TSTP Solution File: SWW678_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW678_1 : TPTP v8.1.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:59:38 EDT 2022
% Result : Theorem 1.54s 1.21s
% Output : Proof 1.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW678_1 : TPTP v8.1.0. Released v6.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 20:38:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.54/1.21 % SZS status Theorem
% 1.54/1.21 % SZS output start Proof
% 1.54/1.21 tff(in_type, type, (
% 1.54/1.21 in: ( $int * 'Tree' ) > $o)).
% 1.54/1.21 tff(tptp_fun__left__Tree__Tree__type, type, (
% 1.54/1.21 tptp_fun__left__Tree__Tree_: 'Tree' > 'Tree')).
% 1.54/1.21 tff(tptp_fun__node__Int_Tree_Tree__Tree__type, type, (
% 1.54/1.21 tptp_fun__node__Int_Tree_Tree__Tree_: ( $int * 'Tree' * 'Tree' ) > 'Tree')).
% 1.54/1.21 tff(tptp_fun__right__Tree__Tree__type, type, (
% 1.54/1.21 tptp_fun__right__Tree__Tree_: 'Tree' > 'Tree')).
% 1.54/1.21 tff(tptp_fun_T_3_type, type, (
% 1.54/1.21 tptp_fun_T_3: 'Tree')).
% 1.54/1.21 tff(tptp_fun__val__Tree__Int__type, type, (
% 1.54/1.21 tptp_fun__val__Tree__Int_: 'Tree' > $int)).
% 1.54/1.21 tff(tptp_fun_V_2_type, type, (
% 1.54/1.21 tptp_fun_V_2: $int)).
% 1.54/1.21 tff(tptp_fun__empty_Tree__type, type, (
% 1.54/1.21 tptp_fun__empty_Tree_: 'Tree')).
% 1.54/1.21 tff(tptp_fun_T_5_5_type, type, (
% 1.54/1.21 tptp_fun_T_5_5: 'Tree')).
% 1.54/1.21 tff(tptp_fun_T_3_4_type, type, (
% 1.54/1.21 tptp_fun_T_3_4: 'Tree')).
% 1.54/1.21 tff(searchtree_type, type, (
% 1.54/1.21 searchtree: 'Tree' > $o)).
% 1.54/1.21 tff(tptp_fun_V_1_type, type, (
% 1.54/1.21 tptp_fun_V_1: 'Tree' > $int)).
% 1.54/1.21 tff(tptp_fun_V_0_type, type, (
% 1.54/1.21 tptp_fun_V_0: 'Tree' > $int)).
% 1.54/1.21 tff(1,plain,
% 1.54/1.21 (^[V: $int, T: 'Tree'] : refl((in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0)))))) <=> (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0)))))))),
% 1.54/1.21 inference(bind,[status(th)],[])).
% 1.54/1.21 tff(2,plain,
% 1.54/1.21 (![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0)))))) <=> ![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))),
% 1.54/1.21 inference(quant_intro,[status(thm)],[1])).
% 1.54/1.21 tff(3,plain,
% 1.54/1.21 (^[V: $int, T: 'Tree'] : rewrite((in(V, T) <=> ((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0)))) <=> (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0)))))))),
% 1.54/1.21 inference(bind,[status(th)],[])).
% 1.54/1.21 tff(4,plain,
% 1.54/1.21 (![V: $int, T: 'Tree'] : (in(V, T) <=> ((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0)))) <=> ![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))),
% 1.54/1.21 inference(quant_intro,[status(thm)],[3])).
% 1.54/1.21 tff(5,plain,
% 1.54/1.21 (^[V: $int, T: 'Tree'] : rewrite((in(V, T) <=> ((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T))) = 0)))) <=> (in(V, T) <=> ((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0)))))),
% 1.54/1.21 inference(bind,[status(th)],[])).
% 1.54/1.21 tff(6,plain,
% 1.54/1.21 (![V: $int, T: 'Tree'] : (in(V, T) <=> ((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T))) = 0)))) <=> ![V: $int, T: 'Tree'] : (in(V, T) <=> ((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))),
% 1.54/1.21 inference(quant_intro,[status(thm)],[5])).
% 1.54/1.21 tff(7,plain,
% 1.54/1.21 (^[V: $int, T: 'Tree'] : rewrite((in(V, T) <=> ((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | (V = tptp_fun__val__Tree__Int_(T))))) <=> (in(V, T) <=> ((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T))) = 0)))))),
% 1.54/1.21 inference(bind,[status(th)],[])).
% 1.54/1.21 tff(8,plain,
% 1.54/1.21 (![V: $int, T: 'Tree'] : (in(V, T) <=> ((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | (V = tptp_fun__val__Tree__Int_(T))))) <=> ![V: $int, T: 'Tree'] : (in(V, T) <=> ((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T))) = 0))))),
% 1.54/1.21 inference(quant_intro,[status(thm)],[7])).
% 1.54/1.21 tff(9,plain,
% 1.54/1.21 (![V: $int, T: 'Tree'] : (in(V, T) <=> ((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | (V = tptp_fun__val__Tree__Int_(T))))) <=> ![V: $int, T: 'Tree'] : (in(V, T) <=> ((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | (V = tptp_fun__val__Tree__Int_(T)))))),
% 1.54/1.21 inference(rewrite,[status(thm)],[])).
% 1.54/1.21 tff(10,plain,
% 1.54/1.21 (^[V: $int, T: 'Tree'] : rewrite((in(V, T) <=> (((T = |'empty:Tree'|) => $false) & ((~(T = |'empty:Tree'|)) => (((V = tptp_fun__val__Tree__Int_(T)) | in(V, tptp_fun__left__Tree__Tree_(T))) | in(V, tptp_fun__right__Tree__Tree_(T)))))) <=> (in(V, T) <=> ((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | (V = tptp_fun__val__Tree__Int_(T))))))),
% 1.54/1.21 inference(bind,[status(th)],[])).
% 1.54/1.21 tff(11,plain,
% 1.54/1.21 (![V: $int, T: 'Tree'] : (in(V, T) <=> (((T = |'empty:Tree'|) => $false) & ((~(T = |'empty:Tree'|)) => (((V = tptp_fun__val__Tree__Int_(T)) | in(V, tptp_fun__left__Tree__Tree_(T))) | in(V, tptp_fun__right__Tree__Tree_(T)))))) <=> ![V: $int, T: 'Tree'] : (in(V, T) <=> ((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | (V = tptp_fun__val__Tree__Int_(T)))))),
% 1.54/1.21 inference(quant_intro,[status(thm)],[10])).
% 1.54/1.21 tff(12,axiom,(![V: $int, T: 'Tree'] : (in(V, T) <=> (((T = |'empty:Tree'|) => $false) & ((~(T = |'empty:Tree'|)) => (((V = tptp_fun__val__Tree__Int_(T)) | in(V, tptp_fun__left__Tree__Tree_(T))) | in(V, tptp_fun__right__Tree__Tree_(T))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','formula_005')).
% 1.54/1.21 tff(13,plain,
% 1.54/1.21 (![V: $int, T: 'Tree'] : (in(V, T) <=> ((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | (V = tptp_fun__val__Tree__Int_(T)))))),
% 1.54/1.21 inference(modus_ponens,[status(thm)],[12, 11])).
% 1.54/1.21 tff(14,plain,
% 1.54/1.21 (![V: $int, T: 'Tree'] : (in(V, T) <=> ((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | (V = tptp_fun__val__Tree__Int_(T)))))),
% 1.54/1.21 inference(modus_ponens,[status(thm)],[13, 9])).
% 1.54/1.21 tff(15,plain,
% 1.54/1.21 (![V: $int, T: 'Tree'] : (in(V, T) <=> ((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T))) = 0))))),
% 1.54/1.21 inference(modus_ponens,[status(thm)],[14, 8])).
% 1.54/1.21 tff(16,plain,
% 1.54/1.21 (![V: $int, T: 'Tree'] : (in(V, T) <=> ((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))),
% 1.54/1.21 inference(modus_ponens,[status(thm)],[15, 6])).
% 1.54/1.21 tff(17,plain,(
% 1.54/1.21 ![V: $int, T: 'Tree'] : (in(V, T) <=> ((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))),
% 1.54/1.21 inference(skolemize,[status(sab)],[16])).
% 1.54/1.21 tff(18,plain,
% 1.54/1.21 (![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))),
% 1.54/1.21 inference(modus_ponens,[status(thm)],[17, 4])).
% 1.54/1.21 tff(19,plain,
% 1.54/1.21 (![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))),
% 1.54/1.21 inference(modus_ponens,[status(thm)],[18, 2])).
% 1.54/1.21 tff(20,plain,
% 1.54/1.21 (((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) <=> (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0))))))) <=> ((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) <=> (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0)))))))),
% 1.54/1.21 inference(rewrite,[status(thm)],[])).
% 1.54/1.21 tff(21,plain,
% 1.54/1.21 ((in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) <=> (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, V!2)) = 0)))))) <=> (in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) <=> (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0))))))),
% 1.54/1.21 inference(rewrite,[status(thm)],[])).
% 1.54/1.21 tff(22,plain,
% 1.54/1.21 (((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) <=> (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, V!2)) = 0))))))) <=> ((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) <=> (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0)))))))),
% 1.54/1.21 inference(monotonicity,[status(thm)],[21])).
% 1.54/1.21 tff(23,plain,
% 1.54/1.21 (((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) <=> (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, V!2)) = 0))))))) <=> ((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) <=> (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0)))))))),
% 1.54/1.21 inference(transitivity,[status(thm)],[22, 20])).
% 1.54/1.21 tff(24,plain,
% 1.54/1.21 ((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) <=> (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, V!2)) = 0))))))),
% 1.54/1.21 inference(quant_inst,[status(thm)],[])).
% 1.54/1.21 tff(25,plain,
% 1.54/1.21 ((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) <=> (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0))))))),
% 1.54/1.21 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.54/1.21 tff(26,plain,
% 1.54/1.21 (in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) <=> (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0)))))),
% 1.54/1.21 inference(unit_resolution,[status(thm)],[25, 19])).
% 1.54/1.21 tff(27,assumption,(in(V!2, |'empty:Tree'|)), introduced(assumption)).
% 1.54/1.21 tff(28,plain,
% 1.54/1.21 (((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (~in(V!2, |'empty:Tree'|))) <=> ((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (~in(V!2, |'empty:Tree'|)))),
% 1.54/1.21 inference(rewrite,[status(thm)],[])).
% 1.54/1.21 tff(29,plain,
% 1.54/1.21 ((in(V!2, |'empty:Tree'|) <=> $false) <=> (~in(V!2, |'empty:Tree'|))),
% 1.54/1.21 inference(rewrite,[status(thm)],[])).
% 1.54/1.21 tff(30,plain,
% 1.54/1.21 ((~$true) <=> $false),
% 1.54/1.21 inference(rewrite,[status(thm)],[])).
% 1.54/1.21 tff(31,plain,
% 1.54/1.21 (($true | $false) <=> $true),
% 1.54/1.21 inference(rewrite,[status(thm)],[])).
% 1.54/1.21 tff(32,plain,
% 1.54/1.21 (($true | in(V!2, tptp_fun__right__Tree__Tree_(|'empty:Tree'|)) | in(V!2, tptp_fun__left__Tree__Tree_(|'empty:Tree'|)) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(|'empty:Tree'|))) = 0)) <=> $true),
% 1.54/1.21 inference(rewrite,[status(thm)],[])).
% 1.54/1.21 tff(33,plain,
% 1.54/1.21 (($sum($product(-1, V!2), tptp_fun__val__Tree__Int_(|'empty:Tree'|)) = 0) <=> ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(|'empty:Tree'|))) = 0)),
% 1.54/1.21 inference(rewrite,[status(thm)],[])).
% 1.54/1.21 tff(34,plain,
% 1.54/1.21 ($sum(tptp_fun__val__Tree__Int_(|'empty:Tree'|), $product(-1, V!2)) = $sum($product(-1, V!2), tptp_fun__val__Tree__Int_(|'empty:Tree'|))),
% 1.54/1.21 inference(rewrite,[status(thm)],[])).
% 1.54/1.21 tff(35,plain,
% 1.54/1.21 (($sum(tptp_fun__val__Tree__Int_(|'empty:Tree'|), $product(-1, V!2)) = 0) <=> ($sum($product(-1, V!2), tptp_fun__val__Tree__Int_(|'empty:Tree'|)) = 0)),
% 1.54/1.21 inference(monotonicity,[status(thm)],[34])).
% 1.54/1.21 tff(36,plain,
% 1.54/1.21 (($sum(tptp_fun__val__Tree__Int_(|'empty:Tree'|), $product(-1, V!2)) = 0) <=> ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(|'empty:Tree'|))) = 0)),
% 1.54/1.21 inference(transitivity,[status(thm)],[35, 33])).
% 1.54/1.21 tff(37,plain,
% 1.54/1.21 ((|'empty:Tree'| = |'empty:Tree'|) <=> $true),
% 1.54/1.21 inference(rewrite,[status(thm)],[])).
% 1.54/1.21 tff(38,plain,
% 1.54/1.21 (((|'empty:Tree'| = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(|'empty:Tree'|)) | in(V!2, tptp_fun__left__Tree__Tree_(|'empty:Tree'|)) | ($sum(tptp_fun__val__Tree__Int_(|'empty:Tree'|), $product(-1, V!2)) = 0)) <=> ($true | in(V!2, tptp_fun__right__Tree__Tree_(|'empty:Tree'|)) | in(V!2, tptp_fun__left__Tree__Tree_(|'empty:Tree'|)) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(|'empty:Tree'|))) = 0))),
% 1.54/1.21 inference(monotonicity,[status(thm)],[37, 36])).
% 1.54/1.21 tff(39,plain,
% 1.54/1.21 (((|'empty:Tree'| = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(|'empty:Tree'|)) | in(V!2, tptp_fun__left__Tree__Tree_(|'empty:Tree'|)) | ($sum(tptp_fun__val__Tree__Int_(|'empty:Tree'|), $product(-1, V!2)) = 0)) <=> $true),
% 1.54/1.21 inference(transitivity,[status(thm)],[38, 32])).
% 1.54/1.21 tff(40,plain,
% 1.54/1.21 ((~((|'empty:Tree'| = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(|'empty:Tree'|)) | in(V!2, tptp_fun__left__Tree__Tree_(|'empty:Tree'|)) | ($sum(tptp_fun__val__Tree__Int_(|'empty:Tree'|), $product(-1, V!2)) = 0))) <=> (~$true)),
% 1.54/1.21 inference(monotonicity,[status(thm)],[39])).
% 1.54/1.21 tff(41,plain,
% 1.54/1.21 ((~((|'empty:Tree'| = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(|'empty:Tree'|)) | in(V!2, tptp_fun__left__Tree__Tree_(|'empty:Tree'|)) | ($sum(tptp_fun__val__Tree__Int_(|'empty:Tree'|), $product(-1, V!2)) = 0))) <=> $false),
% 1.54/1.21 inference(transitivity,[status(thm)],[40, 30])).
% 1.54/1.21 tff(42,plain,
% 1.54/1.21 (((|'empty:Tree'| = |'empty:Tree'|) | (~((|'empty:Tree'| = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(|'empty:Tree'|)) | in(V!2, tptp_fun__left__Tree__Tree_(|'empty:Tree'|)) | ($sum(tptp_fun__val__Tree__Int_(|'empty:Tree'|), $product(-1, V!2)) = 0)))) <=> ($true | $false)),
% 1.54/1.21 inference(monotonicity,[status(thm)],[37, 41])).
% 1.54/1.21 tff(43,plain,
% 1.54/1.21 (((|'empty:Tree'| = |'empty:Tree'|) | (~((|'empty:Tree'| = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(|'empty:Tree'|)) | in(V!2, tptp_fun__left__Tree__Tree_(|'empty:Tree'|)) | ($sum(tptp_fun__val__Tree__Int_(|'empty:Tree'|), $product(-1, V!2)) = 0)))) <=> $true),
% 1.54/1.21 inference(transitivity,[status(thm)],[42, 31])).
% 1.54/1.21 tff(44,plain,
% 1.54/1.21 ((~((|'empty:Tree'| = |'empty:Tree'|) | (~((|'empty:Tree'| = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(|'empty:Tree'|)) | in(V!2, tptp_fun__left__Tree__Tree_(|'empty:Tree'|)) | ($sum(tptp_fun__val__Tree__Int_(|'empty:Tree'|), $product(-1, V!2)) = 0))))) <=> (~$true)),
% 1.54/1.21 inference(monotonicity,[status(thm)],[43])).
% 1.54/1.21 tff(45,plain,
% 1.54/1.21 ((~((|'empty:Tree'| = |'empty:Tree'|) | (~((|'empty:Tree'| = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(|'empty:Tree'|)) | in(V!2, tptp_fun__left__Tree__Tree_(|'empty:Tree'|)) | ($sum(tptp_fun__val__Tree__Int_(|'empty:Tree'|), $product(-1, V!2)) = 0))))) <=> $false),
% 1.54/1.21 inference(transitivity,[status(thm)],[44, 30])).
