%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP704+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:08:31 AM UTC 2025
% Result : Theorem 26.53s 26.70s
% Output : Proof 26.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP704+1 : TPTP v9.0.0. Released v4.0.0.
% 0.00/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 16:56:54 EDT 2025
% 0.13/0.34 % CPUTime :
% 26.53/26.70 % SZS status Theorem
% 26.53/26.70 % SZS output start Proof
% 26.53/26.70 tff(mult_type, type, (
% 26.53/26.70 mult: ( $i * $i ) > $i)).
% 26.53/26.70 tff(tptp_fun_X5_0_type, type, (
% 26.53/26.70 tptp_fun_X5_0: $i)).
% 26.53/26.70 tff(op_f_type, type, (
% 26.53/26.70 op_f: $i)).
% 26.53/26.70 tff(tptp_fun_X4_1_type, type, (
% 26.53/26.70 tptp_fun_X4_1: $i)).
% 26.53/26.70 tff(rd_type, type, (
% 26.53/26.70 rd: ( $i * $i ) > $i)).
% 26.53/26.70 tff(ld_type, type, (
% 26.53/26.70 ld: ( $i * $i ) > $i)).
% 26.53/26.70 tff(op_c_type, type, (
% 26.53/26.70 op_c: $i)).
% 26.53/26.70 tff(op_e_type, type, (
% 26.53/26.70 op_e: $i)).
% 26.53/26.70 tff(op_d_type, type, (
% 26.53/26.70 op_d: $i)).
% 26.53/26.70 tff(1,plain,
% 26.53/26.70 (^[B: $i, A: $i] : refl((rd(mult(A, B), B) = A) <=> (rd(mult(A, B), B) = A))),
% 26.53/26.70 inference(bind,[status(th)],[])).
% 26.53/26.70 tff(2,plain,
% 26.53/26.70 (![B: $i, A: $i] : (rd(mult(A, B), B) = A) <=> ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 26.53/26.70 inference(quant_intro,[status(thm)],[1])).
% 26.53/26.70 tff(3,plain,
% 26.53/26.70 (![B: $i, A: $i] : (rd(mult(A, B), B) = A) <=> ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 26.53/26.70 inference(rewrite,[status(thm)],[])).
% 26.53/26.70 tff(4,axiom,(![B: $i, A: $i] : (rd(mult(A, B), B) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f04')).
% 26.53/26.70 tff(5,plain,
% 26.53/26.70 (![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 26.53/26.70 inference(modus_ponens,[status(thm)],[4, 3])).
% 26.53/26.70 tff(6,plain,(
% 26.53/26.70 ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 26.53/26.70 inference(skolemize,[status(sab)],[5])).
% 26.53/26.70 tff(7,plain,
% 26.53/26.70 (![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 26.53/26.70 inference(modus_ponens,[status(thm)],[6, 2])).
% 26.53/26.70 tff(8,plain,
% 26.53/26.70 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(X4!1, op_f), X5!0), ld(mult(mult(X4!1, op_f), X5!0), op_c)), ld(mult(mult(X4!1, op_f), X5!0), op_c)) = mult(mult(X4!1, op_f), X5!0))),
% 26.53/26.70 inference(quant_inst,[status(thm)],[])).
% 26.53/26.70 tff(9,plain,
% 26.53/26.70 (rd(mult(mult(mult(X4!1, op_f), X5!0), ld(mult(mult(X4!1, op_f), X5!0), op_c)), ld(mult(mult(X4!1, op_f), X5!0), op_c)) = mult(mult(X4!1, op_f), X5!0)),
% 26.53/26.70 inference(unit_resolution,[status(thm)],[8, 7])).
% 26.53/26.70 tff(10,plain,
% 26.53/26.70 (^[B: $i, A: $i] : refl((ld(A, mult(A, B)) = B) <=> (ld(A, mult(A, B)) = B))),
% 26.53/26.70 inference(bind,[status(th)],[])).
% 26.53/26.70 tff(11,plain,
% 26.53/26.70 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 26.53/26.70 inference(quant_intro,[status(thm)],[10])).
% 26.53/26.70 tff(12,plain,
% 26.53/26.70 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 26.53/26.70 inference(rewrite,[status(thm)],[])).
% 26.53/26.70 tff(13,axiom,(![B: $i, A: $i] : (ld(A, mult(A, B)) = B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f02')).
% 26.53/26.70 tff(14,plain,
% 26.53/26.70 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 26.53/26.70 inference(modus_ponens,[status(thm)],[13, 12])).
% 26.53/26.70 tff(15,plain,(
% 26.53/26.70 ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 26.53/26.70 inference(skolemize,[status(sab)],[14])).
% 26.53/26.70 tff(16,plain,
% 26.53/26.70 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 26.53/26.70 inference(modus_ponens,[status(thm)],[15, 11])).
% 26.53/26.70 tff(17,plain,
% 26.53/26.70 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(op_c, X5!0), mult(mult(op_c, X5!0), ld(mult(mult(X4!1, op_f), X5!0), op_c))) = ld(mult(mult(X4!1, op_f), X5!0), op_c))),
% 26.53/26.70 inference(quant_inst,[status(thm)],[])).
% 26.53/26.70 tff(18,plain,
% 26.53/26.70 (ld(mult(op_c, X5!0), mult(mult(op_c, X5!0), ld(mult(mult(X4!1, op_f), X5!0), op_c))) = ld(mult(mult(X4!1, op_f), X5!0), op_c)),
% 26.53/26.70 inference(unit_resolution,[status(thm)],[17, 16])).
% 26.53/26.70 tff(19,plain,
% 26.53/26.70 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(X4!1, mult(X4!1, mult(mult(op_f, X5!0), ld(mult(X4!1, mult(op_f, X5!0)), op_c)))) = mult(mult(op_f, X5!0), ld(mult(X4!1, mult(op_f, X5!0)), op_c)))),
% 26.53/26.70 inference(quant_inst,[status(thm)],[])).
% 26.53/26.70 tff(20,plain,
% 26.53/26.70 (ld(X4!1, mult(X4!1, mult(mult(op_f, X5!0), ld(mult(X4!1, mult(op_f, X5!0)), op_c)))) = mult(mult(op_f, X5!0), ld(mult(X4!1, mult(op_f, X5!0)), op_c))),
% 26.53/26.70 inference(unit_resolution,[status(thm)],[19, 16])).
% 26.53/26.70 tff(21,plain,
% 26.53/26.70 (^[B: $i, A: $i] : refl((op_f = mult(A, mult(B, ld(mult(A, B), op_c)))) <=> (op_f = mult(A, mult(B, ld(mult(A, B), op_c)))))),
% 26.53/26.70 inference(bind,[status(th)],[])).
% 26.53/26.70 tff(22,plain,
% 26.53/26.70 (![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c)))) <=> ![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))),
% 26.53/26.70 inference(quant_intro,[status(thm)],[21])).
% 26.53/26.70 tff(23,plain,
% 26.53/26.70 (![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c)))) <=> ![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))),
% 26.53/26.70 inference(rewrite,[status(thm)],[])).
% 26.53/26.70 tff(24,axiom,(![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f13')).
% 26.53/26.70 tff(25,plain,
% 26.53/26.70 (![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))),
% 26.53/26.70 inference(modus_ponens,[status(thm)],[24, 23])).
% 26.53/26.70 tff(26,plain,(
% 26.53/26.70 ![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))),
% 26.53/26.70 inference(skolemize,[status(sab)],[25])).
% 26.53/26.70 tff(27,plain,
% 26.53/26.70 (![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))),
% 26.53/26.70 inference(modus_ponens,[status(thm)],[26, 22])).
% 26.53/26.70 tff(28,plain,
% 26.53/26.70 ((~![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))) | (op_f = mult(X4!1, mult(mult(op_f, X5!0), ld(mult(X4!1, mult(op_f, X5!0)), op_c))))),
% 26.53/26.70 inference(quant_inst,[status(thm)],[])).
% 26.53/26.70 tff(29,plain,
% 26.53/26.70 (op_f = mult(X4!1, mult(mult(op_f, X5!0), ld(mult(X4!1, mult(op_f, X5!0)), op_c)))),
% 26.53/26.70 inference(unit_resolution,[status(thm)],[28, 27])).
% 26.53/26.70 tff(30,plain,
% 26.53/26.70 ((~![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))) | (op_f = mult(X4!1, mult(mult(op_f, op_c), ld(mult(X4!1, mult(op_f, op_c)), op_c))))),
% 26.53/26.70 inference(quant_inst,[status(thm)],[])).
% 26.53/26.70 tff(31,plain,
% 26.53/26.70 (op_f = mult(X4!1, mult(mult(op_f, op_c), ld(mult(X4!1, mult(op_f, op_c)), op_c)))),
% 26.53/26.70 inference(unit_resolution,[status(thm)],[30, 27])).
% 26.53/26.70 tff(32,plain,
% 26.53/26.70 (mult(X4!1, mult(mult(op_f, op_c), ld(mult(X4!1, mult(op_f, op_c)), op_c))) = op_f),
% 26.53/26.70 inference(symmetry,[status(thm)],[31])).
% 26.53/26.70 tff(33,plain,
% 26.53/26.70 (mult(X4!1, mult(mult(op_f, op_c), ld(mult(X4!1, mult(op_f, op_c)), op_c))) = mult(X4!1, mult(mult(op_f, X5!0), ld(mult(X4!1, mult(op_f, X5!0)), op_c)))),
% 26.53/26.70 inference(transitivity,[status(thm)],[32, 29])).
