TSTP Solution File: DAT105_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT105_1 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 : Fri Sep 16 14:36:45 EDT 2022
% Result : Theorem 0.13s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : DAT105_1 : TPTP v8.1.0. Released v6.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n025.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 : Wed Aug 31 02:01:15 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 % SZS output start Proof
% 0.13/0.41 tff(head_type, type, (
% 0.13/0.41 head: list > $int)).
% 0.13/0.41 tff(cons_type, type, (
% 0.13/0.41 cons: ( $int * list ) > list)).
% 0.13/0.41 tff(tail_type, type, (
% 0.13/0.41 tail: list > list)).
% 0.13/0.41 tff(nil_type, type, (
% 0.13/0.41 nil: list)).
% 0.13/0.41 tff(inRange_type, type, (
% 0.13/0.41 inRange: ( $int * list ) > $o)).
% 0.13/0.41 tff(tptp_fun_T_0_type, type, (
% 0.13/0.41 tptp_fun_T_0: ( list * $int ) > list)).
% 0.13/0.41 tff(tptp_fun_K_1_type, type, (
% 0.13/0.41 tptp_fun_K_1: ( list * $int ) > $int)).
% 0.13/0.41 tff(1,plain,
% 0.13/0.41 (^[K: $int, L: list] : refl((~(cons(K, L) = nil)) <=> (~(cons(K, L) = nil)))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(2,plain,
% 0.13/0.41 (![K: $int, L: list] : (~(cons(K, L) = nil)) <=> ![K: $int, L: list] : (~(cons(K, L) = nil))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.41 tff(3,plain,
% 0.13/0.41 (![K: $int, L: list] : (~(cons(K, L) = nil)) <=> ![K: $int, L: list] : (~(cons(K, L) = nil))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(4,axiom,(![K: $int, L: list] : (~(cons(K, L) = nil))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l4')).
% 0.13/0.41 tff(5,plain,
% 0.13/0.41 (![K: $int, L: list] : (~(cons(K, L) = nil))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.41 tff(6,plain,(
% 0.13/0.41 ![K: $int, L: list] : (~(cons(K, L) = nil))),
% 0.13/0.41 inference(skolemize,[status(sab)],[5])).
% 0.13/0.41 tff(7,plain,
% 0.13/0.41 (![K: $int, L: list] : (~(cons(K, L) = nil))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.41 tff(8,plain,
% 0.13/0.41 ((~![K: $int, L: list] : (~(cons(K, L) = nil))) | (~(cons(0, nil) = nil))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(9,plain,
% 0.13/0.41 (~(cons(0, nil) = nil)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.41 tff(10,plain,
% 0.13/0.41 (^[L: list] : refl(((L = nil) | (L = cons(head(L), tail(L)))) <=> ((L = nil) | (L = cons(head(L), tail(L)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(11,plain,
% 0.13/0.41 (![L: list] : ((L = nil) | (L = cons(head(L), tail(L)))) <=> ![L: list] : ((L = nil) | (L = cons(head(L), tail(L))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[10])).
% 0.13/0.41 tff(12,plain,
% 0.13/0.41 (![L: list] : ((L = nil) | (L = cons(head(L), tail(L)))) <=> ![L: list] : ((L = nil) | (L = cons(head(L), tail(L))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(13,axiom,(![L: list] : ((L = nil) | (L = cons(head(L), tail(L))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l3')).
% 0.13/0.41 tff(14,plain,
% 0.13/0.41 (![L: list] : ((L = nil) | (L = cons(head(L), tail(L))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.13/0.41 tff(15,plain,(
% 0.13/0.41 ![L: list] : ((L = nil) | (L = cons(head(L), tail(L))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[14])).
% 0.13/0.41 tff(16,plain,
% 0.13/0.41 (![L: list] : ((L = nil) | (L = cons(head(L), tail(L))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.13/0.41 tff(17,plain,
% 0.13/0.41 (((~![L: list] : ((L = nil) | (L = cons(head(L), tail(L))))) | ((cons(0, nil) = nil) | (cons(0, nil) = cons(head(cons(0, nil)), tail(cons(0, nil)))))) <=> ((~![L: list] : ((L = nil) | (L = cons(head(L), tail(L))))) | (cons(0, nil) = nil) | (cons(0, nil) = cons(head(cons(0, nil)), tail(cons(0, nil)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(18,plain,
% 0.13/0.41 ((~![L: list] : ((L = nil) | (L = cons(head(L), tail(L))))) | ((cons(0, nil) = nil) | (cons(0, nil) = cons(head(cons(0, nil)), tail(cons(0, nil)))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(19,plain,
% 0.13/0.41 ((~![L: list] : ((L = nil) | (L = cons(head(L), tail(L))))) | (cons(0, nil) = nil) | (cons(0, nil) = cons(head(cons(0, nil)), tail(cons(0, nil))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.13/0.41 tff(20,plain,
% 0.13/0.41 (cons(0, nil) = cons(head(cons(0, nil)), tail(cons(0, nil)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 0.13/0.41 tff(21,plain,
% 0.13/0.41 (cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil)),
% 0.13/0.41 inference(symmetry,[status(thm)],[20])).
% 0.13/0.41 tff(22,assumption,(~inRange(1, nil)), introduced(assumption)).
% 0.13/0.41 tff(23,plain,
% 0.13/0.41 (^[N: $int, L: list] : refl((~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))))) <=> (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(24,plain,
% 0.13/0.41 (![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))))) <=> ![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[23])).