% 1.54/1.21 tff(46,plain,
% 1.54/1.21 ((in(V!2, |'empty:Tree'|) <=> (~((|'empty:Tree'| = |'empty:Tree'|) | (~((|'empty:Tree'| = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(|'empty:Tree'|)) | in(V!2, tptp_fun__left__Tree__Tree_(|'empty:Tree'|)) | ($sum(tptp_fun__val__Tree__Int_(|'empty:Tree'|), $product(-1, V!2)) = 0)))))) <=> (in(V!2, |'empty:Tree'|) <=> $false)),
% 1.54/1.21 inference(monotonicity,[status(thm)],[45])).
% 1.54/1.21 tff(47,plain,
% 1.54/1.21 ((in(V!2, |'empty:Tree'|) <=> (~((|'empty:Tree'| = |'empty:Tree'|) | (~((|'empty:Tree'| = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(|'empty:Tree'|)) | in(V!2, tptp_fun__left__Tree__Tree_(|'empty:Tree'|)) | ($sum(tptp_fun__val__Tree__Int_(|'empty:Tree'|), $product(-1, V!2)) = 0)))))) <=> (~in(V!2, |'empty:Tree'|))),
% 1.54/1.21 inference(transitivity,[status(thm)],[46, 29])).
% 1.54/1.21 tff(48,plain,
% 1.54/1.22 (((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (in(V!2, |'empty:Tree'|) <=> (~((|'empty:Tree'| = |'empty:Tree'|) | (~((|'empty:Tree'| = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(|'empty:Tree'|)) | in(V!2, tptp_fun__left__Tree__Tree_(|'empty:Tree'|)) | ($sum(tptp_fun__val__Tree__Int_(|'empty:Tree'|), $product(-1, V!2)) = 0))))))) <=> ((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (~in(V!2, |'empty:Tree'|)))),
% 1.54/1.22 inference(monotonicity,[status(thm)],[47])).
% 1.54/1.22 tff(49,plain,
% 1.54/1.22 (((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (in(V!2, |'empty:Tree'|) <=> (~((|'empty:Tree'| = |'empty:Tree'|) | (~((|'empty:Tree'| = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(|'empty:Tree'|)) | in(V!2, tptp_fun__left__Tree__Tree_(|'empty:Tree'|)) | ($sum(tptp_fun__val__Tree__Int_(|'empty:Tree'|), $product(-1, V!2)) = 0))))))) <=> ((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (~in(V!2, |'empty:Tree'|)))),
% 1.54/1.22 inference(transitivity,[status(thm)],[48, 28])).
% 1.54/1.22 tff(50,plain,
% 1.54/1.22 ((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (in(V!2, |'empty:Tree'|) <=> (~((|'empty:Tree'| = |'empty:Tree'|) | (~((|'empty:Tree'| = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(|'empty:Tree'|)) | in(V!2, tptp_fun__left__Tree__Tree_(|'empty:Tree'|)) | ($sum(tptp_fun__val__Tree__Int_(|'empty:Tree'|), $product(-1, V!2)) = 0))))))),
% 1.54/1.22 inference(quant_inst,[status(thm)],[])).
% 1.54/1.22 tff(51,plain,
% 1.54/1.22 ((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (~in(V!2, |'empty:Tree'|))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[50, 49])).
% 1.54/1.22 tff(52,plain,
% 1.54/1.22 ($false),
% 1.54/1.22 inference(unit_resolution,[status(thm)],[51, 19, 27])).
% 1.54/1.22 tff(53,plain,(~in(V!2, |'empty:Tree'|)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.22 tff(54,assumption,(T!3 = |'empty:Tree'|), introduced(assumption)).
% 1.54/1.22 tff(55,plain,
% 1.54/1.22 (|'empty:Tree'| = T!3),
% 1.54/1.22 inference(symmetry,[status(thm)],[54])).
% 1.54/1.22 tff(56,plain,
% 1.54/1.22 (in(V!2, |'empty:Tree'|) <=> in(V!2, T!3)),
% 1.54/1.22 inference(monotonicity,[status(thm)],[55])).
% 1.54/1.22 tff(57,plain,
% 1.54/1.22 (in(V!2, T!3) <=> in(V!2, |'empty:Tree'|)),
% 1.54/1.22 inference(symmetry,[status(thm)],[56])).
% 1.54/1.22 tff(58,plain,
% 1.54/1.22 (((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))))))))))) | (~(T!3 = |'empty:Tree'|))),
% 1.54/1.22 inference(tautology,[status(thm)],[])).
% 1.54/1.22 tff(59,plain,
% 1.54/1.22 ((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))))))))))),
% 1.54/1.22 inference(unit_resolution,[status(thm)],[58, 54])).
% 1.54/1.22 tff(60,plain,
% 1.54/1.22 ((in(V!2, T!3) | (~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))))))))))))) <=> (in(V!2, T!3) | (~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3))))))))))))))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(61,plain,
% 1.54/1.22 (((~(T!3 = |'empty:Tree'|)) & ((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3))))))))))) <=> (~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))))))))))))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(62,plain,
% 1.54/1.22 (((T!3 = |'empty:Tree'|) | (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3))))))))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)) <=> ((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3))))))))))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(63,plain,
% 1.54/1.22 ((((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3))))))) <=> (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))))))))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(64,plain,
% 1.54/1.22 (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | ((T_5!5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5!5))) <=> ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3))))))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(65,plain,
% 1.54/1.22 ((((T_3!4 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3!4)) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) <=> ((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(66,plain,
% 1.54/1.22 (((((T_3!4 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3!4)) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | ((T_5!5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5!5)))) <=> (((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))))))),
% 1.54/1.22 inference(monotonicity,[status(thm)],[65, 64])).
% 1.54/1.22 tff(67,plain,
% 1.54/1.22 (((((T_3!4 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3!4)) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | ((T_5!5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5!5)))) <=> (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))))))))),
% 1.54/1.22 inference(transitivity,[status(thm)],[66, 63])).
% 1.54/1.22 tff(68,plain,
% 1.54/1.22 (((T!3 = |'empty:Tree'|) | ((((T_3!4 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3!4)) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | ((T_5!5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5!5)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)) <=> ((T!3 = |'empty:Tree'|) | (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3))))))))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0))),
% 1.54/1.22 inference(monotonicity,[status(thm)],[67])).
% 1.54/1.22 tff(69,plain,
% 1.54/1.22 (((T!3 = |'empty:Tree'|) | ((((T_3!4 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3!4)) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | ((T_5!5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5!5)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)) <=> ((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3))))))))))),
% 1.54/1.22 inference(transitivity,[status(thm)],[68, 62])).
% 1.54/1.22 tff(70,plain,
% 1.54/1.22 (((~(T!3 = |'empty:Tree'|)) & ((T!3 = |'empty:Tree'|) | ((((T_3!4 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3!4)) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | ((T_5!5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5!5)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0))) <=> ((~(T!3 = |'empty:Tree'|)) & ((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))))))))))),
% 1.54/1.22 inference(monotonicity,[status(thm)],[69])).
% 1.54/1.22 tff(71,plain,
% 1.54/1.22 (((~(T!3 = |'empty:Tree'|)) & ((T!3 = |'empty:Tree'|) | ((((T_3!4 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3!4)) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | ((T_5!5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5!5)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0))) <=> (~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))))))))))))),
% 1.54/1.22 inference(transitivity,[status(thm)],[70, 61])).
% 1.54/1.22 tff(72,plain,
% 1.54/1.22 ((in(V!2, T!3) | ((~(T!3 = |'empty:Tree'|)) & ((T!3 = |'empty:Tree'|) | ((((T_3!4 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3!4)) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | ((T_5!5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5!5)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)))) <=> (in(V!2, T!3) | (~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3))))))))))))))),
% 1.54/1.22 inference(monotonicity,[status(thm)],[71])).
% 1.54/1.22 tff(73,plain,
% 1.54/1.22 ((in(V!2, T!3) | ((~(T!3 = |'empty:Tree'|)) & ((T!3 = |'empty:Tree'|) | ((((T_3!4 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3!4)) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | ((T_5!5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5!5)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)))) <=> (in(V!2, T!3) | (~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3))))))))))))))),
% 1.54/1.22 inference(transitivity,[status(thm)],[72, 60])).
% 1.54/1.22 tff(74,plain,
% 1.54/1.22 ((searchtree(T!3) & ((in(V!2, T!3) | ((~(T!3 = |'empty:Tree'|)) & ((T!3 = |'empty:Tree'|) | ((((T_3!4 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3!4)) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | ((T_5!5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5!5)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)))) & ((T!3 = |'empty:Tree'|) | (~in(V!2, T!3)) | ((~(T!3 = |'empty:Tree'|)) & (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_3: 'Tree'] : (~((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3)))) | ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_5: 'Tree'] : (~((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5))))) & (~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)))))) <=> (searchtree(T!3) & (in(V!2, T!3) | ((~(T!3 = |'empty:Tree'|)) & ((T!3 = |'empty:Tree'|) | ((((T_3!4 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3!4)) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | ((T_5!5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5!5)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)))) & ((T!3 = |'empty:Tree'|) | (~in(V!2, T!3)) | ((~(T!3 = |'empty:Tree'|)) & (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_3: 'Tree'] : (~((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3)))) | ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_5: 'Tree'] : (~((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5))))) & (~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)))))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(75,plain,
% 1.54/1.22 (((((~(T!3 = |'empty:Tree'|)) & ((T!3 = |'empty:Tree'|) | (($lesseq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V!2)), 0) | ((T_3!4 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3!4))) & ((~$lesseq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V!2)), 0)) | ((T_5!5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5!5)))) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V!2)) = 0))) | in(V!2, T!3)) & (((~(~(T!3 = |'empty:Tree'|))) | ((~(T!3 = |'empty:Tree'|)) & (((~$lesseq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V!2)), 0)) & ![T_3: 'Tree'] : (~((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3)))) | ((~(~$lesseq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V!2)), 0))) & ![T_5: 'Tree'] : (~((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5))))) & (~($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V!2)) = 0)))) | (~in(V!2, T!3)))) <=> ((in(V!2, T!3) | ((~(T!3 = |'empty:Tree'|)) & ((T!3 = |'empty:Tree'|) | ((((T_3!4 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3!4)) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | ((T_5!5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5!5)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)))) & ((T!3 = |'empty:Tree'|) | (~in(V!2, T!3)) | ((~(T!3 = |'empty:Tree'|)) & (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_3: 'Tree'] : (~((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3)))) | ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_5: 'Tree'] : (~((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5))))) & (~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)))))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(76,plain,
% 1.54/1.22 ((~(~searchtree(T!3))) <=> searchtree(T!3)),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(77,plain,
% 1.54/1.22 (((~(~searchtree(T!3))) & ((((~(T!3 = |'empty:Tree'|)) & ((T!3 = |'empty:Tree'|) | (($lesseq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V!2)), 0) | ((T_3!4 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3!4))) & ((~$lesseq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V!2)), 0)) | ((T_5!5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5!5)))) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V!2)) = 0))) | in(V!2, T!3)) & (((~(~(T!3 = |'empty:Tree'|))) | ((~(T!3 = |'empty:Tree'|)) & (((~$lesseq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V!2)), 0)) & ![T_3: 'Tree'] : (~((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3)))) | ((~(~$lesseq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V!2)), 0))) & ![T_5: 'Tree'] : (~((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5))))) & (~($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V!2)) = 0)))) | (~in(V!2, T!3))))) <=> (searchtree(T!3) & ((in(V!2, T!3) | ((~(T!3 = |'empty:Tree'|)) & ((T!3 = |'empty:Tree'|) | ((((T_3!4 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3!4)) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | ((T_5!5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5!5)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)))) & ((T!3 = |'empty:Tree'|) | (~in(V!2, T!3)) | ((~(T!3 = |'empty:Tree'|)) & (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_3: 'Tree'] : (~((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3)))) | ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_5: 'Tree'] : (~((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5))))) & (~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0))))))),
% 1.54/1.22 inference(monotonicity,[status(thm)],[76, 75])).
% 1.54/1.22 tff(78,plain,
% 1.54/1.22 (((~(~searchtree(T!3))) & ((((~(T!3 = |'empty:Tree'|)) & ((T!3 = |'empty:Tree'|) | (($lesseq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V!2)), 0) | ((T_3!4 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3!4))) & ((~$lesseq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V!2)), 0)) | ((T_5!5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5!5)))) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V!2)) = 0))) | in(V!2, T!3)) & (((~(~(T!3 = |'empty:Tree'|))) | ((~(T!3 = |'empty:Tree'|)) & (((~$lesseq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V!2)), 0)) & ![T_3: 'Tree'] : (~((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3)))) | ((~(~$lesseq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V!2)), 0))) & ![T_5: 'Tree'] : (~((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5))))) & (~($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V!2)) = 0)))) | (~in(V!2, T!3))))) <=> (searchtree(T!3) & (in(V!2, T!3) | ((~(T!3 = |'empty:Tree'|)) & ((T!3 = |'empty:Tree'|) | ((((T_3!4 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3!4)) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | ((T_5!5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5!5)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)))) & ((T!3 = |'empty:Tree'|) | (~in(V!2, T!3)) | ((~(T!3 = |'empty:Tree'|)) & (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_3: 'Tree'] : (~((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3)))) | ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_5: 'Tree'] : (~((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5))))) & (~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)))))),
% 1.54/1.22 inference(transitivity,[status(thm)],[77, 74])).
% 1.54/1.22 tff(79,plain,
% 1.54/1.22 ((~![T: 'Tree', V: $int] : ((~searchtree(T)) | (((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | (($lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0) | ?[T_3: 'Tree'] : ((T_3 = tptp_fun__left__Tree__Tree_(T)) & in(V, T_3))) & ((~$lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) | ?[T_5: 'Tree'] : ((T_5 = tptp_fun__right__Tree__Tree_(T)) & in(V, T_5)))) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))) <=> in(V, T)))) <=> (~![T: 'Tree', V: $int] : ((~searchtree(T)) | (((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | (($lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0) | ?[T_3: 'Tree'] : ((T_3 = tptp_fun__left__Tree__Tree_(T)) & in(V, T_3))) & ((~$lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) | ?[T_5: 'Tree'] : ((T_5 = tptp_fun__right__Tree__Tree_(T)) & in(V, T_5)))) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))) <=> in(V, T))))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(80,plain,
% 1.54/1.22 ((~![T: 'Tree', V: $int] : ((~searchtree(T)) | (((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | (($lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0) | ?[T_3: 'Tree'] : ((T_3 = tptp_fun__left__Tree__Tree_(T)) & in(V, T_3))) & ((~$lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) | ?[T_5: 'Tree'] : ((T_5 = tptp_fun__right__Tree__Tree_(T)) & in(V, T_5)))) | ($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T))) = 0))) <=> in(V, T)))) <=> (~![T: 'Tree', V: $int] : ((~searchtree(T)) | (((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | (($lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0) | ?[T_3: 'Tree'] : ((T_3 = tptp_fun__left__Tree__Tree_(T)) & in(V, T_3))) & ((~$lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) | ?[T_5: 'Tree'] : ((T_5 = tptp_fun__right__Tree__Tree_(T)) & in(V, T_5)))) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))) <=> in(V, T))))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(81,plain,
% 1.54/1.22 ((~![T: 'Tree', V: $int] : ((~searchtree(T)) | (((~(T = |'empty:Tree'|)) & ((V = tptp_fun__val__Tree__Int_(T)) | (T = |'empty:Tree'|) | (($lesseq(tptp_fun__val__Tree__Int_(T), V) | ?[T_3: 'Tree'] : ((T_3 = tptp_fun__left__Tree__Tree_(T)) & in(V, T_3))) & ((~$lesseq(tptp_fun__val__Tree__Int_(T), V)) | ?[T_5: 'Tree'] : ((T_5 = tptp_fun__right__Tree__Tree_(T)) & in(V, T_5)))))) <=> in(V, T)))) <=> (~![T: 'Tree', V: $int] : ((~searchtree(T)) | (((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | (($lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0) | ?[T_3: 'Tree'] : ((T_3 = tptp_fun__left__Tree__Tree_(T)) & in(V, T_3))) & ((~$lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) | ?[T_5: 'Tree'] : ((T_5 = tptp_fun__right__Tree__Tree_(T)) & in(V, T_5)))) | ($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T))) = 0))) <=> in(V, T))))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(82,plain,
% 1.54/1.22 ((~![T: 'Tree', V: $int] : ((~searchtree(T)) | (((~(T = |'empty:Tree'|)) & ((V = tptp_fun__val__Tree__Int_(T)) | (T = |'empty:Tree'|) | (($lesseq(tptp_fun__val__Tree__Int_(T), V) | ?[T_3: 'Tree'] : ((T_3 = tptp_fun__left__Tree__Tree_(T)) & in(V, T_3))) & ((~$lesseq(tptp_fun__val__Tree__Int_(T), V)) | ?[T_5: 'Tree'] : ((T_5 = tptp_fun__right__Tree__Tree_(T)) & in(V, T_5)))))) <=> in(V, T)))) <=> (~![T: 'Tree', V: $int] : ((~searchtree(T)) | (((~(T = |'empty:Tree'|)) & ((V = tptp_fun__val__Tree__Int_(T)) | (T = |'empty:Tree'|) | (($lesseq(tptp_fun__val__Tree__Int_(T), V) | ?[T_3: 'Tree'] : ((T_3 = tptp_fun__left__Tree__Tree_(T)) & in(V, T_3))) & ((~$lesseq(tptp_fun__val__Tree__Int_(T), V)) | ?[T_5: 'Tree'] : ((T_5 = tptp_fun__right__Tree__Tree_(T)) & in(V, T_5)))))) <=> in(V, T))))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(83,plain,
% 1.54/1.22 ((~![T: 'Tree', V: $int] : (searchtree(T) => ((((T = |'empty:Tree'|) => $false) & ((~(T = |'empty:Tree'|)) => (((V = tptp_fun__val__Tree__Int_(T)) => $true) & ((~(V = tptp_fun__val__Tree__Int_(T))) => (($less(V, tptp_fun__val__Tree__Int_(T)) => ?[T_3: 'Tree'] : ((T_3 = tptp_fun__left__Tree__Tree_(T)) & in(V, T_3))) & ((~$less(V, tptp_fun__val__Tree__Int_(T))) => ?[T_5: 'Tree'] : ((T_5 = tptp_fun__right__Tree__Tree_(T)) & in(V, T_5)))))))) <=> in(V, T)))) <=> (~![T: 'Tree', V: $int] : ((~searchtree(T)) | (((~(T = |'empty:Tree'|)) & ((V = tptp_fun__val__Tree__Int_(T)) | (T = |'empty:Tree'|) | (($lesseq(tptp_fun__val__Tree__Int_(T), V) | ?[T_3: 'Tree'] : ((T_3 = tptp_fun__left__Tree__Tree_(T)) & in(V, T_3))) & ((~$lesseq(tptp_fun__val__Tree__Int_(T), V)) | ?[T_5: 'Tree'] : ((T_5 = tptp_fun__right__Tree__Tree_(T)) & in(V, T_5)))))) <=> in(V, T))))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(84,axiom,(~![T: 'Tree', V: $int] : (searchtree(T) => ((((T = |'empty:Tree'|) => $false) & ((~(T = |'empty:Tree'|)) => (((V = tptp_fun__val__Tree__Int_(T)) => $true) & ((~(V = tptp_fun__val__Tree__Int_(T))) => (($less(V, tptp_fun__val__Tree__Int_(T)) => ?[T_3: 'Tree'] : ((T_3 = tptp_fun__left__Tree__Tree_(T)) & in(V, T_3))) & ((~$less(V, tptp_fun__val__Tree__Int_(T))) => ?[T_5: 'Tree'] : ((T_5 = tptp_fun__right__Tree__Tree_(T)) & in(V, T_5)))))))) <=> in(V, T)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','formula_007')).
