TSTP Solution File: SWW679_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW679_1 : TPTP v8.1.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 0.13s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWW679_1 : TPTP v8.1.0. Released v6.4.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Sep 4 20:55:29 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.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(searchtree_type, type, (
% 0.13/0.39 searchtree: 'Tree' > $o)).
% 0.13/0.39 tff(tptp_fun__left__Tree__Tree__type, type, (
% 0.13/0.39 tptp_fun__left__Tree__Tree_: 'Tree' > 'Tree')).
% 0.13/0.39 tff(tptp_fun_T_3_type, type, (
% 0.13/0.39 tptp_fun_T_3: 'Tree')).
% 0.13/0.39 tff(tptp_fun__val__Tree__Int__type, type, (
% 0.13/0.39 tptp_fun__val__Tree__Int_: 'Tree' > $int)).
% 0.13/0.39 tff(in_type, type, (
% 0.13/0.39 in: ( $int * 'Tree' ) > $o)).
% 0.13/0.39 tff(tptp_fun__right__Tree__Tree__type, type, (
% 0.13/0.39 tptp_fun__right__Tree__Tree_: 'Tree' > 'Tree')).
% 0.13/0.39 tff(tptp_fun__empty_Tree__type, type, (
% 0.13/0.39 tptp_fun__empty_Tree_: 'Tree')).
% 0.13/0.39 tff(tptp_fun_V_1_type, type, (
% 0.13/0.39 tptp_fun_V_1: 'Tree' > $int)).
% 0.13/0.39 tff(tptp_fun_V_0_type, type, (
% 0.13/0.39 tptp_fun_V_0: 'Tree' > $int)).
% 0.13/0.39 tff(tptp_fun_V_2_type, type, (
% 0.13/0.39 tptp_fun_V_2: $int)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[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)))))))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![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))))))))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (^[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)))))))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (![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))))))))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![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))))))))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (^[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))))))))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (![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))))))))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (^[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)))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (![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))))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (^[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)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (^[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)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (^[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))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.40 tff(17,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/sandbox2/benchmark/theBenchmark.p','formula_006')).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (![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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[20, 11])).
% 0.19/0.40 tff(22,plain,(
% 0.19/0.40 ![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))))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[21])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (![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))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[22, 9])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (![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))))))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[23, 7])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (![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))))))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[24, 5])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (((~![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!3 = |'empty:Tree'|) | (~searchtree(T!3)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T!3))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T!3))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)))))))) | (~(searchtree(T!3) | (~((T!3 = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~((~in(tptp_fun_V_0(T!3), tptp_fun__left__Tree__Tree_(T!3))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_0(T!3))), 0))) | (~((~in(tptp_fun_V_1(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_1(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))))))))))))) | (~((~((T!3 = |'empty:Tree'|) | (~searchtree(T!3)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T!3))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T!3))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)))))))) | (~(searchtree(T!3) | (~((T!3 = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~((~in(tptp_fun_V_0(T!3), tptp_fun__left__Tree__Tree_(T!3))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_0(T!3))), 0))) | (~((~in(tptp_fun_V_1(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_1(T!3))), 0)))))))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 ((~((~((T!3 = |'empty:Tree'|) | (~searchtree(T!3)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T!3))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T!3))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V)), 0)))))))) | (~(searchtree(T!3) | (~((T!3 = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~((~in(tptp_fun_V_0(T!3), tptp_fun__left__Tree__Tree_(T!3))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_0(T!3))), 0))) | (~((~in(tptp_fun_V_1(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_1(T!3))), 0)))))))))))) <=> (~((~((T!3 = |'empty:Tree'|) | (~searchtree(T!3)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T!3))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T!3))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)))))))) | (~(searchtree(T!3) | (~((T!3 = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~((~in(tptp_fun_V_0(T!3), tptp_fun__left__Tree__Tree_(T!3))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_0(T!3))), 0))) | (~((~in(tptp_fun_V_1(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_1(T!3))), 0))))))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (((~![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!3 = |'empty:Tree'|) | (~searchtree(T!3)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T!3))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T!3))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V)), 0)))))))) | (~(searchtree(T!3) | (~((T!3 = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~((~in(tptp_fun_V_0(T!3), tptp_fun__left__Tree__Tree_(T!3))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_0(T!3))), 0))) | (~((~in(tptp_fun_V_1(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_1(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))))))))))))) | (~((~((T!3 = |'empty:Tree'|) | (~searchtree(T!3)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T!3))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T!3))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)))))))) | (~(searchtree(T!3) | (~((T!3 = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~((~in(tptp_fun_V_0(T!3), tptp_fun__left__Tree__Tree_(T!3))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_0(T!3))), 0))) | (~((~in(tptp_fun_V_1(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_1(T!3))), 0)))))))))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[27])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (((~![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!3 = |'empty:Tree'|) | (~searchtree(T!3)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T!3))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T!3))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V)), 0)))))))) | (~(searchtree(T!3) | (~((T!3 = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~((~in(tptp_fun_V_0(T!3), tptp_fun__left__Tree__Tree_(T!3))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_0(T!3))), 0))) | (~((~in(tptp_fun_V_1(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_1(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))))))))))))) | (~((~((T!3 = |'empty:Tree'|) | (~searchtree(T!3)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T!3))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T!3))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)))))))) | (~(searchtree(T!3) | (~((T!3 = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~((~in(tptp_fun_V_0(T!3), tptp_fun__left__Tree__Tree_(T!3))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_0(T!3))), 0))) | (~((~in(tptp_fun_V_1(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_1(T!3))), 0)))))))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[28, 26])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 ((~![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!3 = |'empty:Tree'|) | (~searchtree(T!3)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T!3))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V)), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T!3))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V)), 0)))))))) | (~(searchtree(T!3) | (~((T!3 = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~((~in(tptp_fun_V_0(T!3), tptp_fun__left__Tree__Tree_(T!3))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_0(T!3))), 0))) | (~((~in(tptp_fun_V_1(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_1(T!3))), 