% 0.13/0.41 tff(25,plain,
% 0.13/0.41 (^[N: $int, L: list] : rewrite((~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))))) <=> (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 (![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))))) <=> ![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[25])).
% 0.13/0.41 tff(27,plain,
% 0.13/0.41 (![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))))) <=> ![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[26, 24])).
% 0.13/0.41 tff(28,plain,
% 0.13/0.41 (^[N: $int, L: list] : trans(monotonicity(trans(monotonicity(rewrite(((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0)) & inRange(N, tptp_fun_T_0(L, N))) <=> (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N)))))), (((L = nil) | (~inRange(N, L)) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0)) & inRange(N, tptp_fun_T_0(L, N)))) <=> ((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N)))))))), rewrite(((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N)))))) <=> ((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))), (((L = nil) | (~inRange(N, L)) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0)) & inRange(N, tptp_fun_T_0(L, N)))) <=> ((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N)))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[K: $int, T: list] : trans(monotonicity(rewrite(((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T)) <=> (~($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))), ((~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T))) <=> (~(~($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))), rewrite((~(~($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))) <=> ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))), ((~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T))) <=> ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))), (![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T))) <=> ![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))), (((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T)))) <=> ((~(L = nil)) & ![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))), rewrite(((~(L = nil)) & ![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))) <=> (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))), (((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T)))) <=> (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))), ((inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T))))) <=> (inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))), rewrite((inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))) <=> (inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))), ((inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T))))) <=> (inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))), ((((L = nil) | (~inRange(N, L)) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0)) & inRange(N, tptp_fun_T_0(L, N)))) & (inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T)))))) <=> (((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N)))))) & (inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))))), rewrite((((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N)))))) & (inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T)))))))) <=> (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))), ((((L = nil) | (~inRange(N, L)) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0)) & inRange(N, tptp_fun_T_0(L, N)))) & (inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T)))))) <=> (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(29,plain,
% 0.13/0.41 (![N: $int, L: list] : (((L = nil) | (~inRange(N, L)) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0)) & inRange(N, tptp_fun_T_0(L, N)))) & (inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T)))))) <=> ![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (^[N: $int, L: list] : rewrite((((~inRange(N, L)) | ((L = nil) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$greatereq($sum(tptp_fun_K_1(L, N), $product(-1, N)), 0)) & inRange(N, tptp_fun_T_0(L, N))))) & (inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T)))))) <=> (((L = nil) | (~inRange(N, L)) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0)) & inRange(N, tptp_fun_T_0(L, N)))) & (inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T)))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (![N: $int, L: list] : (((~inRange(N, L)) | ((L = nil) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$greatereq($sum(tptp_fun_K_1(L, N), $product(-1, N)), 0)) & inRange(N, tptp_fun_T_0(L, N))))) & (inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T)))))) <=> ![N: $int, L: list] : (((L = nil) | (~inRange(N, L)) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0)) & inRange(N, tptp_fun_T_0(L, N)))) & (inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (^[N: $int, L: list] : rewrite((inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $greatereq(K, 0) & (~$lesseq($sum(N, $product(-1, K)), 0)) & inRange(N, T)))) <=> (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 (![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $greatereq(K, 0) & (~$lesseq($sum(N, $product(-1, K)), 0)) & inRange(N, T)))) <=> ![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (^[N: $int, L: list] : rewrite((inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $lesseq(0, K) & (~$lesseq(N, K)) & inRange(N, T)))) <=> (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $greatereq(K, 0) & (~$lesseq($sum(N, $product(-1, K)), 0)) & inRange(N, T)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $lesseq(0, K) & (~$lesseq(N, K)) & inRange(N, T)))) <=> ![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $greatereq(K, 0) & (~$lesseq($sum(N, $product(-1, K)), 0)) & inRange(N, T))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $lesseq(0, K) & (~$lesseq(N, K)) & inRange(N, T)))) <=> ![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $lesseq(0, K) & (~$lesseq(N, K)) & inRange(N, T))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (^[N: $int, L: list] : rewrite((inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((((L = cons(K, T)) & $lesseq(0, K)) & $less(K, N)) & inRange(N, T)))) <=> (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $lesseq(0, K) & (~$lesseq(N, K)) & inRange(N, T)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((((L = cons(K, T)) & $lesseq(0, K)) & $less(K, N)) & inRange(N, T)))) <=> ![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $lesseq(0, K) & (~$lesseq(N, K)) & inRange(N, T))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[37])).
% 0.21/0.41 tff(39,axiom,(![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((((L = cons(K, T)) & $lesseq(0, K)) & $less(K, N)) & inRange(N, T))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','inRange')).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $lesseq(0, K) & (~$lesseq(N, K)) & inRange(N, T))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $lesseq(0, K) & (~$lesseq(N, K)) & inRange(N, T))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $greatereq(K, 0) & (~$lesseq($sum(N, $product(-1, K)), 0)) & inRange(N, T))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[41, 35])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (![N: $int, L: list] : (inRange(N, L) <=> ((L = nil) | ?[K: $int, T: list] : ((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[42, 33])).
