%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE148+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:13:05 AM UTC 2025
% Result : Theorem 0.93s 1.11s
% Output : Proof 0.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : KLE148+1 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n008.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 19:03:48 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.93/1.11 % SZS status Theorem
% 0.93/1.11 % SZS output start Proof
% 0.93/1.11 tff(tptp_fun_X0_1_type, type, (
% 0.93/1.11 tptp_fun_X0_1: $i)).
% 0.93/1.11 tff(multiplication_type, type, (
% 0.93/1.11 multiplication: ( $i * $i ) > $i)).
% 0.93/1.11 tff(strong_iteration_type, type, (
% 0.93/1.11 strong_iteration: $i > $i)).
% 0.93/1.11 tff(tptp_fun_X1_0_type, type, (
% 0.93/1.11 tptp_fun_X1_0: $i)).
% 0.93/1.11 tff(addition_type, type, (
% 0.93/1.11 addition: ( $i * $i ) > $i)).
% 0.93/1.11 tff(zero_type, type, (
% 0.93/1.11 zero: $i)).
% 0.93/1.11 tff(one_type, type, (
% 0.93/1.11 one: $i)).
% 0.93/1.11 tff(1,plain,
% 0.93/1.11 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 0.93/1.11 inference(bind,[status(th)],[])).
% 0.93/1.11 tff(2,plain,
% 0.93/1.11 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.93/1.11 inference(quant_intro,[status(thm)],[1])).
% 0.93/1.11 tff(3,plain,
% 0.93/1.11 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(4,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','additive_identity')).
% 0.93/1.11 tff(5,plain,
% 0.93/1.11 (![A: $i] : (addition(A, zero) = A)),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.93/1.11 tff(6,plain,(
% 0.93/1.11 ![A: $i] : (addition(A, zero) = A)),
% 0.93/1.11 inference(skolemize,[status(sab)],[5])).
% 0.93/1.11 tff(7,plain,
% 0.93/1.11 (![A: $i] : (addition(A, zero) = A)),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.93/1.11 tff(8,plain,
% 0.93/1.11 ((~![A: $i] : (addition(A, zero) = A)) | (addition(X0!1, zero) = X0!1)),
% 0.93/1.11 inference(quant_inst,[status(thm)],[])).
% 0.93/1.11 tff(9,plain,
% 0.93/1.11 (addition(X0!1, zero) = X0!1),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.93/1.11 tff(10,plain,
% 0.93/1.11 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))))),
% 0.93/1.11 inference(bind,[status(th)],[])).
% 0.93/1.11 tff(11,plain,
% 0.93/1.11 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.93/1.11 inference(quant_intro,[status(thm)],[10])).
% 0.93/1.11 tff(12,plain,
% 0.93/1.11 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(13,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','distributivity1')).
% 0.93/1.11 tff(14,plain,
% 0.93/1.11 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.93/1.11 tff(15,plain,(
% 0.93/1.11 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.93/1.11 inference(skolemize,[status(sab)],[14])).
% 0.93/1.11 tff(16,plain,
% 0.93/1.11 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.93/1.11 tff(17,plain,
% 0.93/1.11 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))),
% 0.93/1.11 inference(quant_inst,[status(thm)],[])).
% 0.93/1.11 tff(18,plain,
% 0.93/1.11 (multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.93/1.11 tff(19,plain,
% 0.93/1.11 (^[A: $i] : refl((strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)))),
% 0.93/1.11 inference(bind,[status(th)],[])).
% 0.93/1.11 tff(20,plain,
% 0.93/1.11 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.93/1.11 inference(quant_intro,[status(thm)],[19])).
% 0.93/1.11 tff(21,plain,
% 0.93/1.11 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one)) <=> ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(22,axiom,(![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','infty_unfold1')).
% 0.93/1.11 tff(23,plain,
% 0.93/1.11 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.93/1.11 tff(24,plain,(
% 0.93/1.11 ![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.93/1.11 inference(skolemize,[status(sab)],[23])).
% 0.93/1.11 tff(25,plain,
% 0.93/1.11 (![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.93/1.11 tff(26,plain,
% 0.93/1.11 ((~![A: $i] : (strong_iteration(A) = addition(multiplication(A, strong_iteration(A)), one))) | (strong_iteration(X1!0) = addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 0.93/1.11 inference(quant_inst,[status(thm)],[])).
