%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP715+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 05:08:32 AM UTC 2025
% Result : Theorem 0.68s 0.91s
% Output : Proof 0.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP715+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n014.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 16:57:39 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.68/0.91 % SZS status Theorem
% 0.68/0.91 % SZS output start Proof
% 0.68/0.91 tff(tptp_fun_X0_0_type, type, (
% 0.68/0.91 tptp_fun_X0_0: $i)).
% 0.68/0.91 tff(mult_type, type, (
% 0.68/0.91 mult: ( $i * $i ) > $i)).
% 0.68/0.91 tff(op_a_type, type, (
% 0.68/0.91 op_a: $i)).
% 0.68/0.91 tff(op_b_type, type, (
% 0.68/0.91 op_b: $i)).
% 0.68/0.91 tff(unit_type, type, (
% 0.68/0.91 unit: $i)).
% 0.68/0.91 tff(1,plain,
% 0.68/0.91 (^[A: $i] : refl((mult(A, unit) = A) <=> (mult(A, unit) = A))),
% 0.68/0.91 inference(bind,[status(th)],[])).
% 0.68/0.91 tff(2,plain,
% 0.68/0.91 (![A: $i] : (mult(A, unit) = A) <=> ![A: $i] : (mult(A, unit) = A)),
% 0.68/0.91 inference(quant_intro,[status(thm)],[1])).
% 0.68/0.91 tff(3,plain,
% 0.68/0.91 (![A: $i] : (mult(A, unit) = A) <=> ![A: $i] : (mult(A, unit) = A)),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(4,axiom,(![A: $i] : (mult(A, unit) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f08')).
% 0.68/0.91 tff(5,plain,
% 0.68/0.91 (![A: $i] : (mult(A, unit) = A)),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.68/0.91 tff(6,plain,(
% 0.68/0.91 ![A: $i] : (mult(A, unit) = A)),
% 0.68/0.91 inference(skolemize,[status(sab)],[5])).
% 0.68/0.91 tff(7,plain,
% 0.68/0.91 (![A: $i] : (mult(A, unit) = A)),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.68/0.91 tff(8,plain,
% 0.68/0.91 ((~![A: $i] : (mult(A, unit) = A)) | (mult(X0!0, unit) = X0!0)),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(9,plain,
% 0.68/0.91 (mult(X0!0, unit) = X0!0),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.68/0.91 tff(10,plain,
% 0.68/0.91 (^[A: $i] : refl((mult(unit, A) = A) <=> (mult(unit, A) = A))),
% 0.68/0.91 inference(bind,[status(th)],[])).
% 0.68/0.91 tff(11,plain,
% 0.68/0.91 (![A: $i] : (mult(unit, A) = A) <=> ![A: $i] : (mult(unit, A) = A)),
% 0.68/0.91 inference(quant_intro,[status(thm)],[10])).
% 0.68/0.91 tff(12,plain,
% 0.68/0.91 (![A: $i] : (mult(unit, A) = A) <=> ![A: $i] : (mult(unit, A) = A)),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(13,axiom,(![A: $i] : (mult(unit, A) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f09')).
% 0.68/0.91 tff(14,plain,
% 0.68/0.91 (![A: $i] : (mult(unit, A) = A)),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.68/0.91 tff(15,plain,(
% 0.68/0.91 ![A: $i] : (mult(unit, A) = A)),
% 0.68/0.91 inference(skolemize,[status(sab)],[14])).
% 0.68/0.91 tff(16,plain,
% 0.68/0.91 (![A: $i] : (mult(unit, A) = A)),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.68/0.91 tff(17,plain,
% 0.68/0.91 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, op_b) = op_b)),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(18,plain,
% 0.68/0.91 (mult(unit, op_b) = op_b),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.68/0.91 tff(19,plain,
% 0.68/0.91 ((mult(op_a, op_b) = unit) <=> (mult(op_a, op_b) = unit)),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(20,axiom,(mult(op_a, op_b) = unit), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f10')).
% 0.68/0.91 tff(21,plain,
% 0.68/0.91 (mult(op_a, op_b) = unit),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.68/0.91 tff(22,plain,
% 0.68/0.91 (unit = mult(op_a, op_b)),
% 0.68/0.91 inference(symmetry,[status(thm)],[21])).
% 0.68/0.91 tff(23,plain,
% 0.68/0.91 (mult(unit, op_b) = mult(mult(op_a, op_b), op_b)),
% 0.68/0.91 inference(monotonicity,[status(thm)],[22])).
% 0.68/0.91 tff(24,plain,
% 0.68/0.91 (mult(mult(op_a, op_b), op_b) = mult(unit, op_b)),
% 0.68/0.91 inference(symmetry,[status(thm)],[23])).
% 0.68/0.91 tff(25,plain,
% 0.68/0.91 (mult(mult(op_a, op_b), op_b) = op_b),
% 0.68/0.91 inference(transitivity,[status(thm)],[24, 18])).
% 0.68/0.91 tff(26,plain,
% 0.68/0.91 ((~![A: $i] : (mult(unit, A) = A)) | (mult(unit, op_a) = op_a)),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(27,plain,
% 0.68/0.91 (mult(unit, op_a) = op_a),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[26, 16])).
% 0.68/0.91 tff(28,plain,
% 0.68/0.91 (mult(mult(op_a, op_b), op_a) = mult(unit, op_a)),
% 0.68/0.91 inference(monotonicity,[status(thm)],[21])).
% 0.68/0.91 tff(29,plain,
% 0.68/0.91 ((mult(op_b, op_a) = unit) <=> (mult(op_b, op_a) = unit)),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(30,axiom,(mult(op_b, op_a) = unit), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f11')).
% 0.68/0.91 tff(31,plain,
% 0.68/0.91 (mult(op_b, op_a) = unit),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.68/0.91 tff(32,plain,
% 0.68/0.91 (mult(op_b, op_a) = mult(op_a, op_b)),
% 0.68/0.91 inference(transitivity,[status(thm)],[31, 22])).
% 0.68/0.91 tff(33,plain,
% 0.68/0.91 (mult(mult(op_b, op_a), op_a) = mult(mult(op_a, op_b), op_a)),
% 0.68/0.91 inference(monotonicity,[status(thm)],[32])).
% 0.68/0.91 tff(34,plain,
% 0.68/0.91 (^[B: $i, A: $i] : refl((mult(A, mult(B, B)) = mult(mult(A, B), B)) <=> (mult(A, mult(B, B)) = mult(mult(A, B), B)))),
% 0.68/0.91 inference(bind,[status(th)],[])).
% 0.68/0.91 tff(35,plain,
% 0.68/0.91 (![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B)) <=> ![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))),
% 0.68/0.91 inference(quant_intro,[status(thm)],[34])).
% 0.68/0.91 tff(36,plain,
% 0.68/0.91 (![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B)) <=> ![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(37,axiom,(![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f07')).
