%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG210+2 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 : Sat Jun 21 04:58:43 AM UTC 2025
% Result : Theorem 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG210+2 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 10:48:35 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(times_type, type, (
% 0.18/0.37 times: ( $i * $i ) > $i)).
% 0.18/0.37 tff(tptp_fun_B_0_type, type, (
% 0.18/0.37 tptp_fun_B_0: $i)).
% 0.18/0.37 tff(tptp_fun_A_1_type, type, (
% 0.18/0.37 tptp_fun_A_1: $i)).
% 0.18/0.37 tff(element_type, type, (
% 0.18/0.37 element: $i > $o)).
% 0.18/0.37 tff(1,plain,
% 0.18/0.37 (^[B: $i] : refl((element(B) <=> (times(B, times(B, B)) = B)) <=> (element(B) <=> (times(B, times(B, B)) = B)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 (![B: $i] : (element(B) <=> (times(B, times(B, B)) = B)) <=> ![B: $i] : (element(B) <=> (times(B, times(B, B)) = B))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 (![B: $i] : (element(B) <=> (times(B, times(B, B)) = B)) <=> ![B: $i] : (element(B) <=> (times(B, times(B, B)) = B))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 (^[B: $i] : rewrite((element(B) <=> ?[C: $i] : ((times(B, C) = B) & (times(B, B) = C))) <=> (element(B) <=> (times(B, times(B, B)) = B)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 (![B: $i] : (element(B) <=> ?[C: $i] : ((times(B, C) = B) & (times(B, B) = C))) <=> ![B: $i] : (element(B) <=> (times(B, times(B, B)) = B))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[4])).
% 0.18/0.37 tff(6,axiom,(![B: $i] : (element(B) <=> ?[C: $i] : ((times(B, C) = B) & (times(B, B) = C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_2')).
% 0.18/0.37 tff(7,plain,
% 0.18/0.37 (![B: $i] : (element(B) <=> (times(B, times(B, B)) = B))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 (![B: $i] : (element(B) <=> (times(B, times(B, B)) = B))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.37 tff(9,plain,(
% 0.18/0.37 ![B: $i] : (element(B) <=> (times(B, times(B, B)) = B))),
% 0.18/0.37 inference(skolemize,[status(sab)],[8])).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 (![B: $i] : (element(B) <=> (times(B, times(B, B)) = B))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.18/0.37 tff(11,plain,
% 0.18/0.37 ((~![B: $i] : (element(B) <=> (times(B, times(B, B)) = B))) | (element(B!0) <=> (times(B!0, times(B!0, B!0)) = B!0))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(12,plain,
% 0.18/0.37 (element(B!0) <=> (times(B!0, times(B!0, B!0)) = B!0)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 ((~((~element(A!1)) | element(times(A!1, B!0)) | (~element(B!0)))) <=> (~((~element(A!1)) | element(times(A!1, B!0)) | (~element(B!0))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(14,plain,
% 0.18/0.37 ((~![A: $i, B: $i] : ((~element(A)) | element(times(A, B)) | (~element(B)))) <=> (~![A: $i, B: $i] : ((~element(A)) | element(times(A, B)) | (~element(B))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(15,plain,
% 0.18/0.37 ((~![A: $i, B: $i, C: $i] : (((element(A) & element(B)) & (C = times(A, B))) => element(C))) <=> (~![A: $i, B: $i] : ((~element(A)) | element(times(A, B)) | (~element(B))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(16,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')).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 (~![A: $i, B: $i] : ((~element(A)) | element(times(A, B)) | (~element(B)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.18/0.37 tff(18,plain,
% 0.18/0.37 (~![A: $i, B: $i] : ((~element(A)) | element(times(A, B)) | (~element(B)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 (~![A: $i, B: $i] : ((~element(A)) | element(times(A, B)) | (~element(B)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.18/0.37 tff(20,plain,
% 0.18/0.37 (~![A: $i, B: $i] : ((~element(A)) | element(times(A, B)) | (~element(B)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.18/0.37 tff(21,plain,(
% 0.18/0.37 ~((~element(A!1)) | element(times(A!1, B!0)) | (~element(B!0)))),
% 0.18/0.37 inference(skolemize,[status(sab)],[20])).