% 1.54/1.22 tff(85,plain,
% 1.54/1.22 (~![T: 'Tree', V: $int] : ((~searchtree(T)) | (((~(T = |'empty:Tree'|)) & ((V = tptp_fun__val__Tree__Int_(T)) | (T = |'empty:Tree'|) | (($lesseq(tptp_fun__val__Tree__Int_(T), V) | ?[T_3: 'Tree'] : ((T_3 = tptp_fun__left__Tree__Tree_(T)) & in(V, T_3))) & ((~$lesseq(tptp_fun__val__Tree__Int_(T), V)) | ?[T_5: 'Tree'] : ((T_5 = tptp_fun__right__Tree__Tree_(T)) & in(V, T_5)))))) <=> in(V, T)))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[84, 83])).
% 1.54/1.22 tff(86,plain,
% 1.54/1.22 (~![T: 'Tree', V: $int] : ((~searchtree(T)) | (((~(T = |'empty:Tree'|)) & ((V = tptp_fun__val__Tree__Int_(T)) | (T = |'empty:Tree'|) | (($lesseq(tptp_fun__val__Tree__Int_(T), V) | ?[T_3: 'Tree'] : ((T_3 = tptp_fun__left__Tree__Tree_(T)) & in(V, T_3))) & ((~$lesseq(tptp_fun__val__Tree__Int_(T), V)) | ?[T_5: 'Tree'] : ((T_5 = tptp_fun__right__Tree__Tree_(T)) & in(V, T_5)))))) <=> in(V, T)))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[85, 82])).
% 1.54/1.22 tff(87,plain,
% 1.54/1.22 (~![T: 'Tree', V: $int] : ((~searchtree(T)) | (((~(T = |'empty:Tree'|)) & ((V = tptp_fun__val__Tree__Int_(T)) | (T = |'empty:Tree'|) | (($lesseq(tptp_fun__val__Tree__Int_(T), V) | ?[T_3: 'Tree'] : ((T_3 = tptp_fun__left__Tree__Tree_(T)) & in(V, T_3))) & ((~$lesseq(tptp_fun__val__Tree__Int_(T), V)) | ?[T_5: 'Tree'] : ((T_5 = tptp_fun__right__Tree__Tree_(T)) & in(V, T_5)))))) <=> in(V, T)))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[86, 82])).
% 1.54/1.22 tff(88,plain,
% 1.54/1.22 (~![T: 'Tree', V: $int] : ((~searchtree(T)) | (((~(T = |'empty:Tree'|)) & ((V = tptp_fun__val__Tree__Int_(T)) | (T = |'empty:Tree'|) | (($lesseq(tptp_fun__val__Tree__Int_(T), V) | ?[T_3: 'Tree'] : ((T_3 = tptp_fun__left__Tree__Tree_(T)) & in(V, T_3))) & ((~$lesseq(tptp_fun__val__Tree__Int_(T), V)) | ?[T_5: 'Tree'] : ((T_5 = tptp_fun__right__Tree__Tree_(T)) & in(V, T_5)))))) <=> in(V, T)))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[87, 82])).
% 1.54/1.22 tff(89,plain,
% 1.54/1.22 (~![T: 'Tree', V: $int] : ((~searchtree(T)) | (((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | (($lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0) | ?[T_3: 'Tree'] : ((T_3 = tptp_fun__left__Tree__Tree_(T)) & in(V, T_3))) & ((~$lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) | ?[T_5: 'Tree'] : ((T_5 = tptp_fun__right__Tree__Tree_(T)) & in(V, T_5)))) | ($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T))) = 0))) <=> in(V, T)))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[88, 81])).
% 1.54/1.22 tff(90,plain,
% 1.54/1.22 (~![T: 'Tree', V: $int] : ((~searchtree(T)) | (((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | (($lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0) | ?[T_3: 'Tree'] : ((T_3 = tptp_fun__left__Tree__Tree_(T)) & in(V, T_3))) & ((~$lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) | ?[T_5: 'Tree'] : ((T_5 = tptp_fun__right__Tree__Tree_(T)) & in(V, T_5)))) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))) <=> in(V, T)))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[89, 80])).
% 1.54/1.22 tff(91,plain,
% 1.54/1.22 (~![T: 'Tree', V: $int] : ((~searchtree(T)) | (((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | (($lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0) | ?[T_3: 'Tree'] : ((T_3 = tptp_fun__left__Tree__Tree_(T)) & in(V, T_3))) & ((~$lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) | ?[T_5: 'Tree'] : ((T_5 = tptp_fun__right__Tree__Tree_(T)) & in(V, T_5)))) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))) <=> in(V, T)))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[90, 79])).
% 1.54/1.22 tff(92,plain,
% 1.54/1.22 (~![T: 'Tree', V: $int] : ((~searchtree(T)) | (((~(T = |'empty:Tree'|)) & ((T = |'empty:Tree'|) | (($lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0) | ?[T_3: 'Tree'] : ((T_3 = tptp_fun__left__Tree__Tree_(T)) & in(V, T_3))) & ((~$lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) | ?[T_5: 'Tree'] : ((T_5 = tptp_fun__right__Tree__Tree_(T)) & in(V, T_5)))) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))) <=> in(V, T)))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[91, 79])).
% 1.54/1.22 tff(93,plain,
% 1.54/1.22 (searchtree(T!3) & (in(V!2, T!3) | ((~(T!3 = |'empty:Tree'|)) & ((T!3 = |'empty:Tree'|) | ((((T_3!4 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3!4)) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | ((T_5!5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5!5)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)))) & ((T!3 = |'empty:Tree'|) | (~in(V!2, T!3)) | ((~(T!3 = |'empty:Tree'|)) & (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_3: 'Tree'] : (~((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3)))) | ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_5: 'Tree'] : (~((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5))))) & (~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0))))),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[92, 78])).
% 1.54/1.23 tff(94,plain,
% 1.54/1.23 (in(V!2, T!3) | ((~(T!3 = |'empty:Tree'|)) & ((T!3 = |'empty:Tree'|) | ((((T_3!4 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3!4)) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | ((T_5!5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5!5)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)))),
% 1.54/1.23 inference(and_elim,[status(thm)],[93])).
% 1.54/1.23 tff(95,plain,
% 1.54/1.23 (in(V!2, T!3) | (~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))))))))))))),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[94, 73])).
% 1.54/1.23 tff(96,plain,
% 1.54/1.23 (in(V!2, T!3)),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[95, 59])).
% 1.54/1.23 tff(97,plain,
% 1.54/1.23 (in(V!2, |'empty:Tree'|)),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[96, 57])).
% 1.54/1.23 tff(98,assumption,(~in(V!2, |'empty:Tree'|)), introduced(assumption)).
% 1.54/1.23 tff(99,plain,
% 1.54/1.23 ($false),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[98, 97])).
% 1.54/1.23 tff(100,plain,(in(V!2, |'empty:Tree'|) | (~(T!3 = |'empty:Tree'|))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.23 tff(101,plain,
% 1.54/1.23 (~(T!3 = |'empty:Tree'|)),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[100, 53])).
% 1.54/1.23 tff(102,plain,
% 1.54/1.23 (^[X: 'Tree'] : refl(((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X)))) <=> ((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X)))))),
% 1.54/1.23 inference(bind,[status(th)],[])).
% 1.54/1.23 tff(103,plain,
% 1.54/1.23 (![X: 'Tree'] : ((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X)))) <=> ![X: 'Tree'] : ((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X))))),
% 1.54/1.23 inference(quant_intro,[status(thm)],[102])).
% 1.54/1.23 tff(104,plain,
% 1.54/1.23 (![X: 'Tree'] : ((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X)))) <=> ![X: 'Tree'] : ((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X))))),
% 1.54/1.23 inference(rewrite,[status(thm)],[])).
% 1.54/1.23 tff(105,axiom,(![X: 'Tree'] : ((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','formula')).
% 1.54/1.23 tff(106,plain,
% 1.54/1.23 (![X: 'Tree'] : ((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X))))),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[105, 104])).
% 1.54/1.23 tff(107,plain,(
% 1.54/1.23 ![X: 'Tree'] : ((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X))))),
% 1.54/1.23 inference(skolemize,[status(sab)],[106])).
% 1.54/1.23 tff(108,plain,
% 1.54/1.23 (![X: 'Tree'] : ((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X))))),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[107, 103])).
% 1.54/1.23 tff(109,plain,
% 1.54/1.23 (((~![X: 'Tree'] : ((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X))))) | ((T!3 = |'empty:Tree'|) | (T!3 = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) <=> ((~![X: 'Tree'] : ((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X))))) | (T!3 = |'empty:Tree'|) | (T!3 = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))),
% 1.54/1.23 inference(rewrite,[status(thm)],[])).
% 1.54/1.23 tff(110,plain,
% 1.54/1.23 ((~![X: 'Tree'] : ((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X))))) | ((T!3 = |'empty:Tree'|) | (T!3 = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))),
% 1.54/1.23 inference(quant_inst,[status(thm)],[])).
% 1.54/1.23 tff(111,plain,
% 1.54/1.23 ((~![X: 'Tree'] : ((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X))))) | (T!3 = |'empty:Tree'|) | (T!3 = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.54/1.23 tff(112,plain,
% 1.54/1.23 ((T!3 = |'empty:Tree'|) | (T!3 = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[111, 108])).
% 1.54/1.23 tff(113,plain,
% 1.54/1.23 (T!3 = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[112, 101])).
% 1.54/1.23 tff(114,plain,
% 1.54/1.23 (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = T!3),
% 1.54/1.23 inference(symmetry,[status(thm)],[113])).
% 1.54/1.23 tff(115,plain,
% 1.54/1.23 (in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) <=> in(V!2, T!3)),
% 1.54/1.23 inference(monotonicity,[status(thm)],[114])).
% 1.54/1.23 tff(116,plain,
% 1.54/1.23 (in(V!2, T!3) <=> in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))),
% 1.54/1.23 inference(symmetry,[status(thm)],[115])).
% 1.54/1.23 tff(117,plain,
% 1.54/1.23 ((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5) = |'empty:Tree'|) <=> (|'empty:Tree'| = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5))),
% 1.54/1.23 inference(commutativity,[status(thm)],[])).
% 1.54/1.23 tff(118,plain,
% 1.54/1.23 ((|'empty:Tree'| = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)) <=> (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5) = |'empty:Tree'|)),
% 1.54/1.23 inference(symmetry,[status(thm)],[117])).
% 1.54/1.23 tff(119,plain,
% 1.54/1.23 ((~(|'empty:Tree'| = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5))) <=> (~(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5) = |'empty:Tree'|))),
% 1.54/1.23 inference(monotonicity,[status(thm)],[118])).
% 1.54/1.23 tff(120,plain,
% 1.54/1.23 (^[X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : refl((~(|'empty:Tree'| = tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2))) <=> (~(|'empty:Tree'| = tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2))))),
% 1.54/1.23 inference(bind,[status(th)],[])).
% 1.54/1.23 tff(121,plain,
% 1.54/1.23 (![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (~(|'empty:Tree'| = tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2))) <=> ![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (~(|'empty:Tree'| = tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))),
% 1.54/1.23 inference(quant_intro,[status(thm)],[120])).
% 1.54/1.23 tff(122,plain,
% 1.54/1.23 (![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (~(|'empty:Tree'| = tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2))) <=> ![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (~(|'empty:Tree'| = tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))),
% 1.54/1.23 inference(rewrite,[status(thm)],[])).
% 1.54/1.23 tff(123,axiom,(![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (~(|'empty:Tree'| = tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','formula_004')).
% 1.54/1.23 tff(124,plain,
% 1.54/1.23 (![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (~(|'empty:Tree'| = tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[123, 122])).
% 1.54/1.23 tff(125,plain,(
% 1.54/1.23 ![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (~(|'empty:Tree'| = tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))),
% 1.54/1.23 inference(skolemize,[status(sab)],[124])).
% 1.54/1.23 tff(126,plain,
% 1.54/1.23 (![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (~(|'empty:Tree'| = tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[125, 121])).
% 1.54/1.23 tff(127,plain,
% 1.54/1.23 ((~![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (~(|'empty:Tree'| = tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) | (~(|'empty:Tree'| = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))),
% 1.54/1.23 inference(quant_inst,[status(thm)],[])).
% 1.54/1.23 tff(128,plain,
% 1.54/1.23 (~(|'empty:Tree'| = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5))),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[127, 126])).
% 1.54/1.23 tff(129,plain,
% 1.54/1.23 (~(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5) = |'empty:Tree'|)),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[128, 119])).
% 1.54/1.23 tff(130,plain,
% 1.54/1.23 (((~![X: 'Tree'] : ((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X))))) | ((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5) = |'empty:Tree'|) | (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5) = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))))) <=> ((~![X: 'Tree'] : ((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X))))) | (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5) = |'empty:Tree'|) | (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5) = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))))),
% 1.54/1.23 inference(rewrite,[status(thm)],[])).
% 1.54/1.23 tff(131,plain,
% 1.54/1.23 ((~![X: 'Tree'] : ((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X))))) | ((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5) = |'empty:Tree'|) | (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5) = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))))),
% 1.54/1.23 inference(quant_inst,[status(thm)],[])).
% 1.54/1.23 tff(132,plain,
% 1.54/1.23 ((~![X: 'Tree'] : ((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X))))) | (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5) = |'empty:Tree'|) | (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5) = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5))))),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[131, 130])).
% 1.54/1.23 tff(133,plain,
% 1.54/1.23 ((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5) = |'empty:Tree'|) | (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5) = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5))))),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[132, 108])).
% 1.54/1.23 tff(134,plain,
% 1.54/1.23 (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5) = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[133, 129])).
% 1.54/1.23 tff(135,plain,
% 1.54/1.23 (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5))) = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)),
% 1.54/1.23 inference(symmetry,[status(thm)],[134])).
% 1.54/1.23 tff(136,plain,
% 1.54/1.23 (^[X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : refl((tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_2) <=> (tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_2))),
% 1.54/1.23 inference(bind,[status(th)],[])).
% 1.54/1.23 tff(137,plain,
% 1.54/1.23 (![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_2) <=> ![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_2)),
% 1.54/1.23 inference(quant_intro,[status(thm)],[136])).
% 1.54/1.23 tff(138,plain,
% 1.54/1.23 (![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_2) <=> ![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_2)),
% 1.54/1.23 inference(rewrite,[status(thm)],[])).
