%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG003-1 : TPTP v9.0.0. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 04:57:45 AM UTC 2025
% Result : Unsatisfiable 1.82s 2.05s
% Output : Proof 1.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG003-1 : TPTP v9.0.0. Bugfixed v2.5.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 10:41:54 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.82/2.05 % SZS status Unsatisfiable
% 1.82/2.05 % SZS output start Proof
% 1.82/2.05 tff(multiply_type, type, (
% 1.82/2.05 multiply: ( $i * $i ) > $i)).
% 1.82/2.05 tff(f_type, type, (
% 1.82/2.05 f: $i)).
% 1.82/2.05 tff(e_type, type, (
% 1.82/2.05 e: $i)).
% 1.82/2.05 tff(d_type, type, (
% 1.82/2.05 d: $i)).
% 1.82/2.05 tff(c_type, type, (
% 1.82/2.05 c: $i)).
% 1.82/2.05 tff(b_type, type, (
% 1.82/2.05 b: $i)).
% 1.82/2.05 tff(a_type, type, (
% 1.82/2.05 a: $i)).
% 1.82/2.05 tff(inj_1_type, type, (
% 1.82/2.05 inj_1: ( $i * $i ) > $i)).
% 1.82/2.05 tff(an_element_type, type, (
% 1.82/2.05 an_element: $i)).
% 1.82/2.05 tff(1,plain,
% 1.82/2.05 (^[Z: $i, Y: $i, U: $i, X: $i] : refl((multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U))) <=> (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U))))),
% 1.82/2.05 inference(bind,[status(th)],[])).
% 1.82/2.05 tff(2,plain,
% 1.82/2.05 (![Z: $i, Y: $i, U: $i, X: $i] : (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U))) <=> ![Z: $i, Y: $i, U: $i, X: $i] : (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U)))),
% 1.82/2.05 inference(quant_intro,[status(thm)],[1])).
% 1.82/2.05 tff(3,plain,
% 1.82/2.05 (![Z: $i, Y: $i, U: $i, X: $i] : (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U))) <=> ![Z: $i, Y: $i, U: $i, X: $i] : (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U)))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(4,axiom,(![Z: $i, Y: $i, U: $i, X: $i] : (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','medial_law')).
% 1.82/2.05 tff(5,plain,
% 1.82/2.05 (![Z: $i, Y: $i, U: $i, X: $i] : (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U)))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.82/2.05 tff(6,plain,(
% 1.82/2.05 ![Z: $i, Y: $i, U: $i, X: $i] : (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U)))),
% 1.82/2.05 inference(skolemize,[status(sab)],[5])).
% 1.82/2.05 tff(7,plain,
% 1.82/2.05 (![Z: $i, Y: $i, U: $i, X: $i] : (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U)))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.82/2.05 tff(8,plain,
% 1.82/2.05 ((~![Z: $i, Y: $i, U: $i, X: $i] : (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U)))) | (multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)) = multiply(multiply(a, multiply(d, e)), multiply(multiply(b, c), f)))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(9,plain,
% 1.82/2.05 (multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)) = multiply(multiply(a, multiply(d, e)), multiply(multiply(b, c), f))),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.82/2.05 tff(10,plain,
% 1.82/2.05 (multiply(multiply(a, multiply(d, e)), multiply(multiply(b, c), f)) = multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f))),
% 1.82/2.05 inference(symmetry,[status(thm)],[9])).
% 1.82/2.05 tff(11,plain,
% 1.82/2.05 (![Y: $i, U: $i, X: $i] : ((~(multiply(X, Y) = multiply(X, U))) | (Y = U)) <=> ![Xk!0: $i, Xk!1: $i] : (inj_1(Xk!1, multiply(Xk!1, Xk!0)) = Xk!0)),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(12,plain,
% 1.82/2.05 (![Y: $i, U: $i, X: $i] : ((~(multiply(X, Y) = multiply(X, U))) | (Y = U)) <=> ![Y: $i, U: $i, X: $i] : ((~(multiply(X, Y) = multiply(X, U))) | (Y = U))),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(13,plain,
% 1.82/2.05 (![Z: $i, Y: $i, U: $i, X: $i] : ((~(multiply(X, Y) = multiply(X, U))) | (Y = U)) <=> ![Y: $i, U: $i, X: $i] : ((~(multiply(X, Y) = multiply(X, U))) | (Y = U))),
% 1.82/2.05 inference(elim_unused_vars,[status(thm)],[])).
