%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP702+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:08:30 AM UTC 2025
% Result : Theorem 17.99s 18.20s
% Output : Proof 18.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP702+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 16:56:05 EDT 2025
% 0.12/0.34 % CPUTime :
% 17.99/18.20 % SZS status Theorem
% 17.99/18.20 % SZS output start Proof
% 17.99/18.20 tff(mult_type, type, (
% 17.99/18.20 mult: ( $i * $i ) > $i)).
% 17.99/18.20 tff(tptp_fun_X1_0_type, type, (
% 17.99/18.20 tptp_fun_X1_0: $i)).
% 17.99/18.20 tff(op_d_type, type, (
% 17.99/18.20 op_d: $i)).
% 17.99/18.20 tff(tptp_fun_X0_1_type, type, (
% 17.99/18.20 tptp_fun_X0_1: $i)).
% 17.99/18.20 tff(rd_type, type, (
% 17.99/18.20 rd: ( $i * $i ) > $i)).
% 17.99/18.20 tff(ld_type, type, (
% 17.99/18.20 ld: ( $i * $i ) > $i)).
% 17.99/18.20 tff(op_c_type, type, (
% 17.99/18.20 op_c: $i)).
% 17.99/18.20 tff(op_f_type, type, (
% 17.99/18.20 op_f: $i)).
% 17.99/18.20 tff(1,plain,
% 17.99/18.20 (^[B: $i, A: $i] : refl((rd(mult(A, B), B) = A) <=> (rd(mult(A, B), B) = A))),
% 17.99/18.20 inference(bind,[status(th)],[])).
% 17.99/18.20 tff(2,plain,
% 17.99/18.20 (![B: $i, A: $i] : (rd(mult(A, B), B) = A) <=> ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 17.99/18.20 inference(quant_intro,[status(thm)],[1])).
% 17.99/18.20 tff(3,plain,
% 17.99/18.20 (![B: $i, A: $i] : (rd(mult(A, B), B) = A) <=> ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 17.99/18.20 inference(rewrite,[status(thm)],[])).
% 17.99/18.20 tff(4,axiom,(![B: $i, A: $i] : (rd(mult(A, B), B) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f04')).
% 17.99/18.20 tff(5,plain,
% 17.99/18.20 (![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 17.99/18.20 inference(modus_ponens,[status(thm)],[4, 3])).
% 17.99/18.20 tff(6,plain,(
% 17.99/18.20 ![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 17.99/18.20 inference(skolemize,[status(sab)],[5])).
% 17.99/18.20 tff(7,plain,
% 17.99/18.20 (![B: $i, A: $i] : (rd(mult(A, B), B) = A)),
% 17.99/18.20 inference(modus_ponens,[status(thm)],[6, 2])).
% 17.99/18.20 tff(8,plain,
% 17.99/18.20 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(mult(X0!1, op_d), X1!0), ld(mult(mult(X0!1, op_d), X1!0), op_c)), ld(mult(mult(X0!1, op_d), X1!0), op_c)) = mult(mult(X0!1, op_d), X1!0))),
% 17.99/18.20 inference(quant_inst,[status(thm)],[])).
% 17.99/18.20 tff(9,plain,
% 17.99/18.20 (rd(mult(mult(mult(X0!1, op_d), X1!0), ld(mult(mult(X0!1, op_d), X1!0), op_c)), ld(mult(mult(X0!1, op_d), X1!0), op_c)) = mult(mult(X0!1, op_d), X1!0)),
% 17.99/18.20 inference(unit_resolution,[status(thm)],[8, 7])).
% 17.99/18.20 tff(10,plain,
% 17.99/18.20 (^[B: $i, A: $i] : refl((ld(A, mult(A, B)) = B) <=> (ld(A, mult(A, B)) = B))),
% 17.99/18.20 inference(bind,[status(th)],[])).
% 17.99/18.20 tff(11,plain,
% 17.99/18.20 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 17.99/18.20 inference(quant_intro,[status(thm)],[10])).
% 17.99/18.20 tff(12,plain,
% 17.99/18.20 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B) <=> ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 17.99/18.20 inference(rewrite,[status(thm)],[])).
% 17.99/18.20 tff(13,axiom,(![B: $i, A: $i] : (ld(A, mult(A, B)) = B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f02')).
% 17.99/18.20 tff(14,plain,
% 17.99/18.20 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 17.99/18.20 inference(modus_ponens,[status(thm)],[13, 12])).
% 17.99/18.20 tff(15,plain,(
% 17.99/18.20 ![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 17.99/18.20 inference(skolemize,[status(sab)],[14])).
% 17.99/18.20 tff(16,plain,
% 17.99/18.20 (![B: $i, A: $i] : (ld(A, mult(A, B)) = B)),
% 17.99/18.20 inference(modus_ponens,[status(thm)],[15, 11])).
% 17.99/18.20 tff(17,plain,
% 17.99/18.20 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(op_c, X1!0), mult(mult(op_c, X1!0), ld(mult(mult(X0!1, op_d), X1!0), op_c))) = ld(mult(mult(X0!1, op_d), X1!0), op_c))),
% 17.99/18.20 inference(quant_inst,[status(thm)],[])).
% 17.99/18.20 tff(18,plain,
% 17.99/18.20 (ld(mult(op_c, X1!0), mult(mult(op_c, X1!0), ld(mult(mult(X0!1, op_d), X1!0), op_c))) = ld(mult(mult(X0!1, op_d), X1!0), op_c)),
% 17.99/18.20 inference(unit_resolution,[status(thm)],[17, 16])).
% 17.99/18.20 tff(19,plain,
% 17.99/18.20 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(X0!1, mult(X0!1, mult(mult(op_d, X1!0), ld(mult(X0!1, mult(op_d, X1!0)), op_c)))) = mult(mult(op_d, X1!0), ld(mult(X0!1, mult(op_d, X1!0)), op_c)))),
% 17.99/18.20 inference(quant_inst,[status(thm)],[])).
% 17.99/18.20 tff(20,plain,
% 17.99/18.20 (ld(X0!1, mult(X0!1, mult(mult(op_d, X1!0), ld(mult(X0!1, mult(op_d, X1!0)), op_c)))) = mult(mult(op_d, X1!0), ld(mult(X0!1, mult(op_d, X1!0)), op_c))),
% 17.99/18.20 inference(unit_resolution,[status(thm)],[19, 16])).
% 17.99/18.20 tff(21,plain,
% 17.99/18.20 (^[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)))))),
% 17.99/18.20 inference(bind,[status(th)],[])).
% 17.99/18.20 tff(22,plain,
% 17.99/18.20 (![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))))),
% 17.99/18.20 inference(quant_intro,[status(thm)],[21])).
% 17.99/18.20 tff(23,plain,
% 17.99/18.20 (![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))))),
% 17.99/18.20 inference(rewrite,[status(thm)],[])).
% 17.99/18.20 tff(24,axiom,(![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f13')).
% 17.99/18.20 tff(25,plain,
% 17.99/18.20 (![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))),
% 17.99/18.20 inference(modus_ponens,[status(thm)],[24, 23])).
% 17.99/18.20 tff(26,plain,(
% 17.99/18.20 ![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))),
% 17.99/18.20 inference(skolemize,[status(sab)],[25])).
