%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP775+1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:08:39 AM UTC 2025
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GRP775+1 : TPTP v9.0.0. Released v4.1.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Jun 19 17:06:41 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(l_type, type, (
% 0.21/0.41 l: ( $i * $i ) > $o)).
% 0.21/0.41 tff(tptp_fun_X8_1_type, type, (
% 0.21/0.41 tptp_fun_X8_1: $i)).
% 0.21/0.41 tff(tptp_fun_X6_0_type, type, (
% 0.21/0.41 tptp_fun_X6_0: ( $i * $i ) > $i)).
% 0.21/0.41 tff(tptp_fun_X7_2_type, type, (
% 0.21/0.41 tptp_fun_X7_2: $i)).
% 0.21/0.41 tff(product_type, type, (
% 0.21/0.41 product: ( $i * $i ) > $i)).
% 0.21/0.41 tff(r_type, type, (
% 0.21/0.41 r: ( $i * $i ) > $o)).
% 0.21/0.41 tff(d_type, type, (
% 0.21/0.41 d: ( $i * $i ) > $o)).
% 0.21/0.41 tff(1,plain,
% 0.21/0.41 (^[X0: $i, X1: $i] : refl((~(((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))) <=> l(X0, X1))) <=> (~(((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))) <=> l(X0, X1))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 (![X0: $i, X1: $i] : (~(((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))) <=> l(X0, X1))) <=> ![X0: $i, X1: $i] : (~(((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))) <=> l(X0, X1)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.41 tff(3,plain,
% 0.21/0.41 (^[X0: $i, X1: $i] : trans(trans(monotonicity(rewrite(((product(X0, X1) = X0) & (product(X1, X0) = X1)) <=> (~((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))))), ((l(X0, X1) <=> ((product(X0, X1) = X0) & (product(X1, X0) = X1))) <=> (l(X0, X1) <=> (~((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))))))), rewrite((l(X0, X1) <=> (~((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))))) <=> (~(((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))) <=> l(X0, X1)))), ((l(X0, X1) <=> ((product(X0, X1) = X0) & (product(X1, X0) = X1))) <=> (~(((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))) <=> l(X0, X1))))), rewrite((~(((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))) <=> l(X0, X1))) <=> (~(((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))) <=> l(X0, X1)))), ((l(X0, X1) <=> ((product(X0, X1) = X0) & (product(X1, X0) = X1))) <=> (~(((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))) <=> l(X0, X1)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(4,plain,
% 0.21/0.41 (![X0: $i, X1: $i] : (l(X0, X1) <=> ((product(X0, X1) = X0) & (product(X1, X0) = X1))) <=> ![X0: $i, X1: $i] : (~(((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))) <=> l(X0, X1)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 (![X0: $i, X1: $i] : (l(X0, X1) <=> ((product(X0, X1) = X0) & (product(X1, X0) = X1))) <=> ![X0: $i, X1: $i] : (l(X0, X1) <=> ((product(X0, X1) = X0) & (product(X1, X0) = X1)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(6,axiom,(![X0: $i, X1: $i] : (l(X0, X1) <=> ((product(X0, X1) = X0) & (product(X1, X0) = X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sos03')).
% 0.21/0.41 tff(7,plain,
% 0.21/0.41 (![X0: $i, X1: $i] : (l(X0, X1) <=> ((product(X0, X1) = X0) & (product(X1, X0) = X1)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.41 tff(8,plain,(
% 0.21/0.41 ![X0: $i, X1: $i] : (l(X0, X1) <=> ((product(X0, X1) = X0) & (product(X1, X0) = X1)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[7])).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (![X0: $i, X1: $i] : (~(((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))) <=> l(X0, X1)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 (![X0: $i, X1: $i] : (~(((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))) <=> l(X0, X1)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.21/0.41 tff(11,plain,
% 0.21/0.41 ((~![X0: $i, X1: $i] : (~(((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))) <=> l(X0, X1)))) | (~(((~(product(tptp_fun_X6_0(X8!1, X7!2), X8!1) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(X8!1, tptp_fun_X6_0(X8!1, X7!2)) = X8!1))) <=> l(tptp_fun_X6_0(X8!1, X7!2), X8!1)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 (~(((~(product(tptp_fun_X6_0(X8!1, X7!2), X8!1) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(X8!1, tptp_fun_X6_0(X8!1, X7!2)) = X8!1))) <=> l(tptp_fun_X6_0(X8!1, X7!2), X8!1))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.21/0.41 tff(13,plain,
% 0.21/0.41 (^[X2: $i, X3: $i] : refl((~(((~(product(X2, X3) = X3)) | (~(product(X3, X2) = X2))) <=> r(X2, X3))) <=> (~(((~(product(X2, X3) = X3)) | (~(product(X3, X2) = X2))) <=> r(X2, X3))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(14,plain,
% 0.21/0.41 (![X2: $i, X3: $i] : (~(((~(product(X2, X3) = X3)) | (~(product(X3, X2) = X2))) <=> r(X2, X3))) <=> ![X2: $i, X3: $i] : (~(((~(product(X2, X3) = X3)) | (~(product(X3, X2) = X2))) <=> r(X2, X3)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 (^[X2: $i, X3: $i] : trans(trans(monotonicity(rewrite(((product(X2, X3) = X3) & (product(X3, X2) = X2)) <=> (~((~(product(X2, X3) = X3)) | (~(product(X3, X2) = X2))))), ((r(X2, X3) <=> ((product(X2, X3) = X3) & (product(X3, X2) = X2))) <=> (r(X2, X3) <=> (~((~(product(X2, X3) = X3)) | (~(product(X3, X2) = X2))))))), rewrite((r(X2, X3) <=> (~((~(product(X2, X3) = X3)) | (~(product(X3, X2) = X2))))) <=> (~(((~(product(X2, X3) = X3)) | (~(product(X3, X2) = X2))) <=> r(X2, X3)))), ((r(X2, X3) <=> ((product(X2, X3) = X3) & (product(X3, X2) = X2))) <=> (~(((~(product(X2, X3) = X3)) | (~(product(X3, X2) = X2))) <=> r(X2, X3))))), rewrite((~(((~(product(X2, X3) = X3)) | (~(product(X3, X2) = X2))) <=> r(X2, X3))) <=> (~(((~(product(X2, X3) = X3)) | (~(product(X3, X2) = X2))) <=> r(X2, X3)))), ((r(X2, X3) <=> ((product(X2, X3) = X3) & (product(X3, X2) = X2))) <=> (~(((~(product(X2, X3) = X3)) | (~(product(X3, X2) = X2))) <=> r(X2, X3)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(16,plain,
% 0.21/0.41 (![X2: $i, X3: $i] : (r(X2, X3) <=> ((product(X2, X3) = X3) & (product(X3, X2) = X2))) <=> ![X2: $i, X3: $i] : (~(((~(product(X2, X3) = X3)) | (~(product(X3, X2) = X2))) <=> r(X2, X3)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 (![X2: $i, X3: $i] : (r(X2, X3) <=> ((product(X2, X3) = X3) & (product(X3, X2) = X2))) <=> ![X2: $i, X3: $i] : (r(X2, X3) <=> ((product(X2, X3) = X3) & (product(X3, X2) = X2)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(18,axiom,(![X2: $i, X3: $i] : (r(X2, X3) <=> ((product(X2, X3) = X3) & (product(X3, X2) = X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sos04')).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 (![X2: $i, X3: $i] : (r(X2, X3) <=> ((product(X2, X3) = X3) & (product(X3, X2) = X2)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.41 tff(20,plain,(