% 0.93/1.11 tff(27,plain,
% 0.93/1.11 (strong_iteration(X1!0) = addition(multiplication(X1!0, strong_iteration(X1!0)), one)),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.93/1.11 tff(28,plain,
% 0.93/1.11 (multiplication(X1!0, strong_iteration(X1!0)) = multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[27])).
% 0.93/1.11 tff(29,plain,
% 0.93/1.11 (multiplication(X1!0, strong_iteration(X1!0)) = addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))),
% 0.93/1.11 inference(transitivity,[status(thm)],[28, 18])).
% 0.93/1.11 tff(30,plain,
% 0.93/1.11 (multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0))) = multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[29])).
% 0.93/1.11 tff(31,plain,
% 0.93/1.11 (multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = multiplication(X1!0, strong_iteration(X1!0))),
% 0.93/1.11 inference(symmetry,[status(thm)],[28])).
% 0.93/1.11 tff(32,plain,
% 0.93/1.11 (multiplication(X0!1, multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one))) = multiplication(X0!1, multiplication(X1!0, strong_iteration(X1!0)))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[31])).
% 0.93/1.11 tff(33,plain,
% 0.93/1.11 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)))),
% 0.93/1.11 inference(bind,[status(th)],[])).
% 0.93/1.11 tff(34,plain,
% 0.93/1.11 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.93/1.11 inference(quant_intro,[status(thm)],[33])).
% 0.93/1.11 tff(35,plain,
% 0.93/1.11 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(36,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','multiplicative_associativity')).
% 0.93/1.11 tff(37,plain,
% 0.93/1.11 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.93/1.11 tff(38,plain,(
% 0.93/1.11 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.93/1.11 inference(skolemize,[status(sab)],[37])).
% 0.93/1.11 tff(39,plain,
% 0.93/1.11 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.93/1.11 tff(40,plain,
% 0.93/1.11 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X0!1, multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one))) = multiplication(multiplication(X0!1, X1!0), addition(multiplication(X1!0, strong_iteration(X1!0)), one)))),
% 0.93/1.11 inference(quant_inst,[status(thm)],[])).
% 0.93/1.11 tff(41,plain,
% 0.93/1.11 (multiplication(X0!1, multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one))) = multiplication(multiplication(X0!1, X1!0), addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.93/1.11 tff(42,plain,
% 0.93/1.11 (multiplication(multiplication(X0!1, X1!0), addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = multiplication(X0!1, multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one)))),
% 0.93/1.11 inference(symmetry,[status(thm)],[41])).
% 0.93/1.11 tff(43,plain,
% 0.93/1.11 ((~![X0: $i, X1: $i] : ((~(multiplication(X0, X1) = zero)) | (multiplication(X0, strong_iteration(X1)) = X0))) <=> (~![X0: $i, X1: $i] : ((~(multiplication(X0, X1) = zero)) | (multiplication(X0, strong_iteration(X1)) = X0)))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(44,plain,
% 0.93/1.11 ((~![X0: $i, X1: $i] : ((multiplication(X0, X1) = zero) => (multiplication(X0, strong_iteration(X1)) = X0))) <=> (~![X0: $i, X1: $i] : ((~(multiplication(X0, X1) = zero)) | (multiplication(X0, strong_iteration(X1)) = X0)))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(45,axiom,(~![X0: $i, X1: $i] : ((multiplication(X0, X1) = zero) => (multiplication(X0, strong_iteration(X1)) = X0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.93/1.11 tff(46,plain,
% 0.93/1.11 (~![X0: $i, X1: $i] : ((~(multiplication(X0, X1) = zero)) | (multiplication(X0, strong_iteration(X1)) = X0))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.93/1.11 tff(47,plain,
% 0.93/1.11 (~![X0: $i, X1: $i] : ((~(multiplication(X0, X1) = zero)) | (multiplication(X0, strong_iteration(X1)) = X0))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[46, 43])).
% 0.93/1.11 tff(48,plain,
% 0.93/1.11 (~![X0: $i, X1: $i] : ((~(multiplication(X0, X1) = zero)) | (multiplication(X0, strong_iteration(X1)) = X0))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.93/1.11 tff(49,plain,
% 0.93/1.11 (~![X0: $i, X1: $i] : ((~(multiplication(X0, X1) = zero)) | (multiplication(X0, strong_iteration(X1)) = X0))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[48, 43])).
