TSTP Solution File: ALG210+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG210+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ALG210+1 : TPTP v8.1.0. Released v3.1.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n024.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 : Mon Aug 29 13:55:04 EDT 2022
% 0.13/0.34 % 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.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(times_type, type, (
% 0.20/0.40 times: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_B_1_type, type, (
% 0.20/0.40 tptp_fun_B_1: $i)).
% 0.20/0.40 tff(tptp_fun_A_2_type, type, (
% 0.20/0.40 tptp_fun_A_2: $i)).
% 0.20/0.40 tff(tptp_fun_C_0_type, type, (
% 0.20/0.40 tptp_fun_C_0: $i > $i)).
% 0.20/0.40 tff(element_type, type, (
% 0.20/0.40 element: $i > $o)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[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))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![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)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (^[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))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (![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)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![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)))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (^[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)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![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)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(9,axiom,(![B: $i] : (element(B) <=> ?[C: $i] : ((times(B, C) = B) & (times(B, B) = C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_2')).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (![B: $i] : (element(B) <=> ?[C: $i] : ((times(B, C) = B) & (times(B, B) = C)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.20/0.41 tff(11,plain,(
% 0.20/0.41 ![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)))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[10])).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (![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)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (![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)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 ((~![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!1)) | (~((~(times(B!1, tptp_fun_C_0(B!1)) = B!1)) | (~(times(B!1, B!1) = tptp_fun_C_0(B!1))))))) | (~(element(B!1) | ![C: $i] : ((~(times(B!1, C) = B!1)) | (~(times(B!1, B!1) = C)))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (~((~((~element(B!1)) | (~((~(times(B!1, tptp_fun_C_0(B!1)) = B!1)) | (~(times(B!1, B!1) = tptp_fun_C_0(B!1))))))) | (~(element(B!1) | ![C: $i] : ((~(times(B!1, C) = B!1)) | (~(times(B!1, B!1) = C))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (((~((~element(B!1)) | (~((~(times(B!1, tptp_fun_C_0(B!1)) = B!1)) | (~(times(B!1, B!1) = tptp_fun_C_0(B!1))))))) | (~(element(B!1) | ![C: $i] : ((~(times(B!1, C) = B!1)) | (~(times(B!1, B!1) = C)))))) | ((~element(B!1)) | (~((~(times(B!1, tptp_fun_C_0(B!1)) = B!1)) | (~(times(B!1, B!1) = tptp_fun_C_0(B!1))))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 ((~element(B!1)) | (~((~(times(B!1, tptp_fun_C_0(B!1)) = B!1)) | (~(times(B!1, B!1) = tptp_fun_C_0(B!1)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : (element(times(A, B)) | (~(element(A) & element(B))))) <=> (~![A: $i, B: $i] : (element(times(A, B)) | (~(element(A) & element(B)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : ((element(A) & element(B)) => element(times(A, B)))) <=> (~![A: $i, B: $i] : (element(times(A, B)) | (~(element(A) & element(B)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(20,axiom,(~![A: $i, B: $i] : ((element(A) & element(B)) => element(times(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conjecture_1')).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (~![A: $i, B: $i] : (element(times(A, B)) | (~(element(A) & element(B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (~![A: $i, B: $i] : (element(times(A, B)) | (~(element(A) & element(B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (~![A: $i, B: $i] : (element(times(A, B)) | (~(element(A) & element(B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (~![A: $i, B: $i] : (element(times(A, B)) | (~(element(A) & element(B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (~![A: $i, B: $i] : (element(times(A, B)) | (~(element(A) & element(B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (~![A: $i, B: $i] : (element(times(A, B)) | (~(element(A) & element(B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (~![A: $i, B: $i] : (element(times(A, B)) | (~(element(A) & element(B))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[26, 18])).