% 0.21/0.41 ![X2: $i, X3: $i] : (r(X2, X3) <=> ((product(X2, X3) = X3) & (product(X3, X2) = X2)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[19])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 (![X2: $i, X3: $i] : (~(((~(product(X2, X3) = X3)) | (~(product(X3, X2) = X2))) <=> r(X2, X3)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 (![X2: $i, X3: $i] : (~(((~(product(X2, X3) = X3)) | (~(product(X3, X2) = X2))) <=> r(X2, X3)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 ((~![X2: $i, X3: $i] : (~(((~(product(X2, X3) = X3)) | (~(product(X3, X2) = X2))) <=> r(X2, X3)))) | (~(((~(product(X7!2, product(X7!2, X8!1)) = product(X7!2, X8!1))) | (~(product(product(X7!2, X8!1), X7!2) = X7!2))) <=> r(X7!2, product(X7!2, X8!1))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (~(((~(product(X7!2, product(X7!2, X8!1)) = product(X7!2, X8!1))) | (~(product(product(X7!2, X8!1), X7!2) = X7!2))) <=> r(X7!2, product(X7!2, X8!1)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (^[C: $i, B: $i, A: $i] : refl((product(product(A, B), C) = product(A, product(B, C))) <=> (product(product(A, B), C) = product(A, product(B, C))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (![C: $i, B: $i, A: $i] : (product(product(A, B), C) = product(A, product(B, C))) <=> ![C: $i, B: $i, A: $i] : (product(product(A, B), C) = product(A, product(B, C)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 (![C: $i, B: $i, A: $i] : (product(product(A, B), C) = product(A, product(B, C))) <=> ![C: $i, B: $i, A: $i] : (product(product(A, B), C) = product(A, product(B, C)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(28,axiom,(![C: $i, B: $i, A: $i] : (product(product(A, B), C) = product(A, product(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sos01')).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (![C: $i, B: $i, A: $i] : (product(product(A, B), C) = product(A, product(B, C)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.41 tff(30,plain,(
% 0.21/0.41 ![C: $i, B: $i, A: $i] : (product(product(A, B), C) = product(A, product(B, C)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[29])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (![C: $i, B: $i, A: $i] : (product(product(A, B), C) = product(A, product(B, C)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 ((~![C: $i, B: $i, A: $i] : (product(product(A, B), C) = product(A, product(B, C)))) | (product(product(X7!2, product(X8!1, X7!2)), X8!1) = product(X7!2, product(product(X8!1, X7!2), X8!1)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 (product(product(X7!2, product(X8!1, X7!2)), X8!1) = product(X7!2, product(product(X8!1, X7!2), X8!1))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 ((~![X2: $i, X3: $i] : (~(((~(product(X2, X3) = X3)) | (~(product(X3, X2) = X2))) <=> r(X2, X3)))) | (~(((~(product(X7!2, tptp_fun_X6_0(X8!1, X7!2)) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(tptp_fun_X6_0(X8!1, X7!2), X7!2) = X7!2))) <=> r(X7!2, tptp_fun_X6_0(X8!1, X7!2))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (~(((~(product(X7!2, tptp_fun_X6_0(X8!1, X7!2)) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(tptp_fun_X6_0(X8!1, X7!2), X7!2) = X7!2))) <=> r(X7!2, tptp_fun_X6_0(X8!1, X7!2)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[34, 22])).
% 0.21/0.41 tff(36,assumption,(~(product(X7!2, product(X8!1, X7!2)) = X7!2)), introduced(assumption)).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) | (product(X7!2, product(X8!1, X7!2)) = X7!2)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 ((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 ((~(~(((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) <=> d(X7!2, X8!1)))) <=> (((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) <=> d(X7!2, X8!1))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 ((~(((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) <=> d(X7!2, X8!1))) <=> (~(((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) <=> d(X7!2, X8!1)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 ((d(X7!2, X8!1) <=> (~((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))))) <=> (~(((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) <=> d(X7!2, X8!1)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (((product(X7!2, product(X8!1, X7!2)) = X7!2) & (product(X8!1, product(X7!2, X8!1)) = X8!1)) <=> (~((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 ((d(X7!2, X8!1) <=> ((product(X7!2, product(X8!1, X7!2)) = X7!2) & (product(X8!1, product(X7!2, X8!1)) = X8!1))) <=> (d(X7!2, X8!1) <=> (~((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[42])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 ((d(X7!2, X8!1) <=> ((product(X7!2, product(X8!1, X7!2)) = X7!2) & (product(X8!1, product(X7!2, X8!1)) = X8!1))) <=> (~(((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) <=> d(X7!2, X8!1)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[43, 41])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 ((d(X7!2, X8!1) <=> ((product(X7!2, product(X8!1, X7!2)) = X7!2) & (product(X8!1, product(X7!2, X8!1)) = X8!1))) <=> (~(((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) <=> d(X7!2, X8!1)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[44, 40])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 ((~(d(X7!2, X8!1) <=> ((product(X7!2, product(X8!1, X7!2)) = X7!2) & (product(X8!1, product(X7!2, X8!1)) = X8!1)))) <=> (~(~(((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) <=> d(X7!2, X8!1))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[45])).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 ((~(d(X7!2, X8!1) <=> ((product(X7!2, product(X8!1, X7!2)) = X7!2) & (product(X8!1, product(X7!2, X8!1)) = X8!1)))) <=> (((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) <=> d(X7!2, X8!1))),
% 0.21/0.42 inference(transitivity,[status(thm)],[46, 39])).
% 0.21/0.42 tff(48,plain,
% 0.21/0.42 ((~(d(X7!2, X8!1) <=> ((product(X7!2, product(X8!1, X7!2)) = X7!2) & (product(X8!1, product(X7!2, X8!1)) = X8!1)))) <=> (~(d(X7!2, X8!1) <=> ((product(X7!2, product(X8!1, X7!2)) = X7!2) & (product(X8!1, product(X7!2, X8!1)) = X8!1))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(49,plain,
% 0.21/0.42 ((~![X7: $i, X8: $i] : (d(X7, X8) <=> ((product(X7, product(X8, X7)) = X7) & (product(X8, product(X7, X8)) = X8)))) <=> (~![X7: $i, X8: $i] : (d(X7, X8) <=> ((product(X7, product(X8, X7)) = X7) & (product(X8, product(X7, X8)) = X8))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(50,axiom,(~![X7: $i, X8: $i] : (d(X7, X8) <=> ((product(X7, product(X8, X7)) = X7) & (product(X8, product(X7, X8)) = X8)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.21/0.42 tff(51,plain,
% 0.21/0.42 (~![X7: $i, X8: $i] : (d(X7, X8) <=> ((product(X7, product(X8, X7)) = X7) & (product(X8, product(X7, X8)) = X8)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.42 tff(52,plain,
% 0.21/0.42 (~![X7: $i, X8: $i] : (d(X7, X8) <=> ((product(X7, product(X8, X7)) = X7) & (product(X8, product(X7, X8)) = X8)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[51, 49])).
% 0.21/0.42 tff(53,plain,
% 0.21/0.42 (~![X7: $i, X8: $i] : (d(X7, X8) <=> ((product(X7, product(X8, X7)) = X7) & (product(X8, product(X7, X8)) = X8)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[52, 49])).
% 0.21/0.42 tff(54,plain,
% 0.21/0.42 (~![X7: $i, X8: $i] : (d(X7, X8) <=> ((product(X7, product(X8, X7)) = X7) & (product(X8, product(X7, X8)) = X8)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.21/0.42 tff(55,plain,(
% 0.21/0.42 ~(d(X7!2, X8!1) <=> ((product(X7!2, product(X8!1, X7!2)) = X7!2) & (product(X8!1, product(X7!2, X8!1)) = X8!1)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[54])).
% 0.21/0.42 tff(56,plain,
% 0.21/0.42 (~(d(X7!2, X8!1) <=> ((product(X7!2, product(X8!1, X7!2)) = X7!2) & (product(X8!1, product(X7!2, X8!1)) = X8!1)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.21/0.42 tff(57,plain,
% 0.21/0.42 (((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) <=> d(X7!2, X8!1)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[56, 47])).