% 26.53/26.70 tff(34,plain,
% 26.53/26.70 (ld(X4!1, mult(X4!1, mult(mult(op_f, op_c), ld(mult(X4!1, mult(op_f, op_c)), op_c)))) = ld(X4!1, mult(X4!1, mult(mult(op_f, X5!0), ld(mult(X4!1, mult(op_f, X5!0)), op_c))))),
% 26.53/26.70 inference(monotonicity,[status(thm)],[33])).
% 26.53/26.70 tff(35,plain,
% 26.53/26.70 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(X4!1, mult(X4!1, mult(mult(op_f, op_c), ld(mult(X4!1, mult(op_f, op_c)), op_c)))) = mult(mult(op_f, op_c), ld(mult(X4!1, mult(op_f, op_c)), op_c)))),
% 26.53/26.70 inference(quant_inst,[status(thm)],[])).
% 26.53/26.70 tff(36,plain,
% 26.53/26.70 (ld(X4!1, mult(X4!1, mult(mult(op_f, op_c), ld(mult(X4!1, mult(op_f, op_c)), op_c)))) = mult(mult(op_f, op_c), ld(mult(X4!1, mult(op_f, op_c)), op_c))),
% 26.53/26.70 inference(unit_resolution,[status(thm)],[35, 16])).
% 26.53/26.70 tff(37,plain,
% 26.53/26.70 (mult(mult(op_f, op_c), ld(mult(X4!1, mult(op_f, op_c)), op_c)) = ld(X4!1, mult(X4!1, mult(mult(op_f, op_c), ld(mult(X4!1, mult(op_f, op_c)), op_c))))),
% 26.53/26.70 inference(symmetry,[status(thm)],[36])).
% 26.53/26.70 tff(38,plain,
% 26.53/26.70 (^[B: $i, A: $i] : refl((mult(A, mult(B, op_c)) = mult(mult(A, B), op_c)) <=> (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c)))),
% 26.53/26.70 inference(bind,[status(th)],[])).
% 26.53/26.70 tff(39,plain,
% 26.53/26.70 (![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c)) <=> ![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))),
% 26.53/26.70 inference(quant_intro,[status(thm)],[38])).
% 26.53/26.70 tff(40,plain,
% 26.53/26.70 (![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c)) <=> ![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))),
% 26.53/26.70 inference(rewrite,[status(thm)],[])).
% 26.53/26.70 tff(41,axiom,(![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f09')).
% 26.53/26.70 tff(42,plain,
% 26.53/26.70 (![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))),
% 26.53/26.70 inference(modus_ponens,[status(thm)],[41, 40])).
% 26.53/26.70 tff(43,plain,(
% 26.53/26.70 ![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))),
% 26.53/26.70 inference(skolemize,[status(sab)],[42])).
% 26.53/26.70 tff(44,plain,
% 26.53/26.70 (![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))),
% 26.53/26.70 inference(modus_ponens,[status(thm)],[43, 39])).
% 26.53/26.70 tff(45,plain,
% 26.53/26.70 ((~![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))) | (mult(X4!1, mult(op_f, op_c)) = mult(mult(X4!1, op_f), op_c))),
% 26.53/26.71 inference(quant_inst,[status(thm)],[])).
% 26.53/26.71 tff(46,plain,
% 26.53/26.71 (mult(X4!1, mult(op_f, op_c)) = mult(mult(X4!1, op_f), op_c)),
% 26.53/26.71 inference(unit_resolution,[status(thm)],[45, 44])).
% 26.53/26.71 tff(47,plain,
% 26.53/26.71 (ld(mult(X4!1, mult(op_f, op_c)), op_c) = ld(mult(mult(X4!1, op_f), op_c), op_c)),
% 26.53/26.71 inference(monotonicity,[status(thm)],[46])).
% 26.53/26.71 tff(48,plain,
% 26.53/26.71 (ld(mult(mult(X4!1, op_f), op_c), op_c) = ld(mult(X4!1, mult(op_f, op_c)), op_c)),
% 26.53/26.71 inference(symmetry,[status(thm)],[47])).
% 26.53/26.71 tff(49,plain,
% 26.53/26.71 ((~![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))) | (op_f = mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))))),
% 26.53/26.71 inference(quant_inst,[status(thm)],[])).
% 26.53/26.71 tff(50,plain,
% 26.53/26.71 (op_f = mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))),
% 26.53/26.71 inference(unit_resolution,[status(thm)],[49, 27])).
% 26.53/26.71 tff(51,plain,
% 26.53/26.71 (mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))) = op_f),
% 26.53/26.71 inference(symmetry,[status(thm)],[50])).
% 26.53/26.71 tff(52,plain,
% 26.53/26.71 (mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), op_c) = mult(op_f, op_c)),
% 26.53/26.71 inference(monotonicity,[status(thm)],[51])).
% 26.53/26.71 tff(53,plain,
% 26.53/26.71 (mult(mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), op_c), ld(mult(mult(X4!1, op_f), op_c), op_c)) = mult(mult(op_f, op_c), ld(mult(X4!1, mult(op_f, op_c)), op_c))),
% 26.53/26.71 inference(monotonicity,[status(thm)],[52, 48])).
% 26.53/26.71 tff(54,plain,
% 26.53/26.71 (^[B: $i, A: $i] : refl((mult(A, mult(op_c, B)) = mult(mult(A, op_c), B)) <=> (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B)))),
% 26.53/26.71 inference(bind,[status(th)],[])).
% 26.53/26.71 tff(55,plain,
% 26.53/26.71 (![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B)) <=> ![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))),
% 26.53/26.71 inference(quant_intro,[status(thm)],[54])).
% 26.53/26.71 tff(56,plain,
% 26.53/26.71 (![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B)) <=> ![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))),
% 26.53/26.71 inference(rewrite,[status(thm)],[])).
% 26.53/26.71 tff(57,axiom,(![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f10')).
% 26.53/26.71 tff(58,plain,
% 26.53/26.71 (![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))),
% 26.53/26.71 inference(modus_ponens,[status(thm)],[57, 56])).
% 26.53/26.71 tff(59,plain,(
% 26.53/26.71 ![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))),
% 26.53/26.71 inference(skolemize,[status(sab)],[58])).
% 26.53/26.71 tff(60,plain,
% 26.53/26.71 (![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))),
% 26.53/26.71 inference(modus_ponens,[status(thm)],[59, 55])).
% 26.53/26.71 tff(61,plain,
% 26.53/26.71 ((~![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))) | (mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(op_c, ld(mult(mult(X4!1, op_f), op_c), op_c))) = mult(mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), op_c), ld(mult(mult(X4!1, op_f), op_c), op_c)))),
% 26.53/26.71 inference(quant_inst,[status(thm)],[])).
% 26.53/26.71 tff(62,plain,
% 26.53/26.71 (mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(op_c, ld(mult(mult(X4!1, op_f), op_c), op_c))) = mult(mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), op_c), ld(mult(mult(X4!1, op_f), op_c), op_c))),
% 26.53/26.71 inference(unit_resolution,[status(thm)],[61, 60])).
% 26.53/26.71 tff(63,plain,
% 26.53/26.71 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(X4!1, op_f), mult(mult(X4!1, op_f), mult(op_c, ld(mult(mult(X4!1, op_f), op_c), op_c)))) = mult(op_c, ld(mult(mult(X4!1, op_f), op_c), op_c)))),
% 26.53/26.71 inference(quant_inst,[status(thm)],[])).
% 26.53/26.71 tff(64,plain,
% 26.53/26.71 (ld(mult(X4!1, op_f), mult(mult(X4!1, op_f), mult(op_c, ld(mult(mult(X4!1, op_f), op_c), op_c)))) = mult(op_c, ld(mult(mult(X4!1, op_f), op_c), op_c))),
% 26.53/26.71 inference(unit_resolution,[status(thm)],[63, 16])).
% 26.53/26.71 tff(65,plain,
% 26.53/26.71 ((~![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))) | (op_f = mult(mult(X4!1, op_f), mult(op_c, ld(mult(mult(X4!1, op_f), op_c), op_c))))),
% 26.53/26.71 inference(quant_inst,[status(thm)],[])).
% 26.53/26.71 tff(66,plain,
% 26.53/26.71 (op_f = mult(mult(X4!1, op_f), mult(op_c, ld(mult(mult(X4!1, op_f), op_c), op_c)))),
% 26.53/26.71 inference(unit_resolution,[status(thm)],[65, 27])).
% 26.53/26.71 tff(67,plain,
% 26.53/26.71 (mult(mult(X4!1, op_f), mult(op_c, ld(mult(mult(X4!1, op_f), op_c), op_c))) = op_f),
% 26.53/26.71 inference(symmetry,[status(thm)],[66])).
% 26.53/26.71 tff(68,plain,
% 26.53/26.71 (mult(mult(X4!1, op_f), mult(op_c, ld(mult(mult(X4!1, op_f), op_c), op_c))) = mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))),
% 26.53/26.71 inference(transitivity,[status(thm)],[67, 50])).
% 26.53/26.71 tff(69,plain,
% 26.53/26.71 (ld(mult(X4!1, op_f), mult(mult(X4!1, op_f), mult(op_c, ld(mult(mult(X4!1, op_f), op_c), op_c)))) = ld(mult(X4!1, op_f), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))))),
% 26.53/26.71 inference(monotonicity,[status(thm)],[68])).