% 0.20/0.41 tff(28,plain,(
% 0.20/0.41 ~(element(times(A!2, B!1)) | (~(element(A!2) & element(B!1))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[27])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (element(A!2) & element(B!1)),
% 0.20/0.41 inference(or_elim,[status(thm)],[28])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (element(B!1)),
% 0.20/0.41 inference(and_elim,[status(thm)],[29])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 ((~((~element(B!1)) | (~((~(times(B!1, tptp_fun_C_0(B!1)) = B!1)) | (~(times(B!1, B!1) = tptp_fun_C_0(B!1))))))) | (~element(B!1)) | (~((~(times(B!1, tptp_fun_C_0(B!1)) = B!1)) | (~(times(B!1, B!1) = tptp_fun_C_0(B!1)))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 ((~((~element(B!1)) | (~((~(times(B!1, tptp_fun_C_0(B!1)) = B!1)) | (~(times(B!1, B!1) = tptp_fun_C_0(B!1))))))) | (~((~(times(B!1, tptp_fun_C_0(B!1)) = B!1)) | (~(times(B!1, B!1) = tptp_fun_C_0(B!1)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (~((~(times(B!1, tptp_fun_C_0(B!1)) = B!1)) | (~(times(B!1, B!1) = tptp_fun_C_0(B!1))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[32, 17])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (((~(times(B!1, tptp_fun_C_0(B!1)) = B!1)) | (~(times(B!1, B!1) = tptp_fun_C_0(B!1)))) | (times(B!1, tptp_fun_C_0(B!1)) = B!1)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (times(B!1, tptp_fun_C_0(B!1)) = B!1),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (B!1 = times(B!1, tptp_fun_C_0(B!1))),
% 0.20/0.41 inference(symmetry,[status(thm)],[35])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (times(A!2, B!1) = times(A!2, times(B!1, tptp_fun_C_0(B!1)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[36])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (times(A!2, times(B!1, tptp_fun_C_0(B!1))) = times(A!2, B!1)),
% 0.20/0.41 inference(symmetry,[status(thm)],[37])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(42,axiom,(![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_1')).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.41 tff(44,plain,(
% 0.20/0.41 ![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[43])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(tptp_fun_C_0(B!1), A!2), B!1) = times(A!2, times(B!1, tptp_fun_C_0(B!1))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (times(times(tptp_fun_C_0(B!1), A!2), B!1) = times(A!2, times(B!1, tptp_fun_C_0(B!1)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (times(B!1, times(A!2, times(B!1, tptp_fun_C_0(B!1)))) = times(B!1, times(A!2, B!1))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[38])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (times(B!1, times(A!2, B!1)) = times(B!1, times(A!2, times(B!1, tptp_fun_C_0(B!1))))),
% 0.20/0.41 inference(symmetry,[status(thm)],[48])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(B!1, B!1), A!2) = times(B!1, times(A!2, B!1)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (times(times(B!1, B!1), A!2) = times(B!1, times(A!2, B!1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[50, 45])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (((~(times(B!1, tptp_fun_C_0(B!1)) = B!1)) | (~(times(B!1, B!1) = tptp_fun_C_0(B!1)))) | (times(B!1, B!1) = tptp_fun_C_0(B!1))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (times(B!1, B!1) = tptp_fun_C_0(B!1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[52, 33])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (tptp_fun_C_0(B!1) = times(B!1, B!1)),
% 0.20/0.41 inference(symmetry,[status(thm)],[53])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (times(tptp_fun_C_0(B!1), A!2) = times(times(B!1, B!1), A!2)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[54])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (times(tptp_fun_C_0(B!1), A!2) = times(B!1, times(A!2, times(B!1, tptp_fun_C_0(B!1))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[55, 51, 49])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (times(times(tptp_fun_C_0(B!1), A!2), B!1) = times(times(B!1, times(A!2, times(B!1, tptp_fun_C_0(B!1)))), B!1)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (times(times(B!1, times(A!2, times(B!1, tptp_fun_C_0(B!1)))), B!1) = times(times(tptp_fun_C_0(B!1), A!2), B!1)),
% 0.20/0.41 inference(symmetry,[status(thm)],[57])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(B!1, times(A!2, times(B!1, tptp_fun_C_0(B!1)))), B!1) = times(times(A!2, times(B!1, tptp_fun_C_0(B!1))), times(B!1, B!1)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (times(times(B!1, times(A!2, times(B!1, tptp_fun_C_0(B!1)))), B!1) = times(times(A!2, times(B!1, tptp_fun_C_0(B!1))), times(B!1, B!1))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[59, 45])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (times(times(A!2, times(B!1, tptp_fun_C_0(B!1))), times(B!1, B!1)) = times(times(B!1, times(A!2, times(B!1, tptp_fun_C_0(B!1)))), B!1)),