% 0.21/0.42 tff(58,plain,
% 0.21/0.42 ((~((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1)))) | d(X7!2, X8!1) | (~(((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) <=> d(X7!2, X8!1)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(59,plain,
% 0.21/0.42 ((~((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1)))) | d(X7!2, X8!1)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.21/0.42 tff(60,plain,
% 0.21/0.42 (d(X7!2, X8!1)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[59, 38])).
% 0.21/0.42 tff(61,plain,
% 0.21/0.42 (^[X4: $i, X5: $i] : refl((~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5))))))) <=> (~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(62,plain,
% 0.21/0.42 (![X4: $i, X5: $i] : (~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5))))))) <=> ![X4: $i, X5: $i] : (~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[61])).
% 0.21/0.42 tff(63,plain,
% 0.21/0.42 (^[X4: $i, X5: $i] : rewrite((~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5))))))) <=> (~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(64,plain,
% 0.21/0.42 (![X4: $i, X5: $i] : (~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5))))))) <=> ![X4: $i, X5: $i] : (~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.42 tff(65,plain,
% 0.21/0.42 (![X4: $i, X5: $i] : (~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5))))))) <=> ![X4: $i, X5: $i] : (~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5)))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[64, 62])).
% 0.21/0.42 tff(66,plain,
% 0.21/0.42 (^[X4: $i, X5: $i] : trans(monotonicity(rewrite(((~d(X4, X5)) | (r(X4, tptp_fun_X6_0(X5, X4)) & l(tptp_fun_X6_0(X5, X4), X5))) <=> ((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))), rewrite((d(X4, X5) | ![X6: $i] : (~(r(X4, X6) & l(X6, X5)))) <=> (d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5))))), ((((~d(X4, X5)) | (r(X4, tptp_fun_X6_0(X5, X4)) & l(tptp_fun_X6_0(X5, X4), X5))) & (d(X4, X5) | ![X6: $i] : (~(r(X4, X6) & l(X6, X5))))) <=> (((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5))))) & (d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5))))))), rewrite((((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5))))) & (d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5))))) <=> (~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5)))))))), ((((~d(X4, X5)) | (r(X4, tptp_fun_X6_0(X5, X4)) & l(tptp_fun_X6_0(X5, X4), X5))) & (d(X4, X5) | ![X6: $i] : (~(r(X4, X6) & l(X6, X5))))) <=> (~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5)))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(67,plain,
% 0.21/0.42 (![X4: $i, X5: $i] : (((~d(X4, X5)) | (r(X4, tptp_fun_X6_0(X5, X4)) & l(tptp_fun_X6_0(X5, X4), X5))) & (d(X4, X5) | ![X6: $i] : (~(r(X4, X6) & l(X6, X5))))) <=> ![X4: $i, X5: $i] : (~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[66])).
% 0.21/0.42 tff(68,plain,
% 0.21/0.42 (![X4: $i, X5: $i] : (d(X4, X5) <=> ?[X6: $i] : (r(X4, X6) & l(X6, X5))) <=> ![X4: $i, X5: $i] : (d(X4, X5) <=> ?[X6: $i] : (r(X4, X6) & l(X6, X5)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(69,axiom,(![X4: $i, X5: $i] : (d(X4, X5) <=> ?[X6: $i] : (r(X4, X6) & l(X6, X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sos05')).
% 0.21/0.42 tff(70,plain,
% 0.21/0.42 (![X4: $i, X5: $i] : (d(X4, X5) <=> ?[X6: $i] : (r(X4, X6) & l(X6, X5)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.21/0.42 tff(71,plain,(
% 0.21/0.42 ![X4: $i, X5: $i] : (((~d(X4, X5)) | (r(X4, tptp_fun_X6_0(X5, X4)) & l(tptp_fun_X6_0(X5, X4), X5))) & (d(X4, X5) | ![X6: $i] : (~(r(X4, X6) & l(X6, X5)))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[70])).
% 0.21/0.42 tff(72,plain,
% 0.21/0.42 (![X4: $i, X5: $i] : (~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5)))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 (![X4: $i, X5: $i] : (~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5)))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 (((~![X4: $i, X5: $i] : (~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5)))))))) | (~((~(d(X7!2, X8!1) | ![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1))))) | (~((~d(X7!2, X8!1)) | (~((~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)) | (~r(X7!2, tptp_fun_X6_0(X8!1, X7!2)))))))))) <=> ((~![X4: $i, X5: $i] : (~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5)))))))) | (~((~(d(X7!2, X8!1) | ![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1))))) | (~((~d(X7!2, X8!1)) | (~((~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)) | (~r(X7!2, tptp_fun_X6_0(X8!1, X7!2))))))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 ((~((~((~d(X7!2, X8!1)) | (~((~r(X7!2, tptp_fun_X6_0(X8!1, X7!2))) | (~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)))))) | (~(d(X7!2, X8!1) | ![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1))))))) <=> (~((~(d(X7!2, X8!1) | ![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1))))) | (~((~d(X7!2, X8!1)) | (~((~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)) | (~r(X7!2, tptp_fun_X6_0(X8!1, X7!2)))))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 (((~![X4: $i, X5: $i] : (~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5)))))))) | (~((~((~d(X7!2, X8!1)) | (~((~r(X7!2, tptp_fun_X6_0(X8!1, X7!2))) | (~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)))))) | (~(d(X7!2, X8!1) | ![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1)))))))) <=> ((~![X4: $i, X5: $i] : (~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5)))))))) | (~((~(d(X7!2, X8!1) | ![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1))))) | (~((~d(X7!2, X8!1)) | (~((~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)) | (~r(X7!2, tptp_fun_X6_0(X8!1, X7!2))))))))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[75])).
% 0.21/0.42 tff(77,plain,
% 0.21/0.42 (((~![X4: $i, X5: $i] : (~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5)))))))) | (~((~((~d(X7!2, X8!1)) | (~((~r(X7!2, tptp_fun_X6_0(X8!1, X7!2))) | (~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)))))) | (~(d(X7!2, X8!1) | ![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1)))))))) <=> ((~![X4: $i, X5: $i] : (~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5)))))))) | (~((~(d(X7!2, X8!1) | ![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1))))) | (~((~d(X7!2, X8!1)) | (~((~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)) | (~r(X7!2, tptp_fun_X6_0(X8!1, X7!2))))))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[76, 74])).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 ((~![X4: $i, X5: $i] : (~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5)))))))) | (~((~((~d(X7!2, X8!1)) | (~((~r(X7!2, tptp_fun_X6_0(X8!1, X7!2))) | (~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)))))) | (~(d(X7!2, X8!1) | ![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1)))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(79,plain,
% 0.21/0.42 ((~![X4: $i, X5: $i] : (~((~((~d(X4, X5)) | (~((~r(X4, tptp_fun_X6_0(X5, X4))) | (~l(tptp_fun_X6_0(X5, X4), X5)))))) | (~(d(X4, X5) | ![X6: $i] : ((~r(X4, X6)) | (~l(X6, X5)))))))) | (~((~(d(X7!2, X8!1) | ![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1))))) | (~((~d(X7!2, X8!1)) | (~((~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)) | (~r(X7!2, tptp_fun_X6_0(X8!1, X7!2)))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 (~((~(d(X7!2, X8!1) | ![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1))))) | (~((~d(X7!2, X8!1)) | (~((~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)) | (~r(X7!2, tptp_fun_X6_0(X8!1, X7!2))))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[79, 73])).