% 1.54/1.23 tff(139,axiom,(![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','formula_003')).
% 1.54/1.23 tff(140,plain,
% 1.54/1.23 (![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_2)),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[139, 138])).
% 1.54/1.23 tff(141,plain,(
% 1.54/1.23 ![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_2)),
% 1.54/1.23 inference(skolemize,[status(sab)],[140])).
% 1.54/1.23 tff(142,plain,
% 1.54/1.23 (![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_2)),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[141, 137])).
% 1.54/1.23 tff(143,plain,
% 1.54/1.23 ((~![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_2)) | (tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)) = T_5!5)),
% 1.54/1.23 inference(quant_inst,[status(thm)],[])).
% 1.54/1.23 tff(144,plain,
% 1.54/1.23 (tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)) = T_5!5),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[143, 142])).
% 1.54/1.23 tff(145,plain,
% 1.54/1.23 (T_5!5 = tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5))),
% 1.54/1.23 inference(symmetry,[status(thm)],[144])).
% 1.54/1.23 tff(146,plain,
% 1.54/1.23 (^[X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : refl((tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_1) <=> (tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_1))),
% 1.54/1.23 inference(bind,[status(th)],[])).
% 1.54/1.23 tff(147,plain,
% 1.54/1.23 (![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_1) <=> ![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_1)),
% 1.54/1.23 inference(quant_intro,[status(thm)],[146])).
% 1.54/1.23 tff(148,plain,
% 1.54/1.23 (![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_1) <=> ![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_1)),
% 1.54/1.23 inference(rewrite,[status(thm)],[])).
% 1.54/1.23 tff(149,axiom,(![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','formula_002')).
% 1.54/1.23 tff(150,plain,
% 1.54/1.23 (![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_1)),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[149, 148])).
% 1.54/1.23 tff(151,plain,(
% 1.54/1.23 ![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_1)),
% 1.54/1.23 inference(skolemize,[status(sab)],[150])).
% 1.54/1.23 tff(152,plain,
% 1.54/1.23 (![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_1)),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[151, 147])).
% 1.54/1.23 tff(153,plain,
% 1.54/1.23 ((~![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_1)) | (tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)) = T_5!5)),
% 1.54/1.23 inference(quant_inst,[status(thm)],[])).
% 1.54/1.23 tff(154,plain,
% 1.54/1.23 (tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)) = T_5!5),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[153, 152])).
% 1.54/1.23 tff(155,plain,
% 1.54/1.23 (T_5!5 = tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5))),
% 1.54/1.23 inference(symmetry,[status(thm)],[154])).
% 1.54/1.23 tff(156,plain,
% 1.54/1.23 (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T_5!5, T_5!5) = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))),
% 1.54/1.23 inference(monotonicity,[status(thm)],[155, 145])).
% 1.54/1.23 tff(157,plain,
% 1.54/1.23 (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T_5!5, T_5!5) = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)),
% 1.54/1.23 inference(transitivity,[status(thm)],[156, 135])).
% 1.54/1.23 tff(158,plain,
% 1.54/1.23 (tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T_5!5, T_5!5)) = tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5))),
% 1.54/1.23 inference(monotonicity,[status(thm)],[157])).
% 1.54/1.23 tff(159,plain,
% 1.54/1.23 (^[X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : refl(($sum(X_1_0, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) = 0) <=> ($sum(X_1_0, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) = 0))),
% 1.54/1.23 inference(bind,[status(th)],[])).
% 1.54/1.23 tff(160,plain,
% 1.54/1.23 (![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : ($sum(X_1_0, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) = 0) <=> ![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : ($sum(X_1_0, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) = 0)),
% 1.54/1.23 inference(quant_intro,[status(thm)],[159])).
% 1.54/1.23 tff(161,plain,
% 1.54/1.23 (^[X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : trans(monotonicity(rewrite($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)), $product(-1, X_1_0)) = $sum($product(-1, X_1_0), tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))), (($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)), $product(-1, X_1_0)) = 0) <=> ($sum($product(-1, X_1_0), tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2))) = 0))), rewrite(($sum($product(-1, X_1_0), tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2))) = 0) <=> ($sum(X_1_0, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) = 0)), (($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)), $product(-1, X_1_0)) = 0) <=> ($sum(X_1_0, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) = 0)))),
% 1.54/1.23 inference(bind,[status(th)],[])).
% 1.54/1.23 tff(162,plain,
% 1.54/1.23 (![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : ($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)), $product(-1, X_1_0)) = 0) <=> ![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : ($sum(X_1_0, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) = 0)),
% 1.54/1.23 inference(quant_intro,[status(thm)],[161])).
% 1.54/1.23 tff(163,plain,
% 1.54/1.23 (^[X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : rewrite((tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_0) <=> ($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)), $product(-1, X_1_0)) = 0))),
% 1.54/1.23 inference(bind,[status(th)],[])).
% 1.54/1.23 tff(164,plain,
% 1.54/1.23 (![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_0) <=> ![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : ($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)), $product(-1, X_1_0)) = 0)),
% 1.54/1.23 inference(quant_intro,[status(thm)],[163])).
% 1.54/1.23 tff(165,plain,
% 1.54/1.23 (![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_0) <=> ![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_0)),
% 1.54/1.23 inference(rewrite,[status(thm)],[])).
% 1.54/1.23 tff(166,axiom,(![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','formula_001')).
% 1.54/1.23 tff(167,plain,
% 1.54/1.23 (![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_0)),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[166, 165])).
% 1.54/1.23 tff(168,plain,
% 1.54/1.23 (![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : ($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)), $product(-1, X_1_0)) = 0)),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[167, 164])).
% 1.54/1.23 tff(169,plain,
% 1.54/1.23 (![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : ($sum(X_1_0, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) = 0)),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[168, 162])).
% 1.54/1.23 tff(170,plain,(
% 1.54/1.23 ![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : ($sum(X_1_0, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) = 0)),
% 1.54/1.23 inference(skolemize,[status(sab)],[169])).
% 1.54/1.23 tff(171,plain,
% 1.54/1.23 (![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : ($sum(X_1_0, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) = 0)),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[170, 160])).
% 1.54/1.23 tff(172,plain,
% 1.54/1.23 ((~![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : ($sum(X_1_0, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) = 0)) | ($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T_5!5, T_5!5)))) = 0)),
% 1.54/1.23 inference(quant_inst,[status(thm)],[])).
% 1.54/1.23 tff(173,plain,
% 1.54/1.23 ($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T_5!5, T_5!5)))) = 0),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[172, 171])).
% 1.54/1.23 tff(174,plain,
% 1.54/1.23 ((~($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T_5!5, T_5!5)))) = 0)) | $lesseq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T_5!5, T_5!5)))), 0)),
% 1.54/1.23 inference(theory_lemma,[status(thm)],[])).
% 1.54/1.23 tff(175,plain,
% 1.54/1.23 ($lesseq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T_5!5, T_5!5)))), 0)),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[174, 173])).
% 1.54/1.23 tff(176,plain,
% 1.54/1.23 ((~($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T_5!5, T_5!5)))) = 0)) | $greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T_5!5, T_5!5)))), 0)),
% 1.54/1.23 inference(theory_lemma,[status(thm)],[])).
% 1.54/1.23 tff(177,plain,
% 1.54/1.23 ($greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T_5!5, T_5!5)))), 0)),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[176, 173])).
% 1.54/1.23 tff(178,plain,
% 1.54/1.23 ((~![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : ($sum(X_1_0, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) = 0)) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0)),
% 1.54/1.23 inference(quant_inst,[status(thm)],[])).
% 1.54/1.23 tff(179,plain,
% 1.54/1.23 ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[178, 171])).
% 1.54/1.23 tff(180,plain,
% 1.54/1.23 ((~($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0)) | $lesseq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))), 0)),
% 1.54/1.23 inference(theory_lemma,[status(thm)],[])).
% 1.54/1.23 tff(181,plain,
% 1.54/1.23 ($lesseq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))), 0)),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[180, 179])).
% 1.54/1.23 tff(182,plain,
% 1.54/1.23 ((~($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0)) | $greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))), 0)),
% 1.54/1.23 inference(theory_lemma,[status(thm)],[])).
% 1.54/1.23 tff(183,plain,
% 1.54/1.23 ($greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))), 0)),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[182, 179])).
% 1.54/1.23 tff(184,plain,
% 1.54/1.23 (tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T_5!5, T_5!5)) = $sum(V!2, $product(-1, $sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3)))))),
% 1.54/1.23 inference(theory_lemma,[status(thm)],[183, 181, 177, 175])).
% 1.54/1.23 tff(185,plain,
% 1.54/1.23 ($sum(V!2, $product(-1, $sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))))) = tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T_5!5, T_5!5))),
% 1.54/1.23 inference(symmetry,[status(thm)],[184])).
% 1.54/1.23 tff(186,plain,
% 1.54/1.23 (((~![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : ($sum(X_1_0, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) = 0)) | ($sum(V!2, $sum($product(-1, tptp_fun__val__Tree__Int_(T!3)), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), T_5!5, T_5!5))))) = 0)) <=> ((~![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : ($sum(X_1_0, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) = 0)) | ($sum(V!2, $sum($product(-1, tptp_fun__val__Tree__Int_(T!3)), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), T_5!5, T_5!5))))) = 0))),
% 1.58/1.23 inference(rewrite,[status(thm)],[])).
% 1.58/1.23 tff(187,plain,
% 1.58/1.23 (($sum($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), T_5!5, T_5!5)))) = 0) <=> ($sum(V!2, $sum($product(-1, tptp_fun__val__Tree__Int_(T!3)), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), T_5!5, T_5!5))))) = 0)),
% 1.58/1.23 inference(rewrite,[status(thm)],[])).
% 1.58/1.23 tff(188,plain,
% 1.58/1.23 (((~![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : ($sum(X_1_0, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) = 0)) | ($sum($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), T_5!5, T_5!5)))) = 0)) <=> ((~![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : ($sum(X_1_0, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) = 0)) | ($sum(V!2, $sum($product(-1, tptp_fun__val__Tree__Int_(T!3)), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), T_5!5, T_5!5))))) = 0))),
% 1.58/1.23 inference(monotonicity,[status(thm)],[187])).
% 1.58/1.23 tff(189,plain,
% 1.58/1.23 (((~![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : ($sum(X_1_0, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) = 0)) | ($sum($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), T_5!5, T_5!5)))) = 0)) <=> ((~![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : ($sum(X_1_0, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) = 0)) | ($sum(V!2, $sum($product(-1, tptp_fun__val__Tree__Int_(T!3)), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), T_5!5, T_5!5))))) = 0))),
% 1.58/1.23 inference(transitivity,[status(thm)],[188, 186])).
% 1.58/1.23 tff(190,plain,
% 1.58/1.23 ((~![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : ($sum(X_1_0, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) = 0)) | ($sum($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), T_5!5, T_5!5)))) = 0)),
% 1.58/1.23 inference(quant_inst,[status(thm)],[])).
% 1.58/1.23 tff(191,plain,
% 1.58/1.23 ((~![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : ($sum(X_1_0, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) = 0)) | ($sum(V!2, $sum($product(-1, tptp_fun__val__Tree__Int_(T!3)), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), T_5!5, T_5!5))))) = 0)),
% 1.58/1.23 inference(modus_ponens,[status(thm)],[190, 189])).
% 1.58/1.23 tff(192,plain,
% 1.58/1.23 ($sum(V!2, $sum($product(-1, tptp_fun__val__Tree__Int_(T!3)), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), T_5!5, T_5!5))))) = 0),
% 1.58/1.23 inference(unit_resolution,[status(thm)],[191, 171])).
% 1.58/1.23 tff(193,plain,
% 1.58/1.23 ((~($sum(V!2, $sum($product(-1, tptp_fun__val__Tree__Int_(T!3)), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), T_5!5, T_5!5))))) = 0)) | $lesseq($sum(V!2, $sum($product(-1, tptp_fun__val__Tree__Int_(T!3)), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), T_5!5, T_5!5))))), 0)),
% 1.58/1.23 inference(theory_lemma,[status(thm)],[])).
% 1.58/1.23 tff(194,plain,
% 1.58/1.23 ($lesseq($sum(V!2, $sum($product(-1, tptp_fun__val__Tree__Int_(T!3)), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), T_5!5, T_5!5))))), 0)),
% 1.58/1.23 inference(unit_resolution,[status(thm)],[193, 192])).
% 1.58/1.23 tff(195,plain,
% 1.58/1.23 ((~($sum(V!2, $sum($product(-1, tptp_fun__val__Tree__Int_(T!3)), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), T_5!5, T_5!5))))) = 0)) | $greatereq($sum(V!2, $sum($product(-1, tptp_fun__val__Tree__Int_(T!3)), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), T_5!5, T_5!5))))), 0)),
% 1.58/1.23 inference(theory_lemma,[status(thm)],[])).
% 1.58/1.23 tff(196,plain,
% 1.58/1.23 ($greatereq($sum(V!2, $sum($product(-1, tptp_fun__val__Tree__Int_(T!3)), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), T_5!5, T_5!5))))), 0)),
% 1.58/1.23 inference(unit_resolution,[status(thm)],[195, 192])).
% 1.58/1.23 tff(197,assumption,(~(T!3 = |'empty:Tree'|)), introduced(assumption)).
% 1.58/1.23 tff(198,assumption,(~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3))))))))), introduced(assumption)).
% 1.58/1.23 tff(199,plain,
% 1.58/1.23 (((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))))))) | ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3))))))),
% 1.58/1.23 inference(tautology,[status(thm)],[])).
% 1.58/1.23 tff(200,plain,
% 1.58/1.23 ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))))),
% 1.58/1.23 inference(unit_resolution,[status(thm)],[199, 198])).
% 1.58/1.23 tff(201,plain,
% 1.58/1.23 (T!3 = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))),
% 1.58/1.23 inference(unit_resolution,[status(thm)],[112, 197])).
% 1.58/1.23 tff(202,plain,
% 1.58/1.23 (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = T!3),
% 1.58/1.23 inference(symmetry,[status(thm)],[201])).
% 1.58/1.23 tff(203,plain,
% 1.58/1.23 (in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) <=> in(V!2, T!3)),
% 1.58/1.23 inference(monotonicity,[status(thm)],[202])).
% 1.58/1.23 tff(204,plain,
% 1.58/1.23 (in(V!2, T!3) <=> in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))),
% 1.58/1.23 inference(symmetry,[status(thm)],[203])).
% 1.58/1.23 tff(205,plain,
% 1.58/1.23 ((~in(V!2, T!3)) <=> (~in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))),
% 1.58/1.23 inference(monotonicity,[status(thm)],[204])).
% 1.58/1.23 tff(206,assumption,(~in(V!2, T!3)), introduced(assumption)).
% 1.58/1.23 tff(207,plain,
% 1.58/1.23 (~in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))),
% 1.58/1.23 inference(modus_ponens,[status(thm)],[206, 205])).
% 1.58/1.23 tff(208,plain,
% 1.58/1.23 ((~(in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) <=> (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0))))))) | in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) | ((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0))))),
% 1.58/1.23 inference(tautology,[status(thm)],[])).
% 1.58/1.23 tff(209,plain,
% 1.58/1.23 ((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0)))),
% 1.58/1.23 inference(unit_resolution,[status(thm)],[208, 207, 26])).
% 1.58/1.23 tff(210,assumption,((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))))), introduced(assumption)).
% 1.58/1.23 tff(211,assumption,(~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)), introduced(assumption)).
% 1.58/1.23 tff(212,plain,
% 1.58/1.23 ((~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)),
% 1.58/1.23 inference(theory_lemma,[status(thm)],[])).
% 1.58/1.23 tff(213,plain,
% 1.58/1.23 (~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)),
% 1.58/1.23 inference(unit_resolution,[status(thm)],[212, 211])).
% 1.58/1.23 tff(214,plain,
% 1.58/1.23 (~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3))))))))))))),
% 1.58/1.23 inference(unit_resolution,[status(thm)],[95, 206])).
% 1.58/1.24 tff(215,plain,
% 1.58/1.24 (((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))))))))))) | ((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3))))))))))),
% 1.58/1.24 inference(tautology,[status(thm)],[])).
% 1.58/1.24 tff(216,plain,
% 1.58/1.24 ((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))))))))),
% 1.58/1.24 inference(unit_resolution,[status(thm)],[215, 214])).
% 1.58/1.24 tff(217,plain,
% 1.58/1.24 ((~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3))))))))))) | (T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))))))))),
% 1.58/1.24 inference(tautology,[status(thm)],[])).
% 1.58/1.24 tff(218,plain,
% 1.58/1.24 (~((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3))))))))),
% 1.58/1.24 inference(unit_resolution,[status(thm)],[217, 216, 197, 213])).
% 1.58/1.24 tff(219,plain,
% 1.58/1.24 (((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))))))) | ((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))),
% 1.58/1.24 inference(tautology,[status(thm)],[])).
% 1.58/1.24 tff(220,plain,
% 1.58/1.24 ((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)),
% 1.58/1.24 inference(unit_resolution,[status(thm)],[219, 218])).