% 0.68/0.91 tff(38,plain,
% 0.68/0.91 (![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.68/0.91 tff(39,plain,(
% 0.68/0.91 ![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))),
% 0.68/0.91 inference(skolemize,[status(sab)],[38])).
% 0.68/0.91 tff(40,plain,
% 0.68/0.91 (![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.68/0.91 tff(41,plain,
% 0.68/0.91 ((~![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))) | (mult(op_b, mult(op_a, op_a)) = mult(mult(op_b, op_a), op_a))),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(42,plain,
% 0.68/0.91 (mult(op_b, mult(op_a, op_a)) = mult(mult(op_b, op_a), op_a)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.68/0.91 tff(43,plain,
% 0.68/0.91 (op_a = mult(unit, op_a)),
% 0.68/0.91 inference(symmetry,[status(thm)],[27])).
% 0.68/0.91 tff(44,plain,
% 0.68/0.91 (mult(op_a, op_a) = mult(mult(unit, op_a), op_a)),
% 0.68/0.91 inference(monotonicity,[status(thm)],[43])).
% 0.68/0.91 tff(45,plain,
% 0.68/0.91 (mult(mult(unit, op_a), op_a) = mult(op_a, op_a)),
% 0.68/0.91 inference(symmetry,[status(thm)],[44])).
% 0.68/0.91 tff(46,plain,
% 0.68/0.91 (mult(mult(mult(op_a, op_b), op_b), mult(mult(unit, op_a), op_a)) = mult(op_b, mult(op_a, op_a))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[25, 45])).
% 0.68/0.91 tff(47,plain,
% 0.68/0.91 (mult(mult(mult(op_a, op_b), op_b), mult(mult(unit, op_a), op_a)) = op_a),
% 0.68/0.91 inference(transitivity,[status(thm)],[46, 42, 33, 28, 27])).
% 0.68/0.91 tff(48,plain,
% 0.68/0.91 (mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b)) = mult(op_a, op_b)),
% 0.68/0.91 inference(monotonicity,[status(thm)],[47, 25])).
% 0.68/0.91 tff(49,plain,
% 0.68/0.91 (mult(op_a, op_b) = mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b))),
% 0.68/0.91 inference(symmetry,[status(thm)],[48])).
% 0.68/0.91 tff(50,plain,
% 0.68/0.91 (unit = mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b))),
% 0.68/0.91 inference(transitivity,[status(thm)],[22, 49])).
% 0.68/0.91 tff(51,plain,
% 0.68/0.91 (mult(X0!0, unit) = mult(X0!0, mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b)))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[50])).
% 0.68/0.91 tff(52,plain,
% 0.68/0.91 (mult(X0!0, mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b))) = mult(X0!0, unit)),
% 0.68/0.91 inference(symmetry,[status(thm)],[51])).
% 0.68/0.91 tff(53,plain,
% 0.68/0.91 (^[C: $i, B: $i, A: $i] : refl((mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B))) <=> (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B))))),
% 0.68/0.91 inference(bind,[status(th)],[])).
% 0.68/0.91 tff(54,plain,
% 0.68/0.91 (![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B))) <=> ![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 0.68/0.91 inference(quant_intro,[status(thm)],[53])).
% 0.68/0.91 tff(55,plain,
% 0.68/0.91 (![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B))) <=> ![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 0.68/0.91 inference(rewrite,[status(thm)],[])).
% 0.68/0.91 tff(56,axiom,(![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f06')).
% 0.68/0.91 tff(57,plain,
% 0.68/0.91 (![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.68/0.91 tff(58,plain,(
% 0.68/0.91 ![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 0.68/0.91 inference(skolemize,[status(sab)],[57])).
% 0.68/0.91 tff(59,plain,
% 0.68/0.91 (![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))),
% 0.68/0.91 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.68/0.91 tff(60,plain,
% 0.68/0.91 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_b)), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b)) = mult(X0!0, mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b))))),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(61,plain,
% 0.68/0.91 (mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_b)), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b)) = mult(X0!0, mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b)))),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.68/0.91 tff(62,plain,
% 0.68/0.91 (mult(X0!0, mult(mult(op_a, op_b), op_b)) = mult(X0!0, op_b)),
% 0.68/0.91 inference(monotonicity,[status(thm)],[25])).
% 0.68/0.91 tff(63,plain,
% 0.68/0.91 (mult(mult(X0!0, mult(mult(op_a, op_b), op_b)), mult(mult(unit, op_a), op_a)) = mult(mult(X0!0, op_b), mult(mult(unit, op_a), op_a))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[62])).
% 0.68/0.91 tff(64,plain,
% 0.68/0.91 (mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_b)), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b)) = mult(mult(mult(X0!0, op_b), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[63])).
% 0.68/0.91 tff(65,plain,
% 0.68/0.91 (mult(mult(mult(X0!0, op_b), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b)) = mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_b)), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b))),
% 0.68/0.91 inference(symmetry,[status(thm)],[64])).
% 0.68/0.91 tff(66,plain,
% 0.68/0.91 ((~![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))) | (mult(mult(X0!0, op_b), mult(op_a, op_a)) = mult(mult(mult(X0!0, op_b), op_a), op_a))),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(67,plain,
% 0.68/0.91 (mult(mult(X0!0, op_b), mult(op_a, op_a)) = mult(mult(mult(X0!0, op_b), op_a), op_a)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[66, 40])).
% 0.68/0.91 tff(68,plain,
% 0.68/0.91 (mult(mult(X0!0, op_b), mult(mult(unit, op_a), op_a)) = mult(mult(X0!0, op_b), mult(op_a, op_a))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[45])).
% 0.68/0.91 tff(69,plain,
% 0.68/0.91 (mult(mult(X0!0, op_b), mult(mult(unit, op_a), op_a)) = mult(mult(mult(X0!0, op_b), op_a), op_a)),
% 0.68/0.91 inference(transitivity,[status(thm)],[68, 67])).
% 0.68/0.91 tff(70,plain,
% 0.68/0.91 (mult(mult(mult(X0!0, op_b), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b)) = mult(mult(mult(mult(X0!0, op_b), op_a), op_a), mult(mult(op_a, op_b), op_b))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[69])).
% 0.68/0.91 tff(71,plain,
% 0.68/0.91 (mult(mult(mult(mult(X0!0, op_b), op_a), op_a), mult(mult(op_a, op_b), op_b)) = mult(mult(mult(X0!0, op_b), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b))),
% 0.68/0.91 inference(symmetry,[status(thm)],[70])).
% 0.68/0.91 tff(72,plain,
% 0.68/0.91 ((~![A: $i] : (mult(A, unit) = A)) | (mult(op_a, unit) = op_a)),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(73,plain,
% 0.68/0.91 (mult(op_a, unit) = op_a),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[72, 7])).