0))))))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 ((~![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!3 = |'empty:Tree'|) | (~searchtree(T!3)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T!3))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T!3))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)))))))) | (~(searchtree(T!3) | (~((T!3 = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~((~in(tptp_fun_V_0(T!3), tptp_fun__left__Tree__Tree_(T!3))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_0(T!3))), 0))) | (~((~in(tptp_fun_V_1(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_1(T!3))), 0))))))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (~((~((T!3 = |'empty:Tree'|) | (~searchtree(T!3)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T!3))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T!3))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)))))))) | (~(searchtree(T!3) | (~((T!3 = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~((~in(tptp_fun_V_0(T!3), tptp_fun__left__Tree__Tree_(T!3))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_0(T!3))), 0))) | (~((~in(tptp_fun_V_1(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_1(T!3))), 0)))))))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[31, 25])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (((~((T!3 = |'empty:Tree'|) | (~searchtree(T!3)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T!3))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T!3))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)))))))) | (~(searchtree(T!3) | (~((T!3 = |'empty:Tree'|) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~((~in(tptp_fun_V_0(T!3), tptp_fun__left__Tree__Tree_(T!3))) | $greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_0(T!3))), 0))) | (~((~in(tptp_fun_V_1(T!3), tptp_fun__right__Tree__Tree_(T!3))) | (~$greatereq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, tptp_fun_V_1(T!3))), 0))))))))))) | ((T!3 = |'empty:Tree'|) | (~searchtree(T!3)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T!3))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T!3))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)))))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 ((T!3 = |'empty:Tree'|) | (~searchtree(T!3)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T!3))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T!3))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (((~(T!3 = |'empty:Tree'|)) & (((~$lesseq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V!2)), 0)) & ![T_1: 'Tree'] : (~((T_1 = tptp_fun__left__Tree__Tree_(T!3)) & searchtree(T_1)))) | ((~(~$lesseq($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V!2)), 0))) & ![T_2: 'Tree'] : (~((T_2 = tptp_fun__right__Tree__Tree_(T!3)) & searchtree(T_2))))) & (~(~searchtree(T!3))) & (~($sum(tptp_fun__val__Tree__Int_(T!3), $product(-1, V!2)) = 0))) <=> ((~(T!3 = |'empty:Tree'|)) & (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_1: 'Tree'] : (~((T_1 = tptp_fun__left__Tree__Tree_(T!3)) & searchtree(T_1)))) | ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_2: 'Tree'] : (~((T_2 = tptp_fun__right__Tree__Tree_(T!3)) & searchtree(T_2))))) & searchtree(T!3) & (~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 ((~![T: 'Tree', V: $int] : ((T = |'empty:Tree'|) | (($lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0) | ?[T_1: 'Tree'] : ((T_1 = tptp_fun__left__Tree__Tree_(T)) & searchtree(T_1))) & ((~$lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) | ?[T_2: 'Tree'] : ((T_2 = tptp_fun__right__Tree__Tree_(T)) & searchtree(T_2)))) | (~searchtree(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))) <=> (~![T: 'Tree', V: $int] : ((T = |'empty:Tree'|) | (($lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0) | ?[T_1: 'Tree'] : ((T_1 = tptp_fun__left__Tree__Tree_(T)) & searchtree(T_1))) & ((~$lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) | ?[T_2: 'Tree'] : ((T_2 = tptp_fun__right__Tree__Tree_(T)) & searchtree(T_2)))) | (~searchtree(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 ((~![T: 'Tree', V: $int] : ((T = |'empty:Tree'|) | (($lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0) | ?[T_1: 'Tree'] : ((T_1 = tptp_fun__left__Tree__Tree_(T)) & searchtree(T_1))) & ((~$lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) | ?[T_2: 'Tree'] : ((T_2 = tptp_fun__right__Tree__Tree_(T)) & searchtree(T_2)))) | (~searchtree(T)) | ($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T))) = 0))) <=> (~![T: 'Tree', V: $int] : ((T = |'empty:Tree'|) | (($lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0) | ?[T_1: 'Tree'] : ((T_1 = tptp_fun__left__Tree__Tree_(T)) & searchtree(T_1))) & ((~$lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) | ?