TSTP Solution File: ALG210+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG210+2 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 : Tue Sep 6 16:09:13 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG210+2 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 29 14:07:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(times_type, type, (
% 0.19/0.39 times: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_B_2_type, type, (
% 0.19/0.39 tptp_fun_B_2: $i)).
% 0.19/0.39 tff(tptp_fun_A_3_type, type, (
% 0.19/0.39 tptp_fun_A_3: $i)).
% 0.19/0.39 tff(tptp_fun_C_0_type, type, (
% 0.19/0.39 tptp_fun_C_0: $i > $i)).
% 0.19/0.39 tff(element_type, type, (
% 0.19/0.39 element: $i > $o)).
% 0.19/0.39 tff(tptp_fun_C_1_type, type, (
% 0.19/0.39 tptp_fun_C_1: $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[B: $i] : refl((~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C))))))) <=> (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![B: $i] : (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C))))))) <=> ![B: $i] : (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (^[B: $i] : rewrite((~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C))))))) <=> (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![B: $i] : (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C))))))) <=> ![B: $i] : (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![B: $i] : (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C))))))) <=> ![B: $i] : (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (^[B: $i] : trans(monotonicity(rewrite(((~element(B)) | ((times(B, tptp_fun_C_0(B)) = B) & (times(B, B) = tptp_fun_C_0(B)))) <=> ((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))), rewrite((element(B) | ![C: $i] : (~((times(B, C) = B) & (times(B, B) = C)))) <=> (element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C))))), ((((~element(B)) | ((times(B, tptp_fun_C_0(B)) = B) & (times(B, B) = tptp_fun_C_0(B)))) & (element(B) | ![C: $i] : (~((times(B, C) = B) & (times(B, B) = C))))) <=> (((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B)))))) & (element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C))))))), rewrite((((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B)))))) & (element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C))))) <=> (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C)))))))), ((((~element(B)) | ((times(B, tptp_fun_C_0(B)) = B) & (times(B, B) = tptp_fun_C_0(B)))) & (element(B) | ![C: $i] : (~((times(B, C) = B) & (times(B, B) = C))))) <=> (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (![B: $i] : (((~element(B)) | ((times(B, tptp_fun_C_0(B)) = B) & (times(B, B) = tptp_fun_C_0(B)))) & (element(B) | ![C: $i] : (~((times(B, C) = B) & (times(B, B) = C))))) <=> ![B: $i] : (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (![B: $i] : (element(B) <=> ?[C: $i] : ((times(B, C) = B) & (times(B, B) = C))) <=> ![B: $i] : (element(B) <=> ?[C: $i] : ((times(B, C) = B) & (times(B, B) = C)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(9,axiom,(![B: $i] : (element(B) <=> ?[C: $i] : ((times(B, C) = B) & (times(B, B) = C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_2')).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (![B: $i] : (element(B) <=> ?[C: $i] : ((times(B, C) = B) & (times(B, B) = C)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.40 tff(11,plain,(
% 0.19/0.40 ![B: $i] : (((~element(B)) | ((times(B, tptp_fun_C_0(B)) = B) & (times(B, B) = tptp_fun_C_0(B)))) & (element(B) | ![C: $i] : (~((times(B, C) = B) & (times(B, B) = C)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[10])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (![B: $i] : (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (![B: $i] : (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 ((~![B: $i] : (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C)))))))) | (~((~((~element(B!2)) | (~((~(times(B!2, tptp_fun_C_0(B!2)) = B!2)) | (~(times(B!2, B!2) = tptp_fun_C_0(B!2))))))) | (~(element(B!2) | ![C: $i] : ((~(times(B!2, C) = B!2)) | (~(times(B!2, B!2) = C)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (~((~((~element(B!2)) | (~((~(times(B!2, tptp_fun_C_0(B!2)) = B!2)) | (~(times(B!2, B!2) = tptp_fun_C_0(B!2))))))) | (~(element(B!2) | ![C: $i] : ((~(times(B!2, C) = B!2)) | (~(times(B!2, B!2) = C))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (((~((~element(B!2)) | (~((~(times(B!2, tptp_fun_C_0(B!2)) = B!2)) | (~(times(B!2, B!2) = tptp_fun_C_0(B!2))))))) | (~(element(B!2) | ![C: $i] : ((~(times(B!2, C) = B!2)) | (~(times(B!2, B!2) = C)))))) | ((~element(B!2)) | (~((~(times(B!2, tptp_fun_C_0(B!2)) = B!2)) | (~(times(B!2, B!2) = tptp_fun_C_0(B!2))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 ((~element(B!2)) | (~((~(times(B!2, tptp_fun_C_0(B!2)) = B!2)) | (~(times(B!2, B!2) = tptp_fun_C_0(B!2)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : (element(C) | (~(element(A) & element(B) & (C = times(A, B)))))) <=> (~![A: $i, B: $i, C: $i] : (element(C) | (~(element(A) & element(B) & (C = times(A, B))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : (((element(A) & element(B)) & (C = times(A, B))) => element(C))) <=> (~![A: $i, B: $i, C: $i] : (element(C) | (~(element(A) & element(B) & (C = times(A, B))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(20,axiom,(~![A: $i, B: $i, C: $i] : (((element(A) & element(B)) & (C = times(A, B))) => element(C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conjecture_1')).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (~![A: $i, B: $i, C: $i] : (element(C) | (~(element(A) & element(B) & (C = times(A, B)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (~![A: $i, B: $i, C: $i] : (element(C) | (~(element(A) & element(B) & (C = times(A, B)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (~![A: $i, B: $i, C: $i] : (element(C) | (~(element(A) & element(B) & (C = times(A, B)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (~![A: $i, B: $i, C: $i] : (element(C) | (~(element(A) & element(B) & (C = times(A, B)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (~![A: $i, B: $i, C: $i] : (element(C) | (~(element(A) & element(B) & (C = times(A, B)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (~![A: $i, B: $i, C: $i] : (element(C) | (~(element(A) & element(B) & (C = times(A, B)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (~![A: $i, B: $i, C: $i] : (element(C) | (~(element(A) & element(B) & (C = times(A, B)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[26, 18])).
