%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE114+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:13:02 AM UTC 2025
% Result : Theorem 0.40s 0.57s
% Output : Proof 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KLE114+1 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Jun 19 19:00:23 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.40/0.57 % SZS status Theorem
% 0.40/0.57 % SZS output start Proof
% 0.40/0.57 tff(one_type, type, (
% 0.40/0.57 one: $i)).
% 0.40/0.57 tff(forward_box_type, type, (
% 0.40/0.57 forward_box: ( $i * $i ) > $i)).
% 0.40/0.57 tff(tptp_fun_X0_0_type, type, (
% 0.40/0.57 tptp_fun_X0_0: $i)).
% 0.40/0.57 tff(addition_type, type, (
% 0.40/0.57 addition: ( $i * $i ) > $i)).
% 0.40/0.57 tff(antidomain_type, type, (
% 0.40/0.57 antidomain: $i > $i)).
% 0.40/0.57 tff(zero_type, type, (
% 0.40/0.57 zero: $i)).
% 0.40/0.57 tff(multiplication_type, type, (
% 0.40/0.57 multiplication: ( $i * $i ) > $i)).
% 0.40/0.57 tff(domain_type, type, (
% 0.40/0.57 domain: $i > $i)).
% 0.40/0.57 tff(c_type, type, (
% 0.40/0.57 c: $i > $i)).
% 0.40/0.57 tff(forward_diamond_type, type, (
% 0.40/0.57 forward_diamond: ( $i * $i ) > $i)).
% 0.40/0.57 tff(1,plain,
% 0.40/0.57 (^[X0: $i] : refl((addition(antidomain(antidomain(X0)), antidomain(X0)) = one) <=> (addition(antidomain(antidomain(X0)), antidomain(X0)) = one))),
% 0.40/0.57 inference(bind,[status(th)],[])).
% 0.40/0.57 tff(2,plain,
% 0.40/0.57 (![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one) <=> ![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 0.40/0.57 inference(quant_intro,[status(thm)],[1])).
% 0.40/0.57 tff(3,plain,
% 0.40/0.57 (![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one) <=> ![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(4,axiom,(![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax','domain3')).
% 0.40/0.57 tff(5,plain,
% 0.40/0.57 (![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.40/0.57 tff(6,plain,(
% 0.40/0.57 ![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 0.40/0.57 inference(skolemize,[status(sab)],[5])).
% 0.40/0.57 tff(7,plain,
% 0.40/0.57 (![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.40/0.57 tff(8,plain,
% 0.40/0.57 ((~![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)) | (addition(antidomain(antidomain(one)), antidomain(one)) = one)),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(9,plain,
% 0.40/0.57 (addition(antidomain(antidomain(one)), antidomain(one)) = one),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.40/0.57 tff(10,plain,
% 0.40/0.57 (^[X0: $i] : refl((multiplication(antidomain(X0), X0) = zero) <=> (multiplication(antidomain(X0), X0) = zero))),
% 0.40/0.57 inference(bind,[status(th)],[])).
% 0.40/0.57 tff(11,plain,
% 0.40/0.57 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero) <=> ![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.40/0.57 inference(quant_intro,[status(thm)],[10])).
% 0.40/0.57 tff(12,plain,
% 0.40/0.57 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero) <=> ![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(13,axiom,(![X0: $i] : (multiplication(antidomain(X0), X0) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax','domain1')).
% 0.40/0.57 tff(14,plain,
% 0.40/0.57 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.40/0.57 tff(15,plain,(
% 0.40/0.57 ![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.40/0.57 inference(skolemize,[status(sab)],[14])).
% 0.40/0.57 tff(16,plain,
% 0.40/0.57 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.40/0.57 tff(17,plain,
% 0.40/0.57 ((~![X0: $i] : (multiplication(antidomain(X0), X0) = zero)) | (multiplication(antidomain(one), one) = zero)),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(18,plain,
% 0.40/0.57 (multiplication(antidomain(one), one) = zero),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.40/0.57 tff(19,plain,
% 0.40/0.57 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 0.40/0.57 inference(bind,[status(th)],[])).
% 0.40/0.57 tff(20,plain,
% 0.40/0.57 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.40/0.57 inference(quant_intro,[status(thm)],[19])).