% 0.21/0.42 tff(81,plain,
% 0.21/0.42 (((~(d(X7!2, X8!1) | ![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1))))) | (~((~d(X7!2, X8!1)) | (~((~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)) | (~r(X7!2, tptp_fun_X6_0(X8!1, X7!2)))))))) | ((~d(X7!2, X8!1)) | (~((~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)) | (~r(X7!2, tptp_fun_X6_0(X8!1, X7!2))))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(82,plain,
% 0.21/0.43 ((~d(X7!2, X8!1)) | (~((~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)) | (~r(X7!2, tptp_fun_X6_0(X8!1, X7!2)))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.21/0.43 tff(83,plain,
% 0.21/0.43 ((~((~d(X7!2, X8!1)) | (~((~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)) | (~r(X7!2, tptp_fun_X6_0(X8!1, X7!2))))))) | (~d(X7!2, X8!1)) | (~((~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)) | (~r(X7!2, tptp_fun_X6_0(X8!1, X7!2)))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(84,plain,
% 0.21/0.43 ((~d(X7!2, X8!1)) | (~((~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)) | (~r(X7!2, tptp_fun_X6_0(X8!1, X7!2)))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.21/0.43 tff(85,plain,
% 0.21/0.43 (~((~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)) | (~r(X7!2, tptp_fun_X6_0(X8!1, X7!2))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[84, 60])).
% 0.21/0.43 tff(86,plain,
% 0.21/0.43 (((~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)) | (~r(X7!2, tptp_fun_X6_0(X8!1, X7!2)))) | r(X7!2, tptp_fun_X6_0(X8!1, X7!2))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 (r(X7!2, tptp_fun_X6_0(X8!1, X7!2))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.21/0.43 tff(88,plain,
% 0.21/0.43 ((((~(product(X7!2, tptp_fun_X6_0(X8!1, X7!2)) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(tptp_fun_X6_0(X8!1, X7!2), X7!2) = X7!2))) <=> r(X7!2, tptp_fun_X6_0(X8!1, X7!2))) | (~((~(product(X7!2, tptp_fun_X6_0(X8!1, X7!2)) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(tptp_fun_X6_0(X8!1, X7!2), X7!2) = X7!2)))) | (~r(X7!2, tptp_fun_X6_0(X8!1, X7!2)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 ((((~(product(X7!2, tptp_fun_X6_0(X8!1, X7!2)) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(tptp_fun_X6_0(X8!1, X7!2), X7!2) = X7!2))) <=> r(X7!2, tptp_fun_X6_0(X8!1, X7!2))) | (~((~(product(X7!2, tptp_fun_X6_0(X8!1, X7!2)) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(tptp_fun_X6_0(X8!1, X7!2), X7!2) = X7!2))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.21/0.43 tff(90,plain,
% 0.21/0.43 (~((~(product(X7!2, tptp_fun_X6_0(X8!1, X7!2)) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(tptp_fun_X6_0(X8!1, X7!2), X7!2) = X7!2)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[89, 35])).
% 0.21/0.43 tff(91,plain,
% 0.21/0.43 (((~(product(X7!2, tptp_fun_X6_0(X8!1, X7!2)) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(tptp_fun_X6_0(X8!1, X7!2), X7!2) = X7!2))) | (product(tptp_fun_X6_0(X8!1, X7!2), X7!2) = X7!2)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(92,plain,
% 0.21/0.43 (product(tptp_fun_X6_0(X8!1, X7!2), X7!2) = X7!2),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.21/0.43 tff(93,plain,
% 0.21/0.43 (((~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)) | (~r(X7!2, tptp_fun_X6_0(X8!1, X7!2)))) | l(tptp_fun_X6_0(X8!1, X7!2), X8!1)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(94,plain,
% 0.21/0.43 (l(tptp_fun_X6_0(X8!1, X7!2), X8!1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[93, 85])).
% 0.21/0.43 tff(95,plain,
% 0.21/0.43 ((((~(product(tptp_fun_X6_0(X8!1, X7!2), X8!1) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(X8!1, tptp_fun_X6_0(X8!1, X7!2)) = X8!1))) <=> l(tptp_fun_X6_0(X8!1, X7!2), X8!1)) | (~((~(product(tptp_fun_X6_0(X8!1, X7!2), X8!1) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(X8!1, tptp_fun_X6_0(X8!1, X7!2)) = X8!1)))) | (~l(tptp_fun_X6_0(X8!1, X7!2), X8!1))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(96,plain,
% 0.21/0.43 ((((~(product(tptp_fun_X6_0(X8!1, X7!2), X8!1) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(X8!1, tptp_fun_X6_0(X8!1, X7!2)) = X8!1))) <=> l(tptp_fun_X6_0(X8!1, X7!2), X8!1)) | (~((~(product(tptp_fun_X6_0(X8!1, X7!2), X8!1) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(X8!1, tptp_fun_X6_0(X8!1, X7!2)) = X8!1))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.21/0.43 tff(97,plain,
% 0.21/0.43 (~((~(product(tptp_fun_X6_0(X8!1, X7!2), X8!1) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(X8!1, tptp_fun_X6_0(X8!1, X7!2)) = X8!1)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[96, 12])).
% 0.21/0.43 tff(98,plain,
% 0.21/0.43 (((~(product(tptp_fun_X6_0(X8!1, X7!2), X8!1) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(X8!1, tptp_fun_X6_0(X8!1, X7!2)) = X8!1))) | (product(tptp_fun_X6_0(X8!1, X7!2), X8!1) = tptp_fun_X6_0(X8!1, X7!2))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(99,plain,
% 0.21/0.43 (product(tptp_fun_X6_0(X8!1, X7!2), X8!1) = tptp_fun_X6_0(X8!1, X7!2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.21/0.43 tff(100,plain,
% 0.21/0.43 (tptp_fun_X6_0(X8!1, X7!2) = product(tptp_fun_X6_0(X8!1, X7!2), X8!1)),
% 0.21/0.43 inference(symmetry,[status(thm)],[99])).
% 0.21/0.43 tff(101,plain,
% 0.21/0.43 (product(tptp_fun_X6_0(X8!1, X7!2), X7!2) = product(product(tptp_fun_X6_0(X8!1, X7!2), X8!1), X7!2)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[100])).
% 0.21/0.43 tff(102,plain,
% 0.21/0.43 (product(product(tptp_fun_X6_0(X8!1, X7!2), X8!1), X7!2) = product(tptp_fun_X6_0(X8!1, X7!2), X7!2)),
% 0.21/0.43 inference(symmetry,[status(thm)],[101])).
% 0.21/0.43 tff(103,plain,
% 0.21/0.43 ((~![C: $i, B: $i, A: $i] : (product(product(A, B), C) = product(A, product(B, C)))) | (product(product(tptp_fun_X6_0(X8!1, X7!2), X8!1), X7!2) = product(tptp_fun_X6_0(X8!1, X7!2), product(X8!1, X7!2)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(104,plain,
% 0.21/0.43 (product(product(tptp_fun_X6_0(X8!1, X7!2), X8!1), X7!2) = product(tptp_fun_X6_0(X8!1, X7!2), product(X8!1, X7!2))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[103, 31])).
% 0.21/0.43 tff(105,plain,
% 0.21/0.43 (product(tptp_fun_X6_0(X8!1, X7!2), product(X8!1, X7!2)) = product(product(tptp_fun_X6_0(X8!1, X7!2), X8!1), X7!2)),
% 0.21/0.43 inference(symmetry,[status(thm)],[104])).
% 0.21/0.43 tff(106,plain,
% 0.21/0.43 (^[A: $i] : refl((product(A, A) = A) <=> (product(A, A) = A))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(107,plain,
% 0.21/0.43 (![A: $i] : (product(A, A) = A) <=> ![A: $i] : (product(A, A) = A)),
% 0.21/0.43 inference(quant_intro,[status(thm)],[106])).
% 0.21/0.43 tff(108,plain,
% 0.21/0.43 (![A: $i] : (product(A, A) = A) <=> ![A: $i] : (product(A, A) = A)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(109,axiom,(![A: $i] : (product(A, A) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sos02')).