% 0.21/0.41 tff(44,plain,(
% 0.21/0.41 ![N: $int, L: list] : (((~inRange(N, L)) | ((L = nil) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$greatereq($sum(tptp_fun_K_1(L, N), $product(-1, N)), 0)) & inRange(N, tptp_fun_T_0(L, N))))) & (inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T))))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[43])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (![N: $int, L: list] : (((L = nil) | (~inRange(N, L)) | ((L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N))) & $greatereq(tptp_fun_K_1(L, N), 0) & (~$lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0)) & inRange(N, tptp_fun_T_0(L, N)))) & (inRange(N, L) | ((~(L = nil)) & ![K: $int, T: list] : (~((L = cons(K, T)) & $greatereq(K, 0) & (~$greatereq($sum(K, $product(-1, N)), 0)) & inRange(N, T))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[44, 31])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[45, 29])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[46, 27])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | inRange(1, nil)) <=> ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | inRange(1, nil))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(49,plain,
% 0.21/0.42 ((~(~inRange(1, nil))) <=> inRange(1, nil)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 (($false | (~inRange(1, nil))) <=> (~inRange(1, nil))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(51,plain,
% 0.21/0.42 ((~(inRange(1, nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, 1)), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(1, T)))))))) <=> (~inRange(1, nil))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(52,plain,
% 0.21/0.42 ((~$true) <=> $false),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(53,plain,
% 0.21/0.42 (($true | (~inRange(1, nil)) | (~((~(nil = cons(tptp_fun_K_1(nil, 1), tptp_fun_T_0(nil, 1)))) | (~$greatereq(tptp_fun_K_1(nil, 1), 0)) | (~inRange(1, tptp_fun_T_0(nil, 1))) | $greatereq(tptp_fun_K_1(nil, 1), 1)))) <=> $true),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(54,plain,
% 0.21/0.42 ((~($lesseq($sum(1, $product(-1, tptp_fun_K_1(nil, 1))), 0) | (~(nil = cons(tptp_fun_K_1(nil, 1), tptp_fun_T_0(nil, 1)))) | (~$greatereq(tptp_fun_K_1(nil, 1), 0)) | (~inRange(1, tptp_fun_T_0(nil, 1))))) <=> (~((~(nil = cons(tptp_fun_K_1(nil, 1), tptp_fun_T_0(nil, 1)))) | (~$greatereq(tptp_fun_K_1(nil, 1), 0)) | (~inRange(1, tptp_fun_T_0(nil, 1))) | $greatereq(tptp_fun_K_1(nil, 1), 1)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(55,plain,
% 0.21/0.42 ((nil = nil) <=> $true),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(56,plain,
% 0.21/0.42 (((nil = nil) | (~inRange(1, nil)) | (~($lesseq($sum(1, $product(-1, tptp_fun_K_1(nil, 1))), 0) | (~(nil = cons(tptp_fun_K_1(nil, 1), tptp_fun_T_0(nil, 1)))) | (~$greatereq(tptp_fun_K_1(nil, 1), 0)) | (~inRange(1, tptp_fun_T_0(nil, 1)))))) <=> ($true | (~inRange(1, nil)) | (~((~(nil = cons(tptp_fun_K_1(nil, 1), tptp_fun_T_0(nil, 1)))) | (~$greatereq(tptp_fun_K_1(nil, 1), 0)) | (~inRange(1, tptp_fun_T_0(nil, 1))) | $greatereq(tptp_fun_K_1(nil, 1), 1))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[55, 54])).
% 0.21/0.42 tff(57,plain,
% 0.21/0.42 (((nil = nil) | (~inRange(1, nil)) | (~($lesseq($sum(1, $product(-1, tptp_fun_K_1(nil, 1))), 0) | (~(nil = cons(tptp_fun_K_1(nil, 1), tptp_fun_T_0(nil, 1)))) | (~$greatereq(tptp_fun_K_1(nil, 1), 0)) | (~inRange(1, tptp_fun_T_0(nil, 1)))))) <=> $true),
% 0.21/0.42 inference(transitivity,[status(thm)],[56, 53])).
% 0.21/0.42 tff(58,plain,
% 0.21/0.42 ((~((nil = nil) | (~inRange(1, nil)) | (~($lesseq($sum(1, $product(-1, tptp_fun_K_1(nil, 1))), 0) | (~(nil = cons(tptp_fun_K_1(nil, 1), tptp_fun_T_0(nil, 1)))) | (~$greatereq(tptp_fun_K_1(nil, 1), 0)) | (~inRange(1, tptp_fun_T_0(nil, 1))))))) <=> (~$true)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[57])).
% 0.21/0.42 tff(59,plain,
% 0.21/0.42 ((~((nil = nil) | (~inRange(1, nil)) | (~($lesseq($sum(1, $product(-1, tptp_fun_K_1(nil, 1))), 0) | (~(nil = cons(tptp_fun_K_1(nil, 1), tptp_fun_T_0(nil, 1)))) | (~$greatereq(tptp_fun_K_1(nil, 1), 0)) | (~inRange(1, tptp_fun_T_0(nil, 1))))))) <=> $false),
% 0.21/0.42 inference(transitivity,[status(thm)],[58, 52])).
% 0.21/0.42 tff(60,plain,
% 0.21/0.42 (((~((nil = nil) | (~inRange(1, nil)) | (~($lesseq($sum(1, $product(-1, tptp_fun_K_1(nil, 1))), 0) | (~(nil = cons(tptp_fun_K_1(nil, 1), tptp_fun_T_0(nil, 1)))) | (~$greatereq(tptp_fun_K_1(nil, 1), 0)) | (~inRange(1, tptp_fun_T_0(nil, 1))))))) | (~(inRange(1, nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, 1)), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(1, T))))))))) <=> ($false | (~inRange(1, nil)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[59, 51])).