% 1.82/2.05 tff(14,plain,
% 1.82/2.05 (![Z: $i, Y: $i, U: $i, X: $i] : ((~(multiply(X, Y) = Z)) | (Y = U) | (~(multiply(X, U) = Z))) <=> ![Z: $i, Y: $i, U: $i, X: $i] : ((~(multiply(X, Y) = multiply(X, U))) | (Y = U))),
% 1.82/2.05 inference(destructive_equality_resolution,[status(thm)],[])).
% 1.82/2.05 tff(15,plain,
% 1.82/2.05 (![Z: $i, Y: $i, U: $i, X: $i] : ((~(multiply(X, Y) = Z)) | (Y = U) | (~(multiply(X, U) = Z))) <=> ![Y: $i, U: $i, X: $i] : ((~(multiply(X, Y) = multiply(X, U))) | (Y = U))),
% 1.82/2.05 inference(transitivity,[status(thm)],[14, 13])).
% 1.82/2.05 tff(16,plain,
% 1.82/2.05 (^[Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(rewrite(((~(multiply(X, Y) = Z)) | (~(multiply(X, U) = Z))) <=> ((~(multiply(X, Y) = Z)) | (~(multiply(X, U) = Z)))), ((((~(multiply(X, Y) = Z)) | (~(multiply(X, U) = Z))) | (Y = U)) <=> (((~(multiply(X, Y) = Z)) | (~(multiply(X, U) = Z))) | (Y = U)))), rewrite((((~(multiply(X, Y) = Z)) | (~(multiply(X, U) = Z))) | (Y = U)) <=> ((~(multiply(X, Y) = Z)) | (Y = U) | (~(multiply(X, U) = Z)))), ((((~(multiply(X, Y) = Z)) | (~(multiply(X, U) = Z))) | (Y = U)) <=> ((~(multiply(X, Y) = Z)) | (Y = U) | (~(multiply(X, U) = Z)))))),
% 1.82/2.05 inference(bind,[status(th)],[])).
% 1.82/2.05 tff(17,plain,
% 1.82/2.05 (![Z: $i, Y: $i, U: $i, X: $i] : (((~(multiply(X, Y) = Z)) | (~(multiply(X, U) = Z))) | (Y = U)) <=> ![Z: $i, Y: $i, U: $i, X: $i] : ((~(multiply(X, Y) = Z)) | (Y = U) | (~(multiply(X, U) = Z)))),
% 1.82/2.05 inference(quant_intro,[status(thm)],[16])).
% 1.82/2.05 tff(18,plain,
% 1.82/2.05 (![Z: $i, Y: $i, U: $i, X: $i] : (((~(multiply(X, Y) = Z)) | (~(multiply(X, U) = Z))) | (Y = U)) <=> ![Y: $i, U: $i, X: $i] : ((~(multiply(X, Y) = multiply(X, U))) | (Y = U))),
% 1.82/2.05 inference(transitivity,[status(thm)],[17, 15])).
% 1.82/2.05 tff(19,axiom,(![Z: $i, Y: $i, U: $i, X: $i] : (((~(multiply(X, Y) = Z)) | (~(multiply(X, U) = Z))) | (Y = U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','right_cancellation')).
% 1.82/2.05 tff(20,plain,
% 1.82/2.05 (![Y: $i, U: $i, X: $i] : ((~(multiply(X, Y) = multiply(X, U))) | (Y = U))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[19, 18])).
% 1.82/2.05 tff(21,plain,
% 1.82/2.05 (![Y: $i, U: $i, X: $i] : ((~(multiply(X, Y) = multiply(X, U))) | (Y = U))),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[20, 12])).
% 1.82/2.05 tff(22,plain,(
% 1.82/2.05 ![Y: $i, U: $i, X: $i] : ((~(multiply(X, Y) = multiply(X, U))) | (Y = U))),
% 1.82/2.05 inference(skolemize,[status(sab)],[21])).
% 1.82/2.05 tff(23,plain,
% 1.82/2.05 (![Xk!0: $i, Xk!1: $i] : (inj_1(Xk!1, multiply(Xk!1, Xk!0)) = Xk!0)),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[22, 11])).