% 17.99/18.20 tff(27,plain,
% 17.99/18.20 (![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))),
% 17.99/18.20 inference(modus_ponens,[status(thm)],[26, 22])).
% 17.99/18.20 tff(28,plain,
% 17.99/18.20 ((~![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))) | (op_f = mult(X0!1, mult(mult(op_d, X1!0), ld(mult(X0!1, mult(op_d, X1!0)), op_c))))),
% 17.99/18.20 inference(quant_inst,[status(thm)],[])).
% 17.99/18.20 tff(29,plain,
% 17.99/18.20 (op_f = mult(X0!1, mult(mult(op_d, X1!0), ld(mult(X0!1, mult(op_d, X1!0)), op_c)))),
% 17.99/18.20 inference(unit_resolution,[status(thm)],[28, 27])).
% 17.99/18.20 tff(30,plain,
% 17.99/18.20 ((~![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))) | (op_f = mult(X0!1, mult(mult(op_d, op_c), ld(mult(X0!1, mult(op_d, op_c)), op_c))))),
% 17.99/18.20 inference(quant_inst,[status(thm)],[])).
% 17.99/18.20 tff(31,plain,
% 17.99/18.20 (op_f = mult(X0!1, mult(mult(op_d, op_c), ld(mult(X0!1, mult(op_d, op_c)), op_c)))),
% 17.99/18.20 inference(unit_resolution,[status(thm)],[30, 27])).
% 17.99/18.20 tff(32,plain,
% 17.99/18.20 (mult(X0!1, mult(mult(op_d, op_c), ld(mult(X0!1, mult(op_d, op_c)), op_c))) = op_f),
% 17.99/18.20 inference(symmetry,[status(thm)],[31])).
% 17.99/18.20 tff(33,plain,
% 17.99/18.20 (mult(X0!1, mult(mult(op_d, op_c), ld(mult(X0!1, mult(op_d, op_c)), op_c))) = mult(X0!1, mult(mult(op_d, X1!0), ld(mult(X0!1, mult(op_d, X1!0)), op_c)))),
% 17.99/18.20 inference(transitivity,[status(thm)],[32, 29])).
% 17.99/18.20 tff(34,plain,
% 17.99/18.20 (ld(X0!1, mult(X0!1, mult(mult(op_d, op_c), ld(mult(X0!1, mult(op_d, op_c)), op_c)))) = ld(X0!1, mult(X0!1, mult(mult(op_d, X1!0), ld(mult(X0!1, mult(op_d, X1!0)), op_c))))),
% 17.99/18.20 inference(monotonicity,[status(thm)],[33])).
% 17.99/18.20 tff(35,plain,
% 17.99/18.20 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(X0!1, mult(X0!1, mult(mult(op_d, op_c), ld(mult(X0!1, mult(op_d, op_c)), op_c)))) = mult(mult(op_d, op_c), ld(mult(X0!1, mult(op_d, op_c)), op_c)))),
% 17.99/18.20 inference(quant_inst,[status(thm)],[])).
% 17.99/18.20 tff(36,plain,
% 17.99/18.20 (ld(X0!1, mult(X0!1, mult(mult(op_d, op_c), ld(mult(X0!1, mult(op_d, op_c)), op_c)))) = mult(mult(op_d, op_c), ld(mult(X0!1, mult(op_d, op_c)), op_c))),
% 17.99/18.20 inference(unit_resolution,[status(thm)],[35, 16])).
% 17.99/18.20 tff(37,plain,
% 17.99/18.20 (mult(mult(op_d, op_c), ld(mult(X0!1, mult(op_d, op_c)), op_c)) = ld(X0!1, mult(X0!1, mult(mult(op_d, op_c), ld(mult(X0!1, mult(op_d, op_c)), op_c))))),
% 17.99/18.20 inference(symmetry,[status(thm)],[36])).
% 17.99/18.20 tff(38,plain,
% 17.99/18.20 (^[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)))),
% 17.99/18.20 inference(bind,[status(th)],[])).
% 17.99/18.20 tff(39,plain,
% 17.99/18.20 (![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))),
% 17.99/18.20 inference(quant_intro,[status(thm)],[38])).
% 17.99/18.20 tff(40,plain,
% 17.99/18.20 (![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))),
% 17.99/18.20 inference(rewrite,[status(thm)],[])).
% 17.99/18.20 tff(41,axiom,(![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f09')).
% 17.99/18.20 tff(42,plain,
% 17.99/18.20 (![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))),
% 17.99/18.20 inference(modus_ponens,[status(thm)],[41, 40])).
% 17.99/18.20 tff(43,plain,(
% 17.99/18.20 ![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))),
% 17.99/18.20 inference(skolemize,[status(sab)],[42])).
% 17.99/18.20 tff(44,plain,
% 17.99/18.20 (![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))),
% 17.99/18.20 inference(modus_ponens,[status(thm)],[43, 39])).
% 17.99/18.20 tff(45,plain,
% 17.99/18.20 ((~![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))) | (mult(X0!1, mult(op_d, op_c)) = mult(mult(X0!1, op_d), op_c))),
% 17.99/18.20 inference(quant_inst,[status(thm)],[])).
% 17.99/18.20 tff(46,plain,
% 17.99/18.20 (mult(X0!1, mult(op_d, op_c)) = mult(mult(X0!1, op_d), op_c)),
% 17.99/18.20 inference(unit_resolution,[status(thm)],[45, 44])).
% 17.99/18.20 tff(47,plain,
% 17.99/18.20 (ld(mult(X0!1, mult(op_d, op_c)), op_c) = ld(mult(mult(X0!1, op_d), op_c), op_c)),
% 17.99/18.20 inference(monotonicity,[status(thm)],[46])).
% 17.99/18.20 tff(48,plain,
% 17.99/18.20 (ld(mult(mult(X0!1, op_d), op_c), op_c) = ld(mult(X0!1, mult(op_d, op_c)), op_c)),
% 17.99/18.20 inference(symmetry,[status(thm)],[47])).
% 17.99/18.20 tff(49,plain,
% 17.99/18.20 (mult(mult(op_d, op_c), ld(mult(mult(X0!1, op_d), op_c), op_c)) = mult(mult(op_d, op_c), ld(mult(X0!1, mult(op_d, op_c)), op_c))),
% 17.99/18.20 inference(monotonicity,[status(thm)],[48])).
% 17.99/18.20 tff(50,plain,
% 17.99/18.20 (^[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)))),
% 17.99/18.20 inference(bind,[status(th)],[])).
% 17.99/18.20 tff(51,plain,
% 17.99/18.20 (![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))),
% 17.99/18.20 inference(quant_intro,[status(thm)],[50])).
% 17.99/18.20 tff(52,plain,
% 17.99/18.20 (![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))),
% 17.99/18.20 inference(rewrite,[status(thm)],[])).
% 17.99/18.20 tff(53,axiom,(![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f10')).
% 17.99/18.20 tff(54,plain,
% 17.99/18.20 (![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))),
% 17.99/18.20 inference(modus_ponens,[status(thm)],[53, 52])).