% 0.40/0.57 tff(21,plain,
% 0.40/0.57 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(22,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 0.40/0.57 tff(23,plain,
% 0.40/0.57 (![A: $i] : (multiplication(A, one) = A)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.40/0.57 tff(24,plain,(
% 0.40/0.57 ![A: $i] : (multiplication(A, one) = A)),
% 0.40/0.57 inference(skolemize,[status(sab)],[23])).
% 0.40/0.57 tff(25,plain,
% 0.40/0.57 (![A: $i] : (multiplication(A, one) = A)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.40/0.57 tff(26,plain,
% 0.40/0.57 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(antidomain(one), one) = antidomain(one))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(27,plain,
% 0.40/0.57 (multiplication(antidomain(one), one) = antidomain(one)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.40/0.57 tff(28,plain,
% 0.40/0.57 (antidomain(one) = multiplication(antidomain(one), one)),
% 0.40/0.57 inference(symmetry,[status(thm)],[27])).
% 0.40/0.57 tff(29,plain,
% 0.40/0.57 (antidomain(one) = zero),
% 0.40/0.57 inference(transitivity,[status(thm)],[28, 18])).
% 0.40/0.57 tff(30,plain,
% 0.40/0.57 (^[X0: $i, X1: $i] : refl((forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1)))) <=> (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1)))))),
% 0.40/0.57 inference(bind,[status(th)],[])).
% 0.40/0.57 tff(31,plain,
% 0.40/0.57 (![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1)))) <=> ![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 0.40/0.57 inference(quant_intro,[status(thm)],[30])).
% 0.40/0.57 tff(32,plain,
% 0.40/0.57 (![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1)))) <=> ![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(33,axiom,(![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax','forward_diamond')).
% 0.40/0.57 tff(34,plain,
% 0.40/0.57 (![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.40/0.57 tff(35,plain,(
% 0.40/0.57 ![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 0.40/0.57 inference(skolemize,[status(sab)],[34])).
% 0.40/0.57 tff(36,plain,
% 0.40/0.57 (![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.40/0.57 tff(37,plain,
% 0.40/0.57 ((~![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))) | (forward_diamond(X0!0, c(one)) = domain(multiplication(X0!0, domain(c(one)))))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(38,plain,
% 0.40/0.57 (forward_diamond(X0!0, c(one)) = domain(multiplication(X0!0, domain(c(one))))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.40/0.57 tff(39,plain,
% 0.40/0.57 (domain(forward_diamond(X0!0, c(one))) = domain(domain(multiplication(X0!0, domain(c(one)))))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[38])).
% 0.40/0.57 tff(40,plain,
% 0.40/0.57 (domain(domain(multiplication(X0!0, domain(c(one))))) = domain(forward_diamond(X0!0, c(one)))),
% 0.40/0.57 inference(symmetry,[status(thm)],[39])).
% 0.40/0.57 tff(41,plain,
% 0.40/0.57 (^[X0: $i] : refl((domain(X0) = antidomain(antidomain(X0))) <=> (domain(X0) = antidomain(antidomain(X0))))),
% 0.40/0.57 inference(bind,[status(th)],[])).
% 0.40/0.57 tff(42,plain,
% 0.40/0.57 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0))) <=> ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.40/0.57 inference(quant_intro,[status(thm)],[41])).
% 0.40/0.57 tff(43,plain,
% 0.40/0.57 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0))) <=> ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(44,axiom,(![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax','domain4')).
% 0.40/0.57 tff(45,plain,
% 0.40/0.57 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.40/0.57 tff(46,plain,(
% 0.40/0.57 ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.40/0.57 inference(skolemize,[status(sab)],[45])).
% 0.40/0.57 tff(47,plain,
% 0.40/0.57 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.40/0.57 tff(48,plain,
% 0.40/0.57 ((~![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))) | (domain(domain(multiplication(X0!0, domain(c(one))))) = antidomain(antidomain(domain(multiplication(X0!0, domain(c(one)))))))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(49,plain,
% 0.40/0.57 (domain(domain(multiplication(X0!0, domain(c(one))))) = antidomain(antidomain(domain(multiplication(X0!0, domain(c(one))))))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.40/0.57 tff(50,plain,
% 0.40/0.57 (antidomain(antidomain(domain(multiplication(X0!0, domain(c(one)))))) = domain(domain(multiplication(X0!0, domain(c(one)))))),
% 0.40/0.57 inference(symmetry,[status(thm)],[49])).