[T_2: 'Tree'] : ((T_2 = tptp_fun__right__Tree__Tree_(T)) & searchtree(T_2)))) | (~searchtree(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 ((~![T: 'Tree', V: $int] : ((V = tptp_fun__val__Tree__Int_(T)) | (T = |'empty:Tree'|) | (~searchtree(T)) | (($lesseq(tptp_fun__val__Tree__Int_(T), V) | ?[T_1: 'Tree'] : ((T_1 = tptp_fun__left__Tree__Tree_(T)) & searchtree(T_1))) & ((~$lesseq(tptp_fun__val__Tree__Int_(T), V)) | ?[T_2: 'Tree'] : ((T_2 = tptp_fun__right__Tree__Tree_(T)) & searchtree(T_2)))))) <=> (~![T: 'Tree', V: $int] : ((T = |'empty:Tree'|) | (($lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0) | ?[T_1: 'Tree'] : ((T_1 = tptp_fun__left__Tree__Tree_(T)) & searchtree(T_1))) & ((~$lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) | ?[T_2: 'Tree'] : ((T_2 = tptp_fun__right__Tree__Tree_(T)) & searchtree(T_2)))) | (~searchtree(T)) | ($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T))) = 0)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 ((~![T: 'Tree', V: $int] : ((V = tptp_fun__val__Tree__Int_(T)) | (T = |'empty:Tree'|) | (~searchtree(T)) | (($lesseq(tptp_fun__val__Tree__Int_(T), V) | ?[T_1: 'Tree'] : ((T_1 = tptp_fun__left__Tree__Tree_(T)) & searchtree(T_1))) & ((~$lesseq(tptp_fun__val__Tree__Int_(T), V)) | ?[T_2: 'Tree'] : ((T_2 = tptp_fun__right__Tree__Tree_(T)) & searchtree(T_2)))))) <=> (~![T: 'Tree', V: $int] : ((V = tptp_fun__val__Tree__Int_(T)) | (T = |'empty:Tree'|) | (~searchtree(T)) | (($lesseq(tptp_fun__val__Tree__Int_(T), V) | ?[T_1: 'Tree'] : ((T_1 = tptp_fun__left__Tree__Tree_(T)) & searchtree(T_1))) & ((~$lesseq(tptp_fun__val__Tree__Int_(T), V)) | ?[T_2: 'Tree'] : ((T_2 = tptp_fun__right__Tree__Tree_(T)) & searchtree(T_2))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 ((~![T: 'Tree', V: $int] : (searchtree(T) => (((T = |'empty:Tree'|) => $true) & ((~(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_1: 'Tree'] : ((T_1 = tptp_fun__left__Tree__Tree_(T)) & searchtree(T_1))) & ((~$less(V, tptp_fun__val__Tree__Int_(T))) => ?[T_2: 'Tree'] : ((T_2 = tptp_fun__right__Tree__Tree_(T)) & searchtree(T_2)))))))))) <=> (~![T: 'Tree', V: $int] : ((V = tptp_fun__val__Tree__Int_(T)) | (T = |'empty:Tree'|) | (~searchtree(T)) | (($lesseq(tptp_fun__val__Tree__Int_(T), V) | ?[T_1: 'Tree'] : ((T_1 = tptp_fun__left__Tree__Tree_(T)) & searchtree(T_1))) & ((~$lesseq(tptp_fun__val__Tree__Int_(T), V)) | ?[T_2: 'Tree'] : ((T_2 = tptp_fun__right__Tree__Tree_(T)) & searchtree(T_2))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(41,axiom,(~![T: 'Tree', V: $int] : (searchtree(T) => (((T = |'empty:Tree'|) => $true) & ((~(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_1: 'Tree'] : ((T_1 = tptp_fun__left__Tree__Tree_(T)) & searchtree(T_1))) & ((~$less(V, tptp_fun__val__Tree__Int_(T))) => ?[T_2: 'Tree'] : ((T_2 = tptp_fun__right__Tree__Tree_(T)) & searchtree(T_2)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','formula_007')).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (~![T: 'Tree', V: $int] : ((V = tptp_fun__val__Tree__Int_(T)) | (T = |'empty:Tree'|) | (~searchtree(T)) | (($lesseq(tptp_fun__val__Tree__Int_(T), V) | ?[T_1: 'Tree'] : ((T_1 = tptp_fun__left__Tree__Tree_(T)) & searchtree(T_1))) & ((~$lesseq(tptp_fun__val__Tree__Int_(T), V)) | ?[T_2: 'Tree'] : ((T_2 = tptp_fun__right__Tree__Tree_(T)) & searchtree(T_2)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (~![T: 'Tree', V: $int] : ((V = tptp_fun__val__Tree__Int_(T)) | (T = |'empty:Tree'|) | (~searchtree(T)) | (($lesseq(tptp_fun__val__Tree__Int_(T), V) | ?[T_1: 'Tree'] : ((T_1 = tptp_fun__left__Tree__Tree_(T)) & searchtree(T_1))) & ((~$lesseq(tptp_fun__val__Tree__Int_(T), V)) | ?[T_2: 'Tree'] : ((T_2 = tptp_fun__right__Tree__Tree_(T)) & searchtree(T_2)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[42, 39])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (~![T: 'Tree', V: $int] : ((V = tptp_fun__val__Tree__Int_(T)) | (T = |'empty:Tree'|) | (~searchtree(T)) | (($lesseq(tptp_fun__val__Tree__Int_(T), V) | ?[T_1: 'Tree'] : ((T_1 = tptp_fun__left__Tree__Tree_(T)) & searchtree(T_1))) & ((~$lesseq(tptp_fun__val__Tree__Int_(T), V)) | ?[T_2: 'Tree'] : ((T_2 = tptp_fun__right__Tree__Tree_(T)) & searchtree(T_2)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (~![T: 'Tree', V: $int] : ((V = tptp_fun__val__Tree__Int_(T)) | (T = |'empty:Tree'|) | (~searchtree(T)) | (($lesseq(tptp_fun__val__Tree__Int_(T), V) | ?[T_1: 'Tree'] : ((T_1 = tptp_fun__left__Tree__Tree_(T)) & searchtree(T_1))) & ((~$lesseq(tptp_fun__val__Tree__Int_(T), V)) | ?