% 0.18/0.37 tff(22,plain,
% 0.18/0.37 (~((~element(A!1)) | element(times(A!1, B!0)) | (~element(B!0)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[21, 13])).
% 0.18/0.37 tff(23,plain,
% 0.18/0.37 (element(B!0)),
% 0.18/0.37 inference(or_elim,[status(thm)],[22])).
% 0.18/0.37 tff(24,plain,
% 0.18/0.37 ((~(element(B!0) <=> (times(B!0, times(B!0, B!0)) = B!0))) | (~element(B!0)) | (times(B!0, times(B!0, B!0)) = B!0)),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(25,plain,
% 0.18/0.37 ((~(element(B!0) <=> (times(B!0, times(B!0, B!0)) = B!0))) | (times(B!0, times(B!0, B!0)) = B!0)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.18/0.37 tff(26,plain,
% 0.18/0.37 (times(B!0, times(B!0, B!0)) = B!0),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[25, 12])).
% 0.18/0.37 tff(27,plain,
% 0.18/0.37 (B!0 = times(B!0, times(B!0, B!0))),
% 0.18/0.37 inference(symmetry,[status(thm)],[26])).
% 0.18/0.37 tff(28,plain,
% 0.18/0.37 (times(A!1, B!0) = times(A!1, times(B!0, times(B!0, B!0)))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[27])).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 (times(A!1, times(B!0, times(B!0, B!0))) = times(A!1, B!0)),
% 0.18/0.37 inference(symmetry,[status(thm)],[28])).
% 0.18/0.37 tff(30,plain,
% 0.18/0.37 (^[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))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(31,plain,
% 0.18/0.37 (![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)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[30])).
% 0.18/0.37 tff(32,plain,
% 0.18/0.37 (![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)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(33,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')).
% 0.18/0.37 tff(34,plain,
% 0.18/0.37 (![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.18/0.37 tff(35,plain,(
% 0.18/0.37 ![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))),
% 0.18/0.37 inference(skolemize,[status(sab)],[34])).
% 0.18/0.37 tff(36,plain,
% 0.18/0.37 (![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.18/0.37 tff(37,plain,
% 0.18/0.37 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(times(B!0, B!0), A!1), B!0) = times(A!1, times(B!0, times(B!0, B!0))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(38,plain,
% 0.18/0.37 (times(times(times(B!0, B!0), A!1), B!0) = times(A!1, times(B!0, times(B!0, B!0)))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.18/0.37 tff(39,plain,
% 0.18/0.37 ((~![B: $i] : (element(B) <=> (times(B, times(B, B)) = B))) | (element(A!1) <=> (times(A!1, times(A!1, A!1)) = A!1))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(40,plain,
% 0.18/0.37 (element(A!1) <=> (times(A!1, times(A!1, A!1)) = A!1)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[39, 10])).
% 0.18/0.37 tff(41,plain,
% 0.18/0.37 (element(A!1)),
% 0.18/0.37 inference(or_elim,[status(thm)],[22])).
% 0.18/0.37 tff(42,plain,
% 0.18/0.37 ((~(element(A!1) <=> (times(A!1, times(A!1, A!1)) = A!1))) | (~element(A!1)) | (times(A!1, times(A!1, A!1)) = A!1)),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(43,plain,
% 0.18/0.37 ((~(element(A!1) <=> (times(A!1, times(A!1, A!1)) = A!1))) | (times(A!1, times(A!1, A!1)) = A!1)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.18/0.37 tff(44,plain,
% 0.18/0.37 (times(A!1, times(A!1, A!1)) = A!1),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.18/0.37 tff(45,plain,
% 0.18/0.37 (times(times(A!1, times(A!1, A!1)), B!0) = times(A!1, B!0)),
% 0.18/0.37 inference(monotonicity,[status(thm)],[44])).