% 0.20/0.41 inference(symmetry,[status(thm)],[60])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (times(times(A!2, times(B!1, tptp_fun_C_0(B!1))), times(B!1, B!1)) = times(times(A!2, B!1), tptp_fun_C_0(B!1))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[38, 53])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (times(times(A!2, B!1), tptp_fun_C_0(B!1)) = times(times(A!2, times(B!1, tptp_fun_C_0(B!1))), times(B!1, B!1))),
% 0.20/0.41 inference(symmetry,[status(thm)],[62])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(A!2, B!1), tptp_fun_C_0(B!1)) = times(B!1, times(tptp_fun_C_0(B!1), A!2)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (times(times(A!2, B!1), tptp_fun_C_0(B!1)) = times(B!1, times(tptp_fun_C_0(B!1), A!2))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[64, 45])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (times(B!1, times(tptp_fun_C_0(B!1), A!2)) = times(times(A!2, B!1), tptp_fun_C_0(B!1))),
% 0.20/0.41 inference(symmetry,[status(thm)],[65])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 ((~![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!2)) | (~((~(times(A!2, tptp_fun_C_0(A!2)) = A!2)) | (~(times(A!2, A!2) = tptp_fun_C_0(A!2))))))) | (~(element(A!2) | ![C: $i] : ((~(times(A!2, C) = A!2)) | (~(times(A!2, A!2) = C)))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (~((~((~element(A!2)) | (~((~(times(A!2, tptp_fun_C_0(A!2)) = A!2)) | (~(times(A!2, A!2) = tptp_fun_C_0(A!2))))))) | (~(element(A!2) | ![C: $i] : ((~(times(A!2, C) = A!2)) | (~(times(A!2, A!2) = C))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[67, 13])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 (((~((~element(A!2)) | (~((~(times(A!2, tptp_fun_C_0(A!2)) = A!2)) | (~(times(A!2, A!2) = tptp_fun_C_0(A!2))))))) | (~(element(A!2) | ![C: $i] : ((~(times(A!2, C) = A!2)) | (~(times(A!2, A!2) = C)))))) | ((~element(A!2)) | (~((~(times(A!2, tptp_fun_C_0(A!2)) = A!2)) | (~(times(A!2, A!2) = tptp_fun_C_0(A!2))))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 ((~element(A!2)) | (~((~(times(A!2, tptp_fun_C_0(A!2)) = A!2)) | (~(times(A!2, A!2) = tptp_fun_C_0(A!2)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (element(A!2)),
% 0.20/0.42 inference(and_elim,[status(thm)],[29])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 ((~((~element(A!2)) | (~((~(times(A!2, tptp_fun_C_0(A!2)) = A!2)) | (~(times(A!2, A!2) = tptp_fun_C_0(A!2))))))) | (~element(A!2)) | (~((~(times(A!2, tptp_fun_C_0(A!2)) = A!2)) | (~(times(A!2, A!2) = tptp_fun_C_0(A!2)))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 ((~((~element(A!2)) | (~((~(times(A!2, tptp_fun_C_0(A!2)) = A!2)) | (~(times(A!2, A!2) = tptp_fun_C_0(A!2))))))) | (~((~(times(A!2, tptp_fun_C_0(A!2)) = A!2)) | (~(times(A!2, A!2) = tptp_fun_C_0(A!2)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 (~((~(times(A!2, tptp_fun_C_0(A!2)) = A!2)) | (~(times(A!2, A!2) = tptp_fun_C_0(A!2))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[73, 70])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 (((~(times(A!2, tptp_fun_C_0(A!2)) = A!2)) | (~(times(A!2, A!2) = tptp_fun_C_0(A!2)))) | (times(A!2, tptp_fun_C_0(A!2)) = A!2)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 (times(A!2, tptp_fun_C_0(A!2)) = A!2),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (times(tptp_fun_C_0(B!1), times(A!2, tptp_fun_C_0(A!2))) = times(tptp_fun_C_0(B!1), A!2)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[76])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(tptp_fun_C_0(A!2), tptp_fun_C_0(B!1)), A!2) = times(tptp_fun_C_0(B!1), times(A!2, tptp_fun_C_0(A!2))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 (times(times(tptp_fun_C_0(A!2), tptp_fun_C_0(B!1)), A!2) = times(tptp_fun_C_0(B!1), times(A!2, tptp_fun_C_0(A!2)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[78, 45])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (times(times(tptp_fun_C_0(A!2), tptp_fun_C_0(B!1)), A!2) = times(tptp_fun_C_0(B!1), A!2)),
% 0.20/0.42 inference(transitivity,[status(thm)],[79, 77])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 (times(B!1, times(times(tptp_fun_C_0(A!2), tptp_fun_C_0(B!1)), A!2)) = times(B!1, times(tptp_fun_C_0(B!1), A!2))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[80])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(A!2, B!1), times(tptp_fun_C_0(A!2), tptp_fun_C_0(B!1))) = times(B!1, times(times(tptp_fun_C_0(A!2), tptp_fun_C_0(B!1)), A!2)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (times(times(A!2, B!1), times(tptp_fun_C_0(A!2), tptp_fun_C_0(B!1))) = times(B!1, times(times(tptp_fun_C_0(A!2), tptp_fun_C_0(B!1)), A!2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[82, 45])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (((~(times(A!2, tptp_fun_C_0(A!2)) = A!2)) | (~(times(A!2, A!2) = tptp_fun_C_0(A!2)))) | (times(A!2, A!2) = tptp_fun_C_0(A!2))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 (times(A!2, A!2) = tptp_fun_C_0(A!2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[84, 74])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (tptp_fun_C_0(A!2) = times(A!2, A!2)),