% 26.53/26.71 tff(70,plain,
% 26.53/26.71 (ld(mult(X4!1, op_f), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))) = ld(mult(X4!1, op_f), mult(mult(X4!1, op_f), mult(op_c, ld(mult(mult(X4!1, op_f), op_c), op_c))))),
% 26.53/26.71 inference(symmetry,[status(thm)],[69])).
% 26.53/26.71 tff(71,plain,
% 26.53/26.71 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(X4!1, op_f), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))) = mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))),
% 26.53/26.71 inference(quant_inst,[status(thm)],[])).
% 26.53/26.71 tff(72,plain,
% 26.53/26.71 (ld(mult(X4!1, op_f), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))) = mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))),
% 26.53/26.71 inference(unit_resolution,[status(thm)],[71, 16])).
% 26.53/26.71 tff(73,plain,
% 26.53/26.71 (mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)) = ld(mult(X4!1, op_f), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))))),
% 26.53/26.71 inference(symmetry,[status(thm)],[72])).
% 26.53/26.71 tff(74,plain,
% 26.53/26.71 (mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)) = mult(op_c, ld(mult(mult(X4!1, op_f), op_c), op_c))),
% 26.53/26.71 inference(transitivity,[status(thm)],[73, 70, 64])).
% 26.53/26.71 tff(75,plain,
% 26.53/26.71 ((~![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))) | (op_f = mult(mult(mult(X4!1, op_f), X5!0), mult(op_c, ld(mult(mult(mult(X4!1, op_f), X5!0), op_c), op_c))))),
% 26.53/26.71 inference(quant_inst,[status(thm)],[])).
% 26.53/26.71 tff(76,plain,
% 26.53/26.71 (op_f = mult(mult(mult(X4!1, op_f), X5!0), mult(op_c, ld(mult(mult(mult(X4!1, op_f), X5!0), op_c), op_c)))),
% 26.53/26.71 inference(unit_resolution,[status(thm)],[75, 27])).
% 26.53/26.71 tff(77,plain,
% 26.53/26.71 (mult(mult(mult(X4!1, op_f), X5!0), mult(op_c, ld(mult(mult(mult(X4!1, op_f), X5!0), op_c), op_c))) = op_f),
% 26.53/26.71 inference(symmetry,[status(thm)],[76])).
% 26.53/26.71 tff(78,plain,
% 26.53/26.71 ((~![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))) | (mult(mult(mult(X4!1, op_f), X5!0), mult(op_c, ld(mult(mult(mult(X4!1, op_f), X5!0), op_c), op_c))) = mult(mult(mult(mult(X4!1, op_f), X5!0), op_c), ld(mult(mult(mult(X4!1, op_f), X5!0), op_c), op_c)))),
% 26.53/26.71 inference(quant_inst,[status(thm)],[])).
% 26.53/26.71 tff(79,plain,
% 26.53/26.71 (mult(mult(mult(X4!1, op_f), X5!0), mult(op_c, ld(mult(mult(mult(X4!1, op_f), X5!0), op_c), op_c))) = mult(mult(mult(mult(X4!1, op_f), X5!0), op_c), ld(mult(mult(mult(X4!1, op_f), X5!0), op_c), op_c))),
% 26.53/26.71 inference(unit_resolution,[status(thm)],[78, 60])).
% 26.53/26.71 tff(80,plain,
% 26.53/26.71 (mult(mult(mult(mult(X4!1, op_f), X5!0), op_c), ld(mult(mult(mult(X4!1, op_f), X5!0), op_c), op_c)) = mult(mult(mult(X4!1, op_f), X5!0), mult(op_c, ld(mult(mult(mult(X4!1, op_f), X5!0), op_c), op_c)))),
% 26.53/26.71 inference(symmetry,[status(thm)],[79])).
% 26.53/26.71 tff(81,plain,
% 26.53/26.71 (^[B: $i, A: $i] : refl((mult(A, ld(A, B)) = B) <=> (mult(A, ld(A, B)) = B))),
% 26.53/26.71 inference(bind,[status(th)],[])).
% 26.53/26.71 tff(82,plain,
% 26.53/26.71 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B) <=> ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 26.53/26.71 inference(quant_intro,[status(thm)],[81])).
% 26.53/26.71 tff(83,plain,
% 26.53/26.71 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B) <=> ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 26.53/26.71 inference(rewrite,[status(thm)],[])).
% 26.53/26.71 tff(84,axiom,(![B: $i, A: $i] : (mult(A, ld(A, B)) = B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f01')).
% 26.53/26.71 tff(85,plain,
% 26.53/26.71 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 26.53/26.71 inference(modus_ponens,[status(thm)],[84, 83])).
% 26.53/26.71 tff(86,plain,(
% 26.53/26.71 ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 26.53/26.71 inference(skolemize,[status(sab)],[85])).
% 26.53/26.71 tff(87,plain,
% 26.53/26.71 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 26.53/26.71 inference(modus_ponens,[status(thm)],[86, 82])).
% 26.53/26.71 tff(88,plain,
% 26.53/26.71 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(mult(mult(mult(X4!1, op_f), X5!0), op_c), ld(mult(mult(mult(X4!1, op_f), X5!0), op_c), op_c)) = op_c)),
% 26.53/26.71 inference(quant_inst,[status(thm)],[])).
% 26.53/26.71 tff(89,plain,
% 26.53/26.71 (mult(mult(mult(mult(X4!1, op_f), X5!0), op_c), ld(mult(mult(mult(X4!1, op_f), X5!0), op_c), op_c)) = op_c),
% 26.53/26.71 inference(unit_resolution,[status(thm)],[88, 87])).
% 26.53/26.71 tff(90,plain,
% 26.53/26.71 (op_c = mult(mult(mult(mult(X4!1, op_f), X5!0), op_c), ld(mult(mult(mult(X4!1, op_f), X5!0), op_c), op_c))),
% 26.53/26.71 inference(symmetry,[status(thm)],[89])).
% 26.53/26.71 tff(91,plain,
% 26.53/26.71 (op_c = mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))),
% 26.53/26.71 inference(transitivity,[status(thm)],[90, 80, 77, 50])).
% 26.53/26.71 tff(92,plain,
% 26.53/26.71 (mult(op_c, mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))) = mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(op_c, ld(mult(mult(X4!1, op_f), op_c), op_c)))),
% 26.53/26.71 inference(monotonicity,[status(thm)],[91, 74])).
% 26.53/26.71 tff(93,plain,
% 26.53/26.71 (^[B: $i, A: $i] : refl((mult(op_c, mult(A, B)) = mult(mult(op_c, A), B)) <=> (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B)))),
% 26.53/26.71 inference(bind,[status(th)],[])).
% 26.53/26.71 tff(94,plain,
% 26.53/26.71 (![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B)) <=> ![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))),
% 26.53/26.71 inference(quant_intro,[status(thm)],[93])).
% 26.53/26.71 tff(95,plain,
% 26.53/26.71 (![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B)) <=> ![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))),
% 26.53/26.71 inference(rewrite,[status(thm)],[])).
% 26.53/26.71 tff(96,axiom,(![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f08')).
% 26.53/26.71 tff(97,plain,
% 26.53/26.71 (![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))),
% 26.53/26.71 inference(modus_ponens,[status(thm)],[96, 95])).
% 26.53/26.71 tff(98,plain,(
% 26.53/26.71 ![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))),
% 26.53/26.71 inference(skolemize,[status(sab)],[97])).
% 26.53/26.71 tff(99,plain,
% 26.53/26.71 (![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))),
% 26.53/26.71 inference(modus_ponens,[status(thm)],[98, 94])).
% 26.53/26.71 tff(100,plain,
% 26.53/26.71 ((~![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))) | (mult(op_c, mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))) = mult(mult(op_c, X5!0), ld(mult(mult(X4!1, op_f), X5!0), op_c)))),
% 26.53/26.71 inference(quant_inst,[status(thm)],[])).
% 26.53/26.71 tff(101,plain,
% 26.53/26.71 (mult(op_c, mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))) = mult(mult(op_c, X5!0), ld(mult(mult(X4!1, op_f), X5!0), op_c))),
% 26.53/26.71 inference(unit_resolution,[status(thm)],[100, 99])).
% 26.53/26.71 tff(102,plain,
% 26.53/26.71 (mult(mult(op_c, X5!0), ld(mult(mult(X4!1, op_f), X5!0), op_c)) = mult(op_c, mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))),
% 26.53/26.71 inference(symmetry,[status(thm)],[101])).
% 26.53/26.71 tff(103,plain,
% 26.53/26.71 (mult(mult(op_c, X5!0), ld(mult(mult(X4!1, op_f), X5!0), op_c)) = mult(mult(op_f, X5!0), ld(mult(X4!1, mult(op_f, X5!0)), op_c))),
% 26.53/26.71 inference(transitivity,[status(thm)],[102, 92, 62, 53, 37, 34, 20])).
% 26.53/26.71 tff(104,plain,
% 26.53/26.71 (op_c = op_f),
% 26.53/26.71 inference(transitivity,[status(thm)],[90, 80, 77])).
% 26.53/26.71 tff(105,plain,
% 26.53/26.71 (mult(op_c, X5!0) = mult(op_f, X5!0)),
% 26.53/26.71 inference(monotonicity,[status(thm)],[104])).