% 0.18/0.37 tff(46,plain,
% 0.18/0.37 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(A!1, times(A!1, A!1)), B!0) = times(times(A!1, A!1), times(B!0, A!1)))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(47,plain,
% 0.18/0.37 (times(times(A!1, times(A!1, A!1)), B!0) = times(times(A!1, A!1), times(B!0, A!1))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[46, 36])).
% 0.18/0.37 tff(48,plain,
% 0.18/0.37 (times(times(A!1, A!1), times(B!0, A!1)) = times(times(A!1, times(A!1, A!1)), B!0)),
% 0.18/0.37 inference(symmetry,[status(thm)],[47])).
% 0.18/0.37 tff(49,plain,
% 0.18/0.37 (times(times(A!1, A!1), times(B!0, A!1)) = times(A!1, B!0)),
% 0.18/0.37 inference(transitivity,[status(thm)],[48, 45])).
% 0.18/0.37 tff(50,plain,
% 0.18/0.37 (times(B!0, times(times(A!1, A!1), times(B!0, A!1))) = times(B!0, times(A!1, B!0))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[49])).
% 0.18/0.37 tff(51,plain,
% 0.18/0.37 (times(B!0, times(A!1, B!0)) = times(B!0, times(times(A!1, A!1), times(B!0, A!1)))),
% 0.18/0.37 inference(symmetry,[status(thm)],[50])).
% 0.18/0.37 tff(52,plain,
% 0.18/0.37 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(B!0, B!0), A!1) = times(B!0, times(A!1, B!0)))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(53,plain,
% 0.18/0.37 (times(times(B!0, B!0), A!1) = times(B!0, times(A!1, B!0))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[52, 36])).
% 0.18/0.37 tff(54,plain,
% 0.18/0.37 (times(times(B!0, B!0), A!1) = times(B!0, times(times(A!1, A!1), times(B!0, A!1)))),
% 0.18/0.37 inference(transitivity,[status(thm)],[53, 51])).
% 0.18/0.37 tff(55,plain,
% 0.18/0.37 (times(times(times(B!0, B!0), A!1), B!0) = times(times(B!0, times(times(A!1, A!1), times(B!0, A!1))), B!0)),
% 0.18/0.37 inference(monotonicity,[status(thm)],[54])).
% 0.18/0.37 tff(56,plain,
% 0.18/0.37 (times(times(B!0, times(times(A!1, A!1), times(B!0, A!1))), B!0) = times(times(times(B!0, B!0), A!1), B!0)),
% 0.18/0.37 inference(symmetry,[status(thm)],[55])).
% 0.18/0.37 tff(57,plain,
% 0.18/0.37 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(B!0, times(times(A!1, A!1), times(B!0, A!1))), B!0) = times(times(times(A!1, A!1), times(B!0, A!1)), times(B!0, B!0)))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(58,plain,
% 0.18/0.37 (times(times(B!0, times(times(A!1, A!1), times(B!0, A!1))), B!0) = times(times(times(A!1, A!1), times(B!0, A!1)), times(B!0, B!0))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[57, 36])).
% 0.18/0.37 tff(59,plain,
% 0.18/0.37 (times(times(times(A!1, A!1), times(B!0, A!1)), times(B!0, B!0)) = times(times(B!0, times(times(A!1, A!1), times(B!0, A!1))), B!0)),
% 0.18/0.37 inference(symmetry,[status(thm)],[58])).
% 0.18/0.37 tff(60,plain,
% 0.18/0.37 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(B!0, times(B!0, B!0)), B!0) = times(times(B!0, B!0), times(B!0, B!0)))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(61,plain,
% 0.18/0.37 (times(times(B!0, times(B!0, B!0)), B!0) = times(times(B!0, B!0), times(B!0, B!0))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[60, 36])).