% 0.68/0.91 tff(74,plain,
% 0.68/0.91 (mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b)) = unit),
% 0.68/0.91 inference(transitivity,[status(thm)],[48, 21])).
% 0.68/0.91 tff(75,plain,
% 0.68/0.91 (mult(op_a, mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b))) = mult(op_a, unit)),
% 0.68/0.91 inference(monotonicity,[status(thm)],[74])).
% 0.68/0.91 tff(76,plain,
% 0.68/0.91 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(op_a, mult(mult(op_a, op_b), op_b)), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b)) = mult(op_a, mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b))))),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(77,plain,
% 0.68/0.91 (mult(mult(mult(op_a, mult(mult(op_a, op_b), op_b)), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b)) = mult(op_a, mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b)))),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[76, 59])).
% 0.68/0.91 tff(78,plain,
% 0.68/0.91 (mult(op_a, mult(mult(op_a, op_b), op_b)) = mult(op_a, op_b)),
% 0.68/0.91 inference(monotonicity,[status(thm)],[25])).
% 0.68/0.91 tff(79,plain,
% 0.68/0.91 (mult(op_a, mult(mult(op_a, op_b), op_b)) = unit),
% 0.68/0.91 inference(transitivity,[status(thm)],[78, 21])).
% 0.68/0.91 tff(80,plain,
% 0.68/0.91 (mult(mult(op_a, mult(mult(op_a, op_b), op_b)), mult(mult(unit, op_a), op_a)) = mult(unit, mult(op_a, op_a))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[79, 45])).
% 0.68/0.91 tff(81,plain,
% 0.68/0.91 (mult(unit, mult(op_a, op_a)) = mult(mult(op_a, mult(mult(op_a, op_b), op_b)), mult(mult(unit, op_a), op_a))),
% 0.68/0.91 inference(symmetry,[status(thm)],[80])).
% 0.68/0.91 tff(82,plain,
% 0.68/0.91 ((~![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))) | (mult(unit, mult(op_a, op_a)) = mult(mult(unit, op_a), op_a))),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(83,plain,
% 0.68/0.91 (mult(unit, mult(op_a, op_a)) = mult(mult(unit, op_a), op_a)),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[82, 40])).
% 0.68/0.91 tff(84,plain,
% 0.68/0.91 (mult(mult(unit, op_a), op_a) = mult(unit, mult(op_a, op_a))),
% 0.68/0.91 inference(symmetry,[status(thm)],[83])).
% 0.68/0.91 tff(85,plain,
% 0.68/0.91 (mult(op_a, op_a) = mult(mult(op_a, mult(mult(op_a, op_b), op_b)), mult(mult(unit, op_a), op_a))),
% 0.68/0.91 inference(transitivity,[status(thm)],[44, 84, 81])).
% 0.68/0.91 tff(86,plain,
% 0.68/0.91 (mult(mult(op_a, op_a), mult(mult(op_a, op_b), op_b)) = mult(mult(mult(op_a, mult(mult(op_a, op_b), op_b)), mult(mult(unit, op_a), op_a)), mult(mult(op_a, op_b), op_b))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[85])).
% 0.68/0.91 tff(87,plain,
% 0.68/0.91 (mult(mult(mult(op_a, op_b), op_b), op_a) = mult(op_b, op_a)),
% 0.68/0.91 inference(monotonicity,[status(thm)],[25])).
% 0.68/0.91 tff(88,plain,
% 0.68/0.91 (mult(mult(mult(op_a, op_b), op_b), op_a) = mult(op_a, op_b)),
% 0.68/0.91 inference(transitivity,[status(thm)],[87, 31, 22])).
% 0.68/0.91 tff(89,plain,
% 0.68/0.91 (mult(mult(mult(mult(op_a, op_b), op_b), op_a), op_a) = mult(mult(op_a, op_b), op_a)),
% 0.68/0.91 inference(monotonicity,[status(thm)],[88])).
% 0.68/0.91 tff(90,plain,
% 0.68/0.91 (mult(mult(mult(mult(op_a, op_b), op_b), op_a), op_a) = op_a),
% 0.68/0.91 inference(transitivity,[status(thm)],[89, 28, 27])).
% 0.68/0.91 tff(91,plain,
% 0.68/0.91 (mult(mult(mult(mult(mult(op_a, op_b), op_b), op_a), op_a), op_a) = mult(op_a, op_a)),
% 0.68/0.91 inference(monotonicity,[status(thm)],[90])).
% 0.68/0.91 tff(92,plain,
% 0.68/0.91 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(op_a, op_b), op_b), op_a), op_a), op_a) = mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_a), op_a)))),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(93,plain,
% 0.68/0.91 (mult(mult(mult(mult(mult(op_a, op_b), op_b), op_a), op_a), op_a) = mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_a), op_a))),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[92, 59])).
% 0.68/0.91 tff(94,plain,
% 0.68/0.91 (mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_a), op_a)) = mult(mult(mult(mult(mult(op_a, op_b), op_b), op_a), op_a), op_a)),
% 0.68/0.91 inference(symmetry,[status(thm)],[93])).
% 0.68/0.91 tff(95,plain,
% 0.68/0.91 (mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_a), op_a)) = mult(op_a, op_a)),
% 0.68/0.91 inference(transitivity,[status(thm)],[94, 91])).
% 0.68/0.91 tff(96,plain,
% 0.68/0.91 (mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_a), op_a)), mult(mult(op_a, op_b), op_b)) = mult(mult(op_a, op_a), mult(mult(op_a, op_b), op_b))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[95])).
% 0.68/0.91 tff(97,plain,
% 0.68/0.91 (mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_a), op_a)), mult(mult(op_a, op_b), op_b)) = op_a),
% 0.68/0.91 inference(transitivity,[status(thm)],[96, 86, 77, 75, 73])).
% 0.68/0.91 tff(98,plain,
% 0.68/0.91 (mult(mult(X0!0, op_b), mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_a), op_a)), mult(mult(op_a, op_b), op_b))) = mult(mult(X0!0, op_b), op_a)),
% 0.68/0.91 inference(monotonicity,[status(thm)],[97])).
% 0.68/0.91 tff(99,plain,
% 0.68/0.91 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_a), op_a)), mult(mult(op_a, op_b), op_b)) = mult(mult(X0!0, op_b), mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_a), op_a)), mult(mult(op_a, op_b), op_b))))),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(100,plain,
% 0.68/0.91 (mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_a), op_a)), mult(mult(op_a, op_b), op_b)) = mult(mult(X0!0, op_b), mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_a), op_a)), mult(mult(op_a, op_b), op_b)))),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[99, 59])).
% 0.68/0.91 tff(101,plain,
% 0.68/0.91 (mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_a), op_a)), mult(mult(op_a, op_b), op_b)) = mult(mult(X0!0, op_b), op_a)),
% 0.68/0.91 inference(transitivity,[status(thm)],[100, 98])).