% 0.21/0.43 tff(110,plain,
% 0.21/0.43 (![A: $i] : (product(A, A) = A)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.21/0.43 tff(111,plain,(
% 0.21/0.43 ![A: $i] : (product(A, A) = A)),
% 0.21/0.43 inference(skolemize,[status(sab)],[110])).
% 0.21/0.43 tff(112,plain,
% 0.21/0.43 (![A: $i] : (product(A, A) = A)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.21/0.43 tff(113,plain,
% 0.21/0.43 ((~![A: $i] : (product(A, A) = A)) | (product(product(X8!1, X7!2), product(X8!1, X7!2)) = product(X8!1, X7!2))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(114,plain,
% 0.21/0.43 (product(product(X8!1, X7!2), product(X8!1, X7!2)) = product(X8!1, X7!2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.21/0.43 tff(115,plain,
% 0.21/0.43 (product(X8!1, X7!2) = product(product(X8!1, X7!2), product(X8!1, X7!2))),
% 0.21/0.43 inference(symmetry,[status(thm)],[114])).
% 0.21/0.43 tff(116,plain,
% 0.21/0.43 (product(tptp_fun_X6_0(X8!1, X7!2), product(X8!1, X7!2)) = product(tptp_fun_X6_0(X8!1, X7!2), product(product(X8!1, X7!2), product(X8!1, X7!2)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[115])).
% 0.21/0.43 tff(117,plain,
% 0.21/0.43 (product(tptp_fun_X6_0(X8!1, X7!2), product(product(X8!1, X7!2), product(X8!1, X7!2))) = product(tptp_fun_X6_0(X8!1, X7!2), product(X8!1, X7!2))),
% 0.21/0.43 inference(symmetry,[status(thm)],[116])).
% 0.21/0.43 tff(118,plain,
% 0.21/0.43 ((~![C: $i, B: $i, A: $i] : (product(product(A, B), C) = product(A, product(B, C)))) | (product(product(tptp_fun_X6_0(X8!1, X7!2), product(X8!1, X7!2)), product(X8!1, X7!2)) = product(tptp_fun_X6_0(X8!1, X7!2), product(product(X8!1, X7!2), product(X8!1, X7!2))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(119,plain,
% 0.21/0.43 (product(product(tptp_fun_X6_0(X8!1, X7!2), product(X8!1, X7!2)), product(X8!1, X7!2)) = product(tptp_fun_X6_0(X8!1, X7!2), product(product(X8!1, X7!2), product(X8!1, X7!2)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[118, 31])).
% 0.21/0.43 tff(120,plain,
% 0.21/0.43 (product(tptp_fun_X6_0(X8!1, X7!2), product(X8!1, X7!2)) = X7!2),
% 0.21/0.43 inference(transitivity,[status(thm)],[105, 102, 92])).
% 0.21/0.43 tff(121,plain,
% 0.21/0.43 (product(product(tptp_fun_X6_0(X8!1, X7!2), product(X8!1, X7!2)), product(X8!1, X7!2)) = product(X7!2, product(X8!1, X7!2))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[120])).
% 0.21/0.43 tff(122,plain,
% 0.21/0.43 (product(X7!2, product(X8!1, X7!2)) = product(product(tptp_fun_X6_0(X8!1, X7!2), product(X8!1, X7!2)), product(X8!1, X7!2))),
% 0.21/0.43 inference(symmetry,[status(thm)],[121])).
% 0.21/0.43 tff(123,plain,
% 0.21/0.43 (product(X7!2, product(X8!1, X7!2)) = X7!2),
% 0.21/0.43 inference(transitivity,[status(thm)],[122, 119, 117, 105, 102, 92])).
% 0.21/0.43 tff(124,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[36, 123])).
% 0.21/0.43 tff(125,plain,(product(X7!2, product(X8!1, X7!2)) = X7!2), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(126,plain,
% 0.21/0.43 (product(product(X7!2, product(X8!1, X7!2)), X8!1) = product(X7!2, X8!1)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[125])).
% 0.21/0.43 tff(127,plain,
% 0.21/0.43 (product(X7!2, X8!1) = product(product(X7!2, product(X8!1, X7!2)), X8!1)),
% 0.21/0.43 inference(symmetry,[status(thm)],[126])).
% 0.21/0.43 tff(128,plain,
% 0.21/0.43 (product(X7!2, X8!1) = product(X7!2, product(product(X8!1, X7!2), X8!1))),
% 0.21/0.43 inference(transitivity,[status(thm)],[127, 33])).
% 0.21/0.43 tff(129,plain,
% 0.21/0.43 (product(X7!2, product(product(X8!1, X7!2), X8!1)) = product(product(X7!2, product(X8!1, X7!2)), X8!1)),
% 0.21/0.43 inference(symmetry,[status(thm)],[33])).
% 0.21/0.43 tff(130,plain,
% 0.21/0.43 (product(X7!2, product(product(X8!1, X7!2), X8!1)) = product(X7!2, X8!1)),
% 0.21/0.43 inference(transitivity,[status(thm)],[129, 126])).
% 0.21/0.43 tff(131,plain,
% 0.21/0.43 (product(X7!2, product(X7!2, product(product(X8!1, X7!2), X8!1))) = product(X7!2, product(X7!2, X8!1))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[130])).
% 0.21/0.43 tff(132,plain,
% 0.21/0.43 (product(X7!2, product(X7!2, X8!1)) = product(X7!2, product(X7!2, product(product(X8!1, X7!2), X8!1)))),
% 0.21/0.43 inference(symmetry,[status(thm)],[131])).
% 0.21/0.43 tff(133,plain,
% 0.21/0.43 ((product(X7!2, product(X7!2, X8!1)) = product(X7!2, X8!1)) <=> (product(X7!2, product(X7!2, product(product(X8!1, X7!2), X8!1))) = product(X7!2, product(product(X8!1, X7!2), X8!1)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[132, 128])).
% 0.21/0.43 tff(134,plain,
% 0.21/0.43 ((product(X7!2, product(X7!2, product(product(X8!1, X7!2), X8!1))) = product(X7!2, product(product(X8!1, X7!2), X8!1))) <=> (product(X7!2, product(X7!2, X8!1)) = product(X7!2, X8!1))),
% 0.21/0.43 inference(symmetry,[status(thm)],[133])).
% 0.21/0.43 tff(135,assumption,(product(X7!2, product(X8!1, X7!2)) = X7!2), introduced(assumption)).
% 0.21/0.43 tff(136,plain,
% 0.21/0.43 (product(product(X7!2, product(X8!1, X7!2)), X8!1) = product(X7!2, X8!1)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[135])).
% 0.21/0.43 tff(137,plain,
% 0.21/0.43 (product(X7!2, X8!1) = product(product(X7!2, product(X8!1, X7!2)), X8!1)),
% 0.21/0.43 inference(symmetry,[status(thm)],[136])).
% 0.21/0.43 tff(138,plain,
% 0.21/0.43 ((~![A: $i] : (product(A, A) = A)) | (product(X7!2, X7!2) = X7!2)),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(139,plain,
% 0.21/0.43 (product(X7!2, X7!2) = X7!2),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[138, 112])).
% 0.21/0.43 tff(140,plain,
% 0.21/0.43 (X7!2 = product(X7!2, X7!2)),
% 0.21/0.43 inference(symmetry,[status(thm)],[139])).
% 0.21/0.43 tff(141,plain,
% 0.21/0.43 (product(X7!2, X8!1) = product(product(X7!2, X7!2), X8!1)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[140])).
% 0.21/0.43 tff(142,plain,
% 0.21/0.43 (product(product(X7!2, X7!2), X8!1) = product(X7!2, X8!1)),
% 0.21/0.43 inference(symmetry,[status(thm)],[141])).