% 26.53/26.71 tff(106,plain,
% 26.53/26.71 (ld(mult(op_c, X5!0), mult(mult(op_c, X5!0), ld(mult(mult(X4!1, op_f), X5!0), op_c))) = ld(mult(op_f, X5!0), mult(mult(op_f, X5!0), ld(mult(X4!1, mult(op_f, X5!0)), op_c)))),
% 26.53/26.71 inference(monotonicity,[status(thm)],[105, 103])).
% 26.53/26.71 tff(107,plain,
% 26.53/26.71 (ld(mult(op_f, X5!0), mult(mult(op_f, X5!0), ld(mult(X4!1, mult(op_f, X5!0)), op_c))) = ld(mult(op_c, X5!0), mult(mult(op_c, X5!0), ld(mult(mult(X4!1, op_f), X5!0), op_c)))),
% 26.53/26.71 inference(symmetry,[status(thm)],[106])).
% 26.53/26.71 tff(108,plain,
% 26.53/26.71 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(op_f, X5!0), mult(mult(op_f, X5!0), ld(mult(X4!1, mult(op_f, X5!0)), op_c))) = ld(mult(X4!1, mult(op_f, X5!0)), op_c))),
% 26.53/26.71 inference(quant_inst,[status(thm)],[])).
% 26.53/26.71 tff(109,plain,
% 26.53/26.71 (ld(mult(op_f, X5!0), mult(mult(op_f, X5!0), ld(mult(X4!1, mult(op_f, X5!0)), op_c))) = ld(mult(X4!1, mult(op_f, X5!0)), op_c)),
% 26.53/26.71 inference(unit_resolution,[status(thm)],[108, 16])).
% 26.53/26.71 tff(110,plain,
% 26.53/26.71 (ld(mult(X4!1, mult(op_f, X5!0)), op_c) = ld(mult(op_f, X5!0), mult(mult(op_f, X5!0), ld(mult(X4!1, mult(op_f, X5!0)), op_c)))),
% 26.53/26.71 inference(symmetry,[status(thm)],[109])).
% 26.53/26.71 tff(111,plain,
% 26.53/26.71 (ld(mult(X4!1, mult(op_f, X5!0)), op_c) = ld(mult(mult(X4!1, op_f), X5!0), op_c)),
% 26.53/26.71 inference(transitivity,[status(thm)],[110, 107, 18])).
% 26.53/26.71 tff(112,plain,
% 26.53/26.71 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(mult(mult(X4!1, op_f), X5!0), ld(mult(mult(X4!1, op_f), X5!0), op_c)) = op_c)),
% 26.53/26.71 inference(quant_inst,[status(thm)],[])).
% 26.53/26.71 tff(113,plain,
% 26.53/26.71 (mult(mult(mult(X4!1, op_f), X5!0), ld(mult(mult(X4!1, op_f), X5!0), op_c)) = op_c),
% 26.53/26.71 inference(unit_resolution,[status(thm)],[112, 87])).
% 26.53/26.71 tff(114,plain,
% 26.53/26.71 (op_c = mult(mult(mult(X4!1, op_f), X5!0), ld(mult(mult(X4!1, op_f), X5!0), op_c))),
% 26.53/26.71 inference(symmetry,[status(thm)],[113])).
% 26.53/26.71 tff(115,plain,
% 26.53/26.71 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(mult(X4!1, mult(op_f, X5!0)), ld(mult(X4!1, mult(op_f, X5!0)), op_c)) = op_c)),
% 26.53/26.71 inference(quant_inst,[status(thm)],[])).
% 26.53/26.71 tff(116,plain,
% 26.53/26.71 (mult(mult(X4!1, mult(op_f, X5!0)), ld(mult(X4!1, mult(op_f, X5!0)), op_c)) = op_c),
% 26.53/26.71 inference(unit_resolution,[status(thm)],[115, 87])).
% 26.53/26.71 tff(117,plain,
% 26.53/26.71 (mult(mult(X4!1, mult(op_f, X5!0)), ld(mult(X4!1, mult(op_f, X5!0)), op_c)) = mult(mult(mult(X4!1, op_f), X5!0), ld(mult(mult(X4!1, op_f), X5!0), op_c))),
% 26.53/26.71 inference(transitivity,[status(thm)],[116, 114])).
% 26.53/26.71 tff(118,plain,
% 26.53/26.71 (rd(mult(mult(X4!1, mult(op_f, X5!0)), ld(mult(X4!1, mult(op_f, X5!0)), op_c)), ld(mult(X4!1, mult(op_f, X5!0)), op_c)) = rd(mult(mult(mult(X4!1, op_f), X5!0), ld(mult(mult(X4!1, op_f), X5!0), op_c)), ld(mult(mult(X4!1, op_f), X5!0), op_c))),
% 26.53/26.71 inference(monotonicity,[status(thm)],[117, 111])).
% 26.53/26.71 tff(119,plain,
% 26.53/26.71 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(X4!1, mult(op_f, X5!0)), ld(mult(X4!1, mult(op_f, X5!0)), op_c)), ld(mult(X4!1, mult(op_f, X5!0)), op_c)) = mult(X4!1, mult(op_f, X5!0)))),
% 26.53/26.71 inference(quant_inst,[status(thm)],[])).
% 26.53/26.71 tff(120,plain,
% 26.53/26.71 (rd(mult(mult(X4!1, mult(op_f, X5!0)), ld(mult(X4!1, mult(op_f, X5!0)), op_c)), ld(mult(X4!1, mult(op_f, X5!0)), op_c)) = mult(X4!1, mult(op_f, X5!0))),
% 26.53/26.71 inference(unit_resolution,[status(thm)],[119, 7])).
% 26.53/26.71 tff(121,plain,
% 26.53/26.71 (mult(X4!1, mult(op_f, X5!0)) = rd(mult(mult(X4!1, mult(op_f, X5!0)), ld(mult(X4!1, mult(op_f, X5!0)), op_c)), ld(mult(X4!1, mult(op_f, X5!0)), op_c))),
% 26.53/26.71 inference(symmetry,[status(thm)],[120])).
% 26.53/26.71 tff(122,plain,
% 26.53/26.71 (mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0)),
% 26.53/26.71 inference(transitivity,[status(thm)],[121, 118, 9])).
% 26.53/26.71 tff(123,assumption,(~(mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0))), introduced(assumption)).
% 26.53/26.71 tff(124,plain,
% 26.53/26.71 ($false),
% 26.53/26.71 inference(unit_resolution,[status(thm)],[123, 122])).
% 26.53/26.71 tff(125,plain,(mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0)), inference(lemma,lemma(discharge,[]))).
% 26.53/26.71 tff(126,plain,
% 26.53/26.71 (op_f = op_c),
% 26.53/26.71 inference(transitivity,[status(thm)],[76, 79, 89])).
% 26.53/26.71 tff(127,plain,
% 26.53/26.71 (mult(mult(X4!1, X5!0), op_f) = mult(mult(X4!1, X5!0), op_c)),
% 26.53/26.71 inference(monotonicity,[status(thm)],[126])).
% 26.53/26.71 tff(128,plain,
% 26.53/26.71 (mult(mult(X4!1, X5!0), op_c) = mult(mult(X4!1, X5!0), op_f)),
% 26.53/26.71 inference(symmetry,[status(thm)],[127])).
% 26.53/26.71 tff(129,plain,
% 26.53/26.71 ((~![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))) | (mult(X4!1, mult(X5!0, op_c)) = mult(mult(X4!1, X5!0), op_c))),
% 26.53/26.71 inference(quant_inst,[status(thm)],[])).
% 26.53/26.71 tff(130,plain,
% 26.53/26.71 (mult(X4!1, mult(X5!0, op_c)) = mult(mult(X4!1, X5!0), op_c)),
% 26.53/26.71 inference(unit_resolution,[status(thm)],[129, 44])).
% 26.53/26.71 tff(131,plain,
% 26.53/26.71 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(rd(op_c, mult(op_f, X5!0)), mult(rd(op_c, mult(op_f, X5!0)), mult(op_f, X5!0))) = mult(op_f, X5!0))),
% 26.53/26.71 inference(quant_inst,[status(thm)],[])).
% 26.53/26.71 tff(132,plain,
% 26.53/26.71 (ld(rd(op_c, mult(op_f, X5!0)), mult(rd(op_c, mult(op_f, X5!0)), mult(op_f, X5!0))) = mult(op_f, X5!0)),
% 26.53/26.71 inference(unit_resolution,[status(thm)],[131, 16])).
% 26.53/26.71 tff(133,plain,
% 26.53/26.71 (^[B: $i, A: $i] : refl((mult(rd(A, B), B) = A) <=> (mult(rd(A, B), B) = A))),
% 26.53/26.71 inference(bind,[status(th)],[])).
% 26.53/26.71 tff(134,plain,
% 26.53/26.71 (![B: $i, A: $i] : (mult(rd(A, B), B) = A) <=> ![B: $i, A: $i] : (mult(rd(A, B), B) = A)),
% 26.53/26.71 inference(quant_intro,[status(thm)],[133])).
% 26.53/26.71 tff(135,plain,
% 26.53/26.71 (![B: $i, A: $i] : (mult(rd(A, B), B) = A) <=> ![B: $i, A: $i] : (mult(rd(A, B), B) = A)),
% 26.53/26.71 inference(rewrite,[status(thm)],[])).