% 0.68/0.91 tff(102,plain,
% 0.68/0.91 (mult(mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_a), op_a)), mult(mult(op_a, op_b), op_b)), op_a) = mult(mult(mult(X0!0, op_b), op_a), op_a)),
% 0.68/0.91 inference(monotonicity,[status(thm)],[101])).
% 0.68/0.91 tff(103,plain,
% 0.68/0.91 (mult(mult(mult(X0!0, op_b), op_a), op_a) = mult(mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_a), op_a)), mult(mult(op_a, op_b), op_b)), op_a)),
% 0.68/0.91 inference(symmetry,[status(thm)],[102])).
% 0.68/0.91 tff(104,plain,
% 0.68/0.91 (mult(mult(mult(mult(X0!0, op_b), op_a), op_a), mult(mult(op_a, op_b), op_b)) = mult(mult(mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_a), op_a)), mult(mult(op_a, op_b), op_b)), op_a), mult(mult(op_a, op_b), op_b))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[103])).
% 0.68/0.91 tff(105,plain,
% 0.68/0.91 (mult(mult(mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_a), op_a)), mult(mult(op_a, op_b), op_b)), op_a), mult(mult(op_a, op_b), op_b)) = mult(mult(mult(mult(X0!0, op_b), op_a), op_a), mult(mult(op_a, op_b), op_b))),
% 0.68/0.91 inference(symmetry,[status(thm)],[104])).
% 0.68/0.91 tff(106,plain,
% 0.68/0.91 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_a), op_a)), mult(mult(op_a, op_b), op_b)), op_a), mult(mult(op_a, op_b), op_b)) = mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_a), op_a)), mult(mult(mult(mult(op_a, op_b), op_b), op_a), mult(mult(op_a, op_b), op_b))))),
% 0.68/0.91 inference(quant_inst,[status(thm)],[])).
% 0.68/0.91 tff(107,plain,
% 0.68/0.91 (mult(mult(mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_a), op_a)), mult(mult(op_a, op_b), op_b)), op_a), mult(mult(op_a, op_b), op_b)) = mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_a), op_a)), mult(mult(mult(mult(op_a, op_b), op_b), op_a), mult(mult(op_a, op_b), op_b)))),
% 0.68/0.91 inference(unit_resolution,[status(thm)],[106, 59])).
% 0.68/0.91 tff(108,plain,
% 0.68/0.91 (mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_a), op_a)), mult(mult(mult(mult(op_a, op_b), op_b), op_a), mult(mult(op_a, op_b), op_b))) = mult(mult(mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_a), op_a)), mult(mult(op_a, op_b), op_b)), op_a), mult(mult(op_a, op_b), op_b))),
% 0.68/0.91 inference(symmetry,[status(thm)],[107])).
% 0.68/0.91 tff(109,plain,
% 0.68/0.91 (mult(mult(mult(mult(op_a, op_b), op_b), op_a), mult(mult(op_a, op_b), op_b)) = mult(mult(op_a, op_b), op_b)),
% 0.68/0.91 inference(monotonicity,[status(thm)],[88, 25])).
% 0.68/0.91 tff(110,plain,
% 0.68/0.91 (mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_a), op_a)), mult(mult(mult(mult(op_a, op_b), op_b), op_a), mult(mult(op_a, op_b), op_b))) = mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_a), op_a)), mult(mult(op_a, op_b), op_b))),
% 0.68/0.91 inference(monotonicity,[status(thm)],[109])).
% 0.68/0.91 tff(111,plain,
% 0.68/0.91 (mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_a), op_a)), mult(mult(op_a, op_b), op_b)) = mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_a), op_a)), mult(mult(mult(mult(op_a, op_b), op_b), op_a), mult(mult(op_a, op_b), op_b)))),
% 0.68/0.92 inference(symmetry,[status(thm)],[110])).
% 0.68/0.92 tff(112,plain,
% 0.68/0.92 (mult(mult(X0!0, op_b), mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_a), op_a)), mult(mult(op_a, op_b), op_b))) = mult(mult(mult(mult(X0!0, op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_a), op_a)), mult(mult(op_a, op_b), op_b))),
% 0.68/0.92 inference(symmetry,[status(thm)],[100])).
% 0.68/0.92 tff(113,plain,
% 0.68/0.92 (mult(mult(X0!0, op_b), op_a) = mult(mult(X0!0, op_b), mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_a), op_a)), mult(mult(op_a, op_b), op_b)))),
% 0.68/0.92 inference(symmetry,[status(thm)],[98])).
% 0.68/0.92 tff(114,plain,
% 0.68/0.92 (mult(mult(X0!0, op_b), op_a) = X0!0),
% 0.68/0.92 inference(transitivity,[status(thm)],[113, 112, 111, 108, 105, 71, 65, 61, 52, 9])).
% 0.68/0.92 tff(115,plain,
% 0.68/0.92 ((~![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))) | (mult(op_a, mult(op_b, op_b)) = mult(mult(op_a, op_b), op_b))),
% 0.68/0.92 inference(quant_inst,[status(thm)],[])).
% 0.68/0.92 tff(116,plain,
% 0.68/0.92 (mult(op_a, mult(op_b, op_b)) = mult(mult(op_a, op_b), op_b)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[115, 40])).
% 0.68/0.92 tff(117,plain,
% 0.68/0.92 (mult(op_a, mult(op_b, op_b)) = op_b),
% 0.68/0.92 inference(transitivity,[status(thm)],[116, 24, 18])).
% 0.68/0.92 tff(118,plain,
% 0.68/0.92 (mult(mult(op_a, mult(op_b, op_b)), op_a) = mult(op_b, op_a)),
% 0.68/0.92 inference(monotonicity,[status(thm)],[117])).
% 0.68/0.92 tff(119,plain,
% 0.68/0.92 (mult(mult(op_a, mult(op_b, op_b)), op_a) = unit),
% 0.68/0.92 inference(transitivity,[status(thm)],[118, 31])).
% 0.68/0.92 tff(120,plain,
% 0.68/0.92 (mult(X0!0, mult(mult(op_a, mult(op_b, op_b)), op_a)) = mult(X0!0, unit)),
% 0.68/0.92 inference(monotonicity,[status(thm)],[119])).
% 0.68/0.92 tff(121,plain,
% 0.68/0.92 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(X0!0, op_a), mult(op_b, op_b)), op_a) = mult(X0!0, mult(mult(op_a, mult(op_b, op_b)), op_a)))),
% 0.68/0.92 inference(quant_inst,[status(thm)],[])).
% 0.68/0.92 tff(122,plain,
% 0.68/0.92 (mult(mult(mult(X0!0, op_a), mult(op_b, op_b)), op_a) = mult(X0!0, mult(mult(op_a, mult(op_b, op_b)), op_a))),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[121, 59])).
% 0.68/0.92 tff(123,plain,
% 0.68/0.92 (mult(unit, op_a) = mult(mult(op_a, op_b), op_a)),
% 0.68/0.92 inference(symmetry,[status(thm)],[28])).