% 0.21/0.43 tff(143,plain,
% 0.21/0.43 ((~![C: $i, B: $i, A: $i] : (product(product(A, B), C) = product(A, product(B, C)))) | (product(product(X7!2, X7!2), X8!1) = product(X7!2, product(X7!2, X8!1)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(144,plain,
% 0.21/0.43 (product(product(X7!2, X7!2), X8!1) = product(X7!2, product(X7!2, X8!1))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[143, 31])).
% 0.21/0.43 tff(145,plain,
% 0.21/0.43 (product(X7!2, product(X7!2, X8!1)) = product(product(X7!2, X7!2), X8!1)),
% 0.21/0.43 inference(symmetry,[status(thm)],[144])).
% 0.21/0.43 tff(146,plain,
% 0.21/0.43 (product(X7!2, X8!1) = product(X7!2, product(product(X8!1, X7!2), X8!1))),
% 0.21/0.43 inference(transitivity,[status(thm)],[137, 33])).
% 0.21/0.43 tff(147,plain,
% 0.21/0.43 (product(X7!2, product(X7!2, X8!1)) = product(X7!2, product(X7!2, product(product(X8!1, X7!2), X8!1)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[146])).
% 0.21/0.43 tff(148,plain,
% 0.21/0.43 (product(X7!2, product(X7!2, product(product(X8!1, X7!2), X8!1))) = product(X7!2, product(X7!2, X8!1))),
% 0.21/0.43 inference(symmetry,[status(thm)],[147])).
% 0.21/0.43 tff(149,plain,
% 0.21/0.43 (product(X7!2, product(X7!2, product(product(X8!1, X7!2), X8!1))) = product(X7!2, product(product(X8!1, X7!2), X8!1))),
% 0.21/0.43 inference(transitivity,[status(thm)],[148, 145, 142, 137, 33])).
% 0.21/0.43 tff(150,assumption,(~(product(X7!2, product(X7!2, product(product(X8!1, X7!2), X8!1))) = product(X7!2, product(product(X8!1, X7!2), X8!1)))), introduced(assumption)).
% 0.21/0.43 tff(151,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.21/0.43 tff(152,plain,((product(X7!2, product(X7!2, product(product(X8!1, X7!2), X8!1))) = product(X7!2, product(product(X8!1, X7!2), X8!1))) | (~(product(X7!2, product(X8!1, X7!2)) = X7!2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(153,plain,
% 0.21/0.43 (product(X7!2, product(X7!2, product(product(X8!1, X7!2), X8!1))) = product(X7!2, product(product(X8!1, X7!2), X8!1))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[152, 125])).
% 0.21/0.43 tff(154,plain,
% 0.21/0.43 (product(X7!2, product(X7!2, X8!1)) = product(X7!2, X8!1)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[153, 134])).
% 0.21/0.43 tff(155,plain,
% 0.21/0.43 ((~![C: $i, B: $i, A: $i] : (product(product(A, B), C) = product(A, product(B, C)))) | (product(product(X7!2, X8!1), X7!2) = product(X7!2, product(X8!1, X7!2)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(156,plain,
% 0.21/0.43 (product(product(X7!2, X8!1), X7!2) = product(X7!2, product(X8!1, X7!2))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[155, 31])).
% 0.21/0.43 tff(157,plain,
% 0.21/0.43 (product(product(X7!2, X8!1), X7!2) = X7!2),
% 0.21/0.43 inference(transitivity,[status(thm)],[156, 125])).
% 0.21/0.43 tff(158,plain,
% 0.21/0.43 ((~((~(product(X7!2, product(X7!2, X8!1)) = product(X7!2, X8!1))) | (~(product(product(X7!2, X8!1), X7!2) = X7!2)))) | (~(product(X7!2, product(X7!2, X8!1)) = product(X7!2, X8!1))) | (~(product(product(X7!2, X8!1), X7!2) = X7!2))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(159,plain,
% 0.21/0.43 ((~((~(product(X7!2, product(X7!2, X8!1)) = product(X7!2, X8!1))) | (~(product(product(X7!2, X8!1), X7!2) = X7!2)))) | (~(product(X7!2, product(X7!2, X8!1)) = product(X7!2, X8!1)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.21/0.43 tff(160,plain,
% 0.21/0.43 (~((~(product(X7!2, product(X7!2, X8!1)) = product(X7!2, X8!1))) | (~(product(product(X7!2, X8!1), X7!2) = X7!2)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[159, 154])).
% 0.21/0.43 tff(161,plain,
% 0.21/0.43 ((((~(product(X7!2, product(X7!2, X8!1)) = product(X7!2, X8!1))) | (~(product(product(X7!2, X8!1), X7!2) = X7!2))) <=> r(X7!2, product(X7!2, X8!1))) | ((~(product(X7!2, product(X7!2, X8!1)) = product(X7!2, X8!1))) | (~(product(product(X7!2, X8!1), X7!2) = X7!2))) | r(X7!2, product(X7!2, X8!1))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(162,plain,
% 0.21/0.43 (r(X7!2, product(X7!2, X8!1))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[161, 160, 24])).
% 0.21/0.43 tff(163,assumption,(~((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1)))), introduced(assumption)).
% 0.21/0.43 tff(164,plain,
% 0.21/0.43 (((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) | (product(X8!1, product(X7!2, X8!1)) = X8!1)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(165,plain,
% 0.21/0.43 (product(X8!1, product(X7!2, X8!1)) = X8!1),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.21/0.44 tff(166,plain,
% 0.21/0.44 ((~![A: $i] : (product(A, A) = A)) | (product(X8!1, X8!1) = X8!1)),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(167,plain,
% 0.21/0.44 (product(X8!1, X8!1) = X8!1),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[166, 112])).
% 0.21/0.44 tff(168,plain,
% 0.21/0.44 (X8!1 = product(X8!1, X8!1)),
% 0.21/0.44 inference(symmetry,[status(thm)],[167])).
% 0.21/0.44 tff(169,plain,
% 0.21/0.44 (product(X7!2, X8!1) = product(X7!2, product(X8!1, X8!1))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[168])).
% 0.21/0.44 tff(170,plain,
% 0.21/0.44 (product(X7!2, product(X8!1, X8!1)) = product(X7!2, X8!1)),
% 0.21/0.44 inference(symmetry,[status(thm)],[169])).
% 0.21/0.44 tff(171,plain,
% 0.21/0.44 ((~![C: $i, B: $i, A: $i] : (product(product(A, B), C) = product(A, product(B, C)))) | (product(product(X7!2, X8!1), X8!1) = product(X7!2, product(X8!1, X8!1)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(172,plain,
% 0.21/0.44 (product(product(X7!2, X8!1), X8!1) = product(X7!2, product(X8!1, X8!1))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[171, 31])).
% 0.21/0.44 tff(173,plain,
% 0.22/0.44 (product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1)),
% 0.22/0.44 inference(transitivity,[status(thm)],[172, 170])).
% 0.22/0.44 tff(174,assumption,(~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1))), introduced(assumption)).
% 0.22/0.44 tff(175,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.22/0.44 tff(176,plain,(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.44 tff(177,plain,
% 0.22/0.44 ((~((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1))))) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1)))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(178,plain,
% 0.22/0.44 ((~((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1))))) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.22/0.44 tff(179,plain,
% 0.22/0.44 (~((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[178, 165])).
% 0.22/0.44 tff(180,plain,
% 0.22/0.44 (((~![X0: $i, X1: $i] : (~(((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))) <=> l(X0, X1)))) | (~(((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1)))) <=> l(product(X7!2, X8!1), X8!1)))) <=> ((~![X0: $i, X1: $i] : (~(((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))) <=> l(X0, X1)))) | (~(((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1)))) <=> l(product(X7!2, X8!1), X8!1))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(181,plain,
% 0.22/0.44 ((~(((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1)))) <=> l(product(X7!2, X8!1), X8!1))) <=> (~(((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1)))) <=> l(product(X7!2, X8!1), X8!1)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(182,plain,
% 0.22/0.44 ((((~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1))) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) <=> l(product(X7!2, X8!1), X8!1)) <=> (((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1)))) <=> l(product(X7!2, X8!1), X8!1))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(183,plain,
% 0.22/0.44 ((~(((~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1))) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) <=> l(product(X7!2, X8!1), X8!1))) <=> (~(((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1)))) <=> l(product(X7!2, X8!1), X8!1)))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[182])).