% 0.18/0.37 tff(62,plain,
% 0.18/0.37 (times(B!0, B!0) = times(times(B!0, times(B!0, B!0)), B!0)),
% 0.18/0.37 inference(monotonicity,[status(thm)],[27])).
% 0.18/0.37 tff(63,plain,
% 0.18/0.37 (times(B!0, B!0) = times(times(B!0, B!0), times(B!0, B!0))),
% 0.18/0.37 inference(transitivity,[status(thm)],[62, 61])).
% 0.18/0.37 tff(64,plain,
% 0.18/0.37 (times(times(times(A!1, A!1), times(B!0, A!1)), times(B!0, B!0)) = times(times(times(A!1, A!1), times(B!0, A!1)), times(times(B!0, B!0), times(B!0, B!0)))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[63])).
% 0.18/0.37 tff(65,plain,
% 0.18/0.37 (times(times(times(A!1, A!1), times(B!0, A!1)), times(times(B!0, B!0), times(B!0, B!0))) = times(times(times(A!1, A!1), times(B!0, A!1)), times(B!0, B!0))),
% 0.18/0.37 inference(symmetry,[status(thm)],[64])).
% 0.18/0.37 tff(66,plain,
% 0.18/0.37 (A!1 = times(A!1, times(A!1, A!1))),
% 0.18/0.37 inference(symmetry,[status(thm)],[44])).
% 0.18/0.37 tff(67,plain,
% 0.18/0.37 (times(A!1, A!1) = times(times(A!1, times(A!1, A!1)), A!1)),
% 0.18/0.37 inference(monotonicity,[status(thm)],[66])).
% 0.18/0.37 tff(68,plain,
% 0.18/0.37 (times(times(A!1, times(A!1, A!1)), A!1) = times(A!1, A!1)),
% 0.18/0.37 inference(symmetry,[status(thm)],[67])).
% 0.18/0.37 tff(69,plain,
% 0.18/0.37 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(A!1, times(A!1, A!1)), A!1) = times(times(A!1, A!1), times(A!1, A!1)))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(70,plain,
% 0.18/0.37 (times(times(A!1, times(A!1, A!1)), A!1) = times(times(A!1, A!1), times(A!1, A!1))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[69, 36])).
% 0.18/0.37 tff(71,plain,
% 0.18/0.37 (times(times(A!1, A!1), times(A!1, A!1)) = times(times(A!1, times(A!1, A!1)), A!1)),
% 0.18/0.37 inference(symmetry,[status(thm)],[70])).
% 0.18/0.37 tff(72,plain,
% 0.18/0.37 (times(times(A!1, A!1), times(A!1, A!1)) = times(A!1, A!1)),
% 0.18/0.37 inference(transitivity,[status(thm)],[71, 68])).
% 0.18/0.37 tff(73,plain,
% 0.18/0.37 (times(B!0, times(times(A!1, A!1), times(A!1, A!1))) = times(B!0, times(A!1, A!1))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[72])).
% 0.18/0.37 tff(74,plain,
% 0.18/0.37 (times(B!0, times(A!1, A!1)) = times(B!0, times(times(A!1, A!1), times(A!1, A!1)))),
% 0.18/0.37 inference(symmetry,[status(thm)],[73])).
% 0.18/0.37 tff(75,plain,
% 0.18/0.37 (times(A!1, times(B!0, times(A!1, A!1))) = times(A!1, times(B!0, times(times(A!1, A!1), times(A!1, A!1))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[74])).
% 0.18/0.38 tff(76,plain,
% 0.18/0.38 (times(A!1, times(B!0, times(times(A!1, A!1), times(A!1, A!1)))) = times(A!1, times(B!0, times(A!1, A!1)))),
% 0.18/0.38 inference(symmetry,[status(thm)],[75])).