% 0.21/0.42 tff(61,plain,
% 0.21/0.42 (((~((nil = nil) | (~inRange(1, nil)) | (~($lesseq($sum(1, $product(-1, tptp_fun_K_1(nil, 1))), 0) | (~(nil = cons(tptp_fun_K_1(nil, 1), tptp_fun_T_0(nil, 1)))) | (~$greatereq(tptp_fun_K_1(nil, 1), 0)) | (~inRange(1, tptp_fun_T_0(nil, 1))))))) | (~(inRange(1, nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, 1)), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(1, T))))))))) <=> (~inRange(1, nil))),
% 0.21/0.42 inference(transitivity,[status(thm)],[60, 50])).
% 0.21/0.42 tff(62,plain,
% 0.21/0.42 ((~((~((nil = nil) | (~inRange(1, nil)) | (~($lesseq($sum(1, $product(-1, tptp_fun_K_1(nil, 1))), 0) | (~(nil = cons(tptp_fun_K_1(nil, 1), tptp_fun_T_0(nil, 1)))) | (~$greatereq(tptp_fun_K_1(nil, 1), 0)) | (~inRange(1, tptp_fun_T_0(nil, 1))))))) | (~(inRange(1, nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, 1)), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(1, T)))))))))) <=> (~(~inRange(1, nil)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[61])).
% 0.21/0.42 tff(63,plain,
% 0.21/0.42 ((~((~((nil = nil) | (~inRange(1, nil)) | (~($lesseq($sum(1, $product(-1, tptp_fun_K_1(nil, 1))), 0) | (~(nil = cons(tptp_fun_K_1(nil, 1), tptp_fun_T_0(nil, 1)))) | (~$greatereq(tptp_fun_K_1(nil, 1), 0)) | (~inRange(1, tptp_fun_T_0(nil, 1))))))) | (~(inRange(1, nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, 1)), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(1, T)))))))))) <=> inRange(1, nil)),
% 0.21/0.42 inference(transitivity,[status(thm)],[62, 49])).
% 0.21/0.42 tff(64,plain,
% 0.21/0.42 (((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((nil = nil) | (~inRange(1, nil)) | (~($lesseq($sum(1, $product(-1, tptp_fun_K_1(nil, 1))), 0) | (~(nil = cons(tptp_fun_K_1(nil, 1), tptp_fun_T_0(nil, 1)))) | (~$greatereq(tptp_fun_K_1(nil, 1), 0)) | (~inRange(1, tptp_fun_T_0(nil, 1))))))) | (~(inRange(1, nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, 1)), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(1, T))))))))))) <=> ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | inRange(1, nil))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[63])).
% 0.21/0.42 tff(65,plain,
% 0.21/0.42 (((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((nil = nil) | (~inRange(1, nil)) | (~($lesseq($sum(1, $product(-1, tptp_fun_K_1(nil, 1))), 0) | (~(nil = cons(tptp_fun_K_1(nil, 1), tptp_fun_T_0(nil, 1)))) | (~$greatereq(tptp_fun_K_1(nil, 1), 0)) | (~inRange(1, tptp_fun_T_0(nil, 1))))))) | (~(inRange(1, nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, 1)), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(1, T))))))))))) <=> ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | inRange(1, nil))),
% 0.21/0.42 inference(transitivity,[status(thm)],[64, 48])).
% 0.21/0.42 tff(66,plain,
% 0.21/0.42 ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((nil = nil) | (~inRange(1, nil)) | (~($lesseq($sum(1, $product(-1, tptp_fun_K_1(nil, 1))), 0) | (~(nil = cons(tptp_fun_K_1(nil, 1), tptp_fun_T_0(nil, 1)))) | (~$greatereq(tptp_fun_K_1(nil, 1), 0)) | (~inRange(1, tptp_fun_T_0(nil, 1))))))) | (~(inRange(1, nil) | (~((nil = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, 1)), 0) | (~(nil = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(1, T))))))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(67,plain,
% 0.21/0.42 ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | inRange(1, nil)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.21/0.42 tff(68,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[67, 47, 22])).
% 0.21/0.42 tff(69,plain,(inRange(1, nil)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(70,assumption,(![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))), introduced(assumption)).
% 0.21/0.42 tff(71,plain,
% 0.21/0.42 (((~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))) | ((~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)))) <=> ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(72,plain,
% 0.21/0.42 (($false | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)) | $false) <=> ((~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 ($greatereq(0, 1) <=> $false),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 ($greatereq(0, 0) <=> $true),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 ((~$greatereq(0, 0)) <=> (~$true)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[74])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 ((~$greatereq(0, 0)) <=> $false),
% 0.21/0.42 inference(transitivity,[status(thm)],[75, 52])).
% 0.21/0.42 tff(77,plain,
% 0.21/0.42 (((~$greatereq(0, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)) | $greatereq(0, 1)) <=> ($false | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)) | $false)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[76, 73])).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 (((~$greatereq(0, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)) | $greatereq(0, 1)) <=> ((~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[77, 72])).
% 0.21/0.42 tff(79,plain,
% 0.21/0.42 (((~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))) | ((~$greatereq(0, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)) | $greatereq(0, 1))) <=> ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))) | ((~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[78])).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 (((~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))) | ((~$greatereq(0, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)) | $greatereq(0, 1))) <=> ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[79, 71])).
% 0.21/0.42 tff(81,plain,
% 0.21/0.42 ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))) | ((~$greatereq(0, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil)) | $greatereq(0, 1))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 ((~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(0, nil))) | (~inRange(1, nil))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[82, 70, 69, 21])).