% 0.20/0.42 inference(symmetry,[status(thm)],[85])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (times(tptp_fun_C_0(A!2), tptp_fun_C_0(A!2)) = times(tptp_fun_C_0(A!2), times(A!2, A!2))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[86])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 (times(tptp_fun_C_0(A!2), times(A!2, A!2)) = times(tptp_fun_C_0(A!2), tptp_fun_C_0(A!2))),
% 0.20/0.42 inference(symmetry,[status(thm)],[87])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(A!2, tptp_fun_C_0(A!2)), A!2) = times(tptp_fun_C_0(A!2), times(A!2, A!2)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (times(times(A!2, tptp_fun_C_0(A!2)), A!2) = times(tptp_fun_C_0(A!2), times(A!2, A!2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[89, 45])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 (times(times(A!2, tptp_fun_C_0(A!2)), A!2) = times(A!2, A!2)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[76])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 (times(A!2, A!2) = times(times(A!2, tptp_fun_C_0(A!2)), A!2)),
% 0.20/0.42 inference(symmetry,[status(thm)],[91])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (tptp_fun_C_0(A!2) = times(tptp_fun_C_0(A!2), tptp_fun_C_0(A!2))),
% 0.20/0.42 inference(transitivity,[status(thm)],[86, 92, 90, 88])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (times(tptp_fun_C_0(A!2), tptp_fun_C_0(B!1)) = times(times(tptp_fun_C_0(A!2), tptp_fun_C_0(A!2)), tptp_fun_C_0(B!1))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[93])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (times(times(tptp_fun_C_0(A!2), tptp_fun_C_0(A!2)), tptp_fun_C_0(B!1)) = times(tptp_fun_C_0(A!2), tptp_fun_C_0(B!1))),
% 0.20/0.42 inference(symmetry,[status(thm)],[94])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(tptp_fun_C_0(A!2), tptp_fun_C_0(A!2)), tptp_fun_C_0(B!1)) = times(tptp_fun_C_0(A!2), times(tptp_fun_C_0(B!1), tptp_fun_C_0(A!2))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 (times(times(tptp_fun_C_0(A!2), tptp_fun_C_0(A!2)), tptp_fun_C_0(B!1)) = times(tptp_fun_C_0(A!2), times(tptp_fun_C_0(B!1), tptp_fun_C_0(A!2)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[96, 45])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 (times(tptp_fun_C_0(A!2), times(tptp_fun_C_0(B!1), tptp_fun_C_0(A!2))) = times(times(tptp_fun_C_0(A!2), tptp_fun_C_0(A!2)), tptp_fun_C_0(B!1))),
% 0.20/0.42 inference(symmetry,[status(thm)],[97])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 (times(tptp_fun_C_0(A!2), times(tptp_fun_C_0(B!1), tptp_fun_C_0(A!2))) = times(tptp_fun_C_0(A!2), tptp_fun_C_0(B!1))),
% 0.20/0.42 inference(transitivity,[status(thm)],[98, 95])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 (times(times(A!2, B!1), times(tptp_fun_C_0(A!2), times(tptp_fun_C_0(B!1), tptp_fun_C_0(A!2)))) = times(times(A!2, B!1), times(tptp_fun_C_0(A!2), tptp_fun_C_0(B!1)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[99])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 (times(times(A!2, B!1), times(tptp_fun_C_0(A!2), times(tptp_fun_C_0(B!1), tptp_fun_C_0(A!2)))) = times(A!2, B!1)),
% 0.20/0.42 inference(transitivity,[status(thm)],[100, 83, 81, 66, 63, 61, 58, 47, 38])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 (times(tptp_fun_C_0(A!2), times(B!1, B!1)) = times(tptp_fun_C_0(A!2), tptp_fun_C_0(B!1))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[53])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(B!1, tptp_fun_C_0(A!2)), B!1) = times(tptp_fun_C_0(A!2), times(B!1, B!1)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 (times(times(B!1, tptp_fun_C_0(A!2)), B!1) = times(tptp_fun_C_0(A!2), times(B!1, B!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[103, 45])).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 (times(B!1, tptp_fun_C_0(A!2)) = times(B!1, times(A!2, A!2))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[86])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 (times(B!1, times(A!2, A!2)) = times(B!1, tptp_fun_C_0(A!2))),
% 0.20/0.42 inference(symmetry,[status(thm)],[105])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(A!2, B!1), A!2) = times(B!1, times(A!2, A!2)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 (times(times(A!2, B!1), A!2) = times(B!1, times(A!2, A!2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[107, 45])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 (times(tptp_fun_C_0(B!1), B!1) = times(times(B!1, B!1), B!1)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[54])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 (times(times(B!1, B!1), B!1) = times(tptp_fun_C_0(B!1), B!1)),
% 0.20/0.42 inference(symmetry,[status(thm)],[109])).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(B!1, B!1), B!1) = times(B!1, times(B!1, B!1)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(112,plain,
% 0.20/0.42 (times(times(B!1, B!1), B!1) = times(B!1, times(B!1, B!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[111, 45])).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 (times(B!1, times(B!1, B!1)) = times(times(B!1, B!1), B!1)),
% 0.20/0.42 inference(symmetry,[status(thm)],[112])).
% 0.20/0.42 tff(114,plain,
% 0.20/0.42 (times(B!1, times(B!1, B!1)) = times(B!1, tptp_fun_C_0(B!1))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[53])).