% 0.19/0.40 tff(28,plain,(
% 0.19/0.40 ~(element(C!1) | (~(element(A!3) & element(B!2) & (C!1 = times(A!3, B!2)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[27])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (element(A!3) & element(B!2) & (C!1 = times(A!3, B!2))),
% 0.19/0.40 inference(or_elim,[status(thm)],[28])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (element(B!2)),
% 0.19/0.40 inference(and_elim,[status(thm)],[29])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 ((~((~element(B!2)) | (~((~(times(B!2, tptp_fun_C_0(B!2)) = B!2)) | (~(times(B!2, B!2) = tptp_fun_C_0(B!2))))))) | (~element(B!2)) | (~((~(times(B!2, tptp_fun_C_0(B!2)) = B!2)) | (~(times(B!2, B!2) = tptp_fun_C_0(B!2)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 ((~((~element(B!2)) | (~((~(times(B!2, tptp_fun_C_0(B!2)) = B!2)) | (~(times(B!2, B!2) = tptp_fun_C_0(B!2))))))) | (~((~(times(B!2, tptp_fun_C_0(B!2)) = B!2)) | (~(times(B!2, B!2) = tptp_fun_C_0(B!2)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (~((~(times(B!2, tptp_fun_C_0(B!2)) = B!2)) | (~(times(B!2, B!2) = tptp_fun_C_0(B!2))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[32, 17])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (((~(times(B!2, tptp_fun_C_0(B!2)) = B!2)) | (~(times(B!2, B!2) = tptp_fun_C_0(B!2)))) | (times(B!2, tptp_fun_C_0(B!2)) = B!2)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (times(B!2, tptp_fun_C_0(B!2)) = B!2),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (((~(times(B!2, tptp_fun_C_0(B!2)) = B!2)) | (~(times(B!2, B!2) = tptp_fun_C_0(B!2)))) | (times(B!2, B!2) = tptp_fun_C_0(B!2))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (times(B!2, B!2) = tptp_fun_C_0(B!2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[36, 33])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (times(B!2, times(B!2, B!2)) = times(B!2, tptp_fun_C_0(B!2))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[37])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (^[A: $i, B: $i, C: $i] : refl((times(times(A, B), C) = times(B, times(C, A))) <=> (times(times(A, B), C) = times(B, times(C, A))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A))) <=> ![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A))) <=> ![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(42,axiom,(![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_1')).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.40 tff(44,plain,(
% 0.19/0.40 ![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[43])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(B!2, B!2), B!2) = times(B!2, times(B!2, B!2)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (times(times(B!2, B!2), B!2) = times(B!2, times(B!2, B!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (tptp_fun_C_0(B!2) = times(B!2, B!2)),
% 0.19/0.40 inference(symmetry,[status(thm)],[37])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (times(tptp_fun_C_0(B!2), B!2) = times(times(B!2, B!2), B!2)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[48])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (times(tptp_fun_C_0(B!2), B!2) = B!2),
% 0.19/0.40 inference(transitivity,[status(thm)],[49, 47, 38, 35])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (times(A!3, times(tptp_fun_C_0(B!2), B!2)) = times(A!3, B!2)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[50])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(B!2, A!3), tptp_fun_C_0(B!2)) = times(A!3, times(tptp_fun_C_0(B!2), B!2)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (times(times(B!2, A!3), tptp_fun_C_0(B!2)) = times(A!3, times(tptp_fun_C_0(B!2), B!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[52, 45])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (B!2 = times(B!2, tptp_fun_C_0(B!2))),
% 0.19/0.40 inference(symmetry,[status(thm)],[35])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (times(B!2, A!3) = times(times(B!2, tptp_fun_C_0(B!2)), A!3)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[54])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (times(times(B!2, tptp_fun_C_0(B!2)), A!3) = times(B!2, A!3)),
% 0.19/0.40 inference(symmetry,[status(thm)],[55])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(B!2, tptp_fun_C_0(B!2)), A!3) = times(tptp_fun_C_0(B!2), times(A!3, B!2)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (times(times(B!2, tptp_fun_C_0(B!2)), A!3) = times(tptp_fun_C_0(B!2), times(A!3, B!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[57, 45])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (times(tptp_fun_C_0(B!2), times(A!3, B!2)) = times(times(B!2, tptp_fun_C_0(B!2)), A!3)),
% 0.19/0.40 inference(symmetry,[status(thm)],[58])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (times(tptp_fun_C_0(B!2), times(A!3, B!2)) = times(B!2, A!3)),
% 0.19/0.40 inference(transitivity,[status(thm)],[59, 56])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (times(times(tptp_fun_C_0(B!2), times(A!3, B!2)), tptp_fun_C_0(B!2)) = times(times(B!2, A!3), tptp_fun_C_0(B!2))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[60])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(tptp_fun_C_0(B!2), times(A!3, B!2)), tptp_fun_C_0(B!2)) = times(times(A!3, B!2), times(tptp_fun_C_0(B!2), tptp_fun_C_0(B!2))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (times(times(tptp_fun_C_0(B!2), times(A!3, B!2)), tptp_fun_C_0(B!2)) = times(times(A!3, B!2), times(tptp_fun_C_0(B!2), tptp_fun_C_0(B!2)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[62, 45])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (times(times(A!3, B!2), times(tptp_fun_C_0(B!2), tptp_fun_C_0(B!2))) = times(times(tptp_fun_C_0(B!2), times(A!3, B!2)), tptp_fun_C_0(B!2))),
% 0.19/0.40 inference(symmetry,[status(thm)],[63])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (times(tptp_fun_C_0(B!2), tptp_fun_C_0(B!2)) = times(tptp_fun_C_0(B!2), times(B!2, B!2))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[48])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (times(tptp_fun_C_0(B!2), times(B!2, B!2)) = times(tptp_fun_C_0(B!2), tptp_fun_C_0(B!2))),