% 26.53/26.71 tff(136,axiom,(![B: $i, A: $i] : (mult(rd(A, B), B) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f03')).
% 26.53/26.71 tff(137,plain,
% 26.53/26.71 (![B: $i, A: $i] : (mult(rd(A, B), B) = A)),
% 26.53/26.71 inference(modus_ponens,[status(thm)],[136, 135])).
% 26.53/26.71 tff(138,plain,(
% 26.53/26.71 ![B: $i, A: $i] : (mult(rd(A, B), B) = A)),
% 26.53/26.71 inference(skolemize,[status(sab)],[137])).
% 26.53/26.71 tff(139,plain,
% 26.53/26.71 (![B: $i, A: $i] : (mult(rd(A, B), B) = A)),
% 26.53/26.71 inference(modus_ponens,[status(thm)],[138, 134])).
% 26.53/26.71 tff(140,plain,
% 26.53/26.71 ((~![B: $i, A: $i] : (mult(rd(A, B), B) = A)) | (mult(rd(op_c, mult(op_f, X5!0)), mult(op_f, X5!0)) = op_c)),
% 26.53/26.71 inference(quant_inst,[status(thm)],[])).
% 26.53/26.71 tff(141,plain,
% 26.53/26.71 (mult(rd(op_c, mult(op_f, X5!0)), mult(op_f, X5!0)) = op_c),
% 26.53/26.71 inference(unit_resolution,[status(thm)],[140, 139])).
% 26.53/26.71 tff(142,plain,
% 26.53/26.71 (op_c = mult(rd(op_c, mult(op_f, X5!0)), mult(op_f, X5!0))),
% 26.53/26.71 inference(symmetry,[status(thm)],[141])).
% 26.53/26.71 tff(143,plain,
% 26.53/26.71 ((~![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))) | (op_f = mult(rd(op_c, mult(op_f, X5!0)), mult(X5!0, ld(mult(rd(op_c, mult(op_f, X5!0)), X5!0), op_c))))),
% 26.53/26.71 inference(quant_inst,[status(thm)],[])).
% 26.53/26.71 tff(144,plain,
% 26.53/26.71 (op_f = mult(rd(op_c, mult(op_f, X5!0)), mult(X5!0, ld(mult(rd(op_c, mult(op_f, X5!0)), X5!0), op_c)))),
% 26.53/26.71 inference(unit_resolution,[status(thm)],[143, 27])).
% 26.53/26.71 tff(145,plain,
% 26.53/26.71 (mult(rd(op_c, mult(op_f, X5!0)), mult(X5!0, ld(mult(rd(op_c, mult(op_f, X5!0)), X5!0), op_c))) = op_f),
% 26.53/26.71 inference(symmetry,[status(thm)],[144])).
% 26.53/26.71 tff(146,plain,
% 26.53/26.71 (mult(rd(op_c, mult(op_f, X5!0)), mult(X5!0, ld(mult(rd(op_c, mult(op_f, X5!0)), X5!0), op_c))) = mult(rd(op_c, mult(op_f, X5!0)), mult(op_f, X5!0))),
% 26.53/26.71 inference(transitivity,[status(thm)],[145, 76, 79, 89, 142])).
% 26.53/26.71 tff(147,plain,
% 26.53/26.71 (ld(rd(op_c, mult(op_f, X5!0)), mult(rd(op_c, mult(op_f, X5!0)), mult(X5!0, ld(mult(rd(op_c, mult(op_f, X5!0)), X5!0), op_c)))) = ld(rd(op_c, mult(op_f, X5!0)), mult(rd(op_c, mult(op_f, X5!0)), mult(op_f, X5!0)))),
% 26.53/26.71 inference(monotonicity,[status(thm)],[146])).
% 26.53/26.71 tff(148,plain,
% 26.53/26.71 ((~![B: $i, A: $i] : (mult(rd(A, B), B) = A)) | (mult(rd(op_c, mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))) = op_c)),
% 26.53/26.71 inference(quant_inst,[status(thm)],[])).
% 26.53/26.71 tff(149,plain,
% 26.53/26.71 (mult(rd(op_c, mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))) = op_c),
% 26.53/26.71 inference(unit_resolution,[status(thm)],[148, 139])).
% 26.53/26.71 tff(150,plain,
% 26.53/26.71 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), op_c)) = op_c)),
% 26.53/26.71 inference(quant_inst,[status(thm)],[])).
% 26.53/26.71 tff(151,plain,
% 26.53/26.71 (ld(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), op_c)) = op_c),
% 26.53/26.71 inference(unit_resolution,[status(thm)],[150, 16])).
% 26.53/26.71 tff(152,plain,
% 26.53/26.71 (mult(op_f, op_c) = mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), op_c)),
% 26.53/26.71 inference(symmetry,[status(thm)],[52])).
% 26.53/26.71 tff(153,plain,
% 26.53/26.71 ((~![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))) | (op_f = mult(op_f, mult(X5!0, ld(mult(op_f, X5!0), op_c))))),
% 26.53/26.72 inference(quant_inst,[status(thm)],[])).
% 26.53/26.72 tff(154,plain,
% 26.53/26.72 (op_f = mult(op_f, mult(X5!0, ld(mult(op_f, X5!0), op_c)))),
% 26.53/26.72 inference(unit_resolution,[status(thm)],[153, 27])).
% 26.53/26.72 tff(155,plain,
% 26.53/26.72 (mult(op_f, mult(X5!0, ld(mult(op_f, X5!0), op_c))) = op_f),
% 26.53/26.72 inference(symmetry,[status(thm)],[154])).
% 26.53/26.72 tff(156,plain,
% 26.53/26.72 (mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(X5!0, ld(mult(op_f, X5!0), op_c))) = mult(op_f, mult(X5!0, ld(mult(op_f, X5!0), op_c)))),
% 26.53/26.72 inference(monotonicity,[status(thm)],[51])).
% 26.53/26.72 tff(157,plain,
% 26.53/26.72 (mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(X5!0, ld(mult(op_f, X5!0), op_c))) = op_f),
% 26.53/26.72 inference(transitivity,[status(thm)],[156, 155])).
% 26.53/26.72 tff(158,plain,
% 26.53/26.72 (mult(mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(X5!0, ld(mult(op_f, X5!0), op_c))), op_c) = mult(op_f, op_c)),
% 26.53/26.72 inference(monotonicity,[status(thm)],[157])).
% 26.53/26.72 tff(159,plain,
% 26.53/26.72 ((~![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))) | (mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(mult(X5!0, ld(mult(op_f, X5!0), op_c)), op_c)) = mult(mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(X5!0, ld(mult(op_f, X5!0), op_c))), op_c))),
% 26.53/26.72 inference(quant_inst,[status(thm)],[])).
% 26.53/26.72 tff(160,plain,
% 26.53/26.72 (mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(mult(X5!0, ld(mult(op_f, X5!0), op_c)), op_c)) = mult(mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(X5!0, ld(mult(op_f, X5!0), op_c))), op_c)),
% 26.53/26.72 inference(unit_resolution,[status(thm)],[159, 44])).
% 26.53/26.72 tff(161,plain,
% 26.53/26.72 (mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(mult(X5!0, ld(mult(op_f, X5!0), op_c)), op_c)) = mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), op_c)),
% 26.53/26.72 inference(transitivity,[status(thm)],[160, 158, 152])).
% 26.53/26.72 tff(162,plain,
% 26.53/26.72 (ld(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(mult(X5!0, ld(mult(op_f, X5!0), op_c)), op_c))) = ld(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), op_c))),
% 26.53/26.72 inference(monotonicity,[status(thm)],[161])).
% 26.53/26.72 tff(163,plain,
% 26.53/26.72 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(mult(X5!0, ld(mult(op_f, X5!0), op_c)), op_c))) = mult(mult(X5!0, ld(mult(op_f, X5!0), op_c)), op_c))),
% 26.53/26.72 inference(quant_inst,[status(thm)],[])).
% 26.53/26.72 tff(164,plain,
% 26.53/26.72 (ld(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(mult(X5!0, ld(mult(op_f, X5!0), op_c)), op_c))) = mult(mult(X5!0, ld(mult(op_f, X5!0), op_c)), op_c)),
% 26.53/26.72 inference(unit_resolution,[status(thm)],[163, 16])).
% 26.53/26.72 tff(165,plain,
% 26.53/26.72 (mult(mult(X5!0, ld(mult(op_f, X5!0), op_c)), op_c) = ld(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(mult(X5!0, ld(mult(op_f, X5!0), op_c)), op_c)))),
% 26.53/26.72 inference(symmetry,[status(thm)],[164])).
% 26.53/26.72 tff(166,plain,
% 26.53/26.72 (mult(mult(X5!0, ld(mult(op_f, X5!0), op_c)), op_c) = mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))),
% 26.53/26.72 inference(transitivity,[status(thm)],[165, 162, 151, 90, 80, 77, 50])).
% 26.53/26.72 tff(167,plain,
% 26.53/26.72 (mult(rd(op_c, mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))), mult(mult(X5!0, ld(mult(op_f, X5!0), op_c)), op_c)) = mult(rd(op_c, mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))))),
% 26.53/26.72 inference(monotonicity,[status(thm)],[166])).