% 0.40/0.57 tff(51,plain,
% 0.40/0.57 (antidomain(antidomain(domain(multiplication(X0!0, domain(c(one)))))) = domain(forward_diamond(X0!0, c(one)))),
% 0.40/0.57 inference(transitivity,[status(thm)],[50, 40])).
% 0.40/0.57 tff(52,plain,
% 0.40/0.57 (^[X0: $i] : refl((c(X0) = antidomain(domain(X0))) <=> (c(X0) = antidomain(domain(X0))))),
% 0.40/0.57 inference(bind,[status(th)],[])).
% 0.40/0.57 tff(53,plain,
% 0.40/0.57 (![X0: $i] : (c(X0) = antidomain(domain(X0))) <=> ![X0: $i] : (c(X0) = antidomain(domain(X0)))),
% 0.40/0.57 inference(quant_intro,[status(thm)],[52])).
% 0.40/0.57 tff(54,plain,
% 0.40/0.57 (![X0: $i] : (c(X0) = antidomain(domain(X0))) <=> ![X0: $i] : (c(X0) = antidomain(domain(X0)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(55,axiom,(![X0: $i] : (c(X0) = antidomain(domain(X0)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax','complement')).
% 0.40/0.57 tff(56,plain,
% 0.40/0.57 (![X0: $i] : (c(X0) = antidomain(domain(X0)))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.40/0.57 tff(57,plain,(
% 0.40/0.57 ![X0: $i] : (c(X0) = antidomain(domain(X0)))),
% 0.40/0.57 inference(skolemize,[status(sab)],[56])).
% 0.40/0.57 tff(58,plain,
% 0.40/0.57 (![X0: $i] : (c(X0) = antidomain(domain(X0)))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.40/0.57 tff(59,plain,
% 0.40/0.57 ((~![X0: $i] : (c(X0) = antidomain(domain(X0)))) | (c(forward_diamond(X0!0, c(one))) = antidomain(domain(forward_diamond(X0!0, c(one)))))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(60,plain,
% 0.40/0.57 (c(forward_diamond(X0!0, c(one))) = antidomain(domain(forward_diamond(X0!0, c(one))))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.40/0.57 tff(61,plain,
% 0.40/0.57 (multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one))))))) = multiplication(antidomain(domain(forward_diamond(X0!0, c(one)))), domain(forward_diamond(X0!0, c(one))))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[60, 51])).
% 0.40/0.57 tff(62,plain,
% 0.40/0.57 (multiplication(antidomain(domain(forward_diamond(X0!0, c(one)))), domain(forward_diamond(X0!0, c(one)))) = multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one)))))))),
% 0.40/0.57 inference(symmetry,[status(thm)],[61])).
% 0.40/0.57 tff(63,plain,
% 0.40/0.57 ((~![X0: $i] : (multiplication(antidomain(X0), X0) = zero)) | (multiplication(antidomain(domain(forward_diamond(X0!0, c(one)))), domain(forward_diamond(X0!0, c(one)))) = zero)),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(64,plain,
% 0.40/0.57 (multiplication(antidomain(domain(forward_diamond(X0!0, c(one)))), domain(forward_diamond(X0!0, c(one)))) = zero),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[63, 16])).
% 0.40/0.57 tff(65,plain,
% 0.40/0.57 (zero = multiplication(antidomain(domain(forward_diamond(X0!0, c(one)))), domain(forward_diamond(X0!0, c(one))))),
% 0.40/0.57 inference(symmetry,[status(thm)],[64])).
% 0.40/0.57 tff(66,plain,
% 0.40/0.57 (antidomain(one) = multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one)))))))),
% 0.40/0.57 inference(transitivity,[status(thm)],[28, 18, 65, 62])).
% 0.40/0.57 tff(67,plain,
% 0.40/0.57 (antidomain(antidomain(one)) = antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one))))))))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[66])).