% 17.99/18.20 tff(55,plain,(
% 17.99/18.20 ![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))),
% 17.99/18.20 inference(skolemize,[status(sab)],[54])).
% 17.99/18.20 tff(56,plain,
% 17.99/18.20 (![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))),
% 17.99/18.20 inference(modus_ponens,[status(thm)],[55, 51])).
% 17.99/18.20 tff(57,plain,
% 17.99/18.20 ((~![B: $i, A: $i] : (mult(A, mult(op_c, B)) = mult(mult(A, op_c), B))) | (mult(op_d, mult(op_c, ld(mult(mult(X0!1, op_d), op_c), op_c))) = mult(mult(op_d, op_c), ld(mult(mult(X0!1, op_d), op_c), op_c)))),
% 17.99/18.20 inference(quant_inst,[status(thm)],[])).
% 17.99/18.20 tff(58,plain,
% 17.99/18.20 (mult(op_d, mult(op_c, ld(mult(mult(X0!1, op_d), op_c), op_c))) = mult(mult(op_d, op_c), ld(mult(mult(X0!1, op_d), op_c), op_c))),
% 17.99/18.20 inference(unit_resolution,[status(thm)],[57, 56])).
% 17.99/18.20 tff(59,plain,
% 17.99/18.20 (^[A: $i] : refl((op_d = ld(A, mult(op_c, A))) <=> (op_d = ld(A, mult(op_c, A))))),
% 17.99/18.20 inference(bind,[status(th)],[])).
% 17.99/18.20 tff(60,plain,
% 17.99/18.20 (![A: $i] : (op_d = ld(A, mult(op_c, A))) <=> ![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 17.99/18.20 inference(quant_intro,[status(thm)],[59])).
% 17.99/18.20 tff(61,plain,
% 17.99/18.20 (![A: $i] : (op_d = ld(A, mult(op_c, A))) <=> ![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 17.99/18.20 inference(rewrite,[status(thm)],[])).
% 17.99/18.20 tff(62,axiom,(![A: $i] : (op_d = ld(A, mult(op_c, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f11')).
% 17.99/18.20 tff(63,plain,
% 17.99/18.20 (![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 17.99/18.20 inference(modus_ponens,[status(thm)],[62, 61])).
% 17.99/18.20 tff(64,plain,(
% 17.99/18.20 ![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 17.99/18.20 inference(skolemize,[status(sab)],[63])).
% 17.99/18.20 tff(65,plain,
% 17.99/18.20 (![A: $i] : (op_d = ld(A, mult(op_c, A)))),
% 17.99/18.20 inference(modus_ponens,[status(thm)],[64, 60])).
% 17.99/18.20 tff(66,plain,
% 17.99/18.20 ((~![A: $i] : (op_d = ld(A, mult(op_c, A)))) | (op_d = ld(op_c, mult(op_c, op_c)))),
% 17.99/18.20 inference(quant_inst,[status(thm)],[])).
% 17.99/18.20 tff(67,plain,
% 17.99/18.20 (op_d = ld(op_c, mult(op_c, op_c))),
% 17.99/18.20 inference(unit_resolution,[status(thm)],[66, 65])).
% 17.99/18.20 tff(68,plain,
% 17.99/18.20 (ld(op_c, mult(op_c, op_c)) = op_d),
% 17.99/18.20 inference(symmetry,[status(thm)],[67])).
% 17.99/18.20 tff(69,plain,
% 17.99/18.20 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(op_c, mult(op_c, op_c)) = op_c)),
% 17.99/18.20 inference(quant_inst,[status(thm)],[])).
% 17.99/18.20 tff(70,plain,
% 17.99/18.20 (ld(op_c, mult(op_c, op_c)) = op_c),
% 17.99/18.20 inference(unit_resolution,[status(thm)],[69, 16])).
% 17.99/18.20 tff(71,plain,
% 17.99/18.20 (op_c = ld(op_c, mult(op_c, op_c))),
% 17.99/18.20 inference(symmetry,[status(thm)],[70])).
% 17.99/18.20 tff(72,plain,
% 17.99/18.20 (op_c = op_d),
% 17.99/18.20 inference(transitivity,[status(thm)],[71, 68])).
% 17.99/18.20 tff(73,plain,
% 17.99/18.20 (mult(op_c, mult(op_c, ld(mult(mult(X0!1, op_d), op_c), op_c))) = mult(op_d, mult(op_c, ld(mult(mult(X0!1, op_d), op_c), op_c)))),
% 17.99/18.20 inference(monotonicity,[status(thm)],[72])).
% 17.99/18.20 tff(74,plain,
% 17.99/18.20 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(X0!1, op_d), mult(mult(X0!1, op_d), mult(op_c, ld(mult(mult(X0!1, op_d), op_c), op_c)))) = mult(op_c, ld(mult(mult(X0!1, op_d), op_c), op_c)))),
% 17.99/18.20 inference(quant_inst,[status(thm)],[])).
% 17.99/18.20 tff(75,plain,
% 17.99/18.20 (ld(mult(X0!1, op_d), mult(mult(X0!1, op_d), mult(op_c, ld(mult(mult(X0!1, op_d), op_c), op_c)))) = mult(op_c, ld(mult(mult(X0!1, op_d), op_c), op_c))),
% 17.99/18.20 inference(unit_resolution,[status(thm)],[74, 16])).
% 17.99/18.20 tff(76,plain,
% 17.99/18.20 ((~![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))) | (op_f = mult(mult(X0!1, op_d), mult(X1!0, ld(mult(mult(X0!1, op_d), X1!0), op_c))))),
% 17.99/18.20 inference(quant_inst,[status(thm)],[])).
% 17.99/18.20 tff(77,plain,
% 17.99/18.20 (op_f = mult(mult(X0!1, op_d), mult(X1!0, ld(mult(mult(X0!1, op_d), X1!0), op_c)))),
% 17.99/18.20 inference(unit_resolution,[status(thm)],[76, 27])).
% 17.99/18.20 tff(78,plain,
% 17.99/18.20 ((~![B: $i, A: $i] : (op_f = mult(A, mult(B, ld(mult(A, B), op_c))))) | (op_f = mult(mult(X0!1, op_d), mult(op_c, ld(mult(mult(X0!1, op_d), op_c), op_c))))),
% 17.99/18.20 inference(quant_inst,[status(thm)],[])).
% 17.99/18.20 tff(79,plain,
% 17.99/18.20 (op_f = mult(mult(X0!1, op_d), mult(op_c, ld(mult(mult(X0!1, op_d), op_c), op_c)))),
% 17.99/18.20 inference(unit_resolution,[status(thm)],[78, 27])).
% 17.99/18.20 tff(80,plain,
% 17.99/18.20 (mult(mult(X0!1, op_d), mult(op_c, ld(mult(mult(X0!1, op_d), op_c), op_c))) = op_f),
% 17.99/18.20 inference(symmetry,[status(thm)],[79])).
% 17.99/18.20 tff(81,plain,
% 17.99/18.20 (mult(mult(X0!1, op_d), mult(op_c, ld(mult(mult(X0!1, op_d), op_c), op_c))) = mult(mult(X0!1, op_d), mult(X1!0, ld(mult(mult(X0!1, op_d), X1!0), op_c)))),
% 17.99/18.20 inference(transitivity,[status(thm)],[80, 77])).