% 26.53/26.72 tff(168,plain,
% 26.53/26.72 ((~![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))) | (mult(rd(op_c, mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))), mult(mult(X5!0, ld(mult(op_f, X5!0), op_c)), op_c)) = mult(mult(rd(op_c, mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))), mult(X5!0, ld(mult(op_f, X5!0), op_c))), op_c))),
% 26.53/26.72 inference(quant_inst,[status(thm)],[])).
% 26.53/26.72 tff(169,plain,
% 26.53/26.72 (mult(rd(op_c, mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))), mult(mult(X5!0, ld(mult(op_f, X5!0), op_c)), op_c)) = mult(mult(rd(op_c, mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))), mult(X5!0, ld(mult(op_f, X5!0), op_c))), op_c)),
% 26.53/26.72 inference(unit_resolution,[status(thm)],[168, 44])).
% 26.53/26.72 tff(170,plain,
% 26.53/26.72 (mult(mult(rd(op_c, mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))), mult(X5!0, ld(mult(op_f, X5!0), op_c))), op_c) = mult(rd(op_c, mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))), mult(mult(X5!0, ld(mult(op_f, X5!0), op_c)), op_c))),
% 26.53/26.72 inference(symmetry,[status(thm)],[169])).
% 26.53/26.72 tff(171,plain,
% 26.53/26.72 (mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(X5!0, ld(mult(op_f, X5!0), op_c))) = mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))),
% 26.53/26.72 inference(transitivity,[status(thm)],[156, 155, 50])).
% 26.53/26.72 tff(172,plain,
% 26.53/26.72 (rd(op_c, mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(X5!0, ld(mult(op_f, X5!0), op_c)))) = rd(op_c, mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))))),
% 26.53/26.72 inference(monotonicity,[status(thm)],[171])).
% 26.53/26.72 tff(173,plain,
% 26.53/26.72 (rd(op_c, mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))) = rd(op_c, mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(X5!0, ld(mult(op_f, X5!0), op_c))))),
% 26.53/26.72 inference(symmetry,[status(thm)],[172])).
% 26.53/26.72 tff(174,plain,
% 26.53/26.72 (mult(rd(op_c, mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))), mult(X5!0, ld(mult(op_f, X5!0), op_c))) = mult(rd(op_c, mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(X5!0, ld(mult(op_f, X5!0), op_c)))), mult(X5!0, ld(mult(op_f, X5!0), op_c)))),
% 26.53/26.72 inference(monotonicity,[status(thm)],[173])).
% 26.53/26.72 tff(175,plain,
% 26.53/26.72 (mult(rd(op_c, mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(X5!0, ld(mult(op_f, X5!0), op_c)))), mult(X5!0, ld(mult(op_f, X5!0), op_c))) = mult(rd(op_c, mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))), mult(X5!0, ld(mult(op_f, X5!0), op_c)))),
% 26.53/26.72 inference(symmetry,[status(thm)],[174])).
% 26.53/26.72 tff(176,plain,
% 26.53/26.72 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(rd(op_c, mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(X5!0, ld(mult(op_f, X5!0), op_c)))), mult(X5!0, ld(mult(op_f, X5!0), op_c))), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))) = mult(rd(op_c, mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(X5!0, ld(mult(op_f, X5!0), op_c)))), mult(X5!0, ld(mult(op_f, X5!0), op_c))))),
% 26.53/26.72 inference(quant_inst,[status(thm)],[])).
% 26.53/26.72 tff(177,plain,
% 26.53/26.72 (rd(mult(mult(rd(op_c, mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(X5!0, ld(mult(op_f, X5!0), op_c)))), mult(X5!0, ld(mult(op_f, X5!0), op_c))), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))) = mult(rd(op_c, mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(X5!0, ld(mult(op_f, X5!0), op_c)))), mult(X5!0, ld(mult(op_f, X5!0), op_c)))),
% 26.53/26.72 inference(unit_resolution,[status(thm)],[176, 7])).
% 26.53/26.72 tff(178,plain,
% 26.53/26.72 (^[B: $i, A: $i] : refl((op_e = mult(mult(rd(op_c, mult(A, B)), B), A)) <=> (op_e = mult(mult(rd(op_c, mult(A, B)), B), A)))),
% 26.53/26.72 inference(bind,[status(th)],[])).
% 26.53/26.72 tff(179,plain,
% 26.53/26.72 (![B: $i, A: $i] : (op_e = mult(mult(rd(op_c, mult(A, B)), B), A)) <=> ![B: $i, A: $i] : (op_e = mult(mult(rd(op_c, mult(A, B)), B), A))),
% 26.53/26.72 inference(quant_intro,[status(thm)],[178])).
% 26.53/26.72 tff(180,plain,
% 26.53/26.72 (![B: $i, A: $i] : (op_e = mult(mult(rd(op_c, mult(A, B)), B), A)) <=> ![B: $i, A: $i] : (op_e = mult(mult(rd(op_c, mult(A, B)), B), A))),
% 26.53/26.72 inference(rewrite,[status(thm)],[])).
% 26.53/26.72 tff(181,axiom,(![B: $i, A: $i] : (op_e = mult(mult(rd(op_c, mult(A, B)), B), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f12')).
% 26.53/26.72 tff(182,plain,
% 26.53/26.72 (![B: $i, A: $i] : (op_e = mult(mult(rd(op_c, mult(A, B)), B), A))),
% 26.53/26.72 inference(modus_ponens,[status(thm)],[181, 180])).
% 26.53/26.72 tff(183,plain,(
% 26.53/26.72 ![B: $i, A: $i] : (op_e = mult(mult(rd(op_c, mult(A, B)), B), A))),
% 26.53/26.72 inference(skolemize,[status(sab)],[182])).
% 26.53/26.72 tff(184,plain,
% 26.53/26.72 (![B: $i, A: $i] : (op_e = mult(mult(rd(op_c, mult(A, B)), B), A))),
% 26.53/26.72 inference(modus_ponens,[status(thm)],[183, 179])).
% 26.53/26.72 tff(185,plain,
% 26.53/26.72 ((~![B: $i, A: $i] : (op_e = mult(mult(rd(op_c, mult(A, B)), B), A))) | (op_e = mult(mult(rd(op_c, mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(X5!0, ld(mult(op_f, X5!0), op_c)))), mult(X5!0, ld(mult(op_f, X5!0), op_c))), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))))),
% 26.53/26.72 inference(quant_inst,[status(thm)],[])).
% 26.53/26.72 tff(186,plain,
% 26.53/26.72 (op_e = mult(mult(rd(op_c, mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(X5!0, ld(mult(op_f, X5!0), op_c)))), mult(X5!0, ld(mult(op_f, X5!0), op_c))), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))))),
% 26.53/26.72 inference(unit_resolution,[status(thm)],[185, 184])).
% 26.53/26.72 tff(187,plain,
% 26.53/26.72 ((~![B: $i, A: $i] : (op_e = mult(mult(rd(op_c, mult(A, B)), B), A))) | (op_e = mult(mult(rd(op_c, mult(op_f, X5!0)), X5!0), op_f))),
% 26.53/26.72 inference(quant_inst,[status(thm)],[])).
% 26.53/26.72 tff(188,plain,
% 26.53/26.72 (op_e = mult(mult(rd(op_c, mult(op_f, X5!0)), X5!0), op_f)),
% 26.53/26.72 inference(unit_resolution,[status(thm)],[187, 184])).
% 26.53/26.72 tff(189,plain,
% 26.53/26.72 (mult(mult(rd(op_c, mult(op_f, X5!0)), X5!0), op_f) = op_e),
% 26.53/26.72 inference(symmetry,[status(thm)],[188])).
% 26.53/26.72 tff(190,plain,
% 26.53/26.72 (mult(mult(rd(op_c, mult(op_f, X5!0)), X5!0), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))) = mult(mult(rd(op_c, mult(op_f, X5!0)), X5!0), op_f)),
% 26.53/26.72 inference(monotonicity,[status(thm)],[51])).
% 26.53/26.72 tff(191,plain,
% 26.53/26.72 (mult(mult(rd(op_c, mult(op_f, X5!0)), X5!0), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))) = mult(mult(rd(op_c, mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(X5!0, ld(mult(op_f, X5!0), op_c)))), mult(X5!0, ld(mult(op_f, X5!0), op_c))), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))))),
% 26.53/26.72 inference(transitivity,[status(thm)],[190, 189, 186])).
% 26.53/26.72 tff(192,plain,
% 26.53/26.72 (rd(mult(mult(rd(op_c, mult(op_f, X5!0)), X5!0), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))) = rd(mult(mult(rd(op_c, mult(mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))), mult(X5!0, ld(mult(op_f, X5!0), op_c)))), mult(X5!0, ld(mult(op_f, X5!0), op_c))), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))))),
% 26.53/26.72 inference(monotonicity,[status(thm)],[191])).
% 26.53/26.72 tff(193,plain,
% 26.53/26.72 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(rd(op_c, mult(op_f, X5!0)), X5!0), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))) = mult(rd(op_c, mult(op_f, X5!0)), X5!0))),
% 26.53/26.72 inference(quant_inst,[status(thm)],[])).
% 26.53/26.72 tff(194,plain,
% 26.53/26.72 (rd(mult(mult(rd(op_c, mult(op_f, X5!0)), X5!0), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))) = mult(rd(op_c, mult(op_f, X5!0)), X5!0)),
% 26.53/26.72 inference(unit_resolution,[status(thm)],[193, 7])).