% 0.93/1.11 tff(50,plain,(
% 0.93/1.11 ~((~(multiplication(X0!1, X1!0) = zero)) | (multiplication(X0!1, strong_iteration(X1!0)) = X0!1))),
% 0.93/1.11 inference(skolemize,[status(sab)],[49])).
% 0.93/1.11 tff(51,plain,
% 0.93/1.11 (multiplication(X0!1, X1!0) = zero),
% 0.93/1.11 inference(or_elim,[status(thm)],[50])).
% 0.93/1.11 tff(52,plain,
% 0.93/1.11 (zero = multiplication(X0!1, X1!0)),
% 0.93/1.11 inference(symmetry,[status(thm)],[51])).
% 0.93/1.11 tff(53,plain,
% 0.93/1.11 (multiplication(zero, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = multiplication(multiplication(X0!1, X1!0), addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[52])).
% 0.93/1.11 tff(54,plain,
% 0.93/1.11 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 0.93/1.11 inference(bind,[status(th)],[])).
% 0.93/1.11 tff(55,plain,
% 0.93/1.11 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.93/1.11 inference(quant_intro,[status(thm)],[54])).
% 0.93/1.11 tff(56,plain,
% 0.93/1.11 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(57,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','left_annihilation')).
% 0.93/1.11 tff(58,plain,
% 0.93/1.11 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.93/1.11 tff(59,plain,(
% 0.93/1.11 ![A: $i] : (multiplication(zero, A) = zero)),
% 0.93/1.11 inference(skolemize,[status(sab)],[58])).
% 0.93/1.11 tff(60,plain,
% 0.93/1.11 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.93/1.11 tff(61,plain,
% 0.93/1.11 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = zero)),
% 0.93/1.11 inference(quant_inst,[status(thm)],[])).
% 0.93/1.11 tff(62,plain,
% 0.93/1.11 (multiplication(zero, addition(multiplication(X1!0, strong_iteration(X1!0)), one)) = zero),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.93/1.11 tff(63,plain,
% 0.93/1.11 (zero = multiplication(zero, addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 0.93/1.11 inference(symmetry,[status(thm)],[62])).
% 0.93/1.11 tff(64,plain,
% 0.93/1.11 (zero = multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))),
% 0.93/1.11 inference(transitivity,[status(thm)],[63, 53, 42, 32, 30])).
% 0.93/1.11 tff(65,plain,
% 0.93/1.11 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 0.93/1.11 inference(bind,[status(th)],[])).
% 0.93/1.11 tff(66,plain,
% 0.93/1.11 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.93/1.11 inference(quant_intro,[status(thm)],[65])).
% 0.93/1.11 tff(67,plain,
% 0.93/1.11 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(68,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','multiplicative_right_identity')).
% 0.93/1.11 tff(69,plain,
% 0.93/1.11 (![A: $i] : (multiplication(A, one) = A)),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.93/1.11 tff(70,plain,(
% 0.93/1.11 ![A: $i] : (multiplication(A, one) = A)),
% 0.93/1.11 inference(skolemize,[status(sab)],[69])).
% 0.93/1.11 tff(71,plain,
% 0.93/1.11 (![A: $i] : (multiplication(A, one) = A)),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.93/1.11 tff(72,plain,
% 0.93/1.11 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(X0!1, one) = X0!1)),
% 0.93/1.11 inference(quant_inst,[status(thm)],[])).
% 0.93/1.11 tff(73,plain,
% 0.93/1.11 (multiplication(X0!1, one) = X0!1),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.93/1.11 tff(74,plain,
% 0.93/1.11 (X0!1 = multiplication(X0!1, one)),
% 0.93/1.11 inference(symmetry,[status(thm)],[73])).
% 0.93/1.11 tff(75,plain,
% 0.93/1.11 (addition(X0!1, zero) = addition(multiplication(X0!1, one), multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[74, 64])).
% 0.93/1.11 tff(76,plain,
% 0.93/1.11 (addition(multiplication(X0!1, one), multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))) = addition(X0!1, zero)),
% 0.93/1.11 inference(symmetry,[status(thm)],[75])).
% 0.93/1.11 tff(77,plain,
% 0.93/1.11 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!1, addition(one, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))) = addition(multiplication(X0!1, one), multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))))),
% 0.93/1.11 inference(quant_inst,[status(thm)],[])).