% 17.99/18.20 tff(82,plain,
% 17.99/18.20 (ld(mult(X0!1, op_d), mult(mult(X0!1, op_d), mult(op_c, ld(mult(mult(X0!1, op_d), op_c), op_c)))) = ld(mult(X0!1, op_d), mult(mult(X0!1, op_d), mult(X1!0, ld(mult(mult(X0!1, op_d), X1!0), op_c))))),
% 17.99/18.20 inference(monotonicity,[status(thm)],[81])).
% 17.99/18.20 tff(83,plain,
% 17.99/18.20 (ld(mult(X0!1, op_d), mult(mult(X0!1, op_d), mult(X1!0, ld(mult(mult(X0!1, op_d), X1!0), op_c)))) = ld(mult(X0!1, op_d), mult(mult(X0!1, op_d), mult(op_c, ld(mult(mult(X0!1, op_d), op_c), op_c))))),
% 17.99/18.20 inference(symmetry,[status(thm)],[82])).
% 17.99/18.20 tff(84,plain,
% 17.99/18.20 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(X0!1, op_d), mult(mult(X0!1, op_d), mult(X1!0, ld(mult(mult(X0!1, op_d), X1!0), op_c)))) = mult(X1!0, ld(mult(mult(X0!1, op_d), X1!0), op_c)))),
% 17.99/18.20 inference(quant_inst,[status(thm)],[])).
% 17.99/18.20 tff(85,plain,
% 17.99/18.20 (ld(mult(X0!1, op_d), mult(mult(X0!1, op_d), mult(X1!0, ld(mult(mult(X0!1, op_d), X1!0), op_c)))) = mult(X1!0, ld(mult(mult(X0!1, op_d), X1!0), op_c))),
% 17.99/18.20 inference(unit_resolution,[status(thm)],[84, 16])).
% 17.99/18.20 tff(86,plain,
% 17.99/18.20 (mult(X1!0, ld(mult(mult(X0!1, op_d), X1!0), op_c)) = ld(mult(X0!1, op_d), mult(mult(X0!1, op_d), mult(X1!0, ld(mult(mult(X0!1, op_d), X1!0), op_c))))),
% 17.99/18.20 inference(symmetry,[status(thm)],[85])).
% 17.99/18.20 tff(87,plain,
% 17.99/18.20 (mult(X1!0, ld(mult(mult(X0!1, op_d), X1!0), op_c)) = mult(op_c, ld(mult(mult(X0!1, op_d), op_c), op_c))),
% 17.99/18.20 inference(transitivity,[status(thm)],[86, 83, 75])).
% 17.99/18.20 tff(88,plain,
% 17.99/18.20 (mult(op_c, mult(X1!0, ld(mult(mult(X0!1, op_d), X1!0), op_c))) = mult(op_c, mult(op_c, ld(mult(mult(X0!1, op_d), op_c), op_c)))),
% 17.99/18.20 inference(monotonicity,[status(thm)],[87])).
% 17.99/18.20 tff(89,plain,
% 17.99/18.20 (^[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)))),
% 17.99/18.20 inference(bind,[status(th)],[])).
% 17.99/18.20 tff(90,plain,
% 17.99/18.20 (![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))),
% 17.99/18.20 inference(quant_intro,[status(thm)],[89])).
% 17.99/18.20 tff(91,plain,
% 17.99/18.20 (![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))),
% 17.99/18.20 inference(rewrite,[status(thm)],[])).
% 17.99/18.20 tff(92,axiom,(![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f08')).
% 17.99/18.21 tff(93,plain,
% 17.99/18.21 (![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))),
% 17.99/18.21 inference(modus_ponens,[status(thm)],[92, 91])).
% 17.99/18.21 tff(94,plain,(
% 17.99/18.21 ![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))),
% 17.99/18.21 inference(skolemize,[status(sab)],[93])).
% 17.99/18.21 tff(95,plain,
% 17.99/18.21 (![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))),
% 17.99/18.21 inference(modus_ponens,[status(thm)],[94, 90])).
% 17.99/18.21 tff(96,plain,
% 17.99/18.21 ((~![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))) | (mult(op_c, mult(X1!0, ld(mult(mult(X0!1, op_d), X1!0), op_c))) = mult(mult(op_c, X1!0), ld(mult(mult(X0!1, op_d), X1!0), op_c)))),
% 17.99/18.21 inference(quant_inst,[status(thm)],[])).
% 17.99/18.21 tff(97,plain,
% 17.99/18.21 (mult(op_c, mult(X1!0, ld(mult(mult(X0!1, op_d), X1!0), op_c))) = mult(mult(op_c, X1!0), ld(mult(mult(X0!1, op_d), X1!0), op_c))),
% 17.99/18.21 inference(unit_resolution,[status(thm)],[96, 95])).
% 17.99/18.21 tff(98,plain,
% 17.99/18.21 (mult(mult(op_c, X1!0), ld(mult(mult(X0!1, op_d), X1!0), op_c)) = mult(op_c, mult(X1!0, ld(mult(mult(X0!1, op_d), X1!0), op_c)))),
% 17.99/18.21 inference(symmetry,[status(thm)],[97])).
% 17.99/18.21 tff(99,plain,
% 17.99/18.21 (mult(mult(op_c, X1!0), ld(mult(mult(X0!1, op_d), X1!0), op_c)) = mult(mult(op_d, X1!0), ld(mult(X0!1, mult(op_d, X1!0)), op_c))),
% 17.99/18.21 inference(transitivity,[status(thm)],[98, 88, 73, 58, 49, 37, 34, 20])).
% 17.99/18.21 tff(100,plain,
% 17.99/18.21 (mult(op_c, X1!0) = mult(op_d, X1!0)),
% 17.99/18.21 inference(monotonicity,[status(thm)],[72])).
% 17.99/18.21 tff(101,plain,
% 17.99/18.21 (ld(mult(op_c, X1!0), mult(mult(op_c, X1!0), ld(mult(mult(X0!1, op_d), X1!0), op_c))) = ld(mult(op_d, X1!0), mult(mult(op_d, X1!0), ld(mult(X0!1, mult(op_d, X1!0)), op_c)))),
% 17.99/18.21 inference(monotonicity,[status(thm)],[100, 99])).
% 17.99/18.21 tff(102,plain,
% 17.99/18.21 (ld(mult(op_d, X1!0), mult(mult(op_d, X1!0), ld(mult(X0!1, mult(op_d, X1!0)), op_c))) = ld(mult(op_c, X1!0), mult(mult(op_c, X1!0), ld(mult(mult(X0!1, op_d), X1!0), op_c)))),
% 17.99/18.21 inference(symmetry,[status(thm)],[101])).
% 17.99/18.21 tff(103,plain,
% 17.99/18.21 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(op_d, X1!0), mult(mult(op_d, X1!0), ld(mult(X0!1, mult(op_d, X1!0)), op_c))) = ld(mult(X0!1, mult(op_d, X1!0)), op_c))),
% 17.99/18.21 inference(quant_inst,[status(thm)],[])).