% 0.21/0.42 tff(84,plain,(~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 (((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1)))) | ![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 ((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 (((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((~($greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 1) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1)))) | (~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 0)) | (~inRange(1, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))))) | (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~(inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1)))))))))) <=> ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((~($greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 1) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1)))) | (~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 0)) | (~inRange(1, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))))) | (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~(inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(88,plain,
% 0.21/0.43 ((~((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))) | (~($lesseq($sum(1, $product(-1, tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1)))) | (~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 0)) | (~inRange(1, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))))))) | (~(inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, 1)), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(1, T)))))))))) <=> (~((~((~($greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 1) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1)))) | (~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 0)) | (~inRange(1, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))))) | (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~(inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1)))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 (((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))) | (~($lesseq($sum(1, $product(-1, tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1)))) | (~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 0)) | (~inRange(1, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))))))) | (~(inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, 1)), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(1, T))))))))))) <=> ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((~($greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 1) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1)))) | (~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 0)) | (~inRange(1, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))))) | (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~(inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))))))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[88])).
% 0.21/0.43 tff(90,plain,
% 0.21/0.43 (((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))) | (~($lesseq($sum(1, $product(-1, tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1)))) | (~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 0)) | (~inRange(1, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))))))) | (~(inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, 1)), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(1, T))))))))))) <=> ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((~($greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 1) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1)))) | (~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 0)) | (~inRange(1, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))))) | (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~(inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[89, 87])).
% 0.21/0.43 tff(91,plain,
% 0.21/0.43 ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))) | (~($lesseq($sum(1, $product(-1, tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1)))) | (~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 0)) | (~inRange(1, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))))))) | (~(inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, 1)), 0) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(1, T))))))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(92,plain,
% 0.21/0.43 ((~![N: $int, L: list] : (~((~((L = nil) | (~inRange(N, L)) | (~($lesseq($sum(N, $product(-1, tptp_fun_K_1(L, N))), 0) | (~(L = cons(tptp_fun_K_1(L, N), tptp_fun_T_0(L, N)))) | (~$greatereq(tptp_fun_K_1(L, N), 0)) | (~inRange(N, tptp_fun_T_0(L, N))))))) | (~(inRange(N, L) | (~((L = nil) | (~![K: $int, T: list] : ($greatereq($sum(K, $product(-1, N)), 0) | (~(L = cons(K, T))) | (~$greatereq(K, 0)) | (~inRange(N, T))))))))))) | (~((~((~($greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 1) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1)))) | (~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 0)) | (~inRange(1, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))))) | (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~(inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1)))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.43 tff(93,plain,
% 0.21/0.43 (~((~((~($greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 1) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1)))) | (~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 0)) | (~inRange(1, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))))) | (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~(inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[92, 47])).
% 0.21/0.43 tff(94,plain,
% 0.21/0.43 (((~((~($greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 1) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1)))) | (~$greatereq(tptp_fun_K_1(cons(head(cons(0, nil)), tail(cons(0, nil))), 1), 0)) | (~inRange(1, tptp_fun_T_0(cons(head(cons(0, nil)), tail(cons(0, nil))), 1))))) | (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))) | (~(inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1)))))))) | (inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(95,plain,
% 0.21/0.43 (inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1)))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.21/0.43 tff(96,plain,
% 0.21/0.43 ((~(inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1))))))) | inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1)))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(97,plain,
% 0.21/0.44 (inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))) | (~((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~![K: $int, T: list] : ((~$greatereq(K, 0)) | (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = cons(K, T))) | (~inRange(1, T)) | $greatereq(K, 1)))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.21/0.44 tff(98,plain,
% 0.21/0.44 (inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[97, 86])).
% 0.21/0.44 tff(99,plain,
% 0.21/0.44 ((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) <=> (cons(0, nil) = nil)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[21])).
% 0.21/0.44 tff(100,plain,
% 0.21/0.44 ((cons(0, nil) = nil) <=> (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil)),
% 0.21/0.44 inference(symmetry,[status(thm)],[99])).
% 0.21/0.44 tff(101,plain,
% 0.21/0.44 ((~(cons(0, nil) = nil)) <=> (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = nil))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[100])).
% 0.21/0.44 tff(102,plain,
% 0.21/0.44 (~(cons(head(cons(0, nil)), tail(cons(0, nil))) = nil)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[9, 101])).
% 0.21/0.44 tff(103,plain,
% 0.21/0.44 (^[L: list, N: $int] : refl(((L = nil) | $greatereq($sum(N, $product(-1, head(L))), 2) | (~inRange(N, L))) <=> ((L = nil) | $greatereq($sum(N, $product(-1, head(L))), 2) | (~inRange(N, L))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(104,plain,
% 0.21/0.44 (![L: list, N: $int] : ((L = nil) | $greatereq($sum(N, $product(-1, head(L))), 2) | (~inRange(N, L))) <=> ![L: list, N: $int] : ((L = nil) | $greatereq($sum(N, $product(-1, head(L))), 2) | (~inRange(N, L)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[103])).