% 0.20/0.42 tff(115,plain,
% 0.20/0.42 (times(B!1, tptp_fun_C_0(B!1)) = times(B!1, times(B!1, B!1))),
% 0.20/0.42 inference(symmetry,[status(thm)],[114])).
% 0.20/0.42 tff(116,plain,
% 0.20/0.42 (B!1 = times(tptp_fun_C_0(B!1), B!1)),
% 0.20/0.42 inference(transitivity,[status(thm)],[36, 115, 113, 110])).
% 0.20/0.42 tff(117,plain,
% 0.20/0.42 (times(B!1, A!2) = times(times(tptp_fun_C_0(B!1), B!1), A!2)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[116])).
% 0.20/0.42 tff(118,plain,
% 0.20/0.42 (times(times(tptp_fun_C_0(B!1), B!1), A!2) = times(B!1, A!2)),
% 0.20/0.42 inference(symmetry,[status(thm)],[117])).
% 0.20/0.42 tff(119,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(tptp_fun_C_0(B!1), B!1), A!2) = times(B!1, times(A!2, tptp_fun_C_0(B!1))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(120,plain,
% 0.20/0.42 (times(times(tptp_fun_C_0(B!1), B!1), A!2) = times(B!1, times(A!2, tptp_fun_C_0(B!1)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[119, 45])).
% 0.20/0.42 tff(121,plain,
% 0.20/0.42 (times(B!1, times(A!2, tptp_fun_C_0(B!1))) = times(times(tptp_fun_C_0(B!1), B!1), A!2)),
% 0.20/0.42 inference(symmetry,[status(thm)],[120])).
% 0.20/0.42 tff(122,plain,
% 0.20/0.42 (times(B!1, times(A!2, tptp_fun_C_0(B!1))) = times(B!1, A!2)),
% 0.20/0.42 inference(transitivity,[status(thm)],[121, 118])).
% 0.20/0.42 tff(123,plain,
% 0.20/0.42 (times(tptp_fun_C_0(A!2), times(B!1, times(A!2, tptp_fun_C_0(B!1)))) = times(tptp_fun_C_0(A!2), times(B!1, A!2))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[122])).
% 0.20/0.42 tff(124,plain,
% 0.20/0.42 (times(tptp_fun_C_0(A!2), times(B!1, A!2)) = times(tptp_fun_C_0(A!2), times(B!1, times(A!2, tptp_fun_C_0(B!1))))),
% 0.20/0.42 inference(symmetry,[status(thm)],[123])).
% 0.20/0.42 tff(125,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(A!2, tptp_fun_C_0(A!2)), B!1) = times(tptp_fun_C_0(A!2), times(B!1, A!2)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(126,plain,
% 0.20/0.42 (times(times(A!2, tptp_fun_C_0(A!2)), B!1) = times(tptp_fun_C_0(A!2), times(B!1, A!2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[125, 45])).
% 0.20/0.42 tff(127,plain,
% 0.20/0.42 (times(times(A!2, tptp_fun_C_0(A!2)), B!1) = times(A!2, B!1)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[76])).
% 0.20/0.42 tff(128,plain,
% 0.20/0.42 (times(A!2, B!1) = times(times(A!2, tptp_fun_C_0(A!2)), B!1)),
% 0.20/0.42 inference(symmetry,[status(thm)],[127])).
% 0.20/0.42 tff(129,plain,
% 0.20/0.42 (times(A!2, B!1) = times(tptp_fun_C_0(A!2), times(B!1, times(A!2, tptp_fun_C_0(B!1))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[128, 126, 124])).
% 0.20/0.42 tff(130,plain,
% 0.20/0.42 (times(times(A!2, B!1), A!2) = times(times(tptp_fun_C_0(A!2), times(B!1, times(A!2, tptp_fun_C_0(B!1)))), A!2)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[129])).
% 0.20/0.42 tff(131,plain,
% 0.20/0.42 (times(times(tptp_fun_C_0(A!2), times(B!1, times(A!2, tptp_fun_C_0(B!1)))), A!2) = times(times(A!2, B!1), A!2)),
% 0.20/0.42 inference(symmetry,[status(thm)],[130])).
% 0.20/0.42 tff(132,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(tptp_fun_C_0(A!2), times(B!1, times(A!2, tptp_fun_C_0(B!1)))), A!2) = times(times(B!1, times(A!2, tptp_fun_C_0(B!1))), times(A!2, tptp_fun_C_0(A!2))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(133,plain,
% 0.20/0.42 (times(times(tptp_fun_C_0(A!2), times(B!1, times(A!2, tptp_fun_C_0(B!1)))), A!2) = times(times(B!1, times(A!2, tptp_fun_C_0(B!1))), times(A!2, tptp_fun_C_0(A!2)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[132, 45])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 (times(times(B!1, times(A!2, tptp_fun_C_0(B!1))), times(A!2, tptp_fun_C_0(A!2))) = times(times(tptp_fun_C_0(A!2), times(B!1, times(A!2, tptp_fun_C_0(B!1)))), A!2)),
% 0.20/0.42 inference(symmetry,[status(thm)],[133])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 (times(times(B!1, times(A!2, tptp_fun_C_0(B!1))), times(A!2, tptp_fun_C_0(A!2))) = times(times(B!1, A!2), A!2)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[122, 76])).