% 0.19/0.40 inference(symmetry,[status(thm)],[65])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(B!2, tptp_fun_C_0(B!2)), B!2) = times(tptp_fun_C_0(B!2), times(B!2, B!2)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (times(times(B!2, tptp_fun_C_0(B!2)), B!2) = times(tptp_fun_C_0(B!2), times(B!2, B!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[67, 45])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (times(times(B!2, tptp_fun_C_0(B!2)), B!2) = times(B!2, B!2)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[35])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (times(B!2, B!2) = times(times(B!2, tptp_fun_C_0(B!2)), B!2)),
% 0.19/0.40 inference(symmetry,[status(thm)],[69])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (tptp_fun_C_0(B!2) = times(tptp_fun_C_0(B!2), tptp_fun_C_0(B!2))),
% 0.19/0.40 inference(transitivity,[status(thm)],[48, 70, 68, 66])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (times(times(A!3, B!2), tptp_fun_C_0(B!2)) = times(times(A!3, B!2), times(tptp_fun_C_0(B!2), tptp_fun_C_0(B!2)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[71])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(A!3, B!2), tptp_fun_C_0(B!2)) = times(B!2, times(tptp_fun_C_0(B!2), A!3)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (times(times(A!3, B!2), tptp_fun_C_0(B!2)) = times(B!2, times(tptp_fun_C_0(B!2), A!3))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[73, 45])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (times(B!2, times(tptp_fun_C_0(B!2), A!3)) = times(times(A!3, B!2), tptp_fun_C_0(B!2))),
% 0.19/0.40 inference(symmetry,[status(thm)],[74])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 ((~![B: $i] : (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C)))))))) | (~((~((~element(A!3)) | (~((~(times(A!3, tptp_fun_C_0(A!3)) = A!3)) | (~(times(A!3, A!3) = tptp_fun_C_0(A!3))))))) | (~(element(A!3) | ![C: $i] : ((~(times(A!3, C) = A!3)) | (~(times(A!3, A!3) = C)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (~((~((~element(A!3)) | (~((~(times(A!3, tptp_fun_C_0(A!3)) = A!3)) | (~(times(A!3, A!3) = tptp_fun_C_0(A!3))))))) | (~(element(A!3) | ![C: $i] : ((~(times(A!3, C) = A!3)) | (~(times(A!3, A!3) = C))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[76, 13])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (((~((~element(A!3)) | (~((~(times(A!3, tptp_fun_C_0(A!3)) = A!3)) | (~(times(A!3, A!3) = tptp_fun_C_0(A!3))))))) | (~(element(A!3) | ![C: $i] : ((~(times(A!3, C) = A!3)) | (~(times(A!3, A!3) = C)))))) | ((~element(A!3)) | (~((~(times(A!3, tptp_fun_C_0(A!3)) = A!3)) | (~(times(A!3, A!3) = tptp_fun_C_0(A!3))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 ((~element(A!3)) | (~((~(times(A!3, tptp_fun_C_0(A!3)) = A!3)) | (~(times(A!3, A!3) = tptp_fun_C_0(A!3)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (element(A!3)),
% 0.19/0.40 inference(and_elim,[status(thm)],[29])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 ((~((~element(A!3)) | (~((~(times(A!3, tptp_fun_C_0(A!3)) = A!3)) | (~(times(A!3, A!3) = tptp_fun_C_0(A!3))))))) | (~element(A!3)) | (~((~(times(A!3, tptp_fun_C_0(A!3)) = A!3)) | (~(times(A!3, A!3) = tptp_fun_C_0(A!3)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 ((~((~element(A!3)) | (~((~(times(A!3, tptp_fun_C_0(A!3)) = A!3)) | (~(times(A!3, A!3) = tptp_fun_C_0(A!3))))))) | (~((~(times(A!3, tptp_fun_C_0(A!3)) = A!3)) | (~(times(A!3, A!3) = tptp_fun_C_0(A!3)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (~((~(times(A!3, tptp_fun_C_0(A!3)) = A!3)) | (~(times(A!3, A!3) = tptp_fun_C_0(A!3))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[82, 79])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 (((~(times(A!3, tptp_fun_C_0(A!3)) = A!3)) | (~(times(A!3, A!3) = tptp_fun_C_0(A!3)))) | (times(A!3, tptp_fun_C_0(A!3)) = A!3)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (times(A!3, tptp_fun_C_0(A!3)) = A!3),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (times(tptp_fun_C_0(B!2), times(A!3, tptp_fun_C_0(A!3))) = times(tptp_fun_C_0(B!2), A!3)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[85])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(tptp_fun_C_0(A!3), tptp_fun_C_0(B!2)), A!3) = times(tptp_fun_C_0(B!2), times(A!3, tptp_fun_C_0(A!3))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 (times(times(tptp_fun_C_0(A!3), tptp_fun_C_0(B!2)), A!3) = times(tptp_fun_C_0(B!2), times(A!3, tptp_fun_C_0(A!3)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[87, 45])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 (times(times(tptp_fun_C_0(A!3), tptp_fun_C_0(B!2)), A!3) = times(tptp_fun_C_0(B!2), A!3)),
% 0.19/0.40 inference(transitivity,[status(thm)],[88, 86])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 (times(B!2, times(times(tptp_fun_C_0(A!3), tptp_fun_C_0(B!2)), A!3)) = times(B!2, times(tptp_fun_C_0(B!2), A!3))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[89])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(A!3, B!2), times(tptp_fun_C_0(A!3), tptp_fun_C_0(B!2))) = times(B!2, times(times(tptp_fun_C_0(A!3), tptp_fun_C_0(B!2)), A!3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (times(times(A!3, B!2), times(tptp_fun_C_0(A!3), tptp_fun_C_0(B!2))) = times(B!2, times(times(tptp_fun_C_0(A!3), tptp_fun_C_0(B!2)), A!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[91, 45])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (((~(times(A!3, tptp_fun_C_0(A!3)) = A!3)) | (~(times(A!3, A!3) = tptp_fun_C_0(A!3)))) | (times(A!3, A!3) = tptp_fun_C_0(A!3))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (times(A!3, A!3) = tptp_fun_C_0(A!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[93, 83])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 (tptp_fun_C_0(A!3) = times(A!3, A!3)),
% 0.19/0.41 inference(symmetry,[status(thm)],[94])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (times(tptp_fun_C_0(A!3), tptp_fun_C_0(A!3)) = times(tptp_fun_C_0(A!3), times(A!3, A!3))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 (times(tptp_fun_C_0(A!3), times(A!3, A!3)) = times(tptp_fun_C_0(A!3), tptp_fun_C_0(A!3))),