% 1.58/1.24 tff(221,plain,
% 1.58/1.24 ((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)),
% 1.58/1.24 inference(tautology,[status(thm)],[])).
% 1.58/1.24 tff(222,plain,
% 1.58/1.24 (~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))),
% 1.58/1.24 inference(unit_resolution,[status(thm)],[221, 220, 211])).
% 1.58/1.24 tff(223,plain,
% 1.58/1.24 (((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4))) | (T_3!4 = tptp_fun__left__Tree__Tree_(T!3))),
% 1.58/1.24 inference(tautology,[status(thm)],[])).
% 1.59/1.24 tff(224,plain,
% 1.59/1.24 (T_3!4 = tptp_fun__left__Tree__Tree_(T!3)),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[223, 222])).
% 1.59/1.24 tff(225,plain,
% 1.59/1.24 (tptp_fun__left__Tree__Tree_(T!3) = T_3!4),
% 1.59/1.24 inference(symmetry,[status(thm)],[224])).
% 1.59/1.24 tff(226,plain,
% 1.59/1.24 (tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) = tptp_fun__left__Tree__Tree_(T!3)),
% 1.59/1.24 inference(monotonicity,[status(thm)],[202])).
% 1.59/1.24 tff(227,plain,
% 1.59/1.24 (tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) = T_3!4),
% 1.59/1.24 inference(transitivity,[status(thm)],[226, 225])).
% 1.59/1.24 tff(228,plain,
% 1.59/1.24 (in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) <=> in(V!2, T_3!4)),
% 1.59/1.24 inference(monotonicity,[status(thm)],[227])).
% 1.59/1.24 tff(229,plain,
% 1.59/1.24 (in(V!2, T_3!4) <=> in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.24 inference(symmetry,[status(thm)],[228])).
% 1.59/1.24 tff(230,plain,
% 1.59/1.24 (((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4))) | in(V!2, T_3!4)),
% 1.59/1.24 inference(tautology,[status(thm)],[])).
% 1.59/1.24 tff(231,plain,
% 1.59/1.24 (in(V!2, T_3!4)),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[230, 222])).
% 1.59/1.24 tff(232,plain,
% 1.59/1.24 (in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.24 inference(modus_ponens,[status(thm)],[231, 229])).
% 1.59/1.24 tff(233,plain,
% 1.59/1.24 (((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0)) | (~in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))))),
% 1.59/1.24 inference(tautology,[status(thm)],[])).
% 1.59/1.24 tff(234,plain,
% 1.59/1.24 ((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0)),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[233, 232])).
% 1.59/1.24 tff(235,plain,
% 1.59/1.24 ((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) <=> (T!3 = |'empty:Tree'|)),
% 1.59/1.24 inference(monotonicity,[status(thm)],[202])).
% 1.59/1.24 tff(236,plain,
% 1.59/1.24 ((T!3 = |'empty:Tree'|) <=> (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|)),
% 1.59/1.24 inference(symmetry,[status(thm)],[235])).
% 1.59/1.24 tff(237,plain,
% 1.59/1.24 ((~(T!3 = |'empty:Tree'|)) <=> (~(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|))),
% 1.59/1.24 inference(monotonicity,[status(thm)],[236])).
% 1.59/1.24 tff(238,plain,
% 1.59/1.24 (~(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|)),
% 1.59/1.24 inference(modus_ponens,[status(thm)],[197, 237])).
% 1.59/1.24 tff(239,plain,
% 1.59/1.24 ((~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0))))) | (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0)))),
% 1.59/1.24 inference(tautology,[status(thm)],[])).
% 1.59/1.24 tff(240,plain,
% 1.59/1.24 ((~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0))))) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0)))),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[239, 238])).
% 1.59/1.24 tff(241,plain,
% 1.59/1.24 ($false),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[240, 234, 209])).
% 1.59/1.24 tff(242,plain,(in(V!2, T!3) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (T!3 = |'empty:Tree'|)), inference(lemma,lemma(discharge,[]))).
% 1.59/1.24 tff(243,plain,
% 1.59/1.24 ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[242, 206, 197])).
% 1.59/1.24 tff(244,plain,
% 1.59/1.24 ((~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3))))))) | (~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))))),
% 1.59/1.24 inference(tautology,[status(thm)],[])).
% 1.59/1.24 tff(245,plain,
% 1.59/1.24 (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[244, 243, 210])).
% 1.59/1.24 tff(246,plain,
% 1.59/1.24 (((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))) | (T_5!5 = tptp_fun__right__Tree__Tree_(T!3))),
% 1.59/1.24 inference(tautology,[status(thm)],[])).
% 1.59/1.24 tff(247,plain,
% 1.59/1.24 (T_5!5 = tptp_fun__right__Tree__Tree_(T!3)),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[246, 245])).
% 1.59/1.24 tff(248,plain,
% 1.59/1.24 (tptp_fun__right__Tree__Tree_(T!3) = T_5!5),
% 1.59/1.24 inference(symmetry,[status(thm)],[247])).
% 1.59/1.24 tff(249,plain,
% 1.59/1.24 (tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) = tptp_fun__right__Tree__Tree_(T!3)),
% 1.59/1.24 inference(monotonicity,[status(thm)],[202])).
% 1.59/1.24 tff(250,plain,
% 1.59/1.24 (tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) = T_5!5),
% 1.59/1.24 inference(transitivity,[status(thm)],[249, 248])).
% 1.59/1.24 tff(251,plain,
% 1.59/1.24 (in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) <=> in(V!2, T_5!5)),
% 1.59/1.24 inference(monotonicity,[status(thm)],[250])).
% 1.59/1.24 tff(252,plain,
% 1.59/1.24 (in(V!2, T_5!5) <=> in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.24 inference(symmetry,[status(thm)],[251])).
% 1.59/1.24 tff(253,plain,
% 1.59/1.24 (((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, T_5!5)),
% 1.59/1.24 inference(tautology,[status(thm)],[])).
% 1.59/1.24 tff(254,plain,
% 1.59/1.24 (in(V!2, T_5!5)),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[253, 245])).
% 1.59/1.24 tff(255,plain,
% 1.59/1.24 (in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.24 inference(modus_ponens,[status(thm)],[254, 252])).
% 1.59/1.24 tff(256,plain,
% 1.59/1.24 (((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0)) | (~in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))))),
% 1.59/1.24 inference(tautology,[status(thm)],[])).
% 1.59/1.24 tff(257,plain,
% 1.59/1.24 ((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0)),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[256, 255])).
% 1.59/1.24 tff(258,plain,
% 1.59/1.24 ($false),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[240, 257, 209])).
% 1.59/1.24 tff(259,plain,(in(V!2, T!3) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3))))))) | (T!3 = |'empty:Tree'|)), inference(lemma,lemma(discharge,[]))).
% 1.59/1.24 tff(260,plain,
% 1.59/1.24 (in(V!2, T!3)),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[259, 200, 197])).
% 1.59/1.24 tff(261,plain,
% 1.59/1.24 (((T!3 = |'empty:Tree'|) | (~in(V!2, T!3)) | (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))))))))) <=> ((T!3 = |'empty:Tree'|) | (~in(V!2, T!3)) | (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))))))))))),
% 1.59/1.24 inference(rewrite,[status(thm)],[])).
% 1.59/1.24 tff(262,plain,
% 1.59/1.24 (((T!3 = |'empty:Tree'|) | (~in(V!2, T!3)) | (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))))))))) <=> ((T!3 = |'empty:Tree'|) | (~in(V!2, T!3)) | (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))))))))))),
% 1.59/1.24 inference(rewrite,[status(thm)],[])).
% 1.59/1.24 tff(263,plain,
% 1.59/1.24 (((~(T!3 = |'empty:Tree'|)) & ((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))))) & (~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0))) <=> (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))))))))),
% 1.59/1.24 inference(rewrite,[status(thm)],[])).
% 1.59/1.24 tff(264,plain,
% 1.59/1.24 (((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))))) <=> ((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))))))),
% 1.59/1.24 inference(rewrite,[status(thm)],[])).
% 1.59/1.24 tff(265,plain,
% 1.59/1.24 (($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))) <=> (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))))),
% 1.59/1.24 inference(rewrite,[status(thm)],[])).
% 1.59/1.24 tff(266,plain,
% 1.59/1.24 (^[T_5: 'Tree'] : trans(monotonicity(rewrite(((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5)) <=> (~((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))), ((~((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5))) <=> (~(~((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))))), rewrite((~(~((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))) <=> ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))), ((~((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5))) <=> ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))))),
% 1.59/1.24 inference(bind,[status(th)],[])).
% 1.59/1.24 tff(267,plain,
% 1.59/1.24 (![T_5: 'Tree'] : (~((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5))) <=> ![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.24 inference(quant_intro,[status(thm)],[266])).
% 1.59/1.24 tff(268,plain,
% 1.59/1.24 (($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_5: 'Tree'] : (~((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5)))) <=> ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))),
% 1.59/1.24 inference(monotonicity,[status(thm)],[267])).
% 1.59/1.24 tff(269,plain,
% 1.59/1.24 (($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_5: 'Tree'] : (~((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5)))) <=> (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))))),
% 1.59/1.24 inference(transitivity,[status(thm)],[268, 265])).
% 1.59/1.24 tff(270,plain,
% 1.59/1.24 (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))) <=> (~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3))))))),
% 1.59/1.24 inference(rewrite,[status(thm)],[])).
% 1.59/1.24 tff(271,plain,
% 1.59/1.24 (^[T_3: 'Tree'] : trans(monotonicity(rewrite(((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3)) <=> (~((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3))))), ((~((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3))) <=> (~(~((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3))))))), rewrite((~(~((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3))))) <=> ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))), ((~((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3))) <=> ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))),
% 1.59/1.24 inference(bind,[status(th)],[])).
% 1.59/1.24 tff(272,plain,
% 1.59/1.24 (![T_3: 'Tree'] : (~((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3))) <=> ![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))),
% 1.59/1.24 inference(quant_intro,[status(thm)],[271])).
% 1.59/1.24 tff(273,plain,
% 1.59/1.24 (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_3: 'Tree'] : (~((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3)))) <=> ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3))))),
% 1.59/1.24 inference(monotonicity,[status(thm)],[272])).
% 1.59/1.24 tff(274,plain,
% 1.59/1.24 (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_3: 'Tree'] : (~((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3)))) <=> (~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3))))))),
% 1.59/1.24 inference(transitivity,[status(thm)],[273, 270])).
% 1.59/1.24 tff(275,plain,
% 1.59/1.24 ((((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_3: 'Tree'] : (~((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3)))) | ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_5: 'Tree'] : (~((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5))))) <=> ((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))))))),
% 1.59/1.24 inference(monotonicity,[status(thm)],[274, 269])).
% 1.59/1.24 tff(276,plain,
% 1.59/1.24 ((((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_3: 'Tree'] : (~((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3)))) | ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_5: 'Tree'] : (~((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5))))) <=> ((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))))))),
% 1.59/1.24 inference(transitivity,[status(thm)],[275, 264])).
% 1.59/1.24 tff(277,plain,
% 1.59/1.24 (((~(T!3 = |'empty:Tree'|)) & (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_3: 'Tree'] : (~((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3)))) | ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_5: 'Tree'] : (~((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5))))) & (~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0))) <=> ((~(T!3 = |'empty:Tree'|)) & ((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))))) & (~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)))),
% 1.59/1.24 inference(monotonicity,[status(thm)],[276])).
% 1.59/1.24 tff(278,plain,
% 1.59/1.24 (((~(T!3 = |'empty:Tree'|)) & (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_3: 'Tree'] : (~((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3)))) | ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_5: 'Tree'] : (~((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5))))) & (~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0))) <=> (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))))))))),
% 1.59/1.24 inference(transitivity,[status(thm)],[277, 263])).
% 1.59/1.24 tff(279,plain,
% 1.59/1.24 (((T!3 = |'empty:Tree'|) | (~in(V!2, T!3)) | ((~(T!3 = |'empty:Tree'|)) & (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_3: 'Tree'] : (~((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3)))) | ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_5: 'Tree'] : (~((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5))))) & (~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)))) <=> ((T!3 = |'empty:Tree'|) | (~in(V!2, T!3)) | (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))))))))))),
% 1.59/1.24 inference(monotonicity,[status(thm)],[278])).
% 1.59/1.24 tff(280,plain,
% 1.59/1.24 (((T!3 = |'empty:Tree'|) | (~in(V!2, T!3)) | ((~(T!3 = |'empty:Tree'|)) & (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_3: 'Tree'] : (~((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3)))) | ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_5: 'Tree'] : (~((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5))))) & (~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)))) <=> ((T!3 = |'empty:Tree'|) | (~in(V!2, T!3)) | (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))))))))))),
% 1.59/1.24 inference(transitivity,[status(thm)],[279, 262])).
% 1.59/1.24 tff(281,plain,
% 1.59/1.24 ((T!3 = |'empty:Tree'|) | (~in(V!2, T!3)) | ((~(T!3 = |'empty:Tree'|)) & (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_3: 'Tree'] : (~((T_3 = tptp_fun__left__Tree__Tree_(T!3)) & in(V!2, T_3)))) | ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_5: 'Tree'] : (~((T_5 = tptp_fun__right__Tree__Tree_(T!3)) & in(V!2, T_5))))) & (~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)))),
% 1.59/1.24 inference(and_elim,[status(thm)],[93])).
% 1.59/1.24 tff(282,plain,
% 1.59/1.24 ((T!3 = |'empty:Tree'|) | (~in(V!2, T!3)) | (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))))))))),
% 1.59/1.24 inference(modus_ponens,[status(thm)],[281, 280])).
% 1.59/1.24 tff(283,plain,
% 1.59/1.24 ((T!3 = |'empty:Tree'|) | (~in(V!2, T!3)) | (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))))))))),
% 1.59/1.24 inference(modus_ponens,[status(thm)],[282, 261])).
% 1.59/1.24 tff(284,plain,
% 1.59/1.24 (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))))))))),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[283, 260, 197])).
% 1.59/1.24 tff(285,plain,
% 1.59/1.24 (((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))))))) | ((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))))))),
% 1.59/1.24 inference(tautology,[status(thm)],[])).
% 1.59/1.24 tff(286,plain,
% 1.59/1.24 ((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))))),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[285, 284])).
% 1.59/1.24 tff(287,plain,
% 1.59/1.24 ((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[219, 198])).
% 1.59/1.24 tff(288,assumption,((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)), introduced(assumption)).
% 1.59/1.24 tff(289,plain,
% 1.59/1.24 (~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[221, 211, 288])).
% 1.59/1.24 tff(290,plain,
% 1.59/1.24 (T_3!4 = tptp_fun__left__Tree__Tree_(T!3)),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[223, 289])).
% 1.59/1.24 tff(291,plain,
% 1.59/1.24 (tptp_fun__left__Tree__Tree_(T!3) = T_3!4),
% 1.59/1.24 inference(symmetry,[status(thm)],[290])).
% 1.59/1.24 tff(292,plain,
% 1.59/1.24 (in(V!2, tptp_fun__left__Tree__Tree_(T!3)) <=> in(V!2, T_3!4)),
% 1.59/1.24 inference(monotonicity,[status(thm)],[291])).
% 1.59/1.24 tff(293,plain,
% 1.59/1.24 (in(V!2, T_3!4) <=> in(V!2, tptp_fun__left__Tree__Tree_(T!3))),
% 1.59/1.24 inference(symmetry,[status(thm)],[292])).
% 1.59/1.24 tff(294,plain,
% 1.59/1.24 (in(V!2, T_3!4)),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[230, 289])).
% 1.59/1.24 tff(295,plain,
% 1.59/1.24 (in(V!2, tptp_fun__left__Tree__Tree_(T!3))),
% 1.59/1.24 inference(modus_ponens,[status(thm)],[294, 293])).
% 1.59/1.24 tff(296,assumption,((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))))), introduced(assumption)).
% 1.59/1.24 tff(297,plain,
% 1.59/1.24 (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)),
% 1.59/1.24 inference(tautology,[status(thm)],[])).
% 1.59/1.24 tff(298,plain,
% 1.59/1.24 ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[297, 211])).
% 1.59/1.24 tff(299,plain,
% 1.59/1.24 ((~((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))))))) | (~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))))),
% 1.59/1.24 inference(tautology,[status(thm)],[])).
% 1.59/1.24 tff(300,plain,
% 1.59/1.24 (~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[299, 298, 296])).
% 1.59/1.24 tff(301,plain,
% 1.59/1.24 (($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3))))) | ![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))),
% 1.59/1.24 inference(tautology,[status(thm)],[])).
% 1.59/1.24 tff(302,plain,
% 1.59/1.24 (![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))),
% 1.59/1.24 inference(unit_resolution,[status(thm)],[301, 300])).
% 1.59/1.24 tff(303,plain,
% 1.59/1.24 (((~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))) | (~in(V!2, tptp_fun__left__Tree__Tree_(T!3)))) <=> ((~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))) | (~in(V!2, tptp_fun__left__Tree__Tree_(T!3))))),
% 1.59/1.24 inference(rewrite,[status(thm)],[])).