% 0.20/0.42 tff(136,plain,
% 0.20/0.42 (times(times(B!1, A!2), A!2) = times(times(B!1, times(A!2, tptp_fun_C_0(B!1))), times(A!2, tptp_fun_C_0(A!2)))),
% 0.20/0.42 inference(symmetry,[status(thm)],[135])).
% 0.20/0.42 tff(137,plain,
% 0.20/0.42 (times(times(B!1, A!2), A!2) = times(B!1, tptp_fun_C_0(A!2))),
% 0.20/0.42 inference(transitivity,[status(thm)],[136, 134, 131, 108, 106])).
% 0.20/0.42 tff(138,plain,
% 0.20/0.42 (times(times(times(B!1, A!2), A!2), B!1) = times(times(B!1, tptp_fun_C_0(A!2)), B!1)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[137])).
% 0.20/0.42 tff(139,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(B!1, A!2), A!2) = times(A!2, times(A!2, B!1)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(140,plain,
% 0.20/0.43 (times(times(B!1, A!2), A!2) = times(A!2, times(A!2, B!1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[139, 45])).
% 0.20/0.43 tff(141,plain,
% 0.20/0.43 (times(A!2, times(A!2, B!1)) = times(times(B!1, A!2), A!2)),
% 0.20/0.43 inference(symmetry,[status(thm)],[140])).
% 0.20/0.43 tff(142,plain,
% 0.20/0.43 (times(tptp_fun_C_0(B!1), A!2) = times(B!1, times(A!2, B!1))),
% 0.20/0.43 inference(transitivity,[status(thm)],[55, 51])).
% 0.20/0.43 tff(143,plain,
% 0.20/0.43 (times(B!1, times(tptp_fun_C_0(B!1), A!2)) = times(times(B!1, tptp_fun_C_0(B!1)), times(B!1, times(A!2, B!1)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[36, 142])).
% 0.20/0.43 tff(144,plain,
% 0.20/0.43 (times(times(B!1, tptp_fun_C_0(B!1)), times(B!1, times(A!2, B!1))) = times(B!1, times(tptp_fun_C_0(B!1), A!2))),
% 0.20/0.43 inference(symmetry,[status(thm)],[143])).
% 0.20/0.43 tff(145,plain,
% 0.20/0.43 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(B!1, tptp_fun_C_0(B!1)), times(B!1, times(A!2, B!1))) = times(tptp_fun_C_0(B!1), times(times(B!1, times(A!2, B!1)), B!1)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(146,plain,
% 0.20/0.43 (times(times(B!1, tptp_fun_C_0(B!1)), times(B!1, times(A!2, B!1))) = times(tptp_fun_C_0(B!1), times(times(B!1, times(A!2, B!1)), B!1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[145, 45])).
% 0.20/0.43 tff(147,plain,
% 0.20/0.43 (times(tptp_fun_C_0(B!1), times(times(B!1, times(A!2, B!1)), B!1)) = times(times(B!1, tptp_fun_C_0(B!1)), times(B!1, times(A!2, B!1)))),
% 0.20/0.43 inference(symmetry,[status(thm)],[146])).
% 0.20/0.43 tff(148,plain,
% 0.20/0.43 (times(times(B!1, B!1), A!2) = times(tptp_fun_C_0(B!1), A!2)),
% 0.20/0.43 inference(symmetry,[status(thm)],[55])).
% 0.20/0.43 tff(149,plain,
% 0.20/0.43 (times(B!1, times(A!2, B!1)) = times(times(B!1, B!1), A!2)),
% 0.20/0.43 inference(symmetry,[status(thm)],[51])).
% 0.20/0.43 tff(150,plain,
% 0.20/0.43 (times(B!1, times(A!2, B!1)) = times(tptp_fun_C_0(B!1), A!2)),
% 0.20/0.43 inference(transitivity,[status(thm)],[149, 148])).
% 0.20/0.43 tff(151,plain,
% 0.20/0.43 (times(times(B!1, times(A!2, B!1)), B!1) = times(times(tptp_fun_C_0(B!1), A!2), B!1)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[150])).
% 0.20/0.43 tff(152,plain,
% 0.20/0.43 (times(times(B!1, times(A!2, B!1)), B!1) = times(A!2, B!1)),
% 0.20/0.43 inference(transitivity,[status(thm)],[151, 47, 38])).