% 0.93/1.11 tff(78,plain,
% 0.93/1.11 (multiplication(X0!1, addition(one, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))) = addition(multiplication(X0!1, one), multiplication(X0!1, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))))),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[77, 16])).
% 0.93/1.11 tff(79,plain,
% 0.93/1.11 (addition(multiplication(X1!0, strong_iteration(X1!0)), one) = strong_iteration(X1!0)),
% 0.93/1.11 inference(symmetry,[status(thm)],[27])).
% 0.93/1.11 tff(80,plain,
% 0.93/1.11 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.93/1.11 inference(bind,[status(th)],[])).
% 0.93/1.11 tff(81,plain,
% 0.93/1.11 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.93/1.11 inference(quant_intro,[status(thm)],[80])).
% 0.93/1.11 tff(82,plain,
% 0.93/1.11 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.93/1.11 inference(rewrite,[status(thm)],[])).
% 0.93/1.11 tff(83,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax','additive_commutativity')).
% 0.93/1.11 tff(84,plain,
% 0.93/1.11 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.93/1.11 tff(85,plain,(
% 0.93/1.11 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.93/1.11 inference(skolemize,[status(sab)],[84])).
% 0.93/1.11 tff(86,plain,
% 0.93/1.11 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.93/1.11 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.93/1.11 tff(87,plain,
% 0.93/1.11 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X1!0, strong_iteration(X1!0)), one) = addition(one, multiplication(X1!0, strong_iteration(X1!0))))),
% 0.93/1.11 inference(quant_inst,[status(thm)],[])).
% 0.93/1.11 tff(88,plain,
% 0.93/1.11 (addition(multiplication(X1!0, strong_iteration(X1!0)), one) = addition(one, multiplication(X1!0, strong_iteration(X1!0)))),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.93/1.11 tff(89,plain,
% 0.93/1.11 (addition(one, multiplication(X1!0, strong_iteration(X1!0))) = addition(multiplication(X1!0, strong_iteration(X1!0)), one)),
% 0.93/1.11 inference(symmetry,[status(thm)],[88])).
% 0.93/1.11 tff(90,plain,
% 0.93/1.11 (addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)) = multiplication(X1!0, addition(multiplication(X1!0, strong_iteration(X1!0)), one))),
% 0.93/1.11 inference(symmetry,[status(thm)],[18])).
% 0.93/1.11 tff(91,plain,
% 0.93/1.11 (addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)) = multiplication(X1!0, strong_iteration(X1!0))),
% 0.93/1.11 inference(transitivity,[status(thm)],[90, 31])).
% 0.93/1.11 tff(92,plain,
% 0.93/1.11 (addition(one, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))) = addition(one, multiplication(X1!0, strong_iteration(X1!0)))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[91])).
% 0.93/1.11 tff(93,plain,
% 0.93/1.11 (addition(one, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))) = strong_iteration(X1!0)),
% 0.93/1.11 inference(transitivity,[status(thm)],[92, 89, 79])).
% 0.93/1.11 tff(94,plain,
% 0.93/1.11 (multiplication(X0!1, addition(one, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one)))) = multiplication(X0!1, strong_iteration(X1!0))),
% 0.93/1.11 inference(monotonicity,[status(thm)],[93])).
% 0.93/1.11 tff(95,plain,
% 0.93/1.11 (multiplication(X0!1, strong_iteration(X1!0)) = multiplication(X0!1, addition(one, addition(multiplication(X1!0, multiplication(X1!0, strong_iteration(X1!0))), multiplication(X1!0, one))))),
% 0.93/1.11 inference(symmetry,[status(thm)],[94])).
% 0.93/1.11 tff(96,plain,
% 0.93/1.11 (multiplication(X0!1, strong_iteration(X1!0)) = X0!1),
% 0.93/1.11 inference(transitivity,[status(thm)],[95, 78, 76, 9])).
% 0.93/1.11 tff(97,plain,
% 0.93/1.11 (~(multiplication(X0!1, strong_iteration(X1!0)) = X0!1)),
% 0.93/1.11 inference(or_elim,[status(thm)],[50])).
% 0.93/1.11 tff(98,plain,
% 0.93/1.11 ($false),
% 0.93/1.11 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.93/1.11 % SZS output end Proof
% 0.93/1.11 % E exiting
%------------------------------------------------------------------------------