% 0.21/0.44 tff(105,plain,
% 0.21/0.44 (^[L: list, N: $int] : trans(monotonicity(trans(monotonicity(rewrite(((~(L = nil)) & inRange(N, L)) <=> (~((L = nil) | (~inRange(N, L))))), ((~((~(L = nil)) & inRange(N, L))) <=> (~(~((L = nil) | (~inRange(N, L))))))), rewrite((~(~((L = nil) | (~inRange(N, L))))) <=> ((L = nil) | (~inRange(N, L)))), ((~((~(L = nil)) & inRange(N, L))) <=> ((L = nil) | (~inRange(N, L))))), (((~((~(L = nil)) & inRange(N, L))) | $greatereq($sum(N, $product(-1, head(L))), 2)) <=> (((L = nil) | (~inRange(N, L))) | $greatereq($sum(N, $product(-1, head(L))), 2)))), rewrite((((L = nil) | (~inRange(N, L))) | $greatereq($sum(N, $product(-1, head(L))), 2)) <=> ((L = nil) | $greatereq($sum(N, $product(-1, head(L))), 2) | (~inRange(N, L)))), (((~((~(L = nil)) & inRange(N, L))) | $greatereq($sum(N, $product(-1, head(L))), 2)) <=> ((L = nil) | $greatereq($sum(N, $product(-1, head(L))), 2) | (~inRange(N, L)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(106,plain,
% 0.21/0.44 (![L: list, N: $int] : ((~((~(L = nil)) & inRange(N, L))) | $greatereq($sum(N, $product(-1, head(L))), 2)) <=> ![L: list, N: $int] : ((L = nil) | $greatereq($sum(N, $product(-1, head(L))), 2) | (~inRange(N, L)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[105])).
% 0.21/0.44 tff(107,plain,
% 0.21/0.44 (![L: list, N: $int] : ((~((~(L = nil)) & inRange(N, L))) | $greatereq($sum(N, $product(-1, head(L))), 2)) <=> ![L: list, N: $int] : ((~((~(L = nil)) & inRange(N, L))) | $greatereq($sum(N, $product(-1, head(L))), 2))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(108,plain,
% 0.21/0.44 ((~(~![L: list, N: $int] : ((~((~(L = nil)) & inRange(N, L))) | $greatereq($sum(N, $product(-1, head(L))), 2)))) <=> ![L: list, N: $int] : ((~((~(L = nil)) & inRange(N, L))) | $greatereq($sum(N, $product(-1, head(L))), 2))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(109,plain,
% 0.21/0.44 ((~![L: list, N: $int] : (((~(L = nil)) & inRange(N, L)) => $greatereq($difference(N, head(L)), 2))) <=> (~![L: list, N: $int] : ((~((~(L = nil)) & inRange(N, L))) | $greatereq($sum(N, $product(-1, head(L))), 2)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(110,plain,
% 0.21/0.44 ((~(~![L: list, N: $int] : (((~(L = nil)) & inRange(N, L)) => $greatereq($difference(N, head(L)), 2)))) <=> (~(~![L: list, N: $int] : ((~((~(L = nil)) & inRange(N, L))) | $greatereq($sum(N, $product(-1, head(L))), 2))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[109])).
% 0.21/0.44 tff(111,plain,
% 0.21/0.44 ((~(~![L: list, N: $int] : (((~(L = nil)) & inRange(N, L)) => $greatereq($difference(N, head(L)), 2)))) <=> ![L: list, N: $int] : ((~((~(L = nil)) & inRange(N, L))) | $greatereq($sum(N, $product(-1, head(L))), 2))),
% 0.21/0.44 inference(transitivity,[status(thm)],[110, 108])).
% 0.21/0.44 tff(112,axiom,(~(~![L: list, N: $int] : (((~(L = nil)) & inRange(N, L)) => $greatereq($difference(N, head(L)), 2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c')).
% 0.21/0.44 tff(113,plain,
% 0.21/0.44 (![L: list, N: $int] : ((~((~(L = nil)) & inRange(N, L))) | $greatereq($sum(N, $product(-1, head(L))), 2))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.44 tff(114,plain,
% 0.21/0.44 (![L: list, N: $int] : ((~((~(L = nil)) & inRange(N, L))) | $greatereq($sum(N, $product(-1, head(L))), 2))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[113, 107])).
% 0.21/0.44 tff(115,plain,(
% 0.21/0.44 ![L: list, N: $int] : ((~((~(L = nil)) & inRange(N, L))) | $greatereq($sum(N, $product(-1, head(L))), 2))),
% 0.21/0.44 inference(skolemize,[status(sab)],[114])).
% 0.21/0.44 tff(116,plain,
% 0.21/0.44 (![L: list, N: $int] : ((L = nil) | $greatereq($sum(N, $product(-1, head(L))), 2) | (~inRange(N, L)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[115, 106])).
% 0.21/0.44 tff(117,plain,
% 0.21/0.44 (![L: list, N: $int] : ((L = nil) | $greatereq($sum(N, $product(-1, head(L))), 2) | (~inRange(N, L)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[116, 104])).
% 0.21/0.44 tff(118,plain,
% 0.21/0.44 (((~![L: list, N: $int] : ((L = nil) | $greatereq($sum(N, $product(-1, head(L))), 2) | (~inRange(N, L)))) | ((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))) | $lesseq(head(cons(head(cons(0, nil)), tail(cons(0, nil)))), -1))) <=> ((~![L: list, N: $int] : ((L = nil) | $greatereq($sum(N, $product(-1, head(L))), 2) | (~inRange(N, L)))) | (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))) | $lesseq(head(cons(head(cons(0, nil)), tail(cons(0, nil)))), -1))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(119,plain,
% 0.21/0.44 (((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | $lesseq(head(cons(head(cons(0, nil)), tail(cons(0, nil)))), -1) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))))) <=> ((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))) | $lesseq(head(cons(head(cons(0, nil)), tail(cons(0, nil)))), -1))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(120,plain,
% 0.21/0.44 ($greatereq($sum(1, $product(-1, head(cons(head(cons(0, nil)), tail(cons(0, nil)))))), 2) <=> $lesseq(head(cons(head(cons(0, nil)), tail(cons(0, nil)))), -1)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(121,plain,
% 0.21/0.44 (((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | $greatereq($sum(1, $product(-1, head(cons(head(cons(0, nil)), tail(cons(0, nil)))))), 2) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))))) <=> ((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | $lesseq(head(cons(head(cons(0, nil)), tail(cons(0, nil)))), -1) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[120])).