% 0.22/0.44 tff(184,plain,
% 0.22/0.44 ((~(((~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1))) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) <=> l(product(X7!2, X8!1), X8!1))) <=> (~(((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1)))) <=> l(product(X7!2, X8!1), X8!1)))),
% 0.22/0.44 inference(transitivity,[status(thm)],[183, 181])).
% 0.22/0.44 tff(185,plain,
% 0.22/0.44 (((~![X0: $i, X1: $i] : (~(((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))) <=> l(X0, X1)))) | (~(((~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1))) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) <=> l(product(X7!2, X8!1), X8!1)))) <=> ((~![X0: $i, X1: $i] : (~(((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))) <=> l(X0, X1)))) | (~(((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1)))) <=> l(product(X7!2, X8!1), X8!1))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[184])).
% 0.22/0.44 tff(186,plain,
% 0.22/0.44 (((~![X0: $i, X1: $i] : (~(((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))) <=> l(X0, X1)))) | (~(((~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1))) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) <=> l(product(X7!2, X8!1), X8!1)))) <=> ((~![X0: $i, X1: $i] : (~(((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))) <=> l(X0, X1)))) | (~(((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1)))) <=> l(product(X7!2, X8!1), X8!1))))),
% 0.22/0.44 inference(transitivity,[status(thm)],[185, 180])).
% 0.22/0.44 tff(187,plain,
% 0.22/0.44 ((~![X0: $i, X1: $i] : (~(((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))) <=> l(X0, X1)))) | (~(((~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1))) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) <=> l(product(X7!2, X8!1), X8!1)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(188,plain,
% 0.22/0.44 ((~![X0: $i, X1: $i] : (~(((~(product(X0, X1) = X0)) | (~(product(X1, X0) = X1))) <=> l(X0, X1)))) | (~(((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1)))) <=> l(product(X7!2, X8!1), X8!1)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.22/0.44 tff(189,plain,
% 0.22/0.44 (~(((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1)))) <=> l(product(X7!2, X8!1), X8!1))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[188, 10])).
% 0.22/0.44 tff(190,plain,
% 0.22/0.44 ((((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1)))) <=> l(product(X7!2, X8!1), X8!1)) | ((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1)))) | l(product(X7!2, X8!1), X8!1)),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(191,plain,
% 0.22/0.44 (((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1)))) | l(product(X7!2, X8!1), X8!1)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.22/0.44 tff(192,plain,
% 0.22/0.44 (l(product(X7!2, X8!1), X8!1)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[191, 179])).
% 0.22/0.44 tff(193,plain,
% 0.22/0.44 (((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) | (~d(X7!2, X8!1)) | (~(((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) <=> d(X7!2, X8!1)))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(194,plain,
% 0.22/0.44 (((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))) | (~d(X7!2, X8!1))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[193, 57])).
% 0.22/0.44 tff(195,plain,
% 0.22/0.44 (~d(X7!2, X8!1)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[194, 163])).
% 0.22/0.44 tff(196,plain,
% 0.22/0.44 (((~(d(X7!2, X8!1) | ![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1))))) | (~((~d(X7!2, X8!1)) | (~((~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)) | (~r(X7!2, tptp_fun_X6_0(X8!1, X7!2)))))))) | (d(X7!2, X8!1) | ![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1))))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(197,plain,
% 0.22/0.44 (d(X7!2, X8!1) | ![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1)))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[196, 80])).
% 0.22/0.44 tff(198,plain,
% 0.22/0.44 ((~(d(X7!2, X8!1) | ![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1))))) | d(X7!2, X8!1) | ![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1)))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(199,plain,
% 0.22/0.44 (d(X7!2, X8!1) | ![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1)))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.22/0.44 tff(200,plain,
% 0.22/0.44 (![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1)))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[199, 195])).
% 0.22/0.44 tff(201,plain,
% 0.22/0.44 (((~![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1)))) | ((~l(product(X7!2, X8!1), X8!1)) | (~r(X7!2, product(X7!2, X8!1))))) <=> ((~![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1)))) | (~l(product(X7!2, X8!1), X8!1)) | (~r(X7!2, product(X7!2, X8!1))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(202,plain,
% 0.22/0.44 (((~r(X7!2, product(X7!2, X8!1))) | (~l(product(X7!2, X8!1), X8!1))) <=> ((~l(product(X7!2, X8!1), X8!1)) | (~r(X7!2, product(X7!2, X8!1))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(203,plain,
% 0.22/0.44 (((~![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1)))) | ((~r(X7!2, product(X7!2, X8!1))) | (~l(product(X7!2, X8!1), X8!1)))) <=> ((~![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1)))) | ((~l(product(X7!2, X8!1), X8!1)) | (~r(X7!2, product(X7!2, X8!1)))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[202])).
% 0.22/0.45 tff(204,plain,
% 0.22/0.45 (((~![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1)))) | ((~r(X7!2, product(X7!2, X8!1))) | (~l(product(X7!2, X8!1), X8!1)))) <=> ((~![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1)))) | (~l(product(X7!2, X8!1), X8!1)) | (~r(X7!2, product(X7!2, X8!1))))),
% 0.22/0.45 inference(transitivity,[status(thm)],[203, 201])).
% 0.22/0.45 tff(205,plain,
% 0.22/0.45 ((~![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1)))) | ((~r(X7!2, product(X7!2, X8!1))) | (~l(product(X7!2, X8!1), X8!1)))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(206,plain,
% 0.22/0.45 ((~![X6: $i] : ((~r(X7!2, X6)) | (~l(X6, X8!1)))) | (~l(product(X7!2, X8!1), X8!1)) | (~r(X7!2, product(X7!2, X8!1)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.22/0.45 tff(207,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[206, 200, 192, 162])).
% 0.22/0.45 tff(208,plain,((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.45 tff(209,plain,
% 0.22/0.45 (d(X7!2, X8!1)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[59, 208])).
% 0.22/0.45 tff(210,plain,
% 0.22/0.45 (~((~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)) | (~r(X7!2, tptp_fun_X6_0(X8!1, X7!2))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[84, 209])).
% 0.22/0.45 tff(211,plain,
% 0.22/0.45 (l(tptp_fun_X6_0(X8!1, X7!2), X8!1)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[93, 210])).
% 0.22/0.45 tff(212,plain,
% 0.22/0.45 ((((~(product(tptp_fun_X6_0(X8!1, X7!2), X8!1) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(X8!1, tptp_fun_X6_0(X8!1, X7!2)) = X8!1))) <=> l(tptp_fun_X6_0(X8!1, X7!2), X8!1)) | (~((~(product(tptp_fun_X6_0(X8!1, X7!2), X8!1) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(X8!1, tptp_fun_X6_0(X8!1, X7!2)) = X8!1))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[95, 211])).
% 0.22/0.45 tff(213,plain,
% 0.22/0.45 (~((~(product(tptp_fun_X6_0(X8!1, X7!2), X8!1) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(X8!1, tptp_fun_X6_0(X8!1, X7!2)) = X8!1)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[212, 12])).
% 0.22/0.45 tff(214,plain,
% 0.22/0.45 (((~(product(tptp_fun_X6_0(X8!1, X7!2), X8!1) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(X8!1, tptp_fun_X6_0(X8!1, X7!2)) = X8!1))) | (product(X8!1, tptp_fun_X6_0(X8!1, X7!2)) = X8!1)),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(215,plain,
% 0.22/0.45 (product(X8!1, tptp_fun_X6_0(X8!1, X7!2)) = X8!1),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[214, 213])).