[T_2: 'Tree'] : ((T_2 = tptp_fun__right__Tree__Tree_(T)) & searchtree(T_2)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[44, 39])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (~![T: 'Tree', V: $int] : ((T = |'empty:Tree'|) | (($lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0) | ?[T_1: 'Tree'] : ((T_1 = tptp_fun__left__Tree__Tree_(T)) & searchtree(T_1))) & ((~$lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) | ?[T_2: 'Tree'] : ((T_2 = tptp_fun__right__Tree__Tree_(T)) & searchtree(T_2)))) | (~searchtree(T)) | ($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T))) = 0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (~![T: 'Tree', V: $int] : ((T = |'empty:Tree'|) | (($lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0) | ?[T_1: 'Tree'] : ((T_1 = tptp_fun__left__Tree__Tree_(T)) & searchtree(T_1))) & ((~$lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) | ?[T_2: 'Tree'] : ((T_2 = tptp_fun__right__Tree__Tree_(T)) & searchtree(T_2)))) | (~searchtree(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[46, 37])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (~![T: 'Tree', V: $int] : ((T = |'empty:Tree'|) | (($lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0) | ?[T_1: 'Tree'] : ((T_1 = tptp_fun__left__Tree__Tree_(T)) & searchtree(T_1))) & ((~$lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) | ?[T_2: 'Tree'] : ((T_2 = tptp_fun__right__Tree__Tree_(T)) & searchtree(T_2)))) | (~searchtree(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[47, 36])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (~![T: 'Tree', V: $int] : ((T = |'empty:Tree'|) | (($lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0) | ?[T_1: 'Tree'] : ((T_1 = tptp_fun__left__Tree__Tree_(T)) & searchtree(T_1))) & ((~$lesseq($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)), 0)) | ?[T_2: 'Tree'] : ((T_2 = tptp_fun__right__Tree__Tree_(T)) & searchtree(T_2)))) | (~searchtree(T)) | ($sum(tptp_fun__val__Tree__Int_(T), $product(-1, V)) = 0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[48, 36])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 ((~(T!3 = |'empty:Tree'|)) & (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_1: 'Tree'] : (~((T_1 = tptp_fun__left__Tree__Tree_(T!3)) & searchtree(T_1)))) | ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_2: 'Tree'] : (~((T_2 = tptp_fun__right__Tree__Tree_(T!3)) & searchtree(T_2))))) & searchtree(T!3) & (~($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))) = 0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[49, 35])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (searchtree(T!3)),
% 0.19/0.41 inference(and_elim,[status(thm)],[50])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (~(T!3 = |'empty:Tree'|)),
% 0.19/0.41 inference(and_elim,[status(thm)],[50])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 ((~((T!3 = |'empty:Tree'|) | (~searchtree(T!3)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T!3))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T!3))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)))))))) | (T!3 = |'empty:Tree'|) | (~searchtree(T!3)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T!3))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T!3))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 ((~((T!3 = |'empty:Tree'|) | (~searchtree(T!3)) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T!3))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T!3))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)))))))) | (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T!3))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T!3))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[53, 52, 51])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (~((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T!3))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T!3))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[54, 34])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T!3))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T!3))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))))) | searchtree(tptp_fun__left__Tree__Tree_(T!3))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (searchtree(tptp_fun__left__Tree__Tree_(T!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~![V: $int] : ((~in(V, tptp_fun__left__Tree__Tree_(T!3))) | $lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))) | (~![V: $int] : ((~in(V, tptp_fun__right__Tree__Tree_(T!3))) | (~$lesseq($sum(V, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0))))) | searchtree(tptp_fun__right__Tree__Tree_(T!3))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (searchtree(tptp_fun__right__Tree__Tree_(T!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[58, 55])).