% 1.82/2.05 tff(24,plain,
% 1.82/2.05 ((~![Xk!0: $i, Xk!1: $i] : (inj_1(Xk!1, multiply(Xk!1, Xk!0)) = Xk!0)) | (inj_1(an_element, multiply(an_element, multiply(multiply(a, multiply(d, e)), multiply(multiply(b, c), f)))) = multiply(multiply(a, multiply(d, e)), multiply(multiply(b, c), f)))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(25,plain,
% 1.82/2.05 (inj_1(an_element, multiply(an_element, multiply(multiply(a, multiply(d, e)), multiply(multiply(b, c), f)))) = multiply(multiply(a, multiply(d, e)), multiply(multiply(b, c), f))),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[24, 23])).
% 1.82/2.05 tff(26,plain,
% 1.82/2.05 ((multiply(an_element, an_element) = an_element) <=> (multiply(an_element, an_element) = an_element)),
% 1.82/2.05 inference(rewrite,[status(thm)],[])).
% 1.82/2.05 tff(27,axiom,(multiply(an_element, an_element) = an_element), file('/export/starexec/sandbox/benchmark/theBenchmark.p','idempotent_element')).
% 1.82/2.05 tff(28,plain,
% 1.82/2.05 (multiply(an_element, an_element) = an_element),
% 1.82/2.05 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.82/2.05 tff(29,plain,
% 1.82/2.05 (an_element = multiply(an_element, an_element)),
% 1.82/2.05 inference(symmetry,[status(thm)],[28])).
% 1.82/2.05 tff(30,plain,
% 1.82/2.05 (multiply(an_element, multiply(multiply(a, multiply(d, e)), multiply(multiply(b, c), f))) = multiply(multiply(an_element, an_element), multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)))),
% 1.82/2.05 inference(monotonicity,[status(thm)],[29, 10])).
% 1.82/2.05 tff(31,plain,
% 1.82/2.05 (multiply(multiply(an_element, an_element), multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f))) = multiply(an_element, multiply(multiply(a, multiply(d, e)), multiply(multiply(b, c), f)))),
% 1.82/2.05 inference(symmetry,[status(thm)],[30])).
% 1.82/2.05 tff(32,plain,
% 1.82/2.05 ((~![Z: $i, Y: $i, U: $i, X: $i] : (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U)))) | (multiply(multiply(an_element, an_element), multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f))) = multiply(multiply(an_element, multiply(a, multiply(b, c))), multiply(an_element, multiply(multiply(d, e), f))))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(33,plain,
% 1.82/2.05 (multiply(multiply(an_element, an_element), multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f))) = multiply(multiply(an_element, multiply(a, multiply(b, c))), multiply(an_element, multiply(multiply(d, e), f)))),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[32, 7])).
% 1.82/2.05 tff(34,plain,
% 1.82/2.05 (multiply(multiply(an_element, multiply(a, multiply(b, c))), multiply(an_element, multiply(multiply(d, e), f))) = multiply(multiply(an_element, an_element), multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)))),
% 1.82/2.05 inference(symmetry,[status(thm)],[33])).
% 1.82/2.05 tff(35,plain,
% 1.82/2.05 (multiply(an_element, multiply(a, multiply(b, c))) = multiply(multiply(an_element, an_element), multiply(a, multiply(b, c)))),
% 1.82/2.05 inference(monotonicity,[status(thm)],[29])).
% 1.82/2.05 tff(36,plain,
% 1.82/2.05 (multiply(multiply(an_element, an_element), multiply(a, multiply(b, c))) = multiply(an_element, multiply(a, multiply(b, c)))),
% 1.82/2.05 inference(symmetry,[status(thm)],[35])).
% 1.82/2.05 tff(37,plain,
% 1.82/2.05 ((~![Z: $i, Y: $i, U: $i, X: $i] : (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U)))) | (multiply(multiply(an_element, an_element), multiply(a, multiply(b, c))) = multiply(multiply(an_element, a), multiply(an_element, multiply(b, c))))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(38,plain,
% 1.82/2.05 (multiply(multiply(an_element, an_element), multiply(a, multiply(b, c))) = multiply(multiply(an_element, a), multiply(an_element, multiply(b, c)))),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[37, 7])).
% 1.82/2.05 tff(39,plain,
% 1.82/2.05 (multiply(multiply(an_element, a), multiply(an_element, multiply(b, c))) = multiply(multiply(an_element, an_element), multiply(a, multiply(b, c)))),
% 1.82/2.05 inference(symmetry,[status(thm)],[38])).