% 0.22/0.45 tff(216,plain,
% 0.22/0.45 (product(X7!2, product(X8!1, tptp_fun_X6_0(X8!1, X7!2))) = product(X7!2, X8!1)),
% 0.22/0.45 inference(monotonicity,[status(thm)],[215])).
% 0.22/0.45 tff(217,plain,
% 0.22/0.45 ((~![C: $i, B: $i, A: $i] : (product(product(A, B), C) = product(A, product(B, C)))) | (product(product(X7!2, X8!1), tptp_fun_X6_0(X8!1, X7!2)) = product(X7!2, product(X8!1, tptp_fun_X6_0(X8!1, X7!2))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(218,plain,
% 0.22/0.45 (product(product(X7!2, X8!1), tptp_fun_X6_0(X8!1, X7!2)) = product(X7!2, product(X8!1, tptp_fun_X6_0(X8!1, X7!2)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[217, 31])).
% 0.22/0.45 tff(219,plain,
% 0.22/0.45 (r(X7!2, tptp_fun_X6_0(X8!1, X7!2))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[86, 210])).
% 0.22/0.45 tff(220,plain,
% 0.22/0.45 ((((~(product(X7!2, tptp_fun_X6_0(X8!1, X7!2)) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(tptp_fun_X6_0(X8!1, X7!2), X7!2) = X7!2))) <=> r(X7!2, tptp_fun_X6_0(X8!1, X7!2))) | (~((~(product(X7!2, tptp_fun_X6_0(X8!1, X7!2)) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(tptp_fun_X6_0(X8!1, X7!2), X7!2) = X7!2))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[88, 219])).
% 0.22/0.45 tff(221,plain,
% 0.22/0.45 (~((~(product(X7!2, tptp_fun_X6_0(X8!1, X7!2)) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(tptp_fun_X6_0(X8!1, X7!2), X7!2) = X7!2)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[220, 35])).
% 0.22/0.45 tff(222,plain,
% 0.22/0.45 (((~(product(X7!2, tptp_fun_X6_0(X8!1, X7!2)) = tptp_fun_X6_0(X8!1, X7!2))) | (~(product(tptp_fun_X6_0(X8!1, X7!2), X7!2) = X7!2))) | (product(X7!2, tptp_fun_X6_0(X8!1, X7!2)) = tptp_fun_X6_0(X8!1, X7!2))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(223,plain,
% 0.22/0.45 (product(X7!2, tptp_fun_X6_0(X8!1, X7!2)) = tptp_fun_X6_0(X8!1, X7!2)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[222, 221])).
% 0.22/0.45 tff(224,plain,
% 0.22/0.45 (product(product(X7!2, X8!1), product(X7!2, tptp_fun_X6_0(X8!1, X7!2))) = product(product(X7!2, X8!1), tptp_fun_X6_0(X8!1, X7!2))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[223])).
% 0.22/0.45 tff(225,plain,
% 0.22/0.45 ((~![C: $i, B: $i, A: $i] : (product(product(A, B), C) = product(A, product(B, C)))) | (product(product(product(X7!2, X8!1), X7!2), tptp_fun_X6_0(X8!1, X7!2)) = product(product(X7!2, X8!1), product(X7!2, tptp_fun_X6_0(X8!1, X7!2))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(226,plain,
% 0.22/0.45 (product(product(product(X7!2, X8!1), X7!2), tptp_fun_X6_0(X8!1, X7!2)) = product(product(X7!2, X8!1), product(X7!2, tptp_fun_X6_0(X8!1, X7!2)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[225, 31])).
% 0.22/0.45 tff(227,plain,
% 0.22/0.45 (product(X7!2, product(X8!1, X7!2)) = product(product(X7!2, X8!1), X7!2)),
% 0.22/0.45 inference(symmetry,[status(thm)],[156])).
% 0.22/0.45 tff(228,plain,
% 0.22/0.45 (X7!2 = product(X7!2, product(X8!1, X7!2))),
% 0.22/0.45 inference(symmetry,[status(thm)],[125])).
% 0.22/0.45 tff(229,plain,
% 0.22/0.45 (X7!2 = product(product(X7!2, X8!1), X7!2)),
% 0.22/0.45 inference(transitivity,[status(thm)],[228, 227])).
% 0.22/0.45 tff(230,plain,
% 0.22/0.45 (product(X7!2, tptp_fun_X6_0(X8!1, X7!2)) = product(product(product(X7!2, X8!1), X7!2), tptp_fun_X6_0(X8!1, X7!2))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[229])).
% 0.22/0.45 tff(231,plain,
% 0.22/0.45 (tptp_fun_X6_0(X8!1, X7!2) = product(X7!2, tptp_fun_X6_0(X8!1, X7!2))),
% 0.22/0.45 inference(symmetry,[status(thm)],[223])).
% 0.22/0.45 tff(232,plain,
% 0.22/0.45 (tptp_fun_X6_0(X8!1, X7!2) = product(X7!2, X8!1)),
% 0.22/0.45 inference(transitivity,[status(thm)],[231, 230, 226, 224, 218, 216])).
% 0.22/0.45 tff(233,plain,
% 0.22/0.45 (l(tptp_fun_X6_0(X8!1, X7!2), X8!1) <=> l(product(X7!2, X8!1), X8!1)),
% 0.22/0.45 inference(monotonicity,[status(thm)],[232])).
% 0.22/0.45 tff(234,plain,
% 0.22/0.45 (l(product(X7!2, X8!1), X8!1) <=> l(tptp_fun_X6_0(X8!1, X7!2), X8!1)),
% 0.22/0.45 inference(symmetry,[status(thm)],[233])).
% 0.22/0.45 tff(235,plain,
% 0.22/0.45 ((~l(product(X7!2, X8!1), X8!1)) <=> (~l(tptp_fun_X6_0(X8!1, X7!2), X8!1))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[234])).
% 0.22/0.45 tff(236,plain,
% 0.22/0.45 ((~((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1)))) | (~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(237,plain,
% 0.22/0.45 ((~((~(product(X7!2, product(X8!1, X7!2)) = X7!2)) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1)))) | (~(product(X8!1, product(X7!2, X8!1)) = X8!1))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[236, 125])).
% 0.22/0.45 tff(238,plain,
% 0.22/0.45 (~(product(X8!1, product(X7!2, X8!1)) = X8!1)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[237, 208])).
% 0.22/0.45 tff(239,plain,
% 0.22/0.45 (((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1)))) | (product(X8!1, product(X7!2, X8!1)) = X8!1)),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(240,plain,
% 0.22/0.45 ((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[239, 238])).
% 0.22/0.45 tff(241,plain,
% 0.22/0.45 ((((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1)))) <=> l(product(X7!2, X8!1), X8!1)) | (~((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1))))) | (~l(product(X7!2, X8!1), X8!1))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(242,plain,
% 0.22/0.45 ((~((~(product(X8!1, product(X7!2, X8!1)) = X8!1)) | (~(product(product(X7!2, X8!1), X8!1) = product(X7!2, X8!1))))) | (~l(product(X7!2, X8!1), X8!1))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[241, 189])).
% 0.22/0.45 tff(243,plain,
% 0.22/0.45 (~l(product(X7!2, X8!1), X8!1)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[242, 240])).
% 0.22/0.45 tff(244,plain,
% 0.22/0.45 (~l(tptp_fun_X6_0(X8!1, X7!2), X8!1)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[243, 235])).
% 0.22/0.45 tff(245,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[211, 244])).
% 0.22/0.45 % SZS output end Proof
% 0.22/0.45 % E exiting
%------------------------------------------------------------------------------