% 26.53/26.72 tff(195,plain,
% 26.53/26.72 (mult(rd(op_c, mult(op_f, X5!0)), X5!0) = rd(mult(mult(rd(op_c, mult(op_f, X5!0)), X5!0), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))), mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c))))),
% 26.53/26.72 inference(symmetry,[status(thm)],[194])).
% 26.53/26.72 tff(196,plain,
% 26.53/26.72 (mult(rd(op_c, mult(op_f, X5!0)), X5!0) = mult(rd(op_c, mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))), mult(X5!0, ld(mult(op_f, X5!0), op_c)))),
% 26.53/26.72 inference(transitivity,[status(thm)],[195, 192, 177, 175])).
% 26.53/26.72 tff(197,plain,
% 26.53/26.72 (mult(mult(rd(op_c, mult(op_f, X5!0)), X5!0), op_f) = mult(mult(rd(op_c, mult(mult(X4!1, op_f), mult(X5!0, ld(mult(mult(X4!1, op_f), X5!0), op_c)))), mult(X5!0, ld(mult(op_f, X5!0), op_c))), op_c)),
% 26.53/26.72 inference(monotonicity,[status(thm)],[196, 126])).
% 26.53/26.72 tff(198,plain,
% 26.53/26.72 (mult(mult(rd(op_c, mult(op_f, X5!0)), X5!0), op_c) = mult(mult(rd(op_c, mult(op_f, X5!0)), X5!0), op_f)),
% 26.53/26.72 inference(monotonicity,[status(thm)],[104])).
% 26.53/26.72 tff(199,plain,
% 26.53/26.72 ((~![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))) | (mult(rd(op_c, mult(op_f, X5!0)), mult(X5!0, op_c)) = mult(mult(rd(op_c, mult(op_f, X5!0)), X5!0), op_c))),
% 26.53/26.72 inference(quant_inst,[status(thm)],[])).
% 26.53/26.72 tff(200,plain,
% 26.53/26.72 (mult(rd(op_c, mult(op_f, X5!0)), mult(X5!0, op_c)) = mult(mult(rd(op_c, mult(op_f, X5!0)), X5!0), op_c)),
% 26.53/26.72 inference(unit_resolution,[status(thm)],[199, 44])).
% 26.53/26.72 tff(201,plain,
% 26.53/26.72 (mult(rd(op_c, mult(op_f, X5!0)), mult(X5!0, op_c)) = mult(rd(op_c, mult(op_f, X5!0)), mult(X5!0, ld(mult(rd(op_c, mult(op_f, X5!0)), X5!0), op_c)))),
% 26.53/26.72 inference(transitivity,[status(thm)],[200, 198, 197, 170, 167, 149, 90, 80, 77, 144])).
% 26.53/26.72 tff(202,plain,
% 26.53/26.72 (ld(rd(op_c, mult(op_f, X5!0)), mult(rd(op_c, mult(op_f, X5!0)), mult(X5!0, op_c))) = ld(rd(op_c, mult(op_f, X5!0)), mult(rd(op_c, mult(op_f, X5!0)), mult(X5!0, ld(mult(rd(op_c, mult(op_f, X5!0)), X5!0), op_c))))),
% 26.53/26.72 inference(monotonicity,[status(thm)],[201])).
% 26.53/26.72 tff(203,plain,
% 26.53/26.72 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(rd(op_c, mult(op_f, X5!0)), mult(rd(op_c, mult(op_f, X5!0)), mult(X5!0, op_c))) = mult(X5!0, op_c))),
% 26.53/26.72 inference(quant_inst,[status(thm)],[])).
% 26.53/26.72 tff(204,plain,
% 26.53/26.72 (ld(rd(op_c, mult(op_f, X5!0)), mult(rd(op_c, mult(op_f, X5!0)), mult(X5!0, op_c))) = mult(X5!0, op_c)),
% 26.53/26.72 inference(unit_resolution,[status(thm)],[203, 16])).
% 26.53/26.72 tff(205,plain,
% 26.53/26.72 (mult(X5!0, op_c) = ld(rd(op_c, mult(op_f, X5!0)), mult(rd(op_c, mult(op_f, X5!0)), mult(X5!0, op_c)))),
% 26.53/26.72 inference(symmetry,[status(thm)],[204])).
% 26.53/26.72 tff(206,plain,
% 26.53/26.72 (mult(X5!0, op_c) = mult(op_f, X5!0)),
% 26.53/26.72 inference(transitivity,[status(thm)],[205, 202, 147, 132])).
% 26.53/26.72 tff(207,plain,
% 26.53/26.72 (mult(X4!1, mult(X5!0, op_c)) = mult(X4!1, mult(op_f, X5!0))),
% 26.53/26.72 inference(monotonicity,[status(thm)],[206])).
% 26.53/26.72 tff(208,plain,
% 26.53/26.72 (mult(X4!1, mult(op_f, X5!0)) = mult(X4!1, mult(X5!0, op_c))),
% 26.53/26.72 inference(symmetry,[status(thm)],[207])).
% 26.53/26.72 tff(209,plain,
% 26.53/26.72 (mult(X5!0, op_f) = mult(X5!0, op_c)),
% 26.53/26.72 inference(monotonicity,[status(thm)],[126])).
% 26.53/26.72 tff(210,plain,
% 26.53/26.72 (mult(X5!0, op_f) = mult(op_f, X5!0)),
% 26.53/26.72 inference(transitivity,[status(thm)],[209, 205, 202, 147, 132])).
% 26.53/26.72 tff(211,plain,
% 26.53/26.72 (mult(X4!1, mult(X5!0, op_f)) = mult(X4!1, mult(op_f, X5!0))),
% 26.53/26.72 inference(monotonicity,[status(thm)],[210])).
% 26.53/26.72 tff(212,plain,
% 26.53/26.72 (mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f)),
% 26.53/26.72 inference(transitivity,[status(thm)],[211, 208, 130, 128])).
% 26.53/26.72 tff(213,plain,
% 26.53/26.72 (mult(X4!1, op_c) = mult(X4!1, op_f)),
% 26.53/26.72 inference(monotonicity,[status(thm)],[104])).
% 26.53/26.72 tff(214,plain,
% 26.53/26.72 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(op_c, mult(op_c, op_c)) = op_c)),
% 26.53/26.72 inference(quant_inst,[status(thm)],[])).
% 26.53/26.72 tff(215,plain,
% 26.53/26.72 (ld(op_c, mult(op_c, op_c)) = op_c),
% 26.53/26.72 inference(unit_resolution,[status(thm)],[214, 16])).
% 26.53/26.72 tff(216,plain,
% 26.53/26.72 (^[A: $i] : refl((op_d = ld(A, mult(op_c, A))) <=> (op_d = ld(A, mult(op_c, A))))),
% 26.53/26.72 inference(bind,[status(th)],[])).
% 26.53/26.72 tff(217,plain,
% 26.53/26.72 (![A: $i] : (op_d = ld(A, mult(op_c, A))) <=> ![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 26.53/26.72 inference(quant_intro,[status(thm)],[216])).
% 26.53/26.72 tff(218,plain,
% 26.53/26.72 (![A: $i] : (op_d = ld(A, mult(op_c, A))) <=> ![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 26.53/26.72 inference(rewrite,[status(thm)],[])).
% 26.53/26.72 tff(219,axiom,(![A: $i] : (op_d = ld(A, mult(op_c, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f11')).
% 26.53/26.72 tff(220,plain,
% 26.53/26.72 (![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 26.53/26.72 inference(modus_ponens,[status(thm)],[219, 218])).
% 26.53/26.72 tff(221,plain,(
% 26.53/26.72 ![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 26.53/26.72 inference(skolemize,[status(sab)],[220])).
% 26.53/26.72 tff(222,plain,
% 26.53/26.72 (![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 26.53/26.72 inference(modus_ponens,[status(thm)],[221, 217])).
% 26.53/26.72 tff(223,plain,
% 26.53/26.72 ((~![A: $i] : (op_d = ld(A, mult(op_c, A)))) | (op_d = ld(op_c, mult(op_c, op_c)))),
% 26.53/26.72 inference(quant_inst,[status(thm)],[])).
% 26.53/26.72 tff(224,plain,
% 26.53/26.72 (op_d = ld(op_c, mult(op_c, op_c))),
% 26.53/26.72 inference(unit_resolution,[status(thm)],[223, 222])).
% 26.53/26.72 tff(225,plain,
% 26.53/26.72 ((~![A: $i] : (op_d = ld(A, mult(op_c, A)))) | (op_d = ld(X4!1, mult(op_c, X4!1)))),
% 26.53/26.72 inference(quant_inst,[status(thm)],[])).
% 26.53/26.72 tff(226,plain,
% 26.53/26.72 (op_d = ld(X4!1, mult(op_c, X4!1))),
% 26.53/26.72 inference(unit_resolution,[status(thm)],[225, 222])).
% 26.53/26.72 tff(227,plain,
% 26.53/26.72 (ld(X4!1, mult(op_c, X4!1)) = op_d),
% 26.53/26.72 inference(symmetry,[status(thm)],[226])).
% 26.53/26.72 tff(228,plain,
% 26.53/26.72 (ld(X4!1, mult(op_c, X4!1)) = op_c),
% 26.53/26.72 inference(transitivity,[status(thm)],[227, 224, 215])).
% 26.53/26.72 tff(229,plain,
% 26.53/26.72 (mult(X4!1, ld(X4!1, mult(op_c, X4!1))) = mult(X4!1, op_c)),
% 26.53/26.72 inference(monotonicity,[status(thm)],[228])).