% 1.82/2.05 tff(40,plain,
% 1.82/2.05 (multiply(an_element, multiply(b, c)) = multiply(multiply(an_element, an_element), multiply(b, c))),
% 1.82/2.05 inference(monotonicity,[status(thm)],[29])).
% 1.82/2.05 tff(41,plain,
% 1.82/2.05 (multiply(multiply(an_element, an_element), multiply(b, c)) = multiply(an_element, multiply(b, c))),
% 1.82/2.05 inference(symmetry,[status(thm)],[40])).
% 1.82/2.05 tff(42,plain,
% 1.82/2.05 ((~![Z: $i, Y: $i, U: $i, X: $i] : (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U)))) | (multiply(multiply(an_element, an_element), multiply(b, c)) = multiply(multiply(an_element, b), multiply(an_element, c)))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(43,plain,
% 1.82/2.05 (multiply(multiply(an_element, an_element), multiply(b, c)) = multiply(multiply(an_element, b), multiply(an_element, c))),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[42, 7])).
% 1.82/2.05 tff(44,plain,
% 1.82/2.05 (multiply(multiply(an_element, b), multiply(an_element, c)) = multiply(multiply(an_element, an_element), multiply(b, c))),
% 1.82/2.05 inference(symmetry,[status(thm)],[43])).
% 1.82/2.05 tff(45,plain,
% 1.82/2.05 (multiply(multiply(an_element, b), multiply(an_element, c)) = multiply(an_element, multiply(b, c))),
% 1.82/2.05 inference(transitivity,[status(thm)],[44, 41])).
% 1.82/2.05 tff(46,plain,
% 1.82/2.05 (multiply(multiply(an_element, a), multiply(multiply(an_element, b), multiply(an_element, c))) = multiply(multiply(an_element, a), multiply(an_element, multiply(b, c)))),
% 1.82/2.05 inference(monotonicity,[status(thm)],[45])).
% 1.82/2.05 tff(47,plain,
% 1.82/2.05 (multiply(multiply(an_element, a), multiply(multiply(an_element, b), multiply(an_element, c))) = multiply(an_element, multiply(a, multiply(b, c)))),
% 1.82/2.05 inference(transitivity,[status(thm)],[46, 39, 36])).
% 1.82/2.05 tff(48,plain,
% 1.82/2.05 (multiply(multiply(multiply(an_element, a), multiply(multiply(an_element, b), multiply(an_element, c))), multiply(an_element, multiply(multiply(d, e), f))) = multiply(multiply(an_element, multiply(a, multiply(b, c))), multiply(an_element, multiply(multiply(d, e), f)))),
% 1.82/2.05 inference(monotonicity,[status(thm)],[47])).
% 1.82/2.05 tff(49,plain,
% 1.82/2.05 ((~![Z: $i, Y: $i, U: $i, X: $i] : (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U)))) | (multiply(multiply(multiply(an_element, a), multiply(multiply(an_element, b), multiply(an_element, c))), multiply(an_element, multiply(multiply(d, e), f))) = multiply(multiply(multiply(an_element, a), an_element), multiply(multiply(multiply(an_element, b), multiply(an_element, c)), multiply(multiply(d, e), f))))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(50,plain,
% 1.82/2.05 (multiply(multiply(multiply(an_element, a), multiply(multiply(an_element, b), multiply(an_element, c))), multiply(an_element, multiply(multiply(d, e), f))) = multiply(multiply(multiply(an_element, a), an_element), multiply(multiply(multiply(an_element, b), multiply(an_element, c)), multiply(multiply(d, e), f)))),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[49, 7])).
% 1.82/2.05 tff(51,plain,
% 1.82/2.05 (multiply(multiply(multiply(an_element, a), an_element), multiply(multiply(multiply(an_element, b), multiply(an_element, c)), multiply(multiply(d, e), f))) = multiply(multiply(multiply(an_element, a), multiply(multiply(an_element, b), multiply(an_element, c))), multiply(an_element, multiply(multiply(d, e), f)))),
% 1.82/2.05 inference(symmetry,[status(thm)],[50])).