% 1.59/1.24 tff(304,plain,
% 1.59/1.24 (($false | (~in(V!2, tptp_fun__left__Tree__Tree_(T!3)))) <=> (~in(V!2, tptp_fun__left__Tree__Tree_(T!3)))),
% 1.59/1.24 inference(rewrite,[status(thm)],[])).
% 1.59/1.24 tff(305,plain,
% 1.59/1.24 ((tptp_fun__left__Tree__Tree_(T!3) = tptp_fun__left__Tree__Tree_(T!3)) <=> $true),
% 1.59/1.24 inference(rewrite,[status(thm)],[])).
% 1.59/1.24 tff(306,plain,
% 1.59/1.24 ((~(tptp_fun__left__Tree__Tree_(T!3) = tptp_fun__left__Tree__Tree_(T!3))) <=> (~$true)),
% 1.59/1.24 inference(monotonicity,[status(thm)],[305])).
% 1.59/1.24 tff(307,plain,
% 1.59/1.24 ((~(tptp_fun__left__Tree__Tree_(T!3) = tptp_fun__left__Tree__Tree_(T!3))) <=> $false),
% 1.59/1.24 inference(transitivity,[status(thm)],[306, 30])).
% 1.59/1.24 tff(308,plain,
% 1.59/1.24 (((~(tptp_fun__left__Tree__Tree_(T!3) = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, tptp_fun__left__Tree__Tree_(T!3)))) <=> ($false | (~in(V!2, tptp_fun__left__Tree__Tree_(T!3))))),
% 1.59/1.24 inference(monotonicity,[status(thm)],[307])).
% 1.59/1.24 tff(309,plain,
% 1.59/1.24 (((~(tptp_fun__left__Tree__Tree_(T!3) = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, tptp_fun__left__Tree__Tree_(T!3)))) <=> (~in(V!2, tptp_fun__left__Tree__Tree_(T!3)))),
% 1.59/1.24 inference(transitivity,[status(thm)],[308, 304])).
% 1.59/1.24 tff(310,plain,
% 1.59/1.24 (((~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))) | ((~(tptp_fun__left__Tree__Tree_(T!3) = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, tptp_fun__left__Tree__Tree_(T!3))))) <=> ((~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))) | (~in(V!2, tptp_fun__left__Tree__Tree_(T!3))))),
% 1.59/1.24 inference(monotonicity,[status(thm)],[309])).
% 1.59/1.24 tff(311,plain,
% 1.59/1.24 (((~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))) | ((~(tptp_fun__left__Tree__Tree_(T!3) = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, tptp_fun__left__Tree__Tree_(T!3))))) <=> ((~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))) | (~in(V!2, tptp_fun__left__Tree__Tree_(T!3))))),
% 1.59/1.24 inference(transitivity,[status(thm)],[310, 303])).
% 1.59/1.24 tff(312,plain,
% 1.59/1.24 ((~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))) | ((~(tptp_fun__left__Tree__Tree_(T!3) = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, tptp_fun__left__Tree__Tree_(T!3))))),
% 1.59/1.25 inference(quant_inst,[status(thm)],[])).
% 1.59/1.25 tff(313,plain,
% 1.59/1.25 ((~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))) | (~in(V!2, tptp_fun__left__Tree__Tree_(T!3)))),
% 1.59/1.25 inference(modus_ponens,[status(thm)],[312, 311])).
% 1.59/1.25 tff(314,plain,
% 1.59/1.25 (~in(V!2, tptp_fun__left__Tree__Tree_(T!3))),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[313, 302])).
% 1.59/1.25 tff(315,plain,
% 1.59/1.25 ($false),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[314, 295])).
% 1.59/1.25 tff(316,plain,($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))))))) | (~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)))), inference(lemma,lemma(discharge,[]))).
% 1.59/1.25 tff(317,plain,
% 1.59/1.25 ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[316, 286, 287])).
% 1.59/1.25 tff(318,plain,
% 1.59/1.25 (($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3))))) | (~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))),
% 1.59/1.25 inference(tautology,[status(thm)],[])).
% 1.59/1.25 tff(319,plain,
% 1.59/1.25 ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3))))),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[318, 317])).
% 1.59/1.25 tff(320,plain,
% 1.59/1.25 (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))))),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[299, 319, 286])).
% 1.59/1.25 tff(321,plain,
% 1.59/1.25 (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[244, 317, 200])).
% 1.59/1.25 tff(322,assumption,(~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3))))), introduced(assumption)).
% 1.59/1.25 tff(323,plain,
% 1.59/1.25 (T_5!5 = tptp_fun__right__Tree__Tree_(T!3)),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[246, 322])).
% 1.59/1.25 tff(324,plain,
% 1.59/1.25 (tptp_fun__right__Tree__Tree_(T!3) = T_5!5),
% 1.59/1.25 inference(symmetry,[status(thm)],[323])).
% 1.59/1.25 tff(325,plain,
% 1.59/1.25 (in(V!2, tptp_fun__right__Tree__Tree_(T!3)) <=> in(V!2, T_5!5)),
% 1.59/1.25 inference(monotonicity,[status(thm)],[324])).
% 1.59/1.25 tff(326,plain,
% 1.59/1.25 (in(V!2, T_5!5) <=> in(V!2, tptp_fun__right__Tree__Tree_(T!3))),
% 1.59/1.25 inference(symmetry,[status(thm)],[325])).
% 1.59/1.25 tff(327,plain,
% 1.59/1.25 (in(V!2, T_5!5)),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[253, 322])).
% 1.59/1.25 tff(328,plain,
% 1.59/1.25 (in(V!2, tptp_fun__right__Tree__Tree_(T!3))),
% 1.59/1.25 inference(modus_ponens,[status(thm)],[327, 326])).
% 1.59/1.25 tff(329,assumption,(![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))), introduced(assumption)).
% 1.59/1.25 tff(330,plain,
% 1.59/1.25 (((~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))) | (~in(V!2, tptp_fun__right__Tree__Tree_(T!3)))) <=> ((~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))) | (~in(V!2, tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.25 inference(rewrite,[status(thm)],[])).
% 1.59/1.25 tff(331,plain,
% 1.59/1.25 (((~in(V!2, tptp_fun__right__Tree__Tree_(T!3))) | $false) <=> (~in(V!2, tptp_fun__right__Tree__Tree_(T!3)))),
% 1.59/1.25 inference(rewrite,[status(thm)],[])).
% 1.59/1.25 tff(332,plain,
% 1.59/1.25 ((tptp_fun__right__Tree__Tree_(T!3) = tptp_fun__right__Tree__Tree_(T!3)) <=> $true),
% 1.59/1.25 inference(rewrite,[status(thm)],[])).
% 1.59/1.25 tff(333,plain,
% 1.59/1.25 ((~(tptp_fun__right__Tree__Tree_(T!3) = tptp_fun__right__Tree__Tree_(T!3))) <=> (~$true)),
% 1.59/1.25 inference(monotonicity,[status(thm)],[332])).
% 1.59/1.25 tff(334,plain,
% 1.59/1.25 ((~(tptp_fun__right__Tree__Tree_(T!3) = tptp_fun__right__Tree__Tree_(T!3))) <=> $false),
% 1.59/1.25 inference(transitivity,[status(thm)],[333, 30])).
% 1.59/1.25 tff(335,plain,
% 1.59/1.25 (((~in(V!2, tptp_fun__right__Tree__Tree_(T!3))) | (~(tptp_fun__right__Tree__Tree_(T!3) = tptp_fun__right__Tree__Tree_(T!3)))) <=> ((~in(V!2, tptp_fun__right__Tree__Tree_(T!3))) | $false)),
% 1.59/1.25 inference(monotonicity,[status(thm)],[334])).
% 1.59/1.25 tff(336,plain,
% 1.59/1.25 (((~in(V!2, tptp_fun__right__Tree__Tree_(T!3))) | (~(tptp_fun__right__Tree__Tree_(T!3) = tptp_fun__right__Tree__Tree_(T!3)))) <=> (~in(V!2, tptp_fun__right__Tree__Tree_(T!3)))),
% 1.59/1.25 inference(transitivity,[status(thm)],[335, 331])).
% 1.59/1.25 tff(337,plain,
% 1.59/1.25 (((~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))) | ((~in(V!2, tptp_fun__right__Tree__Tree_(T!3))) | (~(tptp_fun__right__Tree__Tree_(T!3) = tptp_fun__right__Tree__Tree_(T!3))))) <=> ((~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))) | (~in(V!2, tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.25 inference(monotonicity,[status(thm)],[336])).
% 1.59/1.25 tff(338,plain,
% 1.59/1.25 (((~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))) | ((~in(V!2, tptp_fun__right__Tree__Tree_(T!3))) | (~(tptp_fun__right__Tree__Tree_(T!3) = tptp_fun__right__Tree__Tree_(T!3))))) <=> ((~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))) | (~in(V!2, tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.25 inference(transitivity,[status(thm)],[337, 330])).
% 1.59/1.25 tff(339,plain,
% 1.59/1.25 ((~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))) | ((~in(V!2, tptp_fun__right__Tree__Tree_(T!3))) | (~(tptp_fun__right__Tree__Tree_(T!3) = tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.25 inference(quant_inst,[status(thm)],[])).
% 1.59/1.25 tff(340,plain,
% 1.59/1.25 ((~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))) | (~in(V!2, tptp_fun__right__Tree__Tree_(T!3)))),
% 1.59/1.25 inference(modus_ponens,[status(thm)],[339, 338])).
% 1.59/1.25 tff(341,plain,
% 1.59/1.25 (~in(V!2, tptp_fun__right__Tree__Tree_(T!3))),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[340, 329])).
% 1.59/1.25 tff(342,plain,
% 1.59/1.25 ($false),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[341, 328])).
% 1.59/1.25 tff(343,plain,(((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))), inference(lemma,lemma(discharge,[]))).
% 1.59/1.25 tff(344,plain,
% 1.59/1.25 (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[343, 321])).
% 1.59/1.25 tff(345,plain,
% 1.59/1.25 (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))) | ![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.25 inference(tautology,[status(thm)],[])).
% 1.59/1.25 tff(346,plain,
% 1.59/1.25 ($false),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[345, 344, 320])).
% 1.59/1.25 tff(347,plain,(((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))))))) | (T!3 = |'empty:Tree'|)), inference(lemma,lemma(discharge,[]))).
% 1.59/1.25 tff(348,plain,
% 1.59/1.25 ((~((~((~(T_3!4 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3!4)))) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~((~in(V!2, T_5!5)) | (~(T_5!5 = tptp_fun__right__Tree__Tree_(T!3)))))))),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[347, 101])).
% 1.59/1.25 tff(349,plain,
% 1.59/1.25 ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[217, 216, 101, 348])).
% 1.59/1.25 tff(350,plain,
% 1.59/1.25 ((~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)) | $lesseq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)),
% 1.59/1.25 inference(theory_lemma,[status(thm)],[])).
% 1.59/1.25 tff(351,plain,
% 1.59/1.25 ($lesseq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[350, 349])).
% 1.59/1.25 tff(352,plain,
% 1.59/1.25 ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[242, 206, 101])).
% 1.59/1.25 tff(353,plain,
% 1.59/1.25 ($sum(V!2, $product(-1, $sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))))) = $sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), T_5!5, T_5!5))))),
% 1.59/1.25 inference(theory_lemma,[status(thm)],[352, 351, 196, 194])).
% 1.59/1.25 tff(354,plain,
% 1.59/1.25 ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), T_5!5, T_5!5)))) = $sum(V!2, $product(-1, $sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3)))))),
% 1.59/1.25 inference(symmetry,[status(thm)],[353])).
% 1.59/1.25 tff(355,plain,
% 1.59/1.25 (V!2 = $sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), T_5!5, T_5!5))))),
% 1.59/1.25 inference(theory_lemma,[status(thm)],[352, 351, 196, 194])).
% 1.59/1.25 tff(356,plain,
% 1.59/1.25 (V!2 = tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5))),
% 1.59/1.25 inference(transitivity,[status(thm)],[355, 354, 185, 158])).
% 1.59/1.25 tff(357,plain,
% 1.59/1.25 (in(V!2, T!3) <=> in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T!3)),
% 1.59/1.25 inference(monotonicity,[status(thm)],[356])).
% 1.59/1.25 tff(358,plain,
% 1.59/1.25 (in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T!3) <=> in(V!2, T!3)),
% 1.59/1.25 inference(symmetry,[status(thm)],[357])).
% 1.59/1.25 tff(359,plain,
% 1.59/1.25 (((T!3 = |'empty:Tree'|) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(T!3)) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(T!3))) | (~($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0))),
% 1.59/1.25 inference(tautology,[status(thm)],[])).
% 1.59/1.25 tff(360,plain,
% 1.59/1.25 ((T!3 = |'empty:Tree'|) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(T!3)) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(T!3))),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[359, 179])).
% 1.59/1.25 tff(361,plain,
% 1.59/1.25 ((~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(T!3)) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(T!3)))))) | (T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(T!3)) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.25 inference(tautology,[status(thm)],[])).
% 1.59/1.25 tff(362,plain,
% 1.59/1.25 ((~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(T!3)) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(T!3)))))) | (T!3 = |'empty:Tree'|)),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[361, 360])).
% 1.59/1.25 tff(363,plain,
% 1.59/1.25 (~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(T!3)) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(T!3)))))),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[362, 101])).
% 1.59/1.25 tff(364,plain,
% 1.59/1.25 (((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T!3) <=> (~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(T!3)) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(T!3)))))))) <=> ((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T!3) <=> (~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(T!3)) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(T!3))))))))),
% 1.59/1.25 inference(rewrite,[status(thm)],[])).
% 1.59/1.25 tff(365,plain,
% 1.59/1.25 ((in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T!3) <=> (~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(T!3)) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(T!3)) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0)))))) <=> (in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T!3) <=> (~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(T!3)) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(T!3)))))))),
% 1.59/1.25 inference(rewrite,[status(thm)],[])).
% 1.59/1.25 tff(366,plain,
% 1.59/1.25 (((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T!3) <=> (~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(T!3)) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(T!3)) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0))))))) <=> ((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T!3) <=> (~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(T!3)) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(T!3))))))))),
% 1.59/1.25 inference(monotonicity,[status(thm)],[365])).
% 1.59/1.25 tff(367,plain,
% 1.59/1.25 (((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T!3) <=> (~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(T!3)) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(T!3)) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0))))))) <=> ((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T!3) <=> (~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(T!3)) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(T!3))))))))),
% 1.59/1.25 inference(transitivity,[status(thm)],[366, 364])).
% 1.59/1.25 tff(368,plain,
% 1.59/1.25 ((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T!3) <=> (~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(T!3)) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(T!3)) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0))))))),
% 1.59/1.25 inference(quant_inst,[status(thm)],[])).
% 1.59/1.25 tff(369,plain,
% 1.59/1.25 ((~![V: $int, T: 'Tree'] : (in(V, T) <=> (~((T = |'empty:Tree'|) | (~((T = |'empty:Tree'|) | in(V, tptp_fun__right__Tree__Tree_(T)) | in(V, tptp_fun__left__Tree__Tree_(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))))))) | (in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T!3) <=> (~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(T!3)) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(T!3)))))))),
% 1.59/1.25 inference(modus_ponens,[status(thm)],[368, 367])).
% 1.59/1.25 tff(370,plain,
% 1.59/1.25 (in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T!3) <=> (~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(T!3)) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(T!3))))))),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[369, 19])).
% 1.59/1.25 tff(371,plain,
% 1.59/1.25 ((~(in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T!3) <=> (~((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(T!3)) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(T!3)))))))) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T!3) | ((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(T!3)) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(T!3)))))),
% 1.59/1.25 inference(tautology,[status(thm)],[])).
% 1.59/1.25 tff(372,plain,
% 1.59/1.25 (in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T!3) | ((T!3 = |'empty:Tree'|) | (~((T!3 = |'empty:Tree'|) | ($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)))) = 0) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__left__Tree__Tree_(T!3)) | in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), tptp_fun__right__Tree__Tree_(T!3)))))),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[371, 370])).
% 1.59/1.25 tff(373,plain,
% 1.59/1.25 (in(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), T_5!5, T_5!5)), T!3)),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[372, 363])).
% 1.59/1.25 tff(374,plain,
% 1.59/1.25 (in(V!2, T!3)),
% 1.59/1.25 inference(modus_ponens,[status(thm)],[373, 358])).
% 1.59/1.25 tff(375,plain,
% 1.59/1.25 ($false),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[206, 374])).
% 1.59/1.25 tff(376,plain,(in(V!2, T!3)), inference(lemma,lemma(discharge,[]))).
% 1.59/1.25 tff(377,plain,
% 1.59/1.25 (in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))),
% 1.59/1.25 inference(modus_ponens,[status(thm)],[376, 116])).
% 1.59/1.25 tff(378,plain,
% 1.59/1.25 ((~(in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) <=> (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0))))))) | (~in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0)))))),
% 1.59/1.25 inference(tautology,[status(thm)],[])).
% 1.59/1.25 tff(379,plain,
% 1.59/1.25 ((~(in(V!2, tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) <=> (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0))))))) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0)))))),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[378, 377])).