% 0.21/0.44 tff(122,plain,
% 0.21/0.44 (((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | $greatereq($sum(1, $product(-1, head(cons(head(cons(0, nil)), tail(cons(0, nil)))))), 2) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil)))))) <=> ((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))) | $lesseq(head(cons(head(cons(0, nil)), tail(cons(0, nil)))), -1))),
% 0.21/0.44 inference(transitivity,[status(thm)],[121, 119])).
% 0.21/0.44 tff(123,plain,
% 0.21/0.44 (((~![L: list, N: $int] : ((L = nil) | $greatereq($sum(N, $product(-1, head(L))), 2) | (~inRange(N, L)))) | ((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | $greatereq($sum(1, $product(-1, head(cons(head(cons(0, nil)), tail(cons(0, nil)))))), 2) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))) <=> ((~![L: list, N: $int] : ((L = nil) | $greatereq($sum(N, $product(-1, head(L))), 2) | (~inRange(N, L)))) | ((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))) | $lesseq(head(cons(head(cons(0, nil)), tail(cons(0, nil)))), -1)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[122])).
% 0.21/0.44 tff(124,plain,
% 0.21/0.44 (((~![L: list, N: $int] : ((L = nil) | $greatereq($sum(N, $product(-1, head(L))), 2) | (~inRange(N, L)))) | ((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | $greatereq($sum(1, $product(-1, head(cons(head(cons(0, nil)), tail(cons(0, nil)))))), 2) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))) <=> ((~![L: list, N: $int] : ((L = nil) | $greatereq($sum(N, $product(-1, head(L))), 2) | (~inRange(N, L)))) | (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))) | $lesseq(head(cons(head(cons(0, nil)), tail(cons(0, nil)))), -1))),
% 0.21/0.44 inference(transitivity,[status(thm)],[123, 118])).
% 0.21/0.44 tff(125,plain,
% 0.21/0.44 ((~![L: list, N: $int] : ((L = nil) | $greatereq($sum(N, $product(-1, head(L))), 2) | (~inRange(N, L)))) | ((cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | $greatereq($sum(1, $product(-1, head(cons(head(cons(0, nil)), tail(cons(0, nil)))))), 2) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(126,plain,
% 0.21/0.44 ((~![L: list, N: $int] : ((L = nil) | $greatereq($sum(N, $product(-1, head(L))), 2) | (~inRange(N, L)))) | (cons(head(cons(0, nil)), tail(cons(0, nil))) = nil) | (~inRange(1, cons(head(cons(0, nil)), tail(cons(0, nil))))) | $lesseq(head(cons(head(cons(0, nil)), tail(cons(0, nil)))), -1)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.21/0.44 tff(127,plain,
% 0.21/0.44 ($lesseq(head(cons(head(cons(0, nil)), tail(cons(0, nil)))), -1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[126, 117, 102, 98])).
% 0.21/0.44 tff(128,plain,
% 0.21/0.44 ((~$greatereq(head(cons(head(cons(0, nil)), tail(cons(0, nil)))), 0)) | (~$lesseq(head(cons(head(cons(0, nil)), tail(cons(0, nil)))), -1))),
% 0.21/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.44 tff(129,plain,
% 0.21/0.44 (~$greatereq(head(cons(head(cons(0, nil)), tail(cons(0, nil)))), 0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.21/0.44 tff(130,plain,
% 0.21/0.44 (^[K: $int, L: list] : refl(($sum(K, $product(-1, head(cons(K, L)))) = 0) <=> ($sum(K, $product(-1, head(cons(K, L)))) = 0))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(131,plain,
% 0.21/0.44 (![K: $int, L: list] : ($sum(K, $product(-1, head(cons(K, L)))) = 0) <=> ![K: $int, L: list] : ($sum(K, $product(-1, head(cons(K, L)))) = 0)),
% 0.21/0.44 inference(quant_intro,[status(thm)],[130])).
% 0.21/0.44 tff(132,plain,
% 0.21/0.44 (^[K: $int, L: list] : trans(monotonicity(rewrite($sum(head(cons(K, L)), $product(-1, K)) = $sum($product(-1, K), head(cons(K, L)))), (($sum(head(cons(K, L)), $product(-1, K)) = 0) <=> ($sum($product(-1, K), head(cons(K, L))) = 0))), rewrite(($sum($product(-1, K), head(cons(K, L))) = 0) <=> ($sum(K, $product(-1, head(cons(K, L)))) = 0)), (($sum(head(cons(K, L)), $product(-1, K)) = 0) <=> ($sum(K, $product(-1, head(cons(K, L)))) = 0)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(133,plain,
% 0.21/0.44 (![K: $int, L: list] : ($sum(head(cons(K, L)), $product(-1, K)) = 0) <=> ![K: $int, L: list] : ($sum(K, $product(-1, head(cons(K, L)))) = 0)),
% 0.21/0.44 inference(quant_intro,[status(thm)],[132])).