% 0.20/0.43 tff(153,plain,
% 0.20/0.43 (times(tptp_fun_C_0(B!1), times(times(B!1, times(A!2, B!1)), B!1)) = times(tptp_fun_C_0(B!1), times(A!2, B!1))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[152])).
% 0.20/0.43 tff(154,plain,
% 0.20/0.43 (times(tptp_fun_C_0(B!1), times(A!2, B!1)) = times(tptp_fun_C_0(B!1), times(times(B!1, times(A!2, B!1)), B!1))),
% 0.20/0.43 inference(symmetry,[status(thm)],[153])).
% 0.20/0.43 tff(155,plain,
% 0.20/0.43 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(B!1, tptp_fun_C_0(B!1)), A!2) = times(tptp_fun_C_0(B!1), times(A!2, B!1)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(156,plain,
% 0.20/0.43 (times(times(B!1, tptp_fun_C_0(B!1)), A!2) = times(tptp_fun_C_0(B!1), times(A!2, B!1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[155, 45])).
% 0.20/0.43 tff(157,plain,
% 0.20/0.43 (times(times(B!1, tptp_fun_C_0(B!1)), A!2) = times(B!1, A!2)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[35])).
% 0.20/0.43 tff(158,plain,
% 0.20/0.43 (times(B!1, A!2) = times(times(B!1, tptp_fun_C_0(B!1)), A!2)),
% 0.20/0.43 inference(symmetry,[status(thm)],[157])).
% 0.20/0.43 tff(159,plain,
% 0.20/0.43 (times(B!1, times(A!2, tptp_fun_C_0(B!1))) = times(A!2, B!1)),
% 0.20/0.43 inference(transitivity,[status(thm)],[121, 118, 158, 156, 154, 147, 144, 66, 63, 61, 58, 47, 38])).
% 0.20/0.43 tff(160,plain,
% 0.20/0.43 (times(A!2, times(B!1, times(A!2, tptp_fun_C_0(B!1)))) = times(A!2, times(A!2, B!1))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[159])).
% 0.20/0.43 tff(161,plain,
% 0.20/0.43 (times(A!2, times(B!1, times(A!2, tptp_fun_C_0(B!1)))) = times(times(B!1, A!2), A!2)),
% 0.20/0.43 inference(transitivity,[status(thm)],[160, 141])).
% 0.20/0.43 tff(162,plain,
% 0.20/0.43 (times(times(A!2, times(B!1, times(A!2, tptp_fun_C_0(B!1)))), B!1) = times(times(times(B!1, A!2), A!2), B!1)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[161])).
% 0.20/0.43 tff(163,plain,
% 0.20/0.43 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(A!2, times(B!1, times(A!2, tptp_fun_C_0(B!1)))), B!1) = times(times(B!1, times(A!2, tptp_fun_C_0(B!1))), times(B!1, A!2)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(164,plain,
% 0.20/0.43 (times(times(A!2, times(B!1, times(A!2, tptp_fun_C_0(B!1)))), B!1) = times(times(B!1, times(A!2, tptp_fun_C_0(B!1))), times(B!1, A!2))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[163, 45])).
% 0.20/0.43 tff(165,plain,
% 0.20/0.43 (times(times(B!1, times(A!2, tptp_fun_C_0(B!1))), times(B!1, A!2)) = times(times(A!2, times(B!1, times(A!2, tptp_fun_C_0(B!1)))), B!1)),
% 0.20/0.43 inference(symmetry,[status(thm)],[164])).
% 0.20/0.43 tff(166,plain,
% 0.20/0.43 (times(tptp_fun_C_0(B!1), times(A!2, B!1)) = times(times(B!1, tptp_fun_C_0(B!1)), A!2)),
% 0.20/0.43 inference(symmetry,[status(thm)],[156])).
% 0.20/0.43 tff(167,plain,
% 0.20/0.43 (times(A!2, times(B!1, tptp_fun_C_0(B!1))) = times(times(tptp_fun_C_0(B!1), A!2), B!1)),
% 0.20/0.43 inference(symmetry,[status(thm)],[47])).
% 0.20/0.43 tff(168,plain,
% 0.20/0.43 (times(A!2, B!1) = times(B!1, A!2)),
% 0.20/0.43 inference(transitivity,[status(thm)],[37, 167, 57, 60, 62, 65, 143, 146, 153, 166, 157])).
% 0.20/0.43 tff(169,plain,
% 0.20/0.43 (times(A!2, B!1) = times(B!1, times(A!2, tptp_fun_C_0(B!1)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[37, 167, 57, 60, 62, 65, 143, 146, 153, 166, 157, 117, 120])).
% 0.20/0.43 tff(170,plain,
% 0.20/0.43 (times(times(A!2, B!1), times(A!2, B!1)) = times(times(B!1, times(A!2, tptp_fun_C_0(B!1))), times(B!1, A!2))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[169, 168])).