% 17.99/18.21 tff(104,plain,
% 17.99/18.21 (ld(mult(op_d, X1!0), mult(mult(op_d, X1!0), ld(mult(X0!1, mult(op_d, X1!0)), op_c))) = ld(mult(X0!1, mult(op_d, X1!0)), op_c)),
% 17.99/18.21 inference(unit_resolution,[status(thm)],[103, 16])).
% 17.99/18.21 tff(105,plain,
% 17.99/18.21 (ld(mult(X0!1, mult(op_d, X1!0)), op_c) = ld(mult(op_d, X1!0), mult(mult(op_d, X1!0), ld(mult(X0!1, mult(op_d, X1!0)), op_c)))),
% 17.99/18.21 inference(symmetry,[status(thm)],[104])).
% 17.99/18.21 tff(106,plain,
% 17.99/18.21 (ld(mult(X0!1, mult(op_d, X1!0)), op_c) = ld(mult(mult(X0!1, op_d), X1!0), op_c)),
% 17.99/18.21 inference(transitivity,[status(thm)],[105, 102, 18])).
% 17.99/18.21 tff(107,plain,
% 17.99/18.21 (^[B: $i, A: $i] : refl((mult(A, ld(A, B)) = B) <=> (mult(A, ld(A, B)) = B))),
% 17.99/18.21 inference(bind,[status(th)],[])).
% 17.99/18.21 tff(108,plain,
% 17.99/18.21 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B) <=> ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 17.99/18.21 inference(quant_intro,[status(thm)],[107])).
% 17.99/18.21 tff(109,plain,
% 17.99/18.21 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B) <=> ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 17.99/18.21 inference(rewrite,[status(thm)],[])).
% 17.99/18.21 tff(110,axiom,(![B: $i, A: $i] : (mult(A, ld(A, B)) = B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f01')).
% 17.99/18.21 tff(111,plain,
% 17.99/18.21 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 17.99/18.21 inference(modus_ponens,[status(thm)],[110, 109])).
% 17.99/18.21 tff(112,plain,(
% 17.99/18.21 ![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 17.99/18.21 inference(skolemize,[status(sab)],[111])).
% 17.99/18.21 tff(113,plain,
% 17.99/18.21 (![B: $i, A: $i] : (mult(A, ld(A, B)) = B)),
% 17.99/18.21 inference(modus_ponens,[status(thm)],[112, 108])).
% 17.99/18.21 tff(114,plain,
% 17.99/18.21 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(mult(mult(X0!1, op_d), X1!0), ld(mult(mult(X0!1, op_d), X1!0), op_c)) = op_c)),
% 17.99/18.21 inference(quant_inst,[status(thm)],[])).
% 17.99/18.21 tff(115,plain,
% 17.99/18.21 (mult(mult(mult(X0!1, op_d), X1!0), ld(mult(mult(X0!1, op_d), X1!0), op_c)) = op_c),
% 17.99/18.21 inference(unit_resolution,[status(thm)],[114, 113])).
% 17.99/18.21 tff(116,plain,
% 17.99/18.21 (op_c = mult(mult(mult(X0!1, op_d), X1!0), ld(mult(mult(X0!1, op_d), X1!0), op_c))),
% 17.99/18.21 inference(symmetry,[status(thm)],[115])).
% 17.99/18.21 tff(117,plain,
% 17.99/18.21 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(mult(X0!1, mult(op_d, X1!0)), ld(mult(X0!1, mult(op_d, X1!0)), op_c)) = op_c)),
% 17.99/18.21 inference(quant_inst,[status(thm)],[])).
% 17.99/18.21 tff(118,plain,
% 17.99/18.21 (mult(mult(X0!1, mult(op_d, X1!0)), ld(mult(X0!1, mult(op_d, X1!0)), op_c)) = op_c),
% 17.99/18.21 inference(unit_resolution,[status(thm)],[117, 113])).
% 17.99/18.21 tff(119,plain,
% 17.99/18.21 (mult(mult(X0!1, mult(op_d, X1!0)), ld(mult(X0!1, mult(op_d, X1!0)), op_c)) = mult(mult(mult(X0!1, op_d), X1!0), ld(mult(mult(X0!1, op_d), X1!0), op_c))),
% 17.99/18.21 inference(transitivity,[status(thm)],[118, 116])).
% 17.99/18.21 tff(120,plain,
% 17.99/18.21 (rd(mult(mult(X0!1, mult(op_d, X1!0)), ld(mult(X0!1, mult(op_d, X1!0)), op_c)), ld(mult(X0!1, mult(op_d, X1!0)), op_c)) = rd(mult(mult(mult(X0!1, op_d), X1!0), ld(mult(mult(X0!1, op_d), X1!0), op_c)), ld(mult(mult(X0!1, op_d), X1!0), op_c))),
% 17.99/18.21 inference(monotonicity,[status(thm)],[119, 106])).
% 17.99/18.21 tff(121,plain,
% 17.99/18.21 ((~![B: $i, A: $i] : (rd(mult(A, B), B) = A)) | (rd(mult(mult(X0!1, mult(op_d, X1!0)), ld(mult(X0!1, mult(op_d, X1!0)), op_c)), ld(mult(X0!1, mult(op_d, X1!0)), op_c)) = mult(X0!1, mult(op_d, X1!0)))),
% 17.99/18.21 inference(quant_inst,[status(thm)],[])).
% 17.99/18.21 tff(122,plain,
% 17.99/18.21 (rd(mult(mult(X0!1, mult(op_d, X1!0)), ld(mult(X0!1, mult(op_d, X1!0)), op_c)), ld(mult(X0!1, mult(op_d, X1!0)), op_c)) = mult(X0!1, mult(op_d, X1!0))),
% 17.99/18.21 inference(unit_resolution,[status(thm)],[121, 7])).
% 17.99/18.21 tff(123,plain,
% 17.99/18.21 (mult(X0!1, mult(op_d, X1!0)) = rd(mult(mult(X0!1, mult(op_d, X1!0)), ld(mult(X0!1, mult(op_d, X1!0)), op_c)), ld(mult(X0!1, mult(op_d, X1!0)), op_c))),
% 17.99/18.21 inference(symmetry,[status(thm)],[122])).
% 17.99/18.21 tff(124,plain,
% 17.99/18.21 (mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0)),
% 17.99/18.21 inference(transitivity,[status(thm)],[123, 120, 9])).
% 17.99/18.21 tff(125,assumption,(~(mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0))), introduced(assumption)).
% 17.99/18.21 tff(126,plain,
% 17.99/18.21 ($false),
% 17.99/18.21 inference(unit_resolution,[status(thm)],[125, 124])).
% 17.99/18.21 tff(127,plain,(mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0)), inference(lemma,lemma(discharge,[]))).
% 17.99/18.21 tff(128,plain,
% 17.99/18.21 (op_d = op_c),
% 17.99/18.21 inference(transitivity,[status(thm)],[67, 70])).
% 17.99/18.21 tff(129,plain,
% 17.99/18.21 (mult(mult(X0!1, X1!0), op_d) = mult(mult(X0!1, X1!0), op_c)),
% 17.99/18.21 inference(monotonicity,[status(thm)],[128])).