% 0.40/0.57 tff(68,plain,
% 0.40/0.57 (addition(antidomain(antidomain(one)), antidomain(one)) = addition(antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one)))))))), zero)),
% 0.40/0.57 inference(monotonicity,[status(thm)],[67, 29])).
% 0.40/0.57 tff(69,plain,
% 0.40/0.57 (addition(antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one)))))))), zero) = addition(antidomain(antidomain(one)), antidomain(one))),
% 0.40/0.57 inference(symmetry,[status(thm)],[68])).
% 0.40/0.57 tff(70,plain,
% 0.40/0.57 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 0.40/0.57 inference(bind,[status(th)],[])).
% 0.40/0.57 tff(71,plain,
% 0.40/0.57 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.40/0.57 inference(quant_intro,[status(thm)],[70])).
% 0.40/0.57 tff(72,plain,
% 0.40/0.57 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(73,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 0.40/0.57 tff(74,plain,
% 0.40/0.57 (![A: $i] : (addition(A, zero) = A)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.40/0.57 tff(75,plain,(
% 0.40/0.57 ![A: $i] : (addition(A, zero) = A)),
% 0.40/0.57 inference(skolemize,[status(sab)],[74])).
% 0.40/0.57 tff(76,plain,
% 0.40/0.57 (![A: $i] : (addition(A, zero) = A)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.40/0.57 tff(77,plain,
% 0.40/0.57 ((~![A: $i] : (addition(A, zero) = A)) | (addition(antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one)))))))), zero) = antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one)))))))))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(78,plain,
% 0.40/0.57 (addition(antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one)))))))), zero) = antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one))))))))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.40/0.57 tff(79,plain,
% 0.40/0.57 (antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one)))))))) = addition(antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one)))))))), zero)),
% 0.40/0.57 inference(symmetry,[status(thm)],[78])).
% 0.40/0.57 tff(80,plain,
% 0.40/0.57 ((~![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))) | (domain(one) = antidomain(antidomain(one)))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(81,plain,
% 0.40/0.57 (domain(one) = antidomain(antidomain(one))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[80, 47])).
% 0.40/0.57 tff(82,plain,
% 0.40/0.57 (domain(one) = one),
% 0.40/0.57 inference(transitivity,[status(thm)],[81, 67, 79, 69, 9])).
% 0.40/0.57 tff(83,plain,
% 0.40/0.57 (domain(domain(one)) = domain(one)),
% 0.40/0.57 inference(monotonicity,[status(thm)],[82])).
% 0.40/0.57 tff(84,plain,
% 0.40/0.57 ((~![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))) | (domain(domain(one)) = antidomain(antidomain(domain(one))))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(85,plain,
% 0.40/0.57 (domain(domain(one)) = antidomain(antidomain(domain(one)))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[84, 47])).
% 0.40/0.57 tff(86,plain,
% 0.40/0.57 (antidomain(antidomain(domain(one))) = domain(domain(one))),
% 0.40/0.57 inference(symmetry,[status(thm)],[85])).
% 0.40/0.57 tff(87,plain,
% 0.40/0.57 (antidomain(antidomain(one)) = domain(one)),
% 0.40/0.57 inference(symmetry,[status(thm)],[81])).
% 0.40/0.57 tff(88,plain,
% 0.40/0.57 (antidomain(antidomain(antidomain(one))) = antidomain(domain(one))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[87])).
% 0.40/0.57 tff(89,plain,
% 0.40/0.57 ((~![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))) | (domain(antidomain(one)) = antidomain(antidomain(antidomain(one))))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(90,plain,
% 0.40/0.57 (domain(antidomain(one)) = antidomain(antidomain(antidomain(one)))),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[89, 47])).
% 0.40/0.57 tff(91,plain,
% 0.40/0.57 (domain(antidomain(one)) = antidomain(domain(one))),
% 0.40/0.57 inference(transitivity,[status(thm)],[90, 88])).
% 0.40/0.57 tff(92,plain,
% 0.40/0.57 (antidomain(domain(antidomain(one))) = antidomain(antidomain(domain(one)))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[91])).
% 0.40/0.57 tff(93,plain,
% 0.40/0.57 ((~![X0: $i] : (c(X0) = antidomain(domain(X0)))) | (c(antidomain(one)) = antidomain(domain(antidomain(one))))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(94,plain,
% 0.40/0.57 (c(antidomain(one)) = antidomain(domain(antidomain(one)))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[93, 58])).