% 1.82/2.05 tff(52,plain,
% 1.82/2.05 ((~![Z: $i, Y: $i, U: $i, X: $i] : (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U)))) | (multiply(multiply(multiply(an_element, b), multiply(an_element, c)), multiply(multiply(d, e), f)) = multiply(multiply(multiply(an_element, b), multiply(d, e)), multiply(multiply(an_element, c), f)))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(53,plain,
% 1.82/2.05 (multiply(multiply(multiply(an_element, b), multiply(an_element, c)), multiply(multiply(d, e), f)) = multiply(multiply(multiply(an_element, b), multiply(d, e)), multiply(multiply(an_element, c), f))),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[52, 7])).
% 1.82/2.05 tff(54,plain,
% 1.82/2.05 (multiply(multiply(multiply(an_element, b), multiply(d, e)), multiply(multiply(an_element, c), f)) = multiply(multiply(multiply(an_element, b), multiply(an_element, c)), multiply(multiply(d, e), f))),
% 1.82/2.05 inference(symmetry,[status(thm)],[53])).
% 1.82/2.05 tff(55,plain,
% 1.82/2.05 ((~![Z: $i, Y: $i, U: $i, X: $i] : (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U)))) | (multiply(multiply(an_element, d), multiply(b, e)) = multiply(multiply(an_element, b), multiply(d, e)))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(56,plain,
% 1.82/2.05 (multiply(multiply(an_element, d), multiply(b, e)) = multiply(multiply(an_element, b), multiply(d, e))),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[55, 7])).
% 1.82/2.05 tff(57,plain,
% 1.82/2.05 (multiply(multiply(multiply(an_element, d), multiply(b, e)), multiply(multiply(an_element, c), f)) = multiply(multiply(multiply(an_element, b), multiply(d, e)), multiply(multiply(an_element, c), f))),
% 1.82/2.05 inference(monotonicity,[status(thm)],[56])).
% 1.82/2.05 tff(58,plain,
% 1.82/2.05 ((~![Z: $i, Y: $i, U: $i, X: $i] : (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U)))) | (multiply(multiply(multiply(an_element, d), multiply(an_element, c)), multiply(multiply(b, e), f)) = multiply(multiply(multiply(an_element, d), multiply(b, e)), multiply(multiply(an_element, c), f)))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(59,plain,
% 1.82/2.05 (multiply(multiply(multiply(an_element, d), multiply(an_element, c)), multiply(multiply(b, e), f)) = multiply(multiply(multiply(an_element, d), multiply(b, e)), multiply(multiply(an_element, c), f))),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[58, 7])).
% 1.82/2.05 tff(60,plain,
% 1.82/2.05 (multiply(multiply(multiply(an_element, d), multiply(an_element, c)), multiply(multiply(b, e), f)) = multiply(multiply(multiply(an_element, b), multiply(an_element, c)), multiply(multiply(d, e), f))),
% 1.82/2.05 inference(transitivity,[status(thm)],[59, 57, 54])).
% 1.82/2.05 tff(61,plain,
% 1.82/2.05 (multiply(multiply(multiply(an_element, a), an_element), multiply(multiply(multiply(an_element, d), multiply(an_element, c)), multiply(multiply(b, e), f))) = multiply(multiply(multiply(an_element, a), an_element), multiply(multiply(multiply(an_element, b), multiply(an_element, c)), multiply(multiply(d, e), f)))),
% 1.82/2.05 inference(monotonicity,[status(thm)],[60])).
% 1.82/2.05 tff(62,plain,
% 1.82/2.05 ((~![Z: $i, Y: $i, U: $i, X: $i] : (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U)))) | (multiply(multiply(multiply(an_element, a), multiply(multiply(an_element, d), multiply(an_element, c))), multiply(an_element, multiply(multiply(b, e), f))) = multiply(multiply(multiply(an_element, a), an_element), multiply(multiply(multiply(an_element, d), multiply(an_element, c)), multiply(multiply(b, e), f))))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(63,plain,
% 1.82/2.05 (multiply(multiply(multiply(an_element, a), multiply(multiply(an_element, d), multiply(an_element, c))), multiply(an_element, multiply(multiply(b, e), f))) = multiply(multiply(multiply(an_element, a), an_element), multiply(multiply(multiply(an_element, d), multiply(an_element, c)), multiply(multiply(b, e), f)))),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[62, 7])).
% 1.82/2.05 tff(64,plain,
% 1.82/2.05 (multiply(an_element, multiply(d, c)) = multiply(multiply(an_element, an_element), multiply(d, c))),
% 1.82/2.05 inference(monotonicity,[status(thm)],[29])).