% 0.68/0.92 tff(124,plain,
% 0.68/0.92 (op_a = mult(mult(op_a, op_b), op_a)),
% 0.68/0.92 inference(transitivity,[status(thm)],[43, 123])).
% 0.68/0.92 tff(125,plain,
% 0.68/0.92 (mult(X0!0, op_a) = mult(X0!0, mult(mult(op_a, op_b), op_a))),
% 0.68/0.92 inference(monotonicity,[status(thm)],[124])).
% 0.68/0.92 tff(126,plain,
% 0.68/0.92 (mult(mult(X0!0, op_a), mult(op_b, op_b)) = mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), mult(op_b, op_b))),
% 0.68/0.92 inference(monotonicity,[status(thm)],[125])).
% 0.68/0.92 tff(127,plain,
% 0.68/0.92 (mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), mult(op_b, op_b)) = mult(mult(X0!0, op_a), mult(op_b, op_b))),
% 0.68/0.92 inference(symmetry,[status(thm)],[126])).
% 0.68/0.92 tff(128,plain,
% 0.68/0.92 (mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), mult(op_b, op_b)), op_a) = mult(mult(mult(X0!0, op_a), mult(op_b, op_b)), op_a)),
% 0.68/0.92 inference(monotonicity,[status(thm)],[127])).
% 0.68/0.92 tff(129,plain,
% 0.68/0.92 (mult(mult(mult(mult(op_a, op_b), op_b), op_a), mult(mult(op_a, op_b), op_b)) = op_b),
% 0.68/0.92 inference(transitivity,[status(thm)],[109, 24, 18])).
% 0.68/0.92 tff(130,plain,
% 0.68/0.92 (mult(mult(mult(op_a, op_b), op_b), mult(mult(mult(mult(op_a, op_b), op_b), op_a), mult(mult(op_a, op_b), op_b))) = mult(op_b, op_b)),
% 0.68/0.92 inference(monotonicity,[status(thm)],[25, 129])).
% 0.68/0.92 tff(131,plain,
% 0.68/0.92 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), op_a), mult(mult(op_a, op_b), op_b)) = mult(mult(mult(op_a, op_b), op_b), mult(mult(mult(mult(op_a, op_b), op_b), op_a), mult(mult(op_a, op_b), op_b))))),
% 0.68/0.92 inference(quant_inst,[status(thm)],[])).
% 0.68/0.92 tff(132,plain,
% 0.68/0.92 (mult(mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), op_a), mult(mult(op_a, op_b), op_b)) = mult(mult(mult(op_a, op_b), op_b), mult(mult(mult(mult(op_a, op_b), op_b), op_a), mult(mult(op_a, op_b), op_b)))),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[131, 59])).
% 0.68/0.92 tff(133,plain,
% 0.68/0.92 (mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)) = mult(op_b, op_b)),
% 0.68/0.92 inference(monotonicity,[status(thm)],[25, 25])).
% 0.68/0.92 tff(134,plain,
% 0.68/0.92 (mult(op_b, op_b) = mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b))),
% 0.68/0.92 inference(symmetry,[status(thm)],[133])).
% 0.68/0.92 tff(135,plain,
% 0.68/0.92 (mult(mult(mult(op_a, op_b), op_b), op_a) = unit),
% 0.68/0.92 inference(transitivity,[status(thm)],[87, 31])).
% 0.68/0.92 tff(136,plain,
% 0.68/0.92 (mult(mult(mult(mult(op_a, op_b), op_b), op_a), mult(op_b, op_b)) = mult(unit, mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)))),
% 0.68/0.92 inference(monotonicity,[status(thm)],[135, 134])).
% 0.68/0.92 tff(137,plain,
% 0.68/0.92 (mult(unit, mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b))) = mult(mult(mult(mult(op_a, op_b), op_b), op_a), mult(op_b, op_b))),
% 0.68/0.92 inference(symmetry,[status(thm)],[136])).
% 0.68/0.92 tff(138,plain,
% 0.68/0.92 ((~![B: $i, A: $i] : (mult(A, mult(B, B)) = mult(mult(A, B), B))) | (mult(unit, mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b))) = mult(mult(unit, mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b)))),
% 0.68/0.92 inference(quant_inst,[status(thm)],[])).
% 0.68/0.92 tff(139,plain,
% 0.68/0.92 (mult(unit, mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b))) = mult(mult(unit, mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[138, 40])).
% 0.68/0.92 tff(140,plain,
% 0.68/0.92 (mult(mult(unit, mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b)) = mult(unit, mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)))),
% 0.68/0.92 inference(symmetry,[status(thm)],[139])).
% 0.68/0.92 tff(141,plain,
% 0.68/0.92 (mult(unit, mult(mult(op_a, op_b), op_b)) = mult(mult(op_a, op_b), op_b)),
% 0.68/0.92 inference(monotonicity,[status(thm)],[22, 25])).
% 0.68/0.92 tff(142,plain,
% 0.68/0.92 (mult(unit, mult(mult(op_a, op_b), op_b)) = op_b),
% 0.68/0.92 inference(transitivity,[status(thm)],[141, 24, 18])).
% 0.68/0.92 tff(143,plain,
% 0.68/0.92 (mult(mult(unit, mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b)) = mult(op_b, op_b)),
% 0.68/0.92 inference(monotonicity,[status(thm)],[142, 25])).
% 0.68/0.92 tff(144,plain,
% 0.68/0.92 (mult(op_b, op_b) = mult(mult(unit, mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))),
% 0.68/0.92 inference(symmetry,[status(thm)],[143])).
% 0.68/0.92 tff(145,plain,
% 0.68/0.92 (mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)) = mult(mult(mult(mult(op_a, op_b), op_b), op_a), mult(op_b, op_b))),
% 0.68/0.92 inference(transitivity,[status(thm)],[133, 144, 140, 137])).
% 0.68/0.92 tff(146,plain,
% 0.68/0.92 (mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), op_a) = mult(mult(mult(mult(mult(op_a, op_b), op_b), op_a), mult(op_b, op_b)), op_a)),
% 0.68/0.92 inference(monotonicity,[status(thm)],[145])).
% 0.68/0.92 tff(147,plain,
% 0.68/0.92 (mult(mult(mult(mult(mult(op_a, op_b), op_b), op_a), mult(op_b, op_b)), op_a) = mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), op_a)),
% 0.68/0.92 inference(symmetry,[status(thm)],[146])).
% 0.68/0.92 tff(148,plain,
% 0.68/0.92 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(op_a, op_b), op_b), op_a), mult(op_b, op_b)), op_a) = mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, mult(op_b, op_b)), op_a)))),
% 0.68/0.92 inference(quant_inst,[status(thm)],[])).