% 0.19/0.41 tff(60,assumption,(![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3))))), introduced(assumption)).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (((~![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3)))) <=> ((~![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 (((~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | $false) <=> (~searchtree(tptp_fun__right__Tree__Tree_(T!3)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 ((~$true) <=> $false),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 ((tptp_fun__right__Tree__Tree_(T!3) = tptp_fun__right__Tree__Tree_(T!3)) <=> $true),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 ((~(tptp_fun__right__Tree__Tree_(T!3) = tptp_fun__right__Tree__Tree_(T!3))) <=> (~$true)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[64])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 ((~(tptp_fun__right__Tree__Tree_(T!3) = tptp_fun__right__Tree__Tree_(T!3))) <=> $false),
% 0.19/0.42 inference(transitivity,[status(thm)],[65, 63])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 (((~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~(tptp_fun__right__Tree__Tree_(T!3) = tptp_fun__right__Tree__Tree_(T!3)))) <=> ((~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | $false)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.42 tff(68,plain,
% 0.19/0.42 (((~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~(tptp_fun__right__Tree__Tree_(T!3) = tptp_fun__right__Tree__Tree_(T!3)))) <=> (~searchtree(tptp_fun__right__Tree__Tree_(T!3)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[67, 62])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (((~![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3))))) | ((~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~(tptp_fun__right__Tree__Tree_(T!3) = tptp_fun__right__Tree__Tree_(T!3))))) <=> ((~![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[68])).
% 0.19/0.42 tff(70,plain,
% 0.19/0.42 (((~![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3))))) | ((~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~(tptp_fun__right__Tree__Tree_(T!3) = tptp_fun__right__Tree__Tree_(T!3))))) <=> ((~![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[69, 61])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 ((~![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3))))) | ((~searchtree(tptp_fun__right__Tree__Tree_(T!3))) | (~(tptp_fun__right__Tree__Tree_(T!3) = tptp_fun__right__Tree__Tree_(T!3))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 ((~![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__right__Tree__Tree_(T!3)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[72, 60, 59])).
% 0.19/0.42 tff(74,plain,(~![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3)))))) | ![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 (((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3)))))))) <=> ((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 (((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3)))))))) <=> ((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3))))) <=> (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3)))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (^[T_2: 'Tree'] : trans(monotonicity(rewrite(((T_2 = tptp_fun__right__Tree__Tree_(T!3)) & searchtree(T_2)) <=> (~((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3)))))), ((~((T_2 = tptp_fun__right__Tree__Tree_(T!3)) & searchtree(T_2))) <=> (~(~((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3)))))))), rewrite((~(~((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3)))))) <=> ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3))))), ((~((T_2 = tptp_fun__right__Tree__Tree_(T!3)) & searchtree(T_2))) <=> ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (![T_2: 'Tree'] : (~((T_2 = tptp_fun__right__Tree__Tree_(T!3)) & searchtree(T_2))) <=> ![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_2: 'Tree'] : (~((T_2 = tptp_fun__right__Tree__Tree_(T!3)) & searchtree(T_2)))) <=> ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_2: 'Tree'] : (~((T_2 = tptp_fun__right__Tree__Tree_(T!3)) & searchtree(T_2)))) <=> (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3)))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[82, 79])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))) <=> (~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3)))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (^[T_1: 'Tree'] : trans(monotonicity(rewrite(((T_1 = tptp_fun__left__Tree__Tree_(T!3)) & searchtree(T_1)) <=> (~((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3)))))), ((~((T_1 = tptp_fun__left__Tree__Tree_(T!3)) & searchtree(T_1))) <=> (~(~((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3)))))))), rewrite((~(~((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3)))))) <=> ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))), ((~((T_1 = tptp_fun__left__Tree__Tree_(T!3)) & searchtree(T_1))) <=> ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (![T_1: 'Tree'] : (~((T_1 = tptp_fun__left__Tree__Tree_(T!3)) & searchtree(T_1))) <=> ![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[85])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_1: 