% 26.53/26.72 tff(230,plain,
% 26.53/26.72 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(X4!1, ld(X4!1, mult(op_c, X4!1))) = mult(op_c, X4!1))),
% 26.53/26.72 inference(quant_inst,[status(thm)],[])).
% 26.53/26.72 tff(231,plain,
% 26.53/26.72 (mult(X4!1, ld(X4!1, mult(op_c, X4!1))) = mult(op_c, X4!1)),
% 26.53/26.72 inference(unit_resolution,[status(thm)],[230, 87])).
% 26.53/26.72 tff(232,plain,
% 26.53/26.72 (mult(op_c, X4!1) = mult(X4!1, ld(X4!1, mult(op_c, X4!1)))),
% 26.53/26.72 inference(symmetry,[status(thm)],[231])).
% 26.53/26.72 tff(233,plain,
% 26.53/26.72 (mult(op_f, X4!1) = mult(op_c, X4!1)),
% 26.53/26.72 inference(monotonicity,[status(thm)],[126])).
% 26.53/26.72 tff(234,plain,
% 26.53/26.72 (mult(op_f, X4!1) = mult(X4!1, op_f)),
% 26.53/26.72 inference(transitivity,[status(thm)],[233, 232, 229, 213])).
% 26.53/26.72 tff(235,plain,
% 26.53/26.72 (mult(mult(op_f, X4!1), X5!0) = mult(mult(X4!1, op_f), X5!0)),
% 26.53/26.72 inference(monotonicity,[status(thm)],[234])).
% 26.53/26.72 tff(236,plain,
% 26.53/26.72 (mult(mult(X4!1, op_f), X5!0) = mult(mult(op_f, X4!1), X5!0)),
% 26.53/26.72 inference(symmetry,[status(thm)],[235])).
% 26.53/26.72 tff(237,plain,
% 26.53/26.72 (mult(op_c, X4!1) = mult(X4!1, op_f)),
% 26.53/26.72 inference(transitivity,[status(thm)],[232, 229, 213])).
% 26.53/26.72 tff(238,plain,
% 26.53/26.72 (mult(mult(op_c, X4!1), X5!0) = mult(mult(X4!1, op_f), X5!0)),
% 26.53/26.72 inference(monotonicity,[status(thm)],[237])).
% 26.53/26.72 tff(239,plain,
% 26.53/26.72 ((~![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))) | (mult(op_c, mult(X4!1, X5!0)) = mult(mult(op_c, X4!1), X5!0))),
% 26.53/26.72 inference(quant_inst,[status(thm)],[])).
% 26.53/26.72 tff(240,plain,
% 26.53/26.72 (mult(op_c, mult(X4!1, X5!0)) = mult(mult(op_c, X4!1), X5!0)),
% 26.53/26.72 inference(unit_resolution,[status(thm)],[239, 99])).
% 26.53/26.72 tff(241,plain,
% 26.53/26.72 (mult(op_f, mult(X4!1, X5!0)) = mult(op_c, mult(X4!1, X5!0))),
% 26.53/26.72 inference(monotonicity,[status(thm)],[126])).
% 26.53/26.72 tff(242,plain,
% 26.53/26.72 (mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0)),
% 26.53/26.72 inference(transitivity,[status(thm)],[241, 240, 238, 236])).
% 26.53/26.72 tff(243,plain,
% 26.53/26.72 ((~(~((~(mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0))) | (~(mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f))) | (~(mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0)))))) <=> ((~(mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0))) | (~(mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f))) | (~(mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0))))),
% 26.53/26.72 inference(rewrite,[status(thm)],[])).
% 26.53/26.72 tff(244,plain,
% 26.53/26.72 (((mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0)) & (mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f)) & (mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0))) <=> (~((~(mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0))) | (~(mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f))) | (~(mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0)))))),
% 26.53/26.72 inference(rewrite,[status(thm)],[])).
% 26.53/26.72 tff(245,plain,
% 26.53/26.72 ((~((mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0)) & (mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f)) & (mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0)))) <=> (~(~((~(mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0))) | (~(mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f))) | (~(mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0))))))),
% 26.53/26.72 inference(monotonicity,[status(thm)],[244])).
% 26.53/26.72 tff(246,plain,
% 26.53/26.72 ((~((mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0)) & (mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f)) & (mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0)))) <=> ((~(mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0))) | (~(mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f))) | (~(mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0))))),
% 26.53/26.72 inference(transitivity,[status(thm)],[245, 243])).
% 26.53/26.72 tff(247,plain,
% 26.53/26.72 ((~![X4: $i, X5: $i] : ((mult(op_f, mult(X4, X5)) = mult(mult(op_f, X4), X5)) & (mult(X4, mult(X5, op_f)) = mult(mult(X4, X5), op_f)) & (mult(X4, mult(op_f, X5)) = mult(mult(X4, op_f), X5)))) <=> (~![X4: $i, X5: $i] : ((mult(op_f, mult(X4, X5)) = mult(mult(op_f, X4), X5)) & (mult(X4, mult(X5, op_f)) = mult(mult(X4, X5), op_f)) & (mult(X4, mult(op_f, X5)) = mult(mult(X4, op_f), X5))))),
% 26.53/26.72 inference(rewrite,[status(thm)],[])).
% 26.53/26.72 tff(248,plain,
% 26.53/26.72 ((~![X4: $i, X5: $i] : (((mult(op_f, mult(X4, X5)) = mult(mult(op_f, X4), X5)) & (mult(X4, mult(X5, op_f)) = mult(mult(X4, X5), op_f))) & (mult(X4, mult(op_f, X5)) = mult(mult(X4, op_f), X5)))) <=> (~![X4: $i, X5: $i] : ((mult(op_f, mult(X4, X5)) = mult(mult(op_f, X4), X5)) & (mult(X4, mult(X5, op_f)) = mult(mult(X4, X5), op_f)) & (mult(X4, mult(op_f, X5)) = mult(mult(X4, op_f), X5))))),
% 26.53/26.72 inference(rewrite,[status(thm)],[])).
% 26.53/26.72 tff(249,axiom,(~![X4: $i, X5: $i] : (((mult(op_f, mult(X4, X5)) = mult(mult(op_f, X4), X5)) & (mult(X4, mult(X5, op_f)) = mult(mult(X4, X5), op_f))) & (mult(X4, mult(op_f, X5)) = mult(mult(X4, op_f), X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 26.53/26.72 tff(250,plain,
% 26.53/26.72 (~![X4: $i, X5: $i] : ((mult(op_f, mult(X4, X5)) = mult(mult(op_f, X4), X5)) & (mult(X4, mult(X5, op_f)) = mult(mult(X4, X5), op_f)) & (mult(X4, mult(op_f, X5)) = mult(mult(X4, op_f), X5)))),
% 26.53/26.72 inference(modus_ponens,[status(thm)],[249, 248])).
% 26.53/26.72 tff(251,plain,
% 26.53/26.72 (~![X4: $i, X5: $i] : ((mult(op_f, mult(X4, X5)) = mult(mult(op_f, X4), X5)) & (mult(X4, mult(X5, op_f)) = mult(mult(X4, X5), op_f)) & (mult(X4, mult(op_f, X5)) = mult(mult(X4, op_f), X5)))),
% 26.53/26.72 inference(modus_ponens,[status(thm)],[250, 247])).
% 26.53/26.72 tff(252,plain,
% 26.53/26.72 (~![X4: $i, X5: $i] : ((mult(op_f, mult(X4, X5)) = mult(mult(op_f, X4), X5)) & (mult(X4, mult(X5, op_f)) = mult(mult(X4, X5), op_f)) & (mult(X4, mult(op_f, X5)) = mult(mult(X4, op_f), X5)))),
% 26.53/26.72 inference(modus_ponens,[status(thm)],[251, 247])).
% 26.53/26.72 tff(253,plain,
% 26.53/26.72 (~![X4: $i, X5: $i] : ((mult(op_f, mult(X4, X5)) = mult(mult(op_f, X4), X5)) & (mult(X4, mult(X5, op_f)) = mult(mult(X4, X5), op_f)) & (mult(X4, mult(op_f, X5)) = mult(mult(X4, op_f), X5)))),
% 26.53/26.72 inference(modus_ponens,[status(thm)],[252, 247])).
% 26.53/26.72 tff(254,plain,(
% 26.53/26.72 ~((mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0)) & (mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f)) & (mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0)))),
% 26.53/26.72 inference(skolemize,[status(sab)],[253])).
% 26.53/26.72 tff(255,plain,
% 26.53/26.72 ((~(mult(op_f, mult(X4!1, X5!0)) = mult(mult(op_f, X4!1), X5!0))) | (~(mult(X4!1, mult(X5!0, op_f)) = mult(mult(X4!1, X5!0), op_f))) | (~(mult(X4!1, mult(op_f, X5!0)) = mult(mult(X4!1, op_f), X5!0)))),
% 26.53/26.73 inference(modus_ponens,[status(thm)],[254, 246])).
% 26.53/26.73 tff(256,plain,
% 26.53/26.73 ($false),
% 26.53/26.73 inference(unit_resolution,[status(thm)],[255, 242, 212, 125])).
% 26.53/26.73 % SZS output end Proof
% 26.53/26.74 % E exiting
%------------------------------------------------------------------------------