% 1.82/2.05 tff(65,plain,
% 1.82/2.05 (multiply(multiply(an_element, an_element), multiply(d, c)) = multiply(an_element, multiply(d, c))),
% 1.82/2.05 inference(symmetry,[status(thm)],[64])).
% 1.82/2.05 tff(66,plain,
% 1.82/2.05 ((~![Z: $i, Y: $i, U: $i, X: $i] : (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U)))) | (multiply(multiply(an_element, an_element), multiply(d, c)) = multiply(multiply(an_element, d), multiply(an_element, c)))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(67,plain,
% 1.82/2.05 (multiply(multiply(an_element, an_element), multiply(d, c)) = multiply(multiply(an_element, d), multiply(an_element, c))),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[66, 7])).
% 1.82/2.05 tff(68,plain,
% 1.82/2.05 (multiply(multiply(an_element, d), multiply(an_element, c)) = multiply(multiply(an_element, an_element), multiply(d, c))),
% 1.82/2.05 inference(symmetry,[status(thm)],[67])).
% 1.82/2.05 tff(69,plain,
% 1.82/2.05 (multiply(multiply(an_element, d), multiply(an_element, c)) = multiply(an_element, multiply(d, c))),
% 1.82/2.05 inference(transitivity,[status(thm)],[68, 65])).
% 1.82/2.05 tff(70,plain,
% 1.82/2.05 (multiply(multiply(an_element, a), multiply(multiply(an_element, d), multiply(an_element, c))) = multiply(multiply(an_element, a), multiply(an_element, multiply(d, c)))),
% 1.82/2.05 inference(monotonicity,[status(thm)],[69])).
% 1.82/2.05 tff(71,plain,
% 1.82/2.05 (multiply(multiply(an_element, a), multiply(an_element, multiply(d, c))) = multiply(multiply(an_element, a), multiply(multiply(an_element, d), multiply(an_element, c)))),
% 1.82/2.05 inference(symmetry,[status(thm)],[70])).
% 1.82/2.05 tff(72,plain,
% 1.82/2.05 ((~![Z: $i, Y: $i, U: $i, X: $i] : (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U)))) | (multiply(multiply(an_element, an_element), multiply(a, multiply(d, c))) = multiply(multiply(an_element, a), multiply(an_element, multiply(d, c))))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(73,plain,
% 1.82/2.05 (multiply(multiply(an_element, an_element), multiply(a, multiply(d, c))) = multiply(multiply(an_element, a), multiply(an_element, multiply(d, c)))),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[72, 7])).
% 1.82/2.05 tff(74,plain,
% 1.82/2.05 (multiply(an_element, multiply(a, multiply(d, c))) = multiply(multiply(an_element, an_element), multiply(a, multiply(d, c)))),
% 1.82/2.05 inference(monotonicity,[status(thm)],[29])).
% 1.82/2.05 tff(75,plain,
% 1.82/2.05 (multiply(an_element, multiply(a, multiply(d, c))) = multiply(multiply(an_element, a), multiply(multiply(an_element, d), multiply(an_element, c)))),
% 1.82/2.05 inference(transitivity,[status(thm)],[74, 73, 71])).
% 1.82/2.05 tff(76,plain,
% 1.82/2.05 (multiply(multiply(an_element, multiply(a, multiply(d, c))), multiply(an_element, multiply(multiply(b, e), f))) = multiply(multiply(multiply(an_element, a), multiply(multiply(an_element, d), multiply(an_element, c))), multiply(an_element, multiply(multiply(b, e), f)))),
% 1.82/2.05 inference(monotonicity,[status(thm)],[75])).
% 1.82/2.05 tff(77,plain,
% 1.82/2.05 ((~![Z: $i, Y: $i, U: $i, X: $i] : (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U)))) | (multiply(multiply(an_element, an_element), multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f))) = multiply(multiply(an_element, multiply(a, multiply(d, c))), multiply(an_element, multiply(multiply(b, e), f))))),
% 1.82/2.05 inference(quant_inst,[status(thm)],[])).
% 1.82/2.05 tff(78,plain,
% 1.82/2.05 (multiply(multiply(an_element, an_element), multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f))) = multiply(multiply(an_element, multiply(a, multiply(d, c))), multiply(an_element, multiply(multiply(b, e), f)))),
% 1.82/2.05 inference(unit_resolution,[status(thm)],[77, 7])).