% 0.18/0.38 tff(77,plain,
% 0.18/0.38 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(times(times(A!1, A!1), times(A!1, A!1)), A!1), B!0) = times(A!1, times(B!0, times(times(A!1, A!1), times(A!1, A!1)))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(78,plain,
% 0.18/0.38 (times(times(times(times(A!1, A!1), times(A!1, A!1)), A!1), B!0) = times(A!1, times(B!0, times(times(A!1, A!1), times(A!1, A!1))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[77, 36])).
% 0.18/0.38 tff(79,plain,
% 0.18/0.38 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(A!1, A!1), A!1) = times(A!1, times(A!1, A!1)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(80,plain,
% 0.18/0.38 (times(times(A!1, A!1), A!1) = times(A!1, times(A!1, A!1))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[79, 36])).
% 0.18/0.38 tff(81,plain,
% 0.18/0.38 (times(times(times(A!1, A!1), times(A!1, A!1)), A!1) = times(times(A!1, A!1), A!1)),
% 0.18/0.38 inference(monotonicity,[status(thm)],[72])).
% 0.18/0.38 tff(82,plain,
% 0.18/0.38 (times(times(times(A!1, A!1), times(A!1, A!1)), A!1) = A!1),
% 0.18/0.38 inference(transitivity,[status(thm)],[81, 80, 44])).
% 0.18/0.38 tff(83,plain,
% 0.18/0.38 (times(times(times(times(A!1, A!1), times(A!1, A!1)), A!1), B!0) = times(A!1, B!0)),
% 0.18/0.38 inference(monotonicity,[status(thm)],[82])).
% 0.18/0.38 tff(84,plain,
% 0.18/0.38 (times(A!1, B!0) = times(times(times(times(A!1, A!1), times(A!1, A!1)), A!1), B!0)),
% 0.18/0.38 inference(symmetry,[status(thm)],[83])).
% 0.18/0.38 tff(85,plain,
% 0.18/0.38 (times(times(A!1, A!1), times(B!0, A!1)) = times(A!1, times(B!0, times(A!1, A!1)))),
% 0.18/0.38 inference(transitivity,[status(thm)],[48, 45, 84, 78, 76])).
% 0.18/0.38 tff(86,plain,
% 0.18/0.38 (times(times(times(A!1, A!1), times(B!0, A!1)), times(times(B!0, B!0), times(B!0, B!0))) = times(times(A!1, times(B!0, times(A!1, A!1))), times(times(B!0, B!0), times(B!0, B!0)))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[85])).
% 0.18/0.38 tff(87,plain,
% 0.18/0.38 (times(times(A!1, times(B!0, times(A!1, A!1))), times(times(B!0, B!0), times(B!0, B!0))) = times(times(times(A!1, A!1), times(B!0, A!1)), times(times(B!0, B!0), times(B!0, B!0)))),
% 0.18/0.38 inference(symmetry,[status(thm)],[86])).
% 0.18/0.38 tff(88,plain,
% 0.18/0.38 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(A!1, times(B!0, times(A!1, A!1))), times(times(B!0, B!0), times(B!0, B!0))) = times(times(B!0, times(A!1, A!1)), times(times(times(B!0, B!0), times(B!0, B!0)), A!1)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(89,plain,
% 0.18/0.38 (times(times(A!1, times(B!0, times(A!1, A!1))), times(times(B!0, B!0), times(B!0, B!0))) = times(times(B!0, times(A!1, A!1)), times(times(times(B!0, B!0), times(B!0, B!0)), A!1))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[88, 36])).
% 0.18/0.38 tff(90,plain,
% 0.18/0.38 (times(times(B!0, times(A!1, A!1)), times(times(times(B!0, B!0), times(B!0, B!0)), A!1)) = times(times(A!1, times(B!0, times(A!1, A!1))), times(times(B!0, B!0), times(B!0, B!0)))),
% 0.18/0.38 inference(symmetry,[status(thm)],[89])).