% 0.19/0.41 inference(symmetry,[status(thm)],[96])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(A!3, tptp_fun_C_0(A!3)), A!3) = times(tptp_fun_C_0(A!3), times(A!3, A!3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 (times(times(A!3, tptp_fun_C_0(A!3)), A!3) = times(tptp_fun_C_0(A!3), times(A!3, A!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[98, 45])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (times(times(A!3, tptp_fun_C_0(A!3)), A!3) = times(A!3, A!3)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[85])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (times(A!3, A!3) = times(times(A!3, tptp_fun_C_0(A!3)), A!3)),
% 0.19/0.41 inference(symmetry,[status(thm)],[100])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (tptp_fun_C_0(A!3) = times(tptp_fun_C_0(A!3), tptp_fun_C_0(A!3))),
% 0.19/0.41 inference(transitivity,[status(thm)],[95, 101, 99, 97])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (times(tptp_fun_C_0(A!3), tptp_fun_C_0(B!2)) = times(times(tptp_fun_C_0(A!3), tptp_fun_C_0(A!3)), tptp_fun_C_0(B!2))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[102])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (times(times(tptp_fun_C_0(A!3), tptp_fun_C_0(A!3)), tptp_fun_C_0(B!2)) = times(tptp_fun_C_0(A!3), tptp_fun_C_0(B!2))),
% 0.19/0.41 inference(symmetry,[status(thm)],[103])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(tptp_fun_C_0(A!3), tptp_fun_C_0(A!3)), tptp_fun_C_0(B!2)) = times(tptp_fun_C_0(A!3), times(tptp_fun_C_0(B!2), tptp_fun_C_0(A!3))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 (times(times(tptp_fun_C_0(A!3), tptp_fun_C_0(A!3)), tptp_fun_C_0(B!2)) = times(tptp_fun_C_0(A!3), times(tptp_fun_C_0(B!2), tptp_fun_C_0(A!3)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[105, 45])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 (times(tptp_fun_C_0(A!3), times(tptp_fun_C_0(B!2), tptp_fun_C_0(A!3))) = times(times(tptp_fun_C_0(A!3), tptp_fun_C_0(A!3)), tptp_fun_C_0(B!2))),
% 0.19/0.41 inference(symmetry,[status(thm)],[106])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (times(tptp_fun_C_0(A!3), times(tptp_fun_C_0(B!2), tptp_fun_C_0(A!3))) = times(tptp_fun_C_0(A!3), tptp_fun_C_0(B!2))),
% 0.19/0.41 inference(transitivity,[status(thm)],[107, 104])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (times(times(A!3, B!2), times(tptp_fun_C_0(A!3), times(tptp_fun_C_0(B!2), tptp_fun_C_0(A!3)))) = times(times(A!3, B!2), times(tptp_fun_C_0(A!3), tptp_fun_C_0(B!2)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[108])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 (times(times(A!3, B!2), times(tptp_fun_C_0(A!3), times(tptp_fun_C_0(B!2), tptp_fun_C_0(A!3)))) = times(A!3, B!2)),
% 0.19/0.41 inference(transitivity,[status(thm)],[109, 92, 90, 75, 72, 64, 61, 53, 51])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 (times(tptp_fun_C_0(A!3), times(B!2, B!2)) = times(tptp_fun_C_0(A!3), tptp_fun_C_0(B!2))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[37])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(B!2, tptp_fun_C_0(A!3)), B!2) = times(tptp_fun_C_0(A!3), times(B!2, B!2)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 (times(times(B!2, tptp_fun_C_0(A!3)), B!2) = times(tptp_fun_C_0(A!3), times(B!2, B!2))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[112, 45])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (times(B!2, tptp_fun_C_0(A!3)) = times(B!2, times(A!3, A!3))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (times(B!2, times(A!3, A!3)) = times(B!2, tptp_fun_C_0(A!3))),
% 0.19/0.41 inference(symmetry,[status(thm)],[114])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(A!3, B!2), A!3) = times(B!2, times(A!3, A!3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (times(times(A!3, B!2), A!3) = times(B!2, times(A!3, A!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[116, 45])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (times(times(tptp_fun_C_0(B!2), B!2), A!3) = times(B!2, A!3)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[50])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(tptp_fun_C_0(B!2), B!2), A!3) = times(B!2, times(A!3, tptp_fun_C_0(B!2))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (times(times(tptp_fun_C_0(B!2), B!2), A!3) = times(B!2, times(A!3, tptp_fun_C_0(B!2)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[119, 45])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 (times(B!2, times(A!3, tptp_fun_C_0(B!2))) = times(times(tptp_fun_C_0(B!2), B!2), A!3)),
% 0.19/0.41 inference(symmetry,[status(thm)],[120])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 (times(B!2, times(A!3, tptp_fun_C_0(B!2))) = times(B!2, A!3)),
% 0.19/0.41 inference(transitivity,[status(thm)],[121, 118])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 (times(tptp_fun_C_0(A!3), times(B!2, times(A!3, tptp_fun_C_0(B!2)))) = times(tptp_fun_C_0(A!3), times(B!2, A!3))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[122])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (times(tptp_fun_C_0(A!3), times(B!2, A!3)) = times(tptp_fun_C_0(A!3), times(B!2, times(A!3, tptp_fun_C_0(B!2))))),
% 0.19/0.41 inference(symmetry,[status(thm)],[123])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(A!3, tptp_fun_C_0(A!3)), B!2) = times(tptp_fun_C_0(A!3), times(B!2, A!3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 (times(times(A!3, tptp_fun_C_0(A!3)), B!2) = times(tptp_fun_C_0(A!3), times(B!2, A!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[125, 45])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 (times(times(A!3, tptp_fun_C_0(A!3)), B!2) = times(A!3, B!2)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[85])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 (times(A!3, B!2) = times(times(A!3, tptp_fun_C_0(A!3)), B!2)),
% 0.19/0.41 inference(symmetry,[status(thm)],[127])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 (times(A!3, B!2) = times(tptp_fun_C_0(A!3), times(B!2, times(A!3, tptp_fun_C_0(B!2))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[128, 126, 124])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 (times(times(A!3, B!2), A!3) = times(times(tptp_fun_C_0(A!3), times(B!2, times(A!3, tptp_fun_C_0(B!2)))), A!3)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[129])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 (times(times(tptp_fun_C_0(A!3), times(B!2, times(A!3, tptp_fun_C_0(B!2)))), A!3) = times(times(A!3, B!2), A!3)),
% 0.19/0.41 inference(symmetry,[status(thm)],[130])).