% 1.59/1.25 tff(380,plain,
% 1.59/1.25 (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0))))),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[379, 26])).
% 1.59/1.25 tff(381,plain,
% 1.59/1.25 (((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0)))) | ((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0))),
% 1.59/1.25 inference(tautology,[status(thm)],[])).
% 1.59/1.25 tff(382,plain,
% 1.59/1.25 ((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0)),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[381, 380])).
% 1.59/1.25 tff(383,plain,
% 1.59/1.25 (tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) = tptp_fun__val__Tree__Int_(T!3)),
% 1.59/1.25 inference(monotonicity,[status(thm)],[114])).
% 1.59/1.25 tff(384,plain,
% 1.59/1.25 (tptp_fun__val__Tree__Int_(T!3) = tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))),
% 1.59/1.25 inference(symmetry,[status(thm)],[383])).
% 1.59/1.25 tff(385,plain,
% 1.59/1.25 ((~(tptp_fun__val__Tree__Int_(T!3) = tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)),
% 1.59/1.25 inference(theory_lemma,[status(thm)],[])).
% 1.59/1.25 tff(386,plain,
% 1.59/1.25 ($greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[385, 384])).
% 1.59/1.25 tff(387,plain,
% 1.59/1.25 (~((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))))))))),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[283, 376, 101])).
% 1.59/1.25 tff(388,plain,
% 1.59/1.25 (((T!3 = |'empty:Tree'|) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))))))) | (~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0))),
% 1.59/1.25 inference(tautology,[status(thm)],[])).
% 1.59/1.25 tff(389,plain,
% 1.59/1.25 (~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[388, 387])).
% 1.59/1.25 tff(390,plain,
% 1.59/1.25 ((|'empty:Tree'| = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))) <=> (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)) = |'empty:Tree'|)),
% 1.59/1.25 inference(commutativity,[status(thm)],[])).
% 1.59/1.25 tff(391,plain,
% 1.59/1.25 ((~(|'empty:Tree'| = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)))) <=> (~(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)) = |'empty:Tree'|))),
% 1.59/1.25 inference(monotonicity,[status(thm)],[390])).
% 1.59/1.25 tff(392,plain,
% 1.59/1.25 ((~![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (~(|'empty:Tree'| = tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)))) | (~(|'empty:Tree'| = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))))),
% 1.59/1.25 inference(quant_inst,[status(thm)],[])).
% 1.59/1.25 tff(393,plain,
% 1.59/1.25 (~(|'empty:Tree'| = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)))),
% 1.59/1.25 inference(unit_resolution,[status(thm)],[392, 126])).
% 1.59/1.25 tff(394,plain,
% 1.59/1.25 (~(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)) = |'empty:Tree'|)),
% 1.59/1.25 inference(modus_ponens,[status(thm)],[393, 391])).
% 1.59/1.25 tff(395,plain,
% 1.59/1.25 (((~![X: 'Tree'] : ((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X))))) | ((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)) = |'empty:Tree'|) | (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)) = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))))))) <=> ((~![X: 'Tree'] : ((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X))))) | (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)) = |'empty:Tree'|) | (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)) = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))))))),
% 1.59/1.25 inference(rewrite,[status(thm)],[])).
% 1.59/1.25 tff(396,plain,
% 1.59/1.25 ((~![X: 'Tree'] : ((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X))))) | ((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)) = |'empty:Tree'|) | (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)) = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))))))),
% 1.59/1.25 inference(quant_inst,[status(thm)],[])).
% 1.59/1.25 tff(397,plain,
% 1.59/1.25 ((~![X: 'Tree'] : ((X = |'empty:Tree'|) | (X = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(X), tptp_fun__left__Tree__Tree_(X), tptp_fun__right__Tree__Tree_(X))))) | (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)) = |'empty:Tree'|) | (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)) = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)))))),
% 1.59/1.26 inference(modus_ponens,[status(thm)],[396, 395])).
% 1.59/1.26 tff(398,plain,
% 1.59/1.26 ((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)) = |'empty:Tree'|) | (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)) = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)))))),
% 1.59/1.26 inference(unit_resolution,[status(thm)],[397, 108])).
% 1.59/1.26 tff(399,plain,
% 1.59/1.26 (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)) = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))))),
% 1.59/1.26 inference(unit_resolution,[status(thm)],[398, 394])).
% 1.59/1.26 tff(400,plain,
% 1.59/1.26 (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)))) = tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))),
% 1.59/1.26 inference(symmetry,[status(thm)],[399])).
% 1.59/1.26 tff(401,plain,
% 1.59/1.26 (tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))))) = tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)))),
% 1.59/1.26 inference(monotonicity,[status(thm)],[400])).
% 1.59/1.26 tff(402,plain,
% 1.59/1.26 (tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))) = tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)))))),
% 1.59/1.26 inference(symmetry,[status(thm)],[401])).
% 1.59/1.26 tff(403,plain,
% 1.59/1.26 ((~![X_1_0: $int, X_1_1: 'Tree', X_1_2: 'Tree'] : (tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(X_1_0, X_1_1, X_1_2)) = X_1_2)) | (tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))) = tptp_fun__left__Tree__Tree_(T!3))),
% 1.59/1.26 inference(quant_inst,[status(thm)],[])).
% 1.59/1.26 tff(404,plain,
% 1.59/1.26 (tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))) = tptp_fun__left__Tree__Tree_(T!3)),
% 1.59/1.26 inference(unit_resolution,[status(thm)],[403, 142])).
% 1.59/1.26 tff(405,plain,
% 1.59/1.26 (tptp_fun__left__Tree__Tree_(T!3) = tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)))),
% 1.59/1.26 inference(symmetry,[status(thm)],[404])).
% 1.59/1.26 tff(406,plain,
% 1.59/1.26 (tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) = tptp_fun__left__Tree__Tree_(T!3)),
% 1.59/1.26 inference(monotonicity,[status(thm)],[114])).
% 1.59/1.26 tff(407,plain,
% 1.59/1.26 (tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) = tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)))))),
% 1.59/1.26 inference(transitivity,[status(thm)],[406, 405, 402])).
% 1.59/1.26 tff(408,plain,
% 1.59/1.26 (in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) <=> in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))))))),
% 1.59/1.26 inference(monotonicity,[status(thm)],[407])).
% 1.59/1.26 tff(409,plain,
% 1.59/1.26 (in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)))))) <=> in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.26 inference(symmetry,[status(thm)],[408])).
% 1.59/1.26 tff(410,plain,
% 1.59/1.26 ((~in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))))))) <=> (~in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))))),
% 1.59/1.26 inference(monotonicity,[status(thm)],[409])).
% 1.59/1.26 tff(411,plain,
% 1.59/1.26 ((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3)))))))),
% 1.59/1.26 inference(unit_resolution,[status(thm)],[285, 387])).
% 1.59/1.26 tff(412,plain,
% 1.59/1.26 (~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))))),
% 1.59/1.26 inference(unit_resolution,[status(thm)],[299, 298, 411])).
% 1.59/1.26 tff(413,plain,
% 1.59/1.26 (![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))),
% 1.59/1.26 inference(unit_resolution,[status(thm)],[301, 412])).
% 1.59/1.26 tff(414,plain,
% 1.59/1.26 (tptp_fun__left__Tree__Tree_(T!3) = tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)))))),
% 1.59/1.26 inference(transitivity,[status(thm)],[405, 402])).
% 1.59/1.26 tff(415,plain,
% 1.59/1.26 (in(V!2, tptp_fun__left__Tree__Tree_(T!3)) <=> in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))))))),
% 1.59/1.26 inference(monotonicity,[status(thm)],[414])).
% 1.59/1.26 tff(416,plain,
% 1.59/1.26 (in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3)))))) <=> in(V!2, tptp_fun__left__Tree__Tree_(T!3))),
% 1.59/1.26 inference(symmetry,[status(thm)],[415])).
% 1.59/1.26 tff(417,assumption,(in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))))))), introduced(assumption)).
% 1.59/1.26 tff(418,plain,
% 1.59/1.26 (in(V!2, tptp_fun__left__Tree__Tree_(T!3))),
% 1.59/1.26 inference(modus_ponens,[status(thm)],[417, 416])).
% 1.59/1.26 tff(419,assumption,(![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3)))), introduced(assumption)).
% 1.59/1.26 tff(420,plain,
% 1.59/1.26 (~in(V!2, tptp_fun__left__Tree__Tree_(T!3))),
% 1.59/1.26 inference(unit_resolution,[status(thm)],[313, 419])).
% 1.59/1.26 tff(421,plain,
% 1.59/1.26 ($false),
% 1.59/1.26 inference(unit_resolution,[status(thm)],[420, 418])).
% 1.59/1.26 tff(422,plain,((~in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))))))) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3))))), inference(lemma,lemma(discharge,[]))).
% 1.59/1.26 tff(423,plain,
% 1.59/1.26 (~in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(tptp_fun__right__Tree__Tree_(T!3)), |'empty:Tree'|, tptp_fun__left__Tree__Tree_(T!3))))))),
% 1.59/1.26 inference(unit_resolution,[status(thm)],[422, 413])).
% 1.59/1.26 tff(424,plain,
% 1.59/1.26 (~in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.26 inference(modus_ponens,[status(thm)],[423, 410])).
% 1.59/1.26 tff(425,plain,
% 1.59/1.26 ((~(tptp_fun__val__Tree__Int_(T!3) = tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)),
% 1.59/1.26 inference(theory_lemma,[status(thm)],[])).
% 1.59/1.26 tff(426,plain,
% 1.59/1.26 ($lesseq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)),
% 1.59/1.26 inference(unit_resolution,[status(thm)],[425, 384])).
% 1.59/1.26 tff(427,plain,
% 1.59/1.26 ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~$lesseq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))),
% 1.59/1.26 inference(theory_lemma,[status(thm)],[])).
% 1.59/1.26 tff(428,plain,
% 1.59/1.26 (~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)),
% 1.59/1.26 inference(unit_resolution,[status(thm)],[427, 211, 426])).
% 1.59/1.26 tff(429,plain,
% 1.59/1.26 ((~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0)) | $greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)),
% 1.59/1.26 inference(theory_lemma,[status(thm)],[])).
% 1.59/1.26 tff(430,plain,
% 1.59/1.26 (~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0)),
% 1.59/1.26 inference(unit_resolution,[status(thm)],[429, 428])).
% 1.59/1.26 tff(431,plain,
% 1.59/1.26 ((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) <=> (T!3 = |'empty:Tree'|)),
% 1.59/1.26 inference(monotonicity,[status(thm)],[114])).
% 1.59/1.26 tff(432,plain,
% 1.59/1.26 ((T!3 = |'empty:Tree'|) <=> (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|)),
% 1.59/1.26 inference(symmetry,[status(thm)],[431])).
% 1.59/1.26 tff(433,plain,
% 1.59/1.26 ((~(T!3 = |'empty:Tree'|)) <=> (~(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|))),
% 1.59/1.26 inference(monotonicity,[status(thm)],[432])).
% 1.59/1.26 tff(434,plain,
% 1.59/1.26 (~(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|)),
% 1.59/1.26 inference(modus_ponens,[status(thm)],[101, 433])).
% 1.59/1.26 tff(435,plain,
% 1.59/1.26 ((~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0))) | (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0)),
% 1.59/1.26 inference(tautology,[status(thm)],[])).
% 1.59/1.26 tff(436,plain,
% 1.59/1.26 ((~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0))) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.26 inference(unit_resolution,[status(thm)],[435, 434, 430])).
% 1.59/1.26 tff(437,plain,
% 1.59/1.26 (in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.26 inference(unit_resolution,[status(thm)],[436, 424, 382])).
% 1.59/1.26 tff(438,plain,
% 1.59/1.26 (^[T: 'Tree'] : refl((~((~((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0)))))))))))) <=> (~((~((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0)))))))))))))),
% 1.59/1.26 inference(bind,[status(th)],[])).
% 1.59/1.26 tff(439,plain,
% 1.59/1.26 (![T: 'Tree'] : (~((~((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0)))))))))))) <=> ![T: 'Tree'] : (~((~((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0))))))))))))),
% 1.59/1.26 inference(quant_intro,[status(thm)],[438])).
% 1.59/1.26 tff(440,plain,
% 1.59/1.26 (^[T: 'Tree'] : rewrite((~((~((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0)))))))))))) <=> (~((~((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0)))))))))))))),
% 1.59/1.26 inference(bind,[status(th)],[])).
% 1.59/1.26 tff(441,plain,
% 1.59/1.26 (![T: 'Tree'] : (~((~((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0)))))))))))) <=> ![T: 'Tree'] : (~((~((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0))))))))))))),
% 1.59/1.26 inference(quant_intro,[status(thm)],[440])).
% 1.59/1.26 tff(442,plain,
% 1.59/1.26 (![T: 'Tree'] : (~((~((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0)))))))))))) <=> ![T: 'Tree'] : (~((~((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0))))))))))))),
% 1.59/1.26 inference(transitivity,[status(thm)],[441, 439])).
% 1.59/1.26 tff(443,plain,
% 1.59/1.26 (^[T: 'Tree'] : trans(monotonicity(trans(monotonicity(rewrite((searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))) <=> (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))))))), (((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))) | (~searchtree(T))) <=> ((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))) | (~searchtree(T))))), rewrite(((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))) | (~searchtree(T))) <=> ((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))), (((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))) | (~searchtree(T))) <=> ((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))))))))), rewrite((searchtree(T) | ((~(T = |'empty:Tree'|)) & ((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0))))))) <=> (searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0)))))))))), ((((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))) | (~searchtree(T))) & (searchtree(T) | ((~(T = |'empty:Tree'|)) & ((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0)))))))) <=> (((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))))))) & (searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0)))))))))))), rewrite((((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))))))) & (searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0)))))))))) <=> (~((~((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0))))))))))))), ((((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))) | (~searchtree(T))) & (searchtree(T) | ((~(T = |'empty:Tree'|)) & ((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0)))))))) <=> (~((~((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0))))))))))))))),
% 1.59/1.26 inference(bind,[status(th)],[])).
% 1.59/1.26 tff(444,plain,
% 1.59/1.26 (![T: 'Tree'] : (((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))) | (~searchtree(T))) & (searchtree(T) | ((~(T = |'empty:Tree'|)) & ((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0)))))))) <=> ![T: 'Tree'] : (~((~((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0))))))))))))),
% 1.59/1.26 inference(quant_intro,[status(thm)],[443])).
% 1.59/1.26 tff(445,plain,
% 1.59/1.26 (^[T: 'Tree'] : rewrite((((~searchtree(T)) | ((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))) & (searchtree(T) | ((~(T = |'empty:Tree'|)) & ((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0)))))))) <=> (((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))) | (~searchtree(T))) & (searchtree(T) | ((~(T = |'empty:Tree'|)) & ((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0)))))))))),
% 1.59/1.26 inference(bind,[status(th)],[])).
% 1.59/1.26 tff(446,plain,
% 1.59/1.26 (![T: 'Tree'] : (((~searchtree(T)) | ((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))) & (searchtree(T) | ((~(T = |'empty:Tree'|)) & ((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0)))))))) <=> ![T: 'Tree'] : (((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))) | (~searchtree(T))) & (searchtree(T) | ((~(T = |'empty:Tree'|)) & ((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0))))))))),
% 1.59/1.26 inference(quant_intro,[status(thm)],[445])).
% 1.59/1.26 tff(447,plain,
% 1.59/1.26 (^[T: 'Tree'] : rewrite((searchtree(T) <=> ((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T))), 0)) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T))), 0)))))) <=> (searchtree(T) <=> ((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))),
% 1.59/1.26 inference(bind,[status(th)],[])).
% 1.59/1.26 tff(448,plain,
% 1.59/1.26 (![T: 'Tree'] : (searchtree(T) <=> ((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T))), 0)) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T))), 0)))))) <=> ![T: 'Tree'] : (searchtree(T) <=> ((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))))))),
% 1.59/1.26 inference(quant_intro,[status(thm)],[447])).
% 1.59/1.26 tff(449,plain,
% 1.59/1.26 (^[T: 'Tree'] : rewrite((searchtree(T) <=> ((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $lesseq(V, tptp_fun__val__Tree__Int_(T))) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$lesseq(V, tptp_fun__val__Tree__Int_(T))))))) <=> (searchtree(T) <=> ((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T))), 0)) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T))), 0)))))))),
% 1.59/1.26 inference(bind,[status(th)],[])).
% 1.59/1.26 tff(450,plain,
% 1.59/1.26 (![T: 'Tree'] : (searchtree(T) <=> ((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $lesseq(V, tptp_fun__val__Tree__Int_(T))) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$lesseq(V, tptp_fun__val__Tree__Int_(T))))))) <=> ![T: 'Tree'] : (searchtree(T) <=> ((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T))), 0)) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T))), 0))))))),
% 1.59/1.26 inference(quant_intro,[status(thm)],[449])).