% 0.18/0.38 tff(91,plain,
% 0.18/0.38 (times(times(B!0, times(B!0, B!0)), B!0) = times(B!0, B!0)),
% 0.18/0.38 inference(symmetry,[status(thm)],[62])).
% 0.18/0.38 tff(92,plain,
% 0.18/0.38 (times(times(B!0, B!0), times(B!0, B!0)) = times(times(B!0, times(B!0, B!0)), B!0)),
% 0.18/0.38 inference(symmetry,[status(thm)],[61])).
% 0.18/0.38 tff(93,plain,
% 0.18/0.38 (times(times(B!0, B!0), times(B!0, B!0)) = times(B!0, B!0)),
% 0.18/0.38 inference(transitivity,[status(thm)],[92, 91])).
% 0.18/0.38 tff(94,plain,
% 0.18/0.38 (times(times(times(B!0, B!0), times(B!0, B!0)), A!1) = times(times(B!0, B!0), A!1)),
% 0.18/0.38 inference(monotonicity,[status(thm)],[93])).
% 0.18/0.38 tff(95,plain,
% 0.18/0.38 (times(times(times(B!0, B!0), times(B!0, B!0)), A!1) = times(B!0, times(A!1, B!0))),
% 0.18/0.38 inference(transitivity,[status(thm)],[94, 53])).
% 0.18/0.38 tff(96,plain,
% 0.18/0.38 (times(times(B!0, times(A!1, A!1)), times(times(times(B!0, B!0), times(B!0, B!0)), A!1)) = times(times(B!0, times(times(A!1, A!1), times(A!1, A!1))), times(B!0, times(A!1, B!0)))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[74, 95])).
% 0.18/0.38 tff(97,plain,
% 0.18/0.38 (times(times(B!0, times(times(A!1, A!1), times(A!1, A!1))), times(B!0, times(A!1, B!0))) = times(times(B!0, times(A!1, A!1)), times(times(times(B!0, B!0), times(B!0, B!0)), A!1))),
% 0.18/0.38 inference(symmetry,[status(thm)],[96])).
% 0.18/0.38 tff(98,plain,
% 0.18/0.38 (times(A!1, times(times(A!1, A!1), times(B!0, A!1))) = times(A!1, times(A!1, B!0))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[49])).
% 0.18/0.38 tff(99,plain,
% 0.18/0.38 (times(A!1, times(A!1, B!0)) = times(A!1, times(times(A!1, A!1), times(B!0, A!1)))),
% 0.18/0.38 inference(symmetry,[status(thm)],[98])).
% 0.18/0.38 tff(100,plain,
% 0.18/0.38 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(B!0, A!1), A!1) = times(A!1, times(A!1, B!0)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(101,plain,
% 0.18/0.38 (times(times(B!0, A!1), A!1) = times(A!1, times(A!1, B!0))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[100, 36])).
% 0.18/0.38 tff(102,plain,
% 0.18/0.38 (times(A!1, times(times(A!1, A!1), times(A!1, A!1))) = times(A!1, times(A!1, A!1))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[72])).
% 0.18/0.38 tff(103,plain,
% 0.18/0.38 (times(A!1, times(A!1, A!1)) = times(A!1, times(times(A!1, A!1), times(A!1, A!1)))),
% 0.18/0.38 inference(symmetry,[status(thm)],[102])).
% 0.18/0.38 tff(104,plain,
% 0.18/0.38 (A!1 = times(A!1, times(times(A!1, A!1), times(A!1, A!1)))),
% 0.18/0.38 inference(transitivity,[status(thm)],[66, 103])).
% 0.18/0.38 tff(105,plain,
% 0.18/0.38 (times(times(B!0, A!1), A!1) = times(times(B!0, A!1), times(A!1, times(times(A!1, A!1), times(A!1, A!1))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[104])).
% 0.18/0.38 tff(106,plain,
% 0.18/0.38 (times(times(B!0, A!1), times(A!1, times(times(A!1, A!1), times(A!1, A!1)))) = times(times(B!0, A!1), A!1)),
% 0.18/0.38 inference(symmetry,[status(thm)],[105])).