% 0.20/0.43 tff(171,plain,
% 0.20/0.43 (times(times(A!2, B!1), times(A!2, B!1)) = times(tptp_fun_C_0(A!2), times(tptp_fun_C_0(B!1), tptp_fun_C_0(A!2)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[170, 165, 162, 138, 104, 102, 94, 97])).
% 0.20/0.43 tff(172,plain,
% 0.20/0.43 ((~![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!2, B!1))) | (~((~(times(times(A!2, B!1), tptp_fun_C_0(times(A!2, B!1))) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = tptp_fun_C_0(times(A!2, B!1)))))))) | (~(element(times(A!2, B!1)) | ![C: $i] : ((~(times(times(A!2, B!1), C) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = C)))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(173,plain,
% 0.20/0.43 (~((~((~element(times(A!2, B!1))) | (~((~(times(times(A!2, B!1), tptp_fun_C_0(times(A!2, B!1))) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = tptp_fun_C_0(times(A!2, B!1)))))))) | (~(element(times(A!2, B!1)) | ![C: $i] : ((~(times(times(A!2, B!1), C) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = C))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[172, 13])).
% 0.20/0.43 tff(174,plain,
% 0.20/0.43 (((~((~element(times(A!2, B!1))) | (~((~(times(times(A!2, B!1), tptp_fun_C_0(times(A!2, B!1))) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = tptp_fun_C_0(times(A!2, B!1)))))))) | (~(element(times(A!2, B!1)) | ![C: $i] : ((~(times(times(A!2, B!1), C) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = C)))))) | (element(times(A!2, B!1)) | ![C: $i] : ((~(times(times(A!2, B!1), C) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = C))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(175,plain,
% 0.20/0.43 (element(times(A!2, B!1)) | ![C: $i] : ((~(times(times(A!2, B!1), C) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = C)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.20/0.43 tff(176,plain,
% 0.20/0.43 (~element(times(A!2, B!1))),
% 0.20/0.43 inference(or_elim,[status(thm)],[28])).
% 0.20/0.43 tff(177,plain,
% 0.20/0.43 ((~(element(times(A!2, B!1)) | ![C: $i] : ((~(times(times(A!2, B!1), C) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = C))))) | element(times(A!2, B!1)) | ![C: $i] : ((~(times(times(A!2, B!1), C) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = C)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(178,plain,
% 0.20/0.43 ((~(element(times(A!2, B!1)) | ![C: $i] : ((~(times(times(A!2, B!1), C) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = C))))) | ![C: $i] : ((~(times(times(A!2, B!1), C) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = C)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.20/0.43 tff(179,plain,
% 0.20/0.43 (![C: $i] : ((~(times(times(A!2, B!1), C) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = C)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[178, 175])).
% 0.20/0.43 tff(180,plain,
% 0.20/0.43 (((~![C: $i] : ((~(times(times(A!2, B!1), C) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = C)))) | ((~(times(times(A!2, B!1), times(tptp_fun_C_0(A!2), times(tptp_fun_C_0(B!1), tptp_fun_C_0(A!2)))) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = times(tptp_fun_C_0(A!2), times(tptp_fun_C_0(B!1), tptp_fun_C_0(A!2))))))) <=> ((~![C: $i] : ((~(times(times(A!2, B!1), C) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = C)))) | (~(times(times(A!2, B!1), times(tptp_fun_C_0(A!2), times(tptp_fun_C_0(B!1), tptp_fun_C_0(A!2)))) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = times(tptp_fun_C_0(A!2), times(tptp_fun_C_0(B!1), tptp_fun_C_0(A!2))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(181,plain,
% 0.20/0.43 ((~![C: $i] : ((~(times(times(A!2, B!1), C) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = C)))) | ((~(times(times(A!2, B!1), times(tptp_fun_C_0(A!2), times(tptp_fun_C_0(B!1), tptp_fun_C_0(A!2)))) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = times(tptp_fun_C_0(A!2), times(tptp_fun_C_0(B!1), tptp_fun_C_0(A!2))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(182,plain,
% 0.20/0.43 ((~![C: $i] : ((~(times(times(A!2, B!1), C) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = C)))) | (~(times(times(A!2, B!1), times(tptp_fun_C_0(A!2), times(tptp_fun_C_0(B!1), tptp_fun_C_0(A!2)))) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = times(tptp_fun_C_0(A!2), times(tptp_fun_C_0(B!1), tptp_fun_C_0(A!2)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.20/0.43 tff(183,plain,
% 0.20/0.43 ((~(times(times(A!2, B!1), times(tptp_fun_C_0(A!2), times(tptp_fun_C_0(B!1), tptp_fun_C_0(A!2)))) = times(A!2, B!1))) | (~(times(times(A!2, B!1), times(A!2, B!1)) = times(tptp_fun_C_0(A!2), times(tptp_fun_C_0(B!1), tptp_fun_C_0(A!2)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[182, 179])).
% 0.20/0.43 tff(184,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[183, 171, 101])).
% 0.20/0.43 % SZS output end Proof
%------------------------------------------------------------------------------