% 17.99/18.21 tff(130,plain,
% 17.99/18.21 (mult(mult(X0!1, X1!0), op_c) = mult(mult(X0!1, X1!0), op_d)),
% 17.99/18.21 inference(symmetry,[status(thm)],[129])).
% 17.99/18.21 tff(131,plain,
% 17.99/18.21 ((~![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))) | (mult(X0!1, mult(X1!0, op_c)) = mult(mult(X0!1, X1!0), op_c))),
% 17.99/18.21 inference(quant_inst,[status(thm)],[])).
% 17.99/18.21 tff(132,plain,
% 17.99/18.21 (mult(X0!1, mult(X1!0, op_c)) = mult(mult(X0!1, X1!0), op_c)),
% 17.99/18.21 inference(unit_resolution,[status(thm)],[131, 44])).
% 17.99/18.21 tff(133,plain,
% 17.99/18.21 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(op_c, X0!1), mult(mult(op_c, X0!1), mult(op_d, X1!0))) = mult(op_d, X1!0))),
% 17.99/18.21 inference(quant_inst,[status(thm)],[])).
% 17.99/18.21 tff(134,plain,
% 17.99/18.21 (ld(mult(op_c, X0!1), mult(mult(op_c, X0!1), mult(op_d, X1!0))) = mult(op_d, X1!0)),
% 17.99/18.21 inference(unit_resolution,[status(thm)],[133, 16])).
% 17.99/18.21 tff(135,plain,
% 17.99/18.21 ((~![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))) | (mult(op_c, mult(X0!1, mult(op_d, X1!0))) = mult(mult(op_c, X0!1), mult(op_d, X1!0)))),
% 17.99/18.21 inference(quant_inst,[status(thm)],[])).
% 17.99/18.21 tff(136,plain,
% 17.99/18.21 (mult(op_c, mult(X0!1, mult(op_d, X1!0))) = mult(mult(op_c, X0!1), mult(op_d, X1!0))),
% 17.99/18.21 inference(unit_resolution,[status(thm)],[135, 95])).
% 17.99/18.21 tff(137,plain,
% 17.99/18.21 (mult(op_c, mult(X0!1, mult(op_d, X1!0))) = mult(op_c, mult(mult(X0!1, op_d), X1!0))),
% 17.99/18.21 inference(monotonicity,[status(thm)],[127])).
% 17.99/18.21 tff(138,plain,
% 17.99/18.21 (mult(op_c, mult(mult(X0!1, op_d), X1!0)) = mult(op_c, mult(X0!1, mult(op_d, X1!0)))),
% 17.99/18.21 inference(symmetry,[status(thm)],[137])).
% 17.99/18.21 tff(139,plain,
% 17.99/18.21 ((~![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))) | (mult(op_c, mult(mult(X0!1, op_d), X1!0)) = mult(mult(op_c, mult(X0!1, op_d)), X1!0))),
% 17.99/18.21 inference(quant_inst,[status(thm)],[])).
% 17.99/18.21 tff(140,plain,
% 17.99/18.21 (mult(op_c, mult(mult(X0!1, op_d), X1!0)) = mult(mult(op_c, mult(X0!1, op_d)), X1!0)),
% 17.99/18.21 inference(unit_resolution,[status(thm)],[139, 95])).
% 17.99/18.21 tff(141,plain,
% 17.99/18.21 (mult(mult(op_c, mult(X0!1, op_d)), X1!0) = mult(op_c, mult(mult(X0!1, op_d), X1!0))),
% 17.99/18.21 inference(symmetry,[status(thm)],[140])).
% 17.99/18.21 tff(142,plain,
% 17.99/18.21 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(mult(mult(X0!1, op_d), X1!0), ld(mult(mult(X0!1, op_d), X1!0), mult(mult(op_c, mult(X0!1, op_d)), X1!0))) = mult(mult(op_c, mult(X0!1, op_d)), X1!0))),
% 17.99/18.21 inference(quant_inst,[status(thm)],[])).
% 17.99/18.21 tff(143,plain,
% 17.99/18.21 (mult(mult(mult(X0!1, op_d), X1!0), ld(mult(mult(X0!1, op_d), X1!0), mult(mult(op_c, mult(X0!1, op_d)), X1!0))) = mult(mult(op_c, mult(X0!1, op_d)), X1!0)),
% 17.99/18.21 inference(unit_resolution,[status(thm)],[142, 113])).
% 17.99/18.21 tff(144,plain,
% 17.99/18.21 (ld(mult(mult(X0!1, op_d), X1!0), mult(mult(op_c, mult(X0!1, op_d)), X1!0)) = ld(mult(mult(X0!1, op_d), X1!0), mult(op_c, mult(mult(X0!1, op_d), X1!0)))),
% 17.99/18.21 inference(monotonicity,[status(thm)],[141])).
% 17.99/18.21 tff(145,plain,
% 17.99/18.21 (ld(mult(mult(X0!1, op_d), X1!0), mult(op_c, mult(mult(X0!1, op_d), X1!0))) = ld(mult(mult(X0!1, op_d), X1!0), mult(mult(op_c, mult(X0!1, op_d)), X1!0))),
% 17.99/18.21 inference(symmetry,[status(thm)],[144])).
% 17.99/18.21 tff(146,plain,
% 17.99/18.21 ((~![A: $i] : (op_d = ld(A, mult(op_c, A)))) | (op_d = ld(mult(mult(X0!1, op_d), X1!0), mult(op_c, mult(mult(X0!1, op_d), X1!0))))),
% 17.99/18.21 inference(quant_inst,[status(thm)],[])).
% 17.99/18.21 tff(147,plain,
% 17.99/18.21 (op_d = ld(mult(mult(X0!1, op_d), X1!0), mult(op_c, mult(mult(X0!1, op_d), X1!0)))),
% 17.99/18.21 inference(unit_resolution,[status(thm)],[146, 65])).
% 17.99/18.21 tff(148,plain,
% 17.99/18.21 (op_c = ld(mult(mult(X0!1, op_d), X1!0), mult(mult(op_c, mult(X0!1, op_d)), X1!0))),
% 17.99/18.21 inference(transitivity,[status(thm)],[71, 68, 147, 145])).
% 17.99/18.21 tff(149,plain,
% 17.99/18.21 (mult(mult(mult(X0!1, op_d), X1!0), op_c) = mult(mult(mult(X0!1, op_d), X1!0), ld(mult(mult(X0!1, op_d), X1!0), mult(mult(op_c, mult(X0!1, op_d)), X1!0)))),
% 17.99/18.21 inference(monotonicity,[status(thm)],[148])).
% 17.99/18.21 tff(150,plain,
% 17.99/18.21 ((~![B: $i, A: $i] : (mult(A, mult(B, op_c)) = mult(mult(A, B), op_c))) | (mult(mult(X0!1, op_d), mult(X1!0, op_c)) = mult(mult(mult(X0!1, op_d), X1!0), op_c))),
% 17.99/18.21 inference(quant_inst,[status(thm)],[])).
% 17.99/18.21 tff(151,plain,
% 17.99/18.21 (mult(mult(X0!1, op_d), mult(X1!0, op_c)) = mult(mult(mult(X0!1, op_d), X1!0), op_c)),
% 17.99/18.21 inference(unit_resolution,[status(thm)],[150, 44])).