% 0.21/0.44 tff(134,plain,
% 0.21/0.44 (^[K: $int, L: list] : rewrite((head(cons(K, L)) = K) <=> ($sum(head(cons(K, L)), $product(-1, K)) = 0))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(135,plain,
% 0.21/0.44 (![K: $int, L: list] : (head(cons(K, L)) = K) <=> ![K: $int, L: list] : ($sum(head(cons(K, L)), $product(-1, K)) = 0)),
% 0.21/0.44 inference(quant_intro,[status(thm)],[134])).
% 0.21/0.44 tff(136,plain,
% 0.21/0.44 (![K: $int, L: list] : (head(cons(K, L)) = K) <=> ![K: $int, L: list] : (head(cons(K, L)) = K)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(137,axiom,(![K: $int, L: list] : (head(cons(K, L)) = K)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l1')).
% 0.21/0.44 tff(138,plain,
% 0.21/0.44 (![K: $int, L: list] : (head(cons(K, L)) = K)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.21/0.44 tff(139,plain,
% 0.21/0.44 (![K: $int, L: list] : ($sum(head(cons(K, L)), $product(-1, K)) = 0)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[138, 135])).
% 0.21/0.44 tff(140,plain,
% 0.21/0.44 (![K: $int, L: list] : ($sum(K, $product(-1, head(cons(K, L)))) = 0)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[139, 133])).
% 0.21/0.44 tff(141,plain,(
% 0.21/0.44 ![K: $int, L: list] : ($sum(K, $product(-1, head(cons(K, L)))) = 0)),
% 0.21/0.44 inference(skolemize,[status(sab)],[140])).
% 0.21/0.44 tff(142,plain,
% 0.21/0.44 (![K: $int, L: list] : ($sum(K, $product(-1, head(cons(K, L)))) = 0)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[141, 131])).
% 0.21/0.44 tff(143,plain,
% 0.21/0.44 (((~![K: $int, L: list] : ($sum(K, $product(-1, head(cons(K, L)))) = 0)) | (head(cons(0, nil)) = 0)) <=> ((~![K: $int, L: list] : ($sum(K, $product(-1, head(cons(K, L)))) = 0)) | (head(cons(0, nil)) = 0))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(144,plain,
% 0.21/0.44 (($product(-1, head(cons(0, nil))) = 0) <=> (head(cons(0, nil)) = 0)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(145,plain,
% 0.21/0.44 ($sum(0, $product(-1, head(cons(0, nil)))) = $product(-1, head(cons(0, nil)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(146,plain,
% 0.21/0.44 (($sum(0, $product(-1, head(cons(0, nil)))) = 0) <=> ($product(-1, head(cons(0, nil))) = 0)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[145])).
% 0.21/0.44 tff(147,plain,
% 0.21/0.44 (($sum(0, $product(-1, head(cons(0, nil)))) = 0) <=> (head(cons(0, nil)) = 0)),
% 0.21/0.44 inference(transitivity,[status(thm)],[146, 144])).
% 0.21/0.44 tff(148,plain,
% 0.21/0.44 (((~![K: $int, L: list] : ($sum(K, $product(-1, head(cons(K, L)))) = 0)) | ($sum(0, $product(-1, head(cons(0, nil)))) = 0)) <=> ((~![K: $int, L: list] : ($sum(K, $product(-1, head(cons(K, L)))) = 0)) | (head(cons(0, nil)) = 0))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[147])).
% 0.21/0.44 tff(149,plain,
% 0.21/0.44 (((~![K: $int, L: list] : ($sum(K, $product(-1, head(cons(K, L)))) = 0)) | ($sum(0, $product(-1, head(cons(0, nil)))) = 0)) <=> ((~![K: $int, L: list] : ($sum(K, $product(-1, head(cons(K, L)))) = 0)) | (head(cons(0, nil)) = 0))),
% 0.21/0.44 inference(transitivity,[status(thm)],[148, 143])).
% 0.21/0.44 tff(150,plain,
% 0.21/0.44 ((~![K: $int, L: list] : ($sum(K, $product(-1, head(cons(K, L)))) = 0)) | ($sum(0, $product(-1, head(cons(0, nil)))) = 0)),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(151,plain,
% 0.21/0.44 ((~![K: $int, L: list] : ($sum(K, $product(-1, head(cons(K, L)))) = 0)) | (head(cons(0, nil)) = 0)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.21/0.44 tff(152,plain,
% 0.21/0.44 (head(cons(0, nil)) = 0),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[151, 142])).
% 0.21/0.44 tff(153,plain,
% 0.21/0.44 (head(cons(head(cons(0, nil)), tail(cons(0, nil)))) = head(cons(0, nil))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[21])).
% 0.21/0.44 tff(154,plain,
% 0.21/0.44 (head(cons(head(cons(0, nil)), tail(cons(0, nil)))) = 0),
% 0.21/0.44 inference(transitivity,[status(thm)],[153, 152])).
% 0.21/0.44 tff(155,plain,
% 0.21/0.44 ((~(head(cons(head(cons(0, nil)), tail(cons(0, nil)))) = 0)) | $greatereq(head(cons(head(cons(0, nil)), tail(cons(0, nil)))), 0)),
% 0.21/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.44 tff(156,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[155, 154, 129])).
% 0.21/0.44 % SZS output end Proof
%------------------------------------------------------------------------------