% 0.19/0.41 tff(132,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(tptp_fun_C_0(A!3), times(B!2, times(A!3, tptp_fun_C_0(B!2)))), A!3) = times(times(B!2, times(A!3, tptp_fun_C_0(B!2))), times(A!3, tptp_fun_C_0(A!3))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(133,plain,
% 0.19/0.41 (times(times(tptp_fun_C_0(A!3), times(B!2, times(A!3, tptp_fun_C_0(B!2)))), A!3) = times(times(B!2, times(A!3, tptp_fun_C_0(B!2))), times(A!3, tptp_fun_C_0(A!3)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[132, 45])).
% 0.19/0.41 tff(134,plain,
% 0.19/0.41 (times(times(B!2, times(A!3, tptp_fun_C_0(B!2))), times(A!3, tptp_fun_C_0(A!3))) = times(times(tptp_fun_C_0(A!3), times(B!2, times(A!3, tptp_fun_C_0(B!2)))), A!3)),
% 0.19/0.41 inference(symmetry,[status(thm)],[133])).
% 0.19/0.41 tff(135,plain,
% 0.19/0.41 (times(times(B!2, times(A!3, tptp_fun_C_0(B!2))), times(A!3, tptp_fun_C_0(A!3))) = times(times(B!2, A!3), A!3)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[122, 85])).
% 0.19/0.41 tff(136,plain,
% 0.19/0.41 (times(times(B!2, A!3), A!3) = times(times(B!2, times(A!3, tptp_fun_C_0(B!2))), times(A!3, tptp_fun_C_0(A!3)))),
% 0.19/0.41 inference(symmetry,[status(thm)],[135])).
% 0.19/0.41 tff(137,plain,
% 0.19/0.41 (times(times(B!2, A!3), A!3) = times(B!2, tptp_fun_C_0(A!3))),
% 0.19/0.41 inference(transitivity,[status(thm)],[136, 134, 131, 117, 115])).
% 0.19/0.41 tff(138,plain,
% 0.19/0.41 (times(times(times(B!2, A!3), A!3), B!2) = times(times(B!2, tptp_fun_C_0(A!3)), B!2)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[137])).
% 0.19/0.41 tff(139,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(B!2, A!3), A!3) = times(A!3, times(A!3, B!2)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(140,plain,
% 0.19/0.41 (times(times(B!2, A!3), A!3) = times(A!3, times(A!3, B!2))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[139, 45])).
% 0.19/0.41 tff(141,plain,
% 0.19/0.41 (times(A!3, times(A!3, B!2)) = times(times(B!2, A!3), A!3)),
% 0.19/0.41 inference(symmetry,[status(thm)],[140])).
% 0.19/0.41 tff(142,plain,
% 0.19/0.41 (times(times(A!3, times(A!3, B!2)), B!2) = times(times(times(B!2, A!3), A!3), B!2)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[141])).
% 0.19/0.41 tff(143,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(A!3, times(A!3, B!2)), B!2) = times(times(A!3, B!2), times(B!2, A!3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(144,plain,
% 0.19/0.41 (times(times(A!3, times(A!3, B!2)), B!2) = times(times(A!3, B!2), times(B!2, A!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[143, 45])).
% 0.19/0.41 tff(145,plain,
% 0.19/0.41 (times(times(A!3, B!2), times(B!2, A!3)) = times(times(A!3, times(A!3, B!2)), B!2)),
% 0.19/0.41 inference(symmetry,[status(thm)],[144])).
% 0.19/0.41 tff(146,plain,
% 0.19/0.41 (times(tptp_fun_C_0(B!2), A!3) = times(times(B!2, B!2), A!3)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[48])).
% 0.19/0.41 tff(147,plain,
% 0.19/0.41 (times(times(B!2, B!2), A!3) = times(tptp_fun_C_0(B!2), A!3)),
% 0.19/0.41 inference(symmetry,[status(thm)],[146])).
% 0.19/0.41 tff(148,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(B!2, B!2), A!3) = times(B!2, times(A!3, B!2)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(149,plain,
% 0.19/0.41 (times(times(B!2, B!2), A!3) = times(B!2, times(A!3, B!2))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[148, 45])).
% 0.19/0.41 tff(150,plain,
% 0.19/0.41 (times(B!2, times(A!3, B!2)) = times(times(B!2, B!2), A!3)),
% 0.19/0.41 inference(symmetry,[status(thm)],[149])).
% 0.19/0.41 tff(151,plain,
% 0.19/0.41 (times(B!2, times(A!3, B!2)) = times(tptp_fun_C_0(B!2), A!3)),
% 0.19/0.41 inference(transitivity,[status(thm)],[150, 147])).
% 0.19/0.41 tff(152,plain,
% 0.19/0.41 (times(times(B!2, times(A!3, B!2)), B!2) = times(times(tptp_fun_C_0(B!2), A!3), B!2)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[151])).
% 0.19/0.41 tff(153,plain,
% 0.19/0.41 (times(times(tptp_fun_C_0(B!2), A!3), B!2) = times(times(B!2, times(A!3, B!2)), B!2)),
% 0.19/0.41 inference(symmetry,[status(thm)],[152])).