% 0.40/0.58 tff(95,plain,
% 0.40/0.58 (zero = multiplication(antidomain(one), one)),
% 0.40/0.58 inference(symmetry,[status(thm)],[18])).
% 0.40/0.58 tff(96,plain,
% 0.40/0.58 (zero = antidomain(one)),
% 0.40/0.58 inference(transitivity,[status(thm)],[95, 27])).
% 0.40/0.58 tff(97,plain,
% 0.40/0.58 (c(zero) = c(antidomain(one))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[96])).
% 0.40/0.58 tff(98,plain,
% 0.40/0.58 ((~![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)) | (addition(antidomain(antidomain(antidomain(antidomain(antidomain(domain(one)))))), antidomain(antidomain(antidomain(antidomain(domain(one)))))) = one)),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(99,plain,
% 0.40/0.58 (addition(antidomain(antidomain(antidomain(antidomain(antidomain(domain(one)))))), antidomain(antidomain(antidomain(antidomain(domain(one)))))) = one),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[98, 7])).
% 0.40/0.58 tff(100,plain,
% 0.40/0.58 ((~![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))) | (domain(antidomain(domain(one))) = antidomain(antidomain(antidomain(domain(one)))))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(101,plain,
% 0.40/0.58 (domain(antidomain(domain(one))) = antidomain(antidomain(antidomain(domain(one))))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[100, 47])).
% 0.40/0.58 tff(102,plain,
% 0.40/0.58 (antidomain(antidomain(antidomain(domain(one)))) = domain(antidomain(domain(one)))),
% 0.40/0.58 inference(symmetry,[status(thm)],[101])).
% 0.40/0.58 tff(103,plain,
% 0.40/0.58 (antidomain(antidomain(antidomain(antidomain(domain(one))))) = antidomain(domain(antidomain(domain(one))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[102])).
% 0.40/0.58 tff(104,plain,
% 0.40/0.58 (antidomain(domain(antidomain(domain(one)))) = antidomain(antidomain(antidomain(antidomain(domain(one)))))),
% 0.40/0.58 inference(symmetry,[status(thm)],[103])).
% 0.40/0.58 tff(105,plain,
% 0.40/0.58 (addition(antidomain(antidomain(antidomain(antidomain(antidomain(domain(one)))))), antidomain(domain(antidomain(domain(one))))) = addition(antidomain(antidomain(antidomain(antidomain(antidomain(domain(one)))))), antidomain(antidomain(antidomain(antidomain(domain(one))))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[104])).
% 0.40/0.58 tff(106,plain,
% 0.40/0.58 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.40/0.58 inference(bind,[status(th)],[])).
% 0.40/0.58 tff(107,plain,
% 0.40/0.58 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.40/0.58 inference(quant_intro,[status(thm)],[106])).
% 0.40/0.58 tff(108,plain,
% 0.40/0.58 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(109,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 0.40/0.58 tff(110,plain,
% 0.40/0.58 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.40/0.58 tff(111,plain,(
% 0.40/0.58 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.40/0.58 inference(skolemize,[status(sab)],[110])).
% 0.40/0.58 tff(112,plain,
% 0.40/0.58 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.40/0.58 tff(113,plain,
% 0.40/0.58 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(antidomain(antidomain(antidomain(antidomain(antidomain(domain(one)))))), antidomain(domain(antidomain(domain(one))))) = addition(antidomain(domain(antidomain(domain(one)))), antidomain(antidomain(antidomain(antidomain(antidomain(domain(one))))))))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(114,plain,
% 0.40/0.58 (addition(antidomain(antidomain(antidomain(antidomain(antidomain(domain(one)))))), antidomain(domain(antidomain(domain(one))))) = addition(antidomain(domain(antidomain(domain(one)))), antidomain(antidomain(antidomain(antidomain(antidomain(domain(one)))))))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.40/0.58 tff(115,plain,
% 0.40/0.58 (addition(antidomain(domain(antidomain(domain(one)))), antidomain(antidomain(antidomain(antidomain(antidomain(domain(one))))))) = addition(antidomain(antidomain(antidomain(antidomain(antidomain(domain(one)))))), antidomain(domain(antidomain(domain(one)))))),
% 0.40/0.58 inference(symmetry,[status(thm)],[114])).