% 0.68/0.92 tff(149,plain,
% 0.68/0.92 (mult(mult(mult(mult(mult(op_a, op_b), op_b), op_a), mult(op_b, op_b)), op_a) = mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, mult(op_b, op_b)), op_a))),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[148, 59])).
% 0.68/0.92 tff(150,plain,
% 0.68/0.92 (mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, mult(op_b, op_b)), op_a)) = mult(mult(mult(mult(mult(op_a, op_b), op_b), op_a), mult(op_b, op_b)), op_a)),
% 0.68/0.92 inference(symmetry,[status(thm)],[149])).
% 0.68/0.92 tff(151,plain,
% 0.68/0.92 (mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, mult(op_b, op_b)), op_a)) = mult(mult(mult(op_a, op_b), op_b), unit)),
% 0.68/0.92 inference(monotonicity,[status(thm)],[119])).
% 0.68/0.92 tff(152,plain,
% 0.68/0.92 (mult(mult(mult(op_a, op_b), op_b), unit) = mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, mult(op_b, op_b)), op_a))),
% 0.68/0.92 inference(symmetry,[status(thm)],[151])).
% 0.68/0.92 tff(153,plain,
% 0.68/0.92 (mult(mult(mult(op_a, op_b), op_b), unit) = mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), op_a)),
% 0.68/0.92 inference(transitivity,[status(thm)],[152, 150, 147])).
% 0.68/0.92 tff(154,plain,
% 0.68/0.92 (mult(mult(mult(mult(op_a, op_b), op_b), unit), mult(mult(op_a, op_b), op_b)) = mult(mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), op_a), mult(mult(op_a, op_b), op_b))),
% 0.68/0.92 inference(monotonicity,[status(thm)],[153])).
% 0.68/0.92 tff(155,plain,
% 0.68/0.92 (mult(mult(mult(mult(op_a, op_b), op_b), unit), mult(mult(op_a, op_b), op_b)) = mult(op_b, op_b)),
% 0.68/0.92 inference(transitivity,[status(thm)],[154, 132, 130])).
% 0.68/0.92 tff(156,plain,
% 0.68/0.92 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), unit) = mult(X0!0, mult(mult(op_a, op_b), op_a)))),
% 0.68/0.92 inference(quant_inst,[status(thm)],[])).
% 0.68/0.92 tff(157,plain,
% 0.68/0.92 (mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), unit) = mult(X0!0, mult(mult(op_a, op_b), op_a))),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[156, 7])).
% 0.68/0.92 tff(158,plain,
% 0.68/0.92 (mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), unit), mult(mult(mult(mult(op_a, op_b), op_b), unit), mult(mult(op_a, op_b), op_b))) = mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), mult(op_b, op_b))),
% 0.68/0.92 inference(monotonicity,[status(thm)],[157, 155])).
% 0.68/0.92 tff(159,plain,
% 0.68/0.92 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), unit), mult(mult(op_a, op_b), op_b)), unit), mult(mult(op_a, op_b), op_b)) = mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), unit), mult(mult(mult(mult(op_a, op_b), op_b), unit), mult(mult(op_a, op_b), op_b))))),
% 0.68/0.92 inference(quant_inst,[status(thm)],[])).
% 0.68/0.92 tff(160,plain,
% 0.68/0.92 (mult(mult(mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), unit), mult(mult(op_a, op_b), op_b)), unit), mult(mult(op_a, op_b), op_b)) = mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), unit), mult(mult(mult(mult(op_a, op_b), op_b), unit), mult(mult(op_a, op_b), op_b)))),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[159, 59])).
% 0.68/0.92 tff(161,plain,
% 0.68/0.92 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), unit), mult(mult(op_a, op_b), op_b)), unit) = mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), mult(mult(unit, mult(mult(op_a, op_b), op_b)), unit)))),
% 0.68/0.92 inference(quant_inst,[status(thm)],[])).
% 0.68/0.92 tff(162,plain,
% 0.68/0.92 (mult(mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), unit), mult(mult(op_a, op_b), op_b)), unit) = mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), mult(mult(unit, mult(mult(op_a, op_b), op_b)), unit))),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[161, 59])).
% 0.68/0.92 tff(163,plain,
% 0.68/0.92 (mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), mult(mult(unit, mult(mult(op_a, op_b), op_b)), unit)) = mult(mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), unit), mult(mult(op_a, op_b), op_b)), unit)),
% 0.68/0.92 inference(symmetry,[status(thm)],[162])).
% 0.68/0.92 tff(164,plain,
% 0.68/0.92 ((~![A: $i] : (mult(A, unit) = A)) | (mult(mult(mult(op_a, op_b), op_b), unit) = mult(mult(op_a, op_b), op_b))),
% 0.68/0.92 inference(quant_inst,[status(thm)],[])).
% 0.68/0.92 tff(165,plain,
% 0.68/0.92 (mult(mult(mult(op_a, op_b), op_b), unit) = mult(mult(op_a, op_b), op_b)),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[164, 7])).
% 0.68/0.92 tff(166,plain,
% 0.68/0.92 (mult(op_b, op_a) = mult(mult(op_a, mult(op_b, op_b)), op_a)),
% 0.68/0.92 inference(symmetry,[status(thm)],[118])).
% 0.68/0.92 tff(167,plain,
% 0.68/0.92 (unit = mult(op_b, op_a)),
% 0.68/0.92 inference(symmetry,[status(thm)],[31])).
% 0.68/0.92 tff(168,plain,
% 0.68/0.92 (unit = mult(mult(op_a, mult(op_b, op_b)), op_a)),
% 0.68/0.92 inference(transitivity,[status(thm)],[167, 166])).
% 0.68/0.92 tff(169,plain,
% 0.68/0.92 (mult(mult(unit, mult(mult(op_a, op_b), op_b)), unit) = mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, mult(op_b, op_b)), op_a))),
% 0.68/0.92 inference(monotonicity,[status(thm)],[141, 168])).
% 0.68/0.92 tff(170,plain,
% 0.68/0.92 (mult(mult(unit, mult(mult(op_a, op_b), op_b)), unit) = op_b),
% 0.68/0.92 inference(transitivity,[status(thm)],[169, 151, 165, 24, 18])).
% 0.68/0.92 tff(171,plain,
% 0.68/0.92 (mult(X0!0, mult(mult(op_a, op_b), op_a)) = mult(X0!0, op_a)),
% 0.68/0.92 inference(symmetry,[status(thm)],[125])).
% 0.68/0.92 tff(172,plain,
% 0.68/0.92 (mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), mult(mult(unit, mult(mult(op_a, op_b), op_b)), unit)) = mult(mult(X0!0, op_a), op_b)),
% 0.68/0.92 inference(monotonicity,[status(thm)],[171, 170])).
% 0.68/0.92 tff(173,plain,
% 0.68/0.92 (mult(mult(X0!0, op_a), op_b) = mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), mult(mult(unit, mult(mult(op_a, op_b), op_b)), unit))),
% 0.68/0.92 inference(symmetry,[status(thm)],[172])).