% 17.99/18.21 tff(152,plain,
% 17.99/18.21 (mult(mult(X0!1, op_d), mult(X1!0, op_c)) = mult(mult(op_c, X0!1), mult(op_d, X1!0))),
% 17.99/18.21 inference(transitivity,[status(thm)],[151, 149, 143, 141, 138, 136])).
% 17.99/18.21 tff(153,plain,
% 17.99/18.21 ((~![B: $i, A: $i] : (mult(A, ld(A, B)) = B)) | (mult(X0!1, ld(X0!1, mult(op_c, X0!1))) = mult(op_c, X0!1))),
% 17.99/18.21 inference(quant_inst,[status(thm)],[])).
% 17.99/18.21 tff(154,plain,
% 17.99/18.21 (mult(X0!1, ld(X0!1, mult(op_c, X0!1))) = mult(op_c, X0!1)),
% 17.99/18.21 inference(unit_resolution,[status(thm)],[153, 113])).
% 17.99/18.21 tff(155,plain,
% 17.99/18.21 ((~![A: $i] : (op_d = ld(A, mult(op_c, A)))) | (op_d = ld(X0!1, mult(op_c, X0!1)))),
% 17.99/18.21 inference(quant_inst,[status(thm)],[])).
% 17.99/18.21 tff(156,plain,
% 17.99/18.21 (op_d = ld(X0!1, mult(op_c, X0!1))),
% 17.99/18.21 inference(unit_resolution,[status(thm)],[155, 65])).
% 17.99/18.21 tff(157,plain,
% 17.99/18.21 (ld(X0!1, mult(op_c, X0!1)) = op_d),
% 17.99/18.21 inference(symmetry,[status(thm)],[156])).
% 17.99/18.21 tff(158,plain,
% 17.99/18.21 (mult(X0!1, ld(X0!1, mult(op_c, X0!1))) = mult(X0!1, op_d)),
% 17.99/18.21 inference(monotonicity,[status(thm)],[157])).
% 17.99/18.21 tff(159,plain,
% 17.99/18.21 (mult(X0!1, op_d) = mult(X0!1, ld(X0!1, mult(op_c, X0!1)))),
% 17.99/18.21 inference(symmetry,[status(thm)],[158])).
% 17.99/18.21 tff(160,plain,
% 17.99/18.21 (mult(X0!1, op_d) = mult(op_c, X0!1)),
% 17.99/18.21 inference(transitivity,[status(thm)],[159, 154])).
% 17.99/18.21 tff(161,plain,
% 17.99/18.21 (ld(mult(X0!1, op_d), mult(mult(X0!1, op_d), mult(X1!0, op_c))) = ld(mult(op_c, X0!1), mult(mult(op_c, X0!1), mult(op_d, X1!0)))),
% 17.99/18.21 inference(monotonicity,[status(thm)],[160, 152])).
% 17.99/18.21 tff(162,plain,
% 17.99/18.21 ((~![B: $i, A: $i] : (ld(A, mult(A, B)) = B)) | (ld(mult(X0!1, op_d), mult(mult(X0!1, op_d), mult(X1!0, op_c))) = mult(X1!0, op_c))),
% 17.99/18.21 inference(quant_inst,[status(thm)],[])).
% 17.99/18.21 tff(163,plain,
% 17.99/18.21 (ld(mult(X0!1, op_d), mult(mult(X0!1, op_d), mult(X1!0, op_c))) = mult(X1!0, op_c)),
% 17.99/18.21 inference(unit_resolution,[status(thm)],[162, 16])).
% 17.99/18.21 tff(164,plain,
% 17.99/18.21 (mult(X1!0, op_c) = ld(mult(X0!1, op_d), mult(mult(X0!1, op_d), mult(X1!0, op_c)))),
% 17.99/18.21 inference(symmetry,[status(thm)],[163])).
% 17.99/18.21 tff(165,plain,
% 17.99/18.21 (mult(X1!0, op_c) = mult(op_d, X1!0)),
% 17.99/18.21 inference(transitivity,[status(thm)],[164, 161, 134])).
% 17.99/18.21 tff(166,plain,
% 17.99/18.21 (mult(X0!1, mult(X1!0, op_c)) = mult(X0!1, mult(op_d, X1!0))),
% 17.99/18.21 inference(monotonicity,[status(thm)],[165])).
% 17.99/18.21 tff(167,plain,
% 17.99/18.21 (mult(X0!1, mult(op_d, X1!0)) = mult(X0!1, mult(X1!0, op_c))),
% 17.99/18.21 inference(symmetry,[status(thm)],[166])).
% 17.99/18.21 tff(168,plain,
% 17.99/18.21 (mult(X1!0, op_d) = mult(X1!0, op_c)),
% 17.99/18.21 inference(monotonicity,[status(thm)],[128])).
% 17.99/18.21 tff(169,plain,
% 17.99/18.21 (mult(X1!0, op_d) = mult(op_d, X1!0)),
% 17.99/18.21 inference(transitivity,[status(thm)],[168, 164, 161, 134])).
% 17.99/18.21 tff(170,plain,
% 17.99/18.21 (mult(X0!1, mult(X1!0, op_d)) = mult(X0!1, mult(op_d, X1!0))),
% 17.99/18.21 inference(monotonicity,[status(thm)],[169])).
% 17.99/18.21 tff(171,plain,
% 17.99/18.21 (mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d)),
% 17.99/18.21 inference(transitivity,[status(thm)],[170, 167, 132, 130])).
% 17.99/18.21 tff(172,plain,
% 17.99/18.21 (mult(op_c, X0!1) = mult(X0!1, ld(X0!1, mult(op_c, X0!1)))),
% 17.99/18.21 inference(symmetry,[status(thm)],[154])).
% 17.99/18.21 tff(173,plain,
% 17.99/18.21 (mult(op_d, X0!1) = mult(op_c, X0!1)),
% 17.99/18.21 inference(monotonicity,[status(thm)],[128])).
% 17.99/18.21 tff(174,plain,
% 17.99/18.21 (mult(op_d, X0!1) = mult(X0!1, op_d)),
% 17.99/18.21 inference(transitivity,[status(thm)],[173, 172, 158])).
% 17.99/18.21 tff(175,plain,
% 17.99/18.21 (mult(mult(op_d, X0!1), X1!0) = mult(mult(X0!1, op_d), X1!0)),
% 17.99/18.21 inference(monotonicity,[status(thm)],[174])).
% 17.99/18.21 tff(176,plain,
% 17.99/18.21 (mult(mult(X0!1, op_d), X1!0) = mult(mult(op_d, X0!1), X1!0)),
% 17.99/18.21 inference(symmetry,[status(thm)],[175])).
% 17.99/18.21 tff(177,plain,
% 17.99/18.21 (mult(op_c, X0!1) = mult(X0!1, op_d)),
% 17.99/18.21 inference(transitivity,[status(thm)],[172, 158])).
% 17.99/18.21 tff(178,plain,
% 17.99/18.21 (mult(mult(op_c, X0!1), X1!0) = mult(mult(X0!1, op_d), X1!0)),
% 17.99/18.21 inference(monotonicity,[status(thm)],[177])).