% 0.18/0.38 tff(107,plain,
% 0.18/0.38 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(times(times(A!1, A!1), times(A!1, A!1)), times(B!0, A!1)), A!1) = times(times(B!0, A!1), times(A!1, times(times(A!1, A!1), times(A!1, A!1)))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(108,plain,
% 0.18/0.38 (times(times(times(times(A!1, A!1), times(A!1, A!1)), times(B!0, A!1)), A!1) = times(times(B!0, A!1), times(A!1, times(times(A!1, A!1), times(A!1, A!1))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[107, 36])).
% 0.18/0.38 tff(109,plain,
% 0.18/0.38 (times(times(times(A!1, A!1), times(A!1, A!1)), times(B!0, A!1)) = times(times(A!1, A!1), times(B!0, A!1))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[72])).
% 0.18/0.38 tff(110,plain,
% 0.18/0.38 (times(times(times(A!1, A!1), times(A!1, A!1)), times(B!0, A!1)) = times(A!1, B!0)),
% 0.18/0.38 inference(transitivity,[status(thm)],[109, 48, 45])).
% 0.18/0.38 tff(111,plain,
% 0.18/0.38 (times(times(times(times(A!1, A!1), times(A!1, A!1)), times(B!0, A!1)), A!1) = times(times(A!1, B!0), A!1)),
% 0.18/0.38 inference(monotonicity,[status(thm)],[110])).
% 0.18/0.38 tff(112,plain,
% 0.18/0.38 (times(times(A!1, B!0), A!1) = times(times(times(times(A!1, A!1), times(A!1, A!1)), times(B!0, A!1)), A!1)),
% 0.18/0.38 inference(symmetry,[status(thm)],[111])).
% 0.18/0.38 tff(113,plain,
% 0.18/0.38 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(A!1, B!0), A!1) = times(B!0, times(A!1, A!1)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(114,plain,
% 0.18/0.38 (times(times(A!1, B!0), A!1) = times(B!0, times(A!1, A!1))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[113, 36])).
% 0.18/0.38 tff(115,plain,
% 0.18/0.38 (times(B!0, times(A!1, A!1)) = times(times(A!1, B!0), A!1)),
% 0.18/0.38 inference(symmetry,[status(thm)],[114])).
% 0.18/0.38 tff(116,plain,
% 0.18/0.38 (times(B!0, times(times(A!1, A!1), times(A!1, A!1))) = times(A!1, times(times(A!1, A!1), times(B!0, A!1)))),
% 0.18/0.38 inference(transitivity,[status(thm)],[73, 115, 112, 108, 106, 101, 99])).
% 0.18/0.38 tff(117,plain,
% 0.18/0.38 (times(times(B!0, times(times(A!1, A!1), times(A!1, A!1))), times(B!0, times(A!1, B!0))) = times(times(A!1, times(times(A!1, A!1), times(B!0, A!1))), times(B!0, times(A!1, B!0)))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[116])).
% 0.18/0.38 tff(118,plain,
% 0.18/0.38 (times(times(A!1, times(times(A!1, A!1), times(B!0, A!1))), times(B!0, times(A!1, B!0))) = times(times(B!0, times(times(A!1, A!1), times(A!1, A!1))), times(B!0, times(A!1, B!0)))),
% 0.18/0.38 inference(symmetry,[status(thm)],[117])).
% 0.18/0.39 tff(119,plain,
% 0.18/0.39 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(A!1, times(times(A!1, A!1), times(B!0, A!1))), times(B!0, times(A!1, B!0))) = times(times(times(A!1, A!1), times(B!0, A!1)), times(times(B!0, times(A!1, B!0)), A!1)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(120,plain,
% 0.18/0.39 (times(times(A!1, times(times(A!1, A!1), times(B!0, A!1))), times(B!0, times(A!1, B!0))) = times(times(times(A!1, A!1), times(B!0, A!1)), times(times(B!0, times(A!1, B!0)), A!1))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[119, 36])).