% 1.89/2.06 tff(79,plain,
% 1.89/2.06 ((~![Z: $i, Y: $i, U: $i, X: $i] : (multiply(multiply(X, Y), multiply(Z, U)) = multiply(multiply(X, Z), multiply(Y, U)))) | (multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)) = multiply(multiply(a, multiply(b, e)), multiply(multiply(d, c), f)))),
% 1.89/2.06 inference(quant_inst,[status(thm)],[])).
% 1.89/2.06 tff(80,plain,
% 1.89/2.06 (multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)) = multiply(multiply(a, multiply(b, e)), multiply(multiply(d, c), f))),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[79, 7])).
% 1.89/2.06 tff(81,plain,
% 1.89/2.06 (multiply(multiply(a, multiply(b, e)), multiply(multiply(d, c), f)) = multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f))),
% 1.89/2.06 inference(symmetry,[status(thm)],[80])).
% 1.89/2.06 tff(82,plain,
% 1.89/2.06 (multiply(an_element, multiply(multiply(a, multiply(b, e)), multiply(multiply(d, c), f))) = multiply(multiply(an_element, an_element), multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)))),
% 1.89/2.06 inference(monotonicity,[status(thm)],[29, 81])).
% 1.89/2.06 tff(83,plain,
% 1.89/2.06 (multiply(an_element, multiply(multiply(a, multiply(b, e)), multiply(multiply(d, c), f))) = multiply(an_element, multiply(multiply(a, multiply(d, e)), multiply(multiply(b, c), f)))),
% 1.89/2.06 inference(transitivity,[status(thm)],[82, 78, 76, 63, 61, 51, 48, 34, 31])).
% 1.89/2.06 tff(84,plain,
% 1.89/2.06 (inj_1(an_element, multiply(an_element, multiply(multiply(a, multiply(b, e)), multiply(multiply(d, c), f)))) = inj_1(an_element, multiply(an_element, multiply(multiply(a, multiply(d, e)), multiply(multiply(b, c), f))))),
% 1.89/2.06 inference(monotonicity,[status(thm)],[83])).
% 1.89/2.06 tff(85,plain,
% 1.89/2.06 ((~![Xk!0: $i, Xk!1: $i] : (inj_1(Xk!1, multiply(Xk!1, Xk!0)) = Xk!0)) | (inj_1(an_element, multiply(an_element, multiply(multiply(a, multiply(b, e)), multiply(multiply(d, c), f)))) = multiply(multiply(a, multiply(b, e)), multiply(multiply(d, c), f)))),
% 1.89/2.06 inference(quant_inst,[status(thm)],[])).
% 1.89/2.06 tff(86,plain,
% 1.89/2.06 (inj_1(an_element, multiply(an_element, multiply(multiply(a, multiply(b, e)), multiply(multiply(d, c), f)))) = multiply(multiply(a, multiply(b, e)), multiply(multiply(d, c), f))),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[85, 23])).
% 1.89/2.06 tff(87,plain,
% 1.89/2.06 (multiply(multiply(a, multiply(b, e)), multiply(multiply(d, c), f)) = inj_1(an_element, multiply(an_element, multiply(multiply(a, multiply(b, e)), multiply(multiply(d, c), f))))),
% 1.89/2.06 inference(symmetry,[status(thm)],[86])).
% 1.89/2.06 tff(88,plain,
% 1.89/2.06 (multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)) = multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f))),
% 1.89/2.06 inference(transitivity,[status(thm)],[80, 87, 84, 25, 10])).
% 1.89/2.06 tff(89,plain,
% 1.89/2.06 ((~(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)) = multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)))) <=> (~(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)) = multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f))))),
% 1.89/2.06 inference(rewrite,[status(thm)],[])).
% 1.89/2.06 tff(90,axiom,(~(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)) = multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 1.89/2.06 tff(91,plain,
% 1.89/2.06 (~(multiply(multiply(a, multiply(d, c)), multiply(multiply(b, e), f)) = multiply(multiply(a, multiply(b, c)), multiply(multiply(d, e), f)))),
% 1.89/2.06 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.89/2.06 tff(92,plain,
% 1.89/2.06 ($false),
% 1.89/2.06 inference(unit_resolution,[status(thm)],[91, 88])).
% 1.89/2.06 % SZS output end Proof
% 1.89/2.06 % E exiting
%------------------------------------------------------------------------------