% 0.19/0.41 tff(154,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(tptp_fun_C_0(B!2), A!3), B!2) = times(A!3, times(B!2, tptp_fun_C_0(B!2))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(155,plain,
% 0.19/0.41 (times(times(tptp_fun_C_0(B!2), A!3), B!2) = times(A!3, times(B!2, tptp_fun_C_0(B!2)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[154, 45])).
% 0.19/0.41 tff(156,plain,
% 0.19/0.41 (times(A!3, times(B!2, tptp_fun_C_0(B!2))) = times(times(tptp_fun_C_0(B!2), A!3), B!2)),
% 0.19/0.41 inference(symmetry,[status(thm)],[155])).
% 0.19/0.41 tff(157,plain,
% 0.19/0.41 (times(A!3, times(B!2, tptp_fun_C_0(B!2))) = times(A!3, B!2)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[35])).
% 0.19/0.41 tff(158,plain,
% 0.19/0.41 (times(A!3, B!2) = times(A!3, times(B!2, tptp_fun_C_0(B!2)))),
% 0.19/0.41 inference(symmetry,[status(thm)],[157])).
% 0.19/0.41 tff(159,plain,
% 0.19/0.41 (times(A!3, B!2) = times(times(B!2, times(A!3, B!2)), B!2)),
% 0.19/0.41 inference(transitivity,[status(thm)],[158, 156, 153])).
% 0.19/0.41 tff(160,plain,
% 0.19/0.41 (times(tptp_fun_C_0(B!2), times(A!3, B!2)) = times(tptp_fun_C_0(B!2), times(times(B!2, times(A!3, B!2)), B!2))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[159])).
% 0.19/0.41 tff(161,plain,
% 0.19/0.41 (times(tptp_fun_C_0(B!2), times(times(B!2, times(A!3, B!2)), B!2)) = times(tptp_fun_C_0(B!2), times(A!3, B!2))),
% 0.19/0.41 inference(symmetry,[status(thm)],[160])).
% 0.19/0.41 tff(162,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(B!2, tptp_fun_C_0(B!2)), times(B!2, times(A!3, B!2))) = times(tptp_fun_C_0(B!2), times(times(B!2, times(A!3, B!2)), B!2)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(163,plain,
% 0.19/0.42 (times(times(B!2, tptp_fun_C_0(B!2)), times(B!2, times(A!3, B!2))) = times(tptp_fun_C_0(B!2), times(times(B!2, times(A!3, B!2)), B!2))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[162, 45])).
% 0.19/0.42 tff(164,plain,
% 0.19/0.42 (times(times(B!2, tptp_fun_C_0(B!2)), times(B!2, times(A!3, B!2))) = times(B!2, times(tptp_fun_C_0(B!2), A!3))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[35, 151])).
% 0.19/0.42 tff(165,plain,
% 0.19/0.42 (times(B!2, times(tptp_fun_C_0(B!2), A!3)) = times(times(B!2, tptp_fun_C_0(B!2)), times(B!2, times(A!3, B!2)))),
% 0.19/0.42 inference(symmetry,[status(thm)],[164])).
% 0.19/0.42 tff(166,plain,
% 0.19/0.42 (times(times(A!3, B!2), times(tptp_fun_C_0(B!2), tptp_fun_C_0(B!2))) = times(times(A!3, B!2), tptp_fun_C_0(B!2))),
% 0.19/0.42 inference(symmetry,[status(thm)],[72])).
% 0.19/0.42 tff(167,plain,
% 0.19/0.42 (times(times(B!2, A!3), tptp_fun_C_0(B!2)) = times(times(tptp_fun_C_0(B!2), times(A!3, B!2)), tptp_fun_C_0(B!2))),
% 0.19/0.42 inference(symmetry,[status(thm)],[61])).
% 0.19/0.42 tff(168,plain,
% 0.19/0.42 (times(A!3, times(tptp_fun_C_0(B!2), B!2)) = times(times(B!2, A!3), tptp_fun_C_0(B!2))),
% 0.19/0.42 inference(symmetry,[status(thm)],[53])).
% 0.19/0.42 tff(169,plain,
% 0.19/0.42 (times(A!3, B!2) = times(A!3, times(tptp_fun_C_0(B!2), B!2))),
% 0.19/0.42 inference(symmetry,[status(thm)],[51])).
% 0.19/0.42 tff(170,plain,
% 0.19/0.42 (times(A!3, B!2) = times(B!2, A!3)),
% 0.19/0.42 inference(transitivity,[status(thm)],[169, 168, 167, 63, 166, 74, 165, 163, 161, 59, 56])).
% 0.19/0.42 tff(171,plain,
% 0.19/0.42 (times(times(A!3, B!2), times(A!3, B!2)) = times(times(A!3, B!2), times(B!2, A!3))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[170])).
% 0.19/0.42 tff(172,plain,
% 0.19/0.42 (times(times(A!3, B!2), times(A!3, B!2)) = times(tptp_fun_C_0(A!3), times(tptp_fun_C_0(B!2), tptp_fun_C_0(A!3)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[171, 145, 142, 138, 113, 111, 103, 106])).