% 0.18/0.39 tff(121,plain,
% 0.18/0.39 (times(times(times(A!1, A!1), times(B!0, A!1)), times(times(B!0, times(A!1, B!0)), A!1)) = times(times(A!1, times(times(A!1, A!1), times(B!0, A!1))), times(B!0, times(A!1, B!0)))),
% 0.18/0.39 inference(symmetry,[status(thm)],[120])).
% 0.18/0.39 tff(122,plain,
% 0.18/0.39 ((~![A: $i, B: $i, C: $i] : (times(times(A, B), C) = times(B, times(C, A)))) | (times(times(B!0, times(A!1, B!0)), A!1) = times(times(A!1, B!0), times(A!1, B!0)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(123,plain,
% 0.18/0.39 (times(times(B!0, times(A!1, B!0)), A!1) = times(times(A!1, B!0), times(A!1, B!0))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[122, 36])).
% 0.18/0.39 tff(124,plain,
% 0.18/0.39 (times(times(times(A!1, A!1), times(B!0, A!1)), times(times(B!0, times(A!1, B!0)), A!1)) = times(times(A!1, B!0), times(times(A!1, B!0), times(A!1, B!0)))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[49, 123])).
% 0.18/0.39 tff(125,plain,
% 0.18/0.39 (times(times(A!1, B!0), times(times(A!1, B!0), times(A!1, B!0))) = times(times(times(A!1, A!1), times(B!0, A!1)), times(times(B!0, times(A!1, B!0)), A!1))),
% 0.18/0.39 inference(symmetry,[status(thm)],[124])).
% 0.18/0.39 tff(126,plain,
% 0.18/0.39 (times(times(A!1, B!0), times(times(A!1, B!0), times(A!1, B!0))) = times(A!1, B!0)),
% 0.18/0.39 inference(transitivity,[status(thm)],[125, 121, 118, 97, 90, 87, 65, 59, 56, 38, 29])).
% 0.18/0.39 tff(127,plain,
% 0.18/0.39 ((~![B: $i] : (element(B) <=> (times(B, times(B, B)) = B))) | (element(times(A!1, B!0)) <=> (times(times(A!1, B!0), times(times(A!1, B!0), times(A!1, B!0))) = times(A!1, B!0)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(128,plain,
% 0.18/0.39 (element(times(A!1, B!0)) <=> (times(times(A!1, B!0), times(times(A!1, B!0), times(A!1, B!0))) = times(A!1, B!0))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[127, 10])).
% 0.18/0.39 tff(129,plain,
% 0.18/0.39 (~element(times(A!1, B!0))),
% 0.18/0.39 inference(or_elim,[status(thm)],[22])).
% 0.18/0.39 tff(130,plain,
% 0.18/0.39 ((~(element(times(A!1, B!0)) <=> (times(times(A!1, B!0), times(times(A!1, B!0), times(A!1, B!0))) = times(A!1, B!0)))) | element(times(A!1, B!0)) | (~(times(times(A!1, B!0), times(times(A!1, B!0), times(A!1, B!0))) = times(A!1, B!0)))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(131,plain,
% 0.18/0.39 ((~(element(times(A!1, B!0)) <=> (times(times(A!1, B!0), times(times(A!1, B!0), times(A!1, B!0))) = times(A!1, B!0)))) | (~(times(times(A!1, B!0), times(times(A!1, B!0), times(A!1, B!0))) = times(A!1, B!0)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.18/0.39 tff(132,plain,
% 0.18/0.39 (~(times(times(A!1, B!0), times(times(A!1, B!0), times(A!1, B!0))) = times(A!1, B!0))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[131, 128])).
% 0.18/0.39 tff(133,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[132, 126])).
% 0.18/0.39 % SZS output end Proof
% 0.18/0.39 % E exiting
%------------------------------------------------------------------------------