% 0.68/0.92 tff(174,plain,
% 0.68/0.92 (mult(mult(X0!0, op_a), op_b) = mult(mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), unit), mult(mult(op_a, op_b), op_b)), unit)),
% 0.68/0.92 inference(transitivity,[status(thm)],[173, 163])).
% 0.68/0.92 tff(175,plain,
% 0.68/0.92 (mult(mult(mult(X0!0, op_a), op_b), mult(mult(op_a, op_b), op_b)) = mult(mult(mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), unit), mult(mult(op_a, op_b), op_b)), unit), mult(mult(op_a, op_b), op_b))),
% 0.68/0.92 inference(monotonicity,[status(thm)],[174])).
% 0.68/0.92 tff(176,plain,
% 0.68/0.92 (mult(mult(mult(X0!0, op_a), op_b), mult(mult(op_a, op_b), op_b)) = mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), mult(op_b, op_b))),
% 0.68/0.92 inference(transitivity,[status(thm)],[175, 160, 158])).
% 0.68/0.92 tff(177,plain,
% 0.68/0.92 (mult(mult(mult(mult(X0!0, op_a), op_b), mult(mult(op_a, op_b), op_b)), op_a) = mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), mult(op_b, op_b)), op_a)),
% 0.68/0.92 inference(monotonicity,[status(thm)],[176])).
% 0.68/0.92 tff(178,plain,
% 0.68/0.92 (mult(mult(op_a, mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b)) = mult(mult(op_a, op_b), op_b)),
% 0.68/0.92 inference(monotonicity,[status(thm)],[78, 25])).
% 0.68/0.92 tff(179,plain,
% 0.68/0.92 (mult(mult(op_a, mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b)) = op_b),
% 0.68/0.92 inference(transitivity,[status(thm)],[178, 24, 18])).
% 0.68/0.92 tff(180,plain,
% 0.68/0.92 (mult(mult(mult(op_a, mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b)) = mult(op_b, op_b)),
% 0.68/0.92 inference(monotonicity,[status(thm)],[179, 25])).
% 0.68/0.92 tff(181,plain,
% 0.68/0.92 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(op_a, mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b)) = mult(op_a, mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))))),
% 0.68/0.92 inference(quant_inst,[status(thm)],[])).
% 0.68/0.92 tff(182,plain,
% 0.68/0.92 (mult(mult(mult(op_a, mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b)) = mult(op_a, mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b)))),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[181, 59])).
% 0.68/0.92 tff(183,plain,
% 0.68/0.92 (mult(op_a, mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))) = mult(mult(mult(op_a, mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))),
% 0.68/0.92 inference(symmetry,[status(thm)],[182])).
% 0.68/0.92 tff(184,plain,
% 0.68/0.92 (mult(op_a, mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))) = mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b))),
% 0.68/0.92 inference(transitivity,[status(thm)],[183, 180, 134])).
% 0.68/0.92 tff(185,plain,
% 0.68/0.92 (mult(mult(op_a, mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), op_a) = mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), op_a)),
% 0.68/0.92 inference(monotonicity,[status(thm)],[184])).
% 0.68/0.92 tff(186,plain,
% 0.68/0.92 (mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), op_a) = mult(mult(op_a, mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), op_a)),
% 0.68/0.92 inference(symmetry,[status(thm)],[185])).
% 0.68/0.92 tff(187,plain,
% 0.68/0.92 (mult(mult(op_a, op_b), op_b) = mult(mult(mult(op_a, op_b), op_b), unit)),
% 0.68/0.92 inference(symmetry,[status(thm)],[165])).
% 0.68/0.92 tff(188,plain,
% 0.68/0.92 (op_b = mult(unit, op_b)),
% 0.68/0.92 inference(symmetry,[status(thm)],[18])).
% 0.68/0.92 tff(189,plain,
% 0.68/0.92 (op_b = mult(mult(op_a, mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), op_a)),
% 0.68/0.92 inference(transitivity,[status(thm)],[188, 23, 187, 152, 150, 147, 186])).
% 0.68/0.92 tff(190,plain,
% 0.68/0.92 (mult(mult(X0!0, op_a), op_b) = mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), mult(mult(op_a, mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), op_a))),
% 0.68/0.92 inference(monotonicity,[status(thm)],[125, 189])).
% 0.68/0.92 tff(191,plain,
% 0.68/0.92 (mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), mult(mult(op_a, mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), op_a)) = mult(mult(X0!0, op_a), op_b)),
% 0.68/0.92 inference(symmetry,[status(thm)],[190])).
% 0.68/0.92 tff(192,plain,
% 0.68/0.92 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), op_a), mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), op_a) = mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), mult(mult(op_a, mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), op_a)))),
% 0.68/0.92 inference(quant_inst,[status(thm)],[])).
% 0.68/0.92 tff(193,plain,
% 0.68/0.92 (mult(mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), op_a), mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), op_a) = mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), mult(mult(op_a, mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), op_a))),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[192, 59])).
% 0.68/0.92 tff(194,plain,
% 0.68/0.92 (mult(mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), op_a), mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), op_a) = mult(mult(X0!0, op_a), op_b)),
% 0.68/0.92 inference(transitivity,[status(thm)],[193, 191])).
% 0.68/0.92 tff(195,plain,
% 0.68/0.92 (mult(mult(mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), op_a), mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), op_a), mult(mult(op_a, op_b), op_b)) = mult(mult(mult(X0!0, op_a), op_b), mult(mult(op_a, op_b), op_b))),
% 0.68/0.92 inference(monotonicity,[status(thm)],[194])).
% 0.68/0.92 tff(196,plain,
% 0.68/0.92 (mult(mult(mult(mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), op_a), mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), op_a), mult(mult(op_a, op_b), op_b)), op_a) = mult(mult(mult(mult(X0!0, op_a), op_b), mult(mult(op_a, op_b), op_b)), op_a)),
% 0.68/0.92 inference(monotonicity,[status(thm)],[195])).
% 0.68/0.92 tff(197,plain,
% 0.68/0.92 ((~![C: $i, B: $i, A: $i] : (mult(mult(mult(A, B), C), B) = mult(A, mult(mult(B, C), B)))) | (mult(mult(mult(mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), op_a), mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), op_a), mult(mult(op_a, op_b), op_b)), op_a) = mult(mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), op_a), mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), mult(mult(op_a, mult(mult(op_a, op_b), op_b)), op_a)))),
% 0.68/0.92 inference(quant_inst,[status(thm)],[])).
% 0.68/0.92 tff(198,plain,
% 0.68/0.92 (mult(mult(mult(mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), op_a), mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), op_a), mult(mult(op_a, op_b), op_b)), op_a) = mult(mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), op_a), mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), mult(mult(op_a, mult(mult(op_a, op_b), op_b)), op_a))),
% 0.68/0.92 inference(unit_resolution,[status(thm)],[197, 59])).