% 17.99/18.21 tff(179,plain,
% 17.99/18.21 ((~![B: $i, A: $i] : (mult(op_c, mult(A, B)) = mult(mult(op_c, A), B))) | (mult(op_c, mult(X0!1, X1!0)) = mult(mult(op_c, X0!1), X1!0))),
% 17.99/18.21 inference(quant_inst,[status(thm)],[])).
% 17.99/18.21 tff(180,plain,
% 17.99/18.21 (mult(op_c, mult(X0!1, X1!0)) = mult(mult(op_c, X0!1), X1!0)),
% 17.99/18.21 inference(unit_resolution,[status(thm)],[179, 95])).
% 17.99/18.21 tff(181,plain,
% 17.99/18.21 (mult(op_d, mult(X0!1, X1!0)) = mult(op_c, mult(X0!1, X1!0))),
% 17.99/18.21 inference(monotonicity,[status(thm)],[128])).
% 17.99/18.21 tff(182,plain,
% 17.99/18.21 (mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0)),
% 17.99/18.21 inference(transitivity,[status(thm)],[181, 180, 178, 176])).
% 17.99/18.21 tff(183,plain,
% 17.99/18.21 ((~(~((~(mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0))) | (~(mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d))) | (~(mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0)))))) <=> ((~(mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0))) | (~(mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d))) | (~(mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0))))),
% 17.99/18.21 inference(rewrite,[status(thm)],[])).
% 17.99/18.21 tff(184,plain,
% 17.99/18.21 (((mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0)) & (mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d)) & (mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0))) <=> (~((~(mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0))) | (~(mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d))) | (~(mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0)))))),
% 17.99/18.21 inference(rewrite,[status(thm)],[])).
% 17.99/18.21 tff(185,plain,
% 17.99/18.21 ((~((mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0)) & (mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d)) & (mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0)))) <=> (~(~((~(mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0))) | (~(mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d))) | (~(mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0))))))),
% 17.99/18.21 inference(monotonicity,[status(thm)],[184])).
% 17.99/18.21 tff(186,plain,
% 17.99/18.21 ((~((mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0)) & (mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d)) & (mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0)))) <=> ((~(mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0))) | (~(mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d))) | (~(mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0))))),
% 18.07/18.22 inference(transitivity,[status(thm)],[185, 183])).
% 18.07/18.22 tff(187,plain,
% 18.07/18.22 ((~![X0: $i, X1: $i] : ((mult(op_d, mult(X0, X1)) = mult(mult(op_d, X0), X1)) & (mult(X0, mult(X1, op_d)) = mult(mult(X0, X1), op_d)) & (mult(X0, mult(op_d, X1)) = mult(mult(X0, op_d), X1)))) <=> (~![X0: $i, X1: $i] : ((mult(op_d, mult(X0, X1)) = mult(mult(op_d, X0), X1)) & (mult(X0, mult(X1, op_d)) = mult(mult(X0, X1), op_d)) & (mult(X0, mult(op_d, X1)) = mult(mult(X0, op_d), X1))))),
% 18.07/18.22 inference(rewrite,[status(thm)],[])).
% 18.07/18.22 tff(188,plain,
% 18.07/18.22 ((~![X0: $i, X1: $i] : (((mult(op_d, mult(X0, X1)) = mult(mult(op_d, X0), X1)) & (mult(X0, mult(X1, op_d)) = mult(mult(X0, X1), op_d))) & (mult(X0, mult(op_d, X1)) = mult(mult(X0, op_d), X1)))) <=> (~![X0: $i, X1: $i] : ((mult(op_d, mult(X0, X1)) = mult(mult(op_d, X0), X1)) & (mult(X0, mult(X1, op_d)) = mult(mult(X0, X1), op_d)) & (mult(X0, mult(op_d, X1)) = mult(mult(X0, op_d), X1))))),
% 18.07/18.22 inference(rewrite,[status(thm)],[])).
% 18.07/18.22 tff(189,axiom,(~![X0: $i, X1: $i] : (((mult(op_d, mult(X0, X1)) = mult(mult(op_d, X0), X1)) & (mult(X0, mult(X1, op_d)) = mult(mult(X0, X1), op_d))) & (mult(X0, mult(op_d, X1)) = mult(mult(X0, op_d), X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 18.07/18.22 tff(190,plain,
% 18.07/18.22 (~![X0: $i, X1: $i] : ((mult(op_d, mult(X0, X1)) = mult(mult(op_d, X0), X1)) & (mult(X0, mult(X1, op_d)) = mult(mult(X0, X1), op_d)) & (mult(X0, mult(op_d, X1)) = mult(mult(X0, op_d), X1)))),
% 18.07/18.22 inference(modus_ponens,[status(thm)],[189, 188])).
% 18.07/18.22 tff(191,plain,
% 18.07/18.22 (~![X0: $i, X1: $i] : ((mult(op_d, mult(X0, X1)) = mult(mult(op_d, X0), X1)) & (mult(X0, mult(X1, op_d)) = mult(mult(X0, X1), op_d)) & (mult(X0, mult(op_d, X1)) = mult(mult(X0, op_d), X1)))),
% 18.07/18.22 inference(modus_ponens,[status(thm)],[190, 187])).
% 18.07/18.22 tff(192,plain,
% 18.07/18.22 (~![X0: $i, X1: $i] : ((mult(op_d, mult(X0, X1)) = mult(mult(op_d, X0), X1)) & (mult(X0, mult(X1, op_d)) = mult(mult(X0, X1), op_d)) & (mult(X0, mult(op_d, X1)) = mult(mult(X0, op_d), X1)))),
% 18.07/18.22 inference(modus_ponens,[status(thm)],[191, 187])).
% 18.07/18.22 tff(193,plain,
% 18.07/18.22 (~![X0: $i, X1: $i] : ((mult(op_d, mult(X0, X1)) = mult(mult(op_d, X0), X1)) & (mult(X0, mult(X1, op_d)) = mult(mult(X0, X1), op_d)) & (mult(X0, mult(op_d, X1)) = mult(mult(X0, op_d), X1)))),
% 18.07/18.22 inference(modus_ponens,[status(thm)],[192, 187])).
% 18.07/18.22 tff(194,plain,(
% 18.07/18.22 ~((mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0)) & (mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d)) & (mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0)))),
% 18.07/18.22 inference(skolemize,[status(sab)],[193])).
% 18.07/18.22 tff(195,plain,
% 18.07/18.22 ((~(mult(op_d, mult(X0!1, X1!0)) = mult(mult(op_d, X0!1), X1!0))) | (~(mult(X0!1, mult(X1!0, op_d)) = mult(mult(X0!1, X1!0), op_d))) | (~(mult(X0!1, mult(op_d, X1!0)) = mult(mult(X0!1, op_d), X1!0)))),
% 18.07/18.22 inference(modus_ponens,[status(thm)],[194, 186])).
% 18.07/18.22 tff(196,plain,
% 18.07/18.22 ($false),
% 18.07/18.22 inference(unit_resolution,[status(thm)],[195, 182, 171, 127])).
% 18.07/18.22 % SZS output end Proof
% 18.07/18.22 % E exiting
%------------------------------------------------------------------------------