% 1.59/1.26 tff(451,plain,
% 1.59/1.26 (![T: 'Tree'] : (searchtree(T) <=> ((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $lesseq(V, tptp_fun__val__Tree__Int_(T))) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$lesseq(V, tptp_fun__val__Tree__Int_(T))))))) <=> ![T: 'Tree'] : (searchtree(T) <=> ((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $lesseq(V, tptp_fun__val__Tree__Int_(T))) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$lesseq(V, tptp_fun__val__Tree__Int_(T)))))))),
% 1.59/1.26 inference(rewrite,[status(thm)],[])).
% 1.59/1.26 tff(452,plain,
% 1.59/1.26 (^[T: 'Tree'] : rewrite((searchtree(T) <=> (((T = |'empty:Tree'|) => $true) & ((~(T = |'empty:Tree'|)) => (((searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T))) & ![V: $int] : (in(V, tptp_fun__left__Tree__Tree_(T)) => $lesseq(V, tptp_fun__val__Tree__Int_(T)))) & ![V: $int] : (in(V, tptp_fun__right__Tree__Tree_(T)) => $greater(V, tptp_fun__val__Tree__Int_(T))))))) <=> (searchtree(T) <=> ((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $lesseq(V, tptp_fun__val__Tree__Int_(T))) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$lesseq(V, tptp_fun__val__Tree__Int_(T))))))))),
% 1.59/1.26 inference(bind,[status(th)],[])).
% 1.59/1.26 tff(453,plain,
% 1.59/1.26 (![T: 'Tree'] : (searchtree(T) <=> (((T = |'empty:Tree'|) => $true) & ((~(T = |'empty:Tree'|)) => (((searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T))) & ![V: $int] : (in(V, tptp_fun__left__Tree__Tree_(T)) => $lesseq(V, tptp_fun__val__Tree__Int_(T)))) & ![V: $int] : (in(V, tptp_fun__right__Tree__Tree_(T)) => $greater(V, tptp_fun__val__Tree__Int_(T))))))) <=> ![T: 'Tree'] : (searchtree(T) <=> ((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $lesseq(V, tptp_fun__val__Tree__Int_(T))) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$lesseq(V, tptp_fun__val__Tree__Int_(T)))))))),
% 1.59/1.26 inference(quant_intro,[status(thm)],[452])).
% 1.59/1.26 tff(454,axiom,(![T: 'Tree'] : (searchtree(T) <=> (((T = |'empty:Tree'|) => $true) & ((~(T = |'empty:Tree'|)) => (((searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T))) & ![V: $int] : (in(V, tptp_fun__left__Tree__Tree_(T)) => $lesseq(V, tptp_fun__val__Tree__Int_(T)))) & ![V: $int] : (in(V, tptp_fun__right__Tree__Tree_(T)) => $greater(V, tptp_fun__val__Tree__Int_(T)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','formula_006')).
% 1.59/1.26 tff(455,plain,
% 1.59/1.26 (![T: 'Tree'] : (searchtree(T) <=> ((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $lesseq(V, tptp_fun__val__Tree__Int_(T))) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$lesseq(V, tptp_fun__val__Tree__Int_(T)))))))),
% 1.59/1.26 inference(modus_ponens,[status(thm)],[454, 453])).
% 1.59/1.26 tff(456,plain,
% 1.59/1.26 (![T: 'Tree'] : (searchtree(T) <=> ((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $lesseq(V, tptp_fun__val__Tree__Int_(T))) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$lesseq(V, tptp_fun__val__Tree__Int_(T)))))))),
% 1.59/1.26 inference(modus_ponens,[status(thm)],[455, 451])).
% 1.59/1.26 tff(457,plain,
% 1.59/1.26 (![T: 'Tree'] : (searchtree(T) <=> ((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T))), 0)) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T))), 0))))))),
% 1.59/1.26 inference(modus_ponens,[status(thm)],[456, 450])).
% 1.59/1.26 tff(458,plain,
% 1.59/1.26 (![T: 'Tree'] : (searchtree(T) <=> ((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))))))),
% 1.59/1.26 inference(modus_ponens,[status(thm)],[457, 448])).
% 1.59/1.26 tff(459,plain,(
% 1.59/1.26 ![T: 'Tree'] : (((~searchtree(T)) | ((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))) & (searchtree(T) | ((~(T = |'empty:Tree'|)) & ((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0))))))))),
% 1.59/1.26 inference(skolemize,[status(sab)],[458])).
% 1.59/1.26 tff(460,plain,
% 1.59/1.26 (![T: 'Tree'] : (((T = |'empty:Tree'|) | (searchtree(tptp_fun__left__Tree__Tree_(T)) & searchtree(tptp_fun__right__Tree__Tree_(T)) & ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) & ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))) | (~searchtree(T))) & (searchtree(T) | ((~(T = |'empty:Tree'|)) & ((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0))))))))),
% 1.59/1.26 inference(modus_ponens,[status(thm)],[459, 446])).
% 1.59/1.26 tff(461,plain,
% 1.59/1.26 (![T: 'Tree'] : (~((~((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0))))))))))))),
% 1.59/1.26 inference(modus_ponens,[status(thm)],[460, 444])).
% 1.59/1.26 tff(462,plain,
% 1.59/1.26 (![T: 'Tree'] : (~((~((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0))))))))))))),
% 1.59/1.26 inference(modus_ponens,[status(thm)],[461, 442])).
% 1.59/1.26 tff(463,plain,
% 1.59/1.26 (((~![T: 'Tree'] : (~((~((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0))))))))))))) | (~((~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))))))) | (~(searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~((~in(tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~((~in(tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))))))))))))) <=> ((~![T: 'Tree'] : (~((~((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0))))))))))))) | (~((~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))))))) | (~(searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~((~in(tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~((~in(tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))))))))))))),
% 1.59/1.26 inference(rewrite,[status(thm)],[])).
% 1.59/1.26 tff(464,plain,
% 1.59/1.26 ((~((~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | 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tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~((~in(tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))))))))))) <=> (~((~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))))))) | (~(searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~((~in(tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~((~in(tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))))))))))))),
% 1.59/1.27 inference(rewrite,[status(thm)],[])).
% 1.59/1.27 tff(465,plain,
% 1.59/1.27 (((~![T: 'Tree'] : (~((~((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0))))))))))))) | (~((~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, V)), 0)))))))) | (~(searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~((~in(tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~((~in(tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), 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V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0))))))))))))) | (~((~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))))))) | (~(searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~((~in(tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~((~in(tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))))))))))))),
% 1.59/1.27 inference(monotonicity,[status(thm)],[464])).
% 1.59/1.27 tff(466,plain,
% 1.59/1.27 (((~![T: 'Tree'] : (~((~((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0))))))))))))) | (~((~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, V)), 0)))))))) | (~(searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~((~in(tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~((~in(tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), 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V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0))))))))))))) | (~((~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))))))) | (~(searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~((~in(tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~((~in(tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))))))))))))),
% 1.59/1.27 inference(transitivity,[status(thm)],[465, 463])).
% 1.59/1.27 tff(467,plain,
% 1.59/1.27 ((~![T: 'Tree'] : (~((~((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0))))))))))))) | (~((~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, V)), 0)))))))) | (~(searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~((~in(tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~((~in(tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))))))))))))),
% 1.59/1.27 inference(quant_inst,[status(thm)],[])).
% 1.59/1.27 tff(468,plain,
% 1.59/1.27 ((~![T: 'Tree'] : (~((~((T = |'empty:Tree'|) | (~searchtree(T)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)))))))) | (~(searchtree(T) | (~((T = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T))) | (~searchtree(tptp_fun__right__Tree__Tree_(T))) | (~((~in(tptp_fun_V_0(T), tptp_fun__left__Tree__Tree_(T))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_0(T))), 0))) | (~((~in(tptp_fun_V_1(T), tptp_fun__right__Tree__Tree_(T))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, tptp_fun_V_1(T))), 0))))))))))))) | (~((~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))))))) | (~(searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~((~in(tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~((~in(tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))))))))))))),
% 1.59/1.27 inference(modus_ponens,[status(thm)],[467, 466])).
% 1.59/1.27 tff(469,plain,
% 1.59/1.27 (~((~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))))))) | (~(searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~((~in(tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~((~in(tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))))))))))),
% 1.59/1.27 inference(unit_resolution,[status(thm)],[468, 462])).
% 1.59/1.27 tff(470,plain,
% 1.59/1.27 (((~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))))))) | (~(searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~((~in(tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, tptp_fun_V_0(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~((~in(tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))), $product(-1, tptp_fun_V_1(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))))))))))) | ((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))))))),
% 1.59/1.27 inference(tautology,[status(thm)],[])).
% 1.59/1.27 tff(471,plain,
% 1.59/1.27 ((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))))))),
% 1.59/1.27 inference(unit_resolution,[status(thm)],[470, 469])).
% 1.59/1.27 tff(472,plain,
% 1.59/1.27 (searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) <=> searchtree(T!3)),
% 1.59/1.27 inference(monotonicity,[status(thm)],[114])).
% 1.59/1.27 tff(473,plain,
% 1.59/1.27 (searchtree(T!3) <=> searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))),
% 1.59/1.27 inference(symmetry,[status(thm)],[472])).
% 1.59/1.27 tff(474,plain,
% 1.59/1.27 (searchtree(T!3)),
% 1.59/1.27 inference(and_elim,[status(thm)],[93])).
% 1.59/1.27 tff(475,plain,
% 1.59/1.27 (searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))),
% 1.59/1.27 inference(modus_ponens,[status(thm)],[474, 473])).
% 1.59/1.27 tff(476,plain,
% 1.59/1.27 ((~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))))))) | (tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | (~searchtree(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))))))),
% 1.59/1.27 inference(tautology,[status(thm)],[])).
% 1.59/1.27 tff(477,plain,
% 1.59/1.27 (~((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))))),
% 1.59/1.27 inference(unit_resolution,[status(thm)],[476, 475, 434, 471])).
% 1.59/1.27 tff(478,plain,
% 1.59/1.27 (((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))))) | ![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))),
% 1.59/1.27 inference(tautology,[status(thm)],[])).
% 1.59/1.27 tff(479,plain,
% 1.59/1.27 (![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))),
% 1.59/1.27 inference(unit_resolution,[status(thm)],[478, 477])).
% 1.59/1.27 tff(480,plain,
% 1.59/1.27 ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | $lesseq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)),
% 1.59/1.27 inference(theory_lemma,[status(thm)],[])).
% 1.59/1.27 tff(481,plain,
% 1.59/1.27 ($lesseq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)),
% 1.59/1.27 inference(unit_resolution,[status(thm)],[480, 211])).
% 1.59/1.27 tff(482,plain,
% 1.59/1.27 ($lesseq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0) | (~$lesseq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~$lesseq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))),
% 1.59/1.27 inference(theory_lemma,[status(thm)],[])).
% 1.59/1.27 tff(483,plain,
% 1.59/1.27 ($lesseq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)),
% 1.59/1.27 inference(unit_resolution,[status(thm)],[482, 481, 426])).
% 1.59/1.27 tff(484,plain,
% 1.59/1.27 (((~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))) | ((~in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))) <=> ((~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))) | (~in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))),
% 1.59/1.27 inference(rewrite,[status(thm)],[])).
% 1.59/1.27 tff(485,plain,
% 1.59/1.27 ((~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))) | ((~in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))),
% 1.59/1.27 inference(quant_inst,[status(thm)],[])).
% 1.59/1.27 tff(486,plain,
% 1.59/1.27 ((~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)))) | (~in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))),
% 1.59/1.27 inference(modus_ponens,[status(thm)],[485, 484])).
% 1.59/1.27 tff(487,plain,
% 1.59/1.27 ($false),
% 1.59/1.27 inference(unit_resolution,[status(thm)],[486, 483, 479, 437])).
% 1.59/1.27 tff(488,plain,($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)), inference(lemma,lemma(discharge,[]))).
% 1.59/1.27 tff(489,plain,
% 1.59/1.27 (($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0) | (~$lesseq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))),
% 1.59/1.27 inference(theory_lemma,[status(thm)],[])).
% 1.59/1.27 tff(490,plain,
% 1.59/1.27 (~$lesseq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)),
% 1.59/1.27 inference(unit_resolution,[status(thm)],[489, 488, 389])).
% 1.59/1.27 tff(491,plain,
% 1.59/1.27 ((~$lesseq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)) | $lesseq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))),
% 1.59/1.27 inference(theory_lemma,[status(thm)],[])).
% 1.59/1.27 tff(492,plain,
% 1.59/1.27 (~$lesseq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)),
% 1.59/1.27 inference(unit_resolution,[status(thm)],[491, 490, 386])).
% 1.59/1.27 tff(493,plain,
% 1.59/1.27 ((~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0)) | $lesseq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)),
% 1.59/1.27 inference(theory_lemma,[status(thm)],[])).
% 1.59/1.27 tff(494,plain,
% 1.59/1.27 (~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0)),
% 1.59/1.27 inference(unit_resolution,[status(thm)],[493, 492])).
% 1.59/1.27 tff(495,plain,
% 1.59/1.27 (tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))) = tptp_fun__right__Tree__Tree_(T!3)),
% 1.59/1.27 inference(monotonicity,[status(thm)],[114])).
% 1.59/1.27 tff(496,plain,
% 1.59/1.27 (tptp_fun__right__Tree__Tree_(T!3) = tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))),
% 1.59/1.27 inference(symmetry,[status(thm)],[495])).
% 1.59/1.27 tff(497,plain,
% 1.59/1.27 (in(V!2, tptp_fun__right__Tree__Tree_(T!3)) <=> in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.27 inference(monotonicity,[status(thm)],[496])).
% 1.59/1.27 tff(498,plain,
% 1.59/1.27 (in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) <=> in(V!2, tptp_fun__right__Tree__Tree_(T!3))),
% 1.59/1.27 inference(symmetry,[status(thm)],[497])).
% 1.59/1.27 tff(499,assumption,(in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), introduced(assumption)).
% 1.59/1.27 tff(500,plain,
% 1.59/1.27 (in(V!2, tptp_fun__right__Tree__Tree_(T!3))),
% 1.59/1.27 inference(modus_ponens,[status(thm)],[499, 498])).
% 1.59/1.27 tff(501,plain,
% 1.59/1.27 ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_3: 'Tree'] : ((~(T_3 = tptp_fun__left__Tree__Tree_(T!3))) | (~in(V!2, T_3))))),
% 1.59/1.27 inference(unit_resolution,[status(thm)],[318, 488])).
% 1.59/1.27 tff(502,plain,
% 1.59/1.27 (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))))),
% 1.59/1.27 inference(unit_resolution,[status(thm)],[299, 501, 411])).
% 1.59/1.27 tff(503,plain,
% 1.59/1.27 (![T_5: 'Tree'] : ((~in(V!2, T_5)) | (~(T_5 = tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.28 inference(unit_resolution,[status(thm)],[345, 502])).
% 1.59/1.28 tff(504,plain,
% 1.59/1.28 (~in(V!2, tptp_fun__right__Tree__Tree_(T!3))),
% 1.59/1.28 inference(unit_resolution,[status(thm)],[340, 503])).
% 1.59/1.28 tff(505,plain,
% 1.59/1.28 ($false),
% 1.59/1.28 inference(unit_resolution,[status(thm)],[504, 500])).
% 1.59/1.28 tff(506,plain,(~in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), inference(lemma,lemma(discharge,[]))).
% 1.59/1.28 tff(507,plain,
% 1.59/1.28 ((~((tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)) = |'empty:Tree'|) | in(V!2, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3)))) | ($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) = 0))) | in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.28 inference(unit_resolution,[status(thm)],[435, 434, 506, 494])).
% 1.59/1.28 tff(508,plain,
% 1.59/1.28 (in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))),
% 1.59/1.28 inference(unit_resolution,[status(thm)],[507, 382])).
% 1.59/1.28 tff(509,plain,
% 1.59/1.28 (((~searchtree(tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))))) | ![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))),
% 1.59/1.28 inference(tautology,[status(thm)],[])).
% 1.59/1.28 tff(510,plain,
% 1.59/1.28 (![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))),
% 1.59/1.28 inference(unit_resolution,[status(thm)],[509, 477])).
% 1.59/1.28 tff(511,plain,
% 1.59/1.28 (((~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | ((~in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) <=> ((~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))),
% 1.59/1.28 inference(rewrite,[status(thm)],[])).
% 1.59/1.28 tff(512,plain,
% 1.59/1.28 ((~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | ((~in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))),
% 1.59/1.28 inference(quant_inst,[status(thm)],[])).
% 1.59/1.28 tff(513,plain,
% 1.59/1.28 ((~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0))) | (~in(V!2, tptp_fun__left__Tree__Tree_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))) | $lesseq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(tptp_fun__node__Int_Tree_Tree__Tree_(tptp_fun__val__Tree__Int_(T!3), tptp_fun__left__Tree__Tree_(T!3), tptp_fun__right__Tree__Tree_(T!3))))), 0)),
% 1.59/1.28 inference(modus_ponens,[status(thm)],[512, 511])).
% 1.59/1.28 tff(514,plain,
% 1.59/1.28 ($false),
% 1.59/1.28 inference(unit_resolution,[status(thm)],[513, 492, 510, 508])).
% 1.59/1.28 % SZS output end Proof
%------------------------------------------------------------------------------