'Tree'] : (~((T_1 = tptp_fun__left__Tree__Tree_(T!3)) & searchtree(T_1)))) <=> ((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[86])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_1: 'Tree'] : (~((T_1 = tptp_fun__left__Tree__Tree_(T!3)) & searchtree(T_1)))) <=> (~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3)))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[87, 84])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 ((((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_1: 'Tree'] : (~((T_1 = tptp_fun__left__Tree__Tree_(T!3)) & searchtree(T_1)))) | ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_2: 'Tree'] : (~((T_2 = tptp_fun__right__Tree__Tree_(T!3)) & searchtree(T_2))))) <=> ((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3))))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[88, 83])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 ((((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_1: 'Tree'] : (~((T_1 = tptp_fun__left__Tree__Tree_(T!3)) & searchtree(T_1)))) | ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_2: 'Tree'] : (~((T_2 = tptp_fun__right__Tree__Tree_(T!3)) & searchtree(T_2))))) <=> ((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[89, 78])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) & ![T_1: 'Tree'] : (~((T_1 = tptp_fun__left__Tree__Tree_(T!3)) & searchtree(T_1)))) | ($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) & ![T_2: 'Tree'] : (~((T_2 = tptp_fun__right__Tree__Tree_(T!3)) & searchtree(T_2))))),
% 0.19/0.42 inference(and_elim,[status(thm)],[50])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 ((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3)))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 ((~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))))) | (~((~$greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0)) | (~![T_2: 'Tree'] : ((~searchtree(T_2)) | (~(T_2 = tptp_fun__right__Tree__Tree_(T!3)))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[92, 77])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (~($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[93, 76])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 (($greatereq($sum(V!2, $product(-1, tptp_fun__val__Tree__Int_(T!3))), 0) | (~![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3)))))) | ![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 (((~![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__left__Tree__Tree_(T!3)))) <=> ((~![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__left__Tree__Tree_(T!3))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | $false) <=> (~searchtree(tptp_fun__left__Tree__Tree_(T!3)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 ((tptp_fun__left__Tree__Tree_(T!3) = tptp_fun__left__Tree__Tree_(T!3)) <=> $true),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 ((~(tptp_fun__left__Tree__Tree_(T!3) = tptp_fun__left__Tree__Tree_(T!3))) <=> (~$true)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[99])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 ((~(tptp_fun__left__Tree__Tree_(T!3) = tptp_fun__left__Tree__Tree_(T!3))) <=> $false),
% 0.19/0.42 inference(transitivity,[status(thm)],[100, 63])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 (((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~(tptp_fun__left__Tree__Tree_(T!3) = tptp_fun__left__Tree__Tree_(T!3)))) <=> ((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | $false)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[101])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 (((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~(tptp_fun__left__Tree__Tree_(T!3) = tptp_fun__left__Tree__Tree_(T!3)))) <=> (~searchtree(tptp_fun__left__Tree__Tree_(T!3)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[102, 98])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 (((~![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))) | ((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~(tptp_fun__left__Tree__Tree_(T!3) = tptp_fun__left__Tree__Tree_(T!3))))) <=> ((~![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__left__Tree__Tree_(T!3))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[103])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 (((~![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))) | ((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~(tptp_fun__left__Tree__Tree_(T!3) = tptp_fun__left__Tree__Tree_(T!3))))) <=> ((~![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__left__Tree__Tree_(T!3))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[104, 97])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 ((~![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))) | ((~searchtree(tptp_fun__left__Tree__Tree_(T!3))) | (~(tptp_fun__left__Tree__Tree_(T!3) = tptp_fun__left__Tree__Tree_(T!3))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 ((~![T_1: 'Tree'] : ((~searchtree(T_1)) | (~(T_1 = tptp_fun__left__Tree__Tree_(T!3))))) | (~searchtree(tptp_fun__left__Tree__Tree_(T!3)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[107, 96, 57])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------