% 0.68/0.92 tff(199,plain,
% 0.68/0.92 (mult(mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), op_a), mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), mult(mult(op_a, mult(mult(op_a, op_b), op_b)), op_a)) = mult(mult(mult(mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), op_a), mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), op_a), mult(mult(op_a, op_b), op_b)), op_a)),
% 0.68/0.93 inference(symmetry,[status(thm)],[198])).
% 0.68/0.93 tff(200,plain,
% 0.68/0.93 (mult(mult(op_a, mult(mult(op_a, op_b), op_b)), op_a) = mult(mult(op_a, op_b), op_a)),
% 0.68/0.93 inference(monotonicity,[status(thm)],[78])).
% 0.68/0.93 tff(201,plain,
% 0.68/0.93 (mult(mult(op_a, op_b), op_a) = mult(mult(op_a, mult(mult(op_a, op_b), op_b)), op_a)),
% 0.68/0.93 inference(symmetry,[status(thm)],[200])).
% 0.68/0.93 tff(202,plain,
% 0.68/0.93 (op_a = mult(mult(op_a, mult(mult(op_a, op_b), op_b)), op_a)),
% 0.68/0.93 inference(transitivity,[status(thm)],[43, 123, 201])).
% 0.68/0.93 tff(203,plain,
% 0.68/0.93 (mult(mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), op_a), mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), op_a) = mult(mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), op_a), mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), mult(mult(op_a, mult(mult(op_a, op_b), op_b)), op_a))),
% 0.68/0.93 inference(monotonicity,[status(thm)],[202])).
% 0.68/0.93 tff(204,plain,
% 0.68/0.93 (mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), mult(mult(op_a, mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), op_a)) = mult(mult(mult(mult(X0!0, mult(mult(op_a, op_b), op_a)), op_a), mult(mult(mult(mult(op_a, op_b), op_b), mult(mult(op_a, op_b), op_b)), mult(mult(op_a, op_b), op_b))), op_a)),
% 0.68/0.93 inference(symmetry,[status(thm)],[193])).
% 0.68/0.93 tff(205,plain,
% 0.68/0.93 (mult(mult(X0!0, op_a), op_b) = X0!0),
% 0.68/0.93 inference(transitivity,[status(thm)],[190, 204, 203, 199, 196, 177, 128, 122, 120, 9])).
% 0.68/0.93 tff(206,plain,
% 0.68/0.93 ((~(~((~(mult(mult(X0!0, op_a), op_b) = X0!0)) | (~(mult(mult(X0!0, op_b), op_a) = X0!0))))) <=> ((~(mult(mult(X0!0, op_a), op_b) = X0!0)) | (~(mult(mult(X0!0, op_b), op_a) = X0!0)))),
% 0.68/0.93 inference(rewrite,[status(thm)],[])).
% 0.68/0.93 tff(207,plain,
% 0.68/0.93 (((mult(mult(X0!0, op_a), op_b) = X0!0) & (mult(mult(X0!0, op_b), op_a) = X0!0)) <=> (~((~(mult(mult(X0!0, op_a), op_b) = X0!0)) | (~(mult(mult(X0!0, op_b), op_a) = X0!0))))),
% 0.68/0.93 inference(rewrite,[status(thm)],[])).
% 0.68/0.93 tff(208,plain,
% 0.68/0.93 ((~((mult(mult(X0!0, op_a), op_b) = X0!0) & (mult(mult(X0!0, op_b), op_a) = X0!0))) <=> (~(~((~(mult(mult(X0!0, op_a), op_b) = X0!0)) | (~(mult(mult(X0!0, op_b), op_a) = X0!0)))))),
% 0.68/0.93 inference(monotonicity,[status(thm)],[207])).
% 0.68/0.93 tff(209,plain,
% 0.68/0.93 ((~((mult(mult(X0!0, op_a), op_b) = X0!0) & (mult(mult(X0!0, op_b), op_a) = X0!0))) <=> ((~(mult(mult(X0!0, op_a), op_b) = X0!0)) | (~(mult(mult(X0!0, op_b), op_a) = X0!0)))),
% 0.68/0.93 inference(transitivity,[status(thm)],[208, 206])).
% 0.68/0.93 tff(210,plain,
% 0.68/0.93 ((~![X0: $i] : ((mult(mult(X0, op_a), op_b) = X0) & (mult(mult(X0, op_b), op_a) = X0))) <=> (~![X0: $i] : ((mult(mult(X0, op_a), op_b) = X0) & (mult(mult(X0, op_b), op_a) = X0)))),
% 0.68/0.93 inference(rewrite,[status(thm)],[])).
% 0.68/0.93 tff(211,axiom,(~![X0: $i] : ((mult(mult(X0, op_a), op_b) = X0) & (mult(mult(X0, op_b), op_a) = X0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.68/0.93 tff(212,plain,
% 0.68/0.93 (~![X0: $i] : ((mult(mult(X0, op_a), op_b) = X0) & (mult(mult(X0, op_b), op_a) = X0))),
% 0.68/0.93 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.68/0.93 tff(213,plain,
% 0.68/0.93 (~![X0: $i] : ((mult(mult(X0, op_a), op_b) = X0) & (mult(mult(X0, op_b), op_a) = X0))),
% 0.68/0.93 inference(modus_ponens,[status(thm)],[212, 210])).
% 0.68/0.93 tff(214,plain,
% 0.68/0.93 (~![X0: $i] : ((mult(mult(X0, op_a), op_b) = X0) & (mult(mult(X0, op_b), op_a) = X0))),
% 0.68/0.93 inference(modus_ponens,[status(thm)],[213, 210])).
% 0.68/0.93 tff(215,plain,
% 0.68/0.93 (~![X0: $i] : ((mult(mult(X0, op_a), op_b) = X0) & (mult(mult(X0, op_b), op_a) = X0))),
% 0.68/0.93 inference(modus_ponens,[status(thm)],[214, 210])).
% 0.68/0.93 tff(216,plain,(
% 0.68/0.93 ~((mult(mult(X0!0, op_a), op_b) = X0!0) & (mult(mult(X0!0, op_b), op_a) = X0!0))),
% 0.68/0.93 inference(skolemize,[status(sab)],[215])).
% 0.68/0.93 tff(217,plain,
% 0.68/0.93 ((~(mult(mult(X0!0, op_a), op_b) = X0!0)) | (~(mult(mult(X0!0, op_b), op_a) = X0!0))),
% 0.68/0.93 inference(modus_ponens,[status(thm)],[216, 209])).
% 0.68/0.93 tff(218,plain,
% 0.68/0.93 ($false),
% 0.68/0.93 inference(unit_resolution,[status(thm)],[217, 205, 114])).
% 0.68/0.93 % SZS output end Proof
% 0.76/0.93 % E exiting
%------------------------------------------------------------------------------