% 0.19/0.42 tff(173,plain,
% 0.19/0.42 (((~![B: $i] : (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C)))))))) | (~((~((~element(times(A!3, B!2))) | (~((~(times(times(A!3, B!2), tptp_fun_C_0(times(A!3, B!2))) = times(A!3, B!2))) | (~(times(times(A!3, B!2), times(A!3, B!2)) = tptp_fun_C_0(times(A!3, B!2)))))))) | (~(element(times(A!3, B!2)) | ![C: $i] : ((~(times(times(A!3, B!2), times(A!3, B!2)) = C)) | (~(times(times(A!3, B!2), C) = times(A!3, B!2))))))))) <=> ((~![B: $i] : (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C)))))))) | (~((~((~element(times(A!3, B!2))) | (~((~(times(times(A!3, B!2), tptp_fun_C_0(times(A!3, B!2))) = times(A!3, B!2))) | (~(times(times(A!3, B!2), times(A!3, B!2)) = tptp_fun_C_0(times(A!3, B!2)))))))) | (~(element(times(A!3, B!2)) | ![C: $i] : ((~(times(times(A!3, B!2), times(A!3, B!2)) = C)) | (~(times(times(A!3, B!2), C) = times(A!3, B!2)))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(174,plain,
% 0.19/0.42 ((~((~((~element(times(A!3, B!2))) | (~((~(times(times(A!3, B!2), tptp_fun_C_0(times(A!3, B!2))) = times(A!3, B!2))) | (~(times(times(A!3, B!2), times(A!3, B!2)) = tptp_fun_C_0(times(A!3, B!2)))))))) | (~(element(times(A!3, B!2)) | ![C: $i] : ((~(times(times(A!3, B!2), C) = times(A!3, B!2))) | (~(times(times(A!3, B!2), times(A!3, B!2)) = C))))))) <=> (~((~((~element(times(A!3, B!2))) | (~((~(times(times(A!3, B!2), tptp_fun_C_0(times(A!3, B!2))) = times(A!3, B!2))) | (~(times(times(A!3, B!2), times(A!3, B!2)) = tptp_fun_C_0(times(A!3, B!2)))))))) | (~(element(times(A!3, B!2)) | ![C: $i] : ((~(times(times(A!3, B!2), times(A!3, B!2)) = C)) | (~(times(times(A!3, B!2), C) = times(A!3, B!2))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(175,plain,
% 0.19/0.42 (((~![B: $i] : (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C)))))))) | (~((~((~element(times(A!3, B!2))) | (~((~(times(times(A!3, B!2), tptp_fun_C_0(times(A!3, B!2))) = times(A!3, B!2))) | (~(times(times(A!3, B!2), times(A!3, B!2)) = tptp_fun_C_0(times(A!3, B!2)))))))) | (~(element(times(A!3, B!2)) | ![C: $i] : ((~(times(times(A!3, B!2), C) = times(A!3, B!2))) | (~(times(times(A!3, B!2), times(A!3, B!2)) = C)))))))) <=> ((~![B: $i] : (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C)))))))) | (~((~((~element(times(A!3, B!2))) | (~((~(times(times(A!3, B!2), tptp_fun_C_0(times(A!3, B!2))) = times(A!3, B!2))) | (~(times(times(A!3, B!2), times(A!3, B!2)) = tptp_fun_C_0(times(A!3, B!2)))))))) | (~(element(times(A!3, B!2)) | ![C: $i] : ((~(times(times(A!3, B!2), times(A!3, B!2)) = C)) | (~(times(times(A!3, B!2), C) = times(A!3, B!2)))))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[174])).
% 0.19/0.42 tff(176,plain,
% 0.19/0.42 (((~![B: $i] : (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C)))))))) | (~((~((~element(times(A!3, B!2))) | (~((~(times(times(A!3, B!2), tptp_fun_C_0(times(A!3, B!2))) = times(A!3, B!2))) | (~(times(times(A!3, B!2), times(A!3, B!2)) = tptp_fun_C_0(times(A!3, B!2)))))))) | (~(element(times(A!3, B!2)) | ![C: $i] : ((~(times(times(A!3, B!2), C) = times(A!3, B!2))) | (~(times(times(A!3, B!2), times(A!3, B!2)) = C)))))))) <=> ((~![B: $i] : (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C)))))))) | (~((~((~element(times(A!3, B!2))) | (~((~(times(times(A!3, B!2), tptp_fun_C_0(times(A!3, B!2))) = times(A!3, B!2))) | (~(times(times(A!3, B!2), times(A!3, B!2)) = tptp_fun_C_0(times(A!3, B!2)))))))) | (~(element(times(A!3, B!2)) | ![C: $i] : ((~(times(times(A!3, B!2), times(A!3, B!2)) = C)) | (~(times(times(A!3, B!2), C) = times(A!3, B!2)))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[175, 173])).
% 0.19/0.42 tff(177,plain,
% 0.19/0.42 ((~![B: $i] : (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C)))))))) | (~((~((~element(times(A!3, B!2))) | (~((~(times(times(A!3, B!2), tptp_fun_C_0(times(A!3, B!2))) = times(A!3, B!2))) | (~(times(times(A!3, B!2), times(A!3, B!2)) = tptp_fun_C_0(times(A!3, B!2)))))))) | (~(element(times(A!3, B!2)) | ![C: $i] : ((~(times(times(A!3, B!2), C) = times(A!3, B!2))) | (~(times(times(A!3, B!2), times(A!3, B!2)) = C)))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(178,plain,
% 0.19/0.42 ((~![B: $i] : (~((~((~element(B)) | (~((~(times(B, tptp_fun_C_0(B)) = B)) | (~(times(B, B) = tptp_fun_C_0(B))))))) | (~(element(B) | ![C: $i] : ((~(times(B, C) = B)) | (~(times(B, B) = C)))))))) | (~((~((~element(times(A!3, B!2))) | (~((~(times(times(A!3, B!2), tptp_fun_C_0(times(A!3, B!2))) = times(A!3, B!2))) | (~(times(times(A!3, B!2), times(A!3, B!2)) = tptp_fun_C_0(times(A!3, B!2)))))))) | (~(element(times(A!3, B!2)) | ![C: $i] : ((~(times(times(A!3, B!2), times(A!3, B!2)) = C)) | (~(times(times(A!3, B!2), C) = times(A!3, B!2))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.19/0.42 tff(179,plain,
% 0.19/0.42 (~((~((~element(times(A!3, B!2))) | (~((~(times(times(A!3, B!2), tptp_fun_C_0(times(A!3, B!2))) = times(A!3, B!2))) | (~(times(times(A!3, B!2), times(A!3, B!2)) = tptp_fun_C_0(times(A!3, B!2)))))))) | (~(element(times(A!3, B!2)) | ![C: $i] : ((~(times(times(A!3, B!2), times(A!3, B!2)) = C)) | (~(times(times(A!3, B!2), C) = times(A!3, B!2)))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[178, 13])).
% 0.19/0.42 tff(180,plain,
% 0.19/0.42 (((~((~element(times(A!3, B!2))) | (~((~(times(times(A!3, B!2), tptp_fun_C_0(times(A!3, B!2))) = times(A!3, B!2))) | (~(times(times(A!3, B!2), times(A!3, B!2)) = tptp_fun_C_0(times(A!3, B!2)))))))) | (~(element(times(A!3, B!2)) | ![C: $i] : ((~(times(times(A!3, B!2), times(A!3, B!2)) = C)) | (~(times(times(A!3, B!2), C) = times(A!3, B!2))))))) | (element(times(A!3, B!2)) | ![C: $i] : ((~(times(times(A!3, B!2), times(A!3, B!2)) = C)) | (~(times(times(A!3, B!2), C) = times(A!3, B!2)))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(181,plain,
% 0.19/0.43 (element(times(A!3, B!2)) | ![C: $i] : ((~(times(times(A!3, B!2), times(A!3, B!2)) = C)) | (~(times(times(A!3, B!2), C) = times(A!3, B!2))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.19/0.43 tff(182,plain,
% 0.19/0.43 (C!1 = times(A!3, B!2)),
% 0.19/0.43 inference(and_elim,[status(thm)],[29])).
% 0.19/0.43 tff(183,plain,
% 0.19/0.43 (times(A!3, B!2) = C!1),
% 0.19/0.43 inference(symmetry,[status(thm)],[182])).
% 0.19/0.43 tff(184,plain,
% 0.19/0.43 (element(times(A!3, B!2)) <=> element(C!1)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[183])).
% 0.19/0.43 tff(185,plain,
% 0.19/0.43 (element(C!1) <=> element(times(A!3, B!2))),
% 0.19/0.43 inference(symmetry,[status(thm)],[184])).
% 0.19/0.43 tff(186,plain,
% 0.19/0.43 ((~element(C!1)) <=> (~element(times(A!3, B!2)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[185])).
% 0.19/0.43 tff(187,plain,
% 0.19/0.43 (~element(C!1)),
% 0.19/0.43 inference(or_elim,[status(thm)],[28])).
% 0.19/0.43 tff(188,plain,
% 0.19/0.43 (~element(times(A!3, B!2))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.19/0.43 tff(189,plain,
% 0.19/0.43 ((~(element(times(A!3, B!2)) | ![C: $i] : ((~(times(times(A!3, B!2), times(A!3, B!2)) = C)) | (~(times(times(A!3, B!2), C) = times(A!3, B!2)))))) | element(times(A!3, B!2)) | ![C: $i] : ((~(times(times(A!3, B!2), times(A!3, B!2)) = C)) | (~(times(times(A!3, B!2), C) = times(A!3, B!2))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(190,plain,
% 0.19/0.43 (![C: $i] : ((~(times(times(A!3, B!2), times(A!3, B!2)) = C)) | (~(times(times(A!3, B!2), C) = times(A!3, B!2))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[189, 188, 181])).
% 0.19/0.43 tff(191,plain,
% 0.19/0.43 (((~![C: $i] : ((~(times(times(A!3, B!2), times(A!3, B!2)) = C)) | (~(times(times(A!3, B!2), C) = times(A!3, B!2))))) | ((~(times(times(A!3, B!2), times(A!3, B!2)) = times(tptp_fun_C_0(A!3), times(tptp_fun_C_0(B!2), tptp_fun_C_0(A!3))))) | (~(times(times(A!3, B!2), times(tptp_fun_C_0(A!3), times(tptp_fun_C_0(B!2), tptp_fun_C_0(A!3)))) = times(A!3, B!2))))) <=> ((~![C: $i] : ((~(times(times(A!3, B!2), times(A!3, B!2)) = C)) | (~(times(times(A!3, B!2), C) = times(A!3, B!2))))) | (~(times(times(A!3, B!2), times(A!3, B!2)) = times(tptp_fun_C_0(A!3), times(tptp_fun_C_0(B!2), tptp_fun_C_0(A!3))))) | (~(times(times(A!3, B!2), times(tptp_fun_C_0(A!3), times(tptp_fun_C_0(B!2), tptp_fun_C_0(A!3)))) = times(A!3, B!2))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(192,plain,
% 0.19/0.43 ((~![C: $i] : ((~(times(times(A!3, B!2), times(A!3, B!2)) = C)) | (~(times(times(A!3, B!2), C) = times(A!3, B!2))))) | ((~(times(times(A!3, B!2), times(A!3, B!2)) = times(tptp_fun_C_0(A!3), times(tptp_fun_C_0(B!2), tptp_fun_C_0(A!3))))) | (~(times(times(A!3, B!2), times(tptp_fun_C_0(A!3), times(tptp_fun_C_0(B!2), tptp_fun_C_0(A!3)))) = times(A!3, B!2))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(193,plain,
% 0.19/0.43 ((~![C: $i] : ((~(times(times(A!3, B!2), times(A!3, B!2)) = C)) | (~(times(times(A!3, B!2), C) = times(A!3, B!2))))) | (~(times(times(A!3, B!2), times(A!3, B!2)) = times(tptp_fun_C_0(A!3), times(tptp_fun_C_0(B!2), tptp_fun_C_0(A!3))))) | (~(times(times(A!3, B!2), times(tptp_fun_C_0(A!3), times(tptp_fun_C_0(B!2), tptp_fun_C_0(A!3)))) = times(A!3, B!2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.19/0.43 tff(194,plain,
% 0.19/0.43 ((~(times(times(A!3, B!2), times(A!3, B!2)) = times(tptp_fun_C_0(A!3), times(tptp_fun_C_0(B!2), tptp_fun_C_0(A!3))))) | (~(times(times(A!3, B!2), times(tptp_fun_C_0(A!3), times(tptp_fun_C_0(B!2), tptp_fun_C_0(A!3)))) = times(A!3, B!2)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[193, 190])).
% 0.19/0.43 tff(195,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[194, 172, 110])).
% 0.19/0.43 % SZS output end Proof
%------------------------------------------------------------------------------