% 0.40/0.58 tff(116,plain,
% 0.40/0.58 (addition(antidomain(domain(antidomain(domain(one)))), antidomain(antidomain(antidomain(antidomain(antidomain(domain(one))))))) = one),
% 0.40/0.58 inference(transitivity,[status(thm)],[115, 105, 99])).
% 0.40/0.58 tff(117,plain,
% 0.40/0.58 (multiplication(zero, addition(antidomain(domain(antidomain(domain(one)))), antidomain(antidomain(antidomain(antidomain(antidomain(domain(one)))))))) = multiplication(antidomain(one), one)),
% 0.40/0.58 inference(monotonicity,[status(thm)],[96, 116])).
% 0.40/0.58 tff(118,plain,
% 0.40/0.58 (^[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))))),
% 0.40/0.58 inference(bind,[status(th)],[])).
% 0.40/0.58 tff(119,plain,
% 0.40/0.58 (![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)))),
% 0.40/0.58 inference(quant_intro,[status(thm)],[118])).
% 0.40/0.58 tff(120,plain,
% 0.40/0.58 (![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)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(121,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','right_distributivity')).
% 0.40/0.58 tff(122,plain,
% 0.40/0.58 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.40/0.58 tff(123,plain,(
% 0.40/0.58 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.40/0.58 inference(skolemize,[status(sab)],[122])).
% 0.40/0.58 tff(124,plain,
% 0.40/0.58 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.40/0.58 tff(125,plain,
% 0.40/0.58 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(zero, addition(antidomain(domain(antidomain(domain(one)))), antidomain(antidomain(antidomain(antidomain(antidomain(domain(one)))))))) = addition(multiplication(zero, antidomain(domain(antidomain(domain(one))))), multiplication(zero, antidomain(antidomain(antidomain(antidomain(antidomain(domain(one)))))))))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(126,plain,
% 0.40/0.58 (multiplication(zero, addition(antidomain(domain(antidomain(domain(one)))), antidomain(antidomain(antidomain(antidomain(antidomain(domain(one)))))))) = addition(multiplication(zero, antidomain(domain(antidomain(domain(one))))), multiplication(zero, antidomain(antidomain(antidomain(antidomain(antidomain(domain(one))))))))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.40/0.58 tff(127,plain,
% 0.40/0.58 (addition(multiplication(zero, antidomain(domain(antidomain(domain(one))))), multiplication(zero, antidomain(antidomain(antidomain(antidomain(antidomain(domain(one)))))))) = multiplication(zero, addition(antidomain(domain(antidomain(domain(one)))), antidomain(antidomain(antidomain(antidomain(antidomain(domain(one))))))))),
% 0.40/0.58 inference(symmetry,[status(thm)],[126])).
% 0.40/0.58 tff(128,plain,
% 0.40/0.58 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 0.40/0.58 inference(bind,[status(th)],[])).
% 0.40/0.58 tff(129,plain,
% 0.40/0.58 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.40/0.58 inference(quant_intro,[status(thm)],[128])).
% 0.40/0.58 tff(130,plain,
% 0.40/0.58 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(131,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','left_annihilation')).
% 0.40/0.58 tff(132,plain,
% 0.40/0.58 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.40/0.58 tff(133,plain,(
% 0.40/0.58 ![A: $i] : (multiplication(zero, A) = zero)),
% 0.40/0.58 inference(skolemize,[status(sab)],[132])).
% 0.40/0.58 tff(134,plain,
% 0.40/0.58 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.40/0.58 tff(135,plain,
% 0.40/0.58 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, antidomain(antidomain(antidomain(antidomain(antidomain(domain(one))))))) = zero)),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(136,plain,
% 0.40/0.58 (multiplication(zero, antidomain(antidomain(antidomain(antidomain(antidomain(domain(one))))))) = zero),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.40/0.58 tff(137,plain,
% 0.40/0.58 (zero = multiplication(zero, antidomain(antidomain(antidomain(antidomain(antidomain(domain(one)))))))),
% 0.40/0.58 inference(symmetry,[status(thm)],[136])).
% 0.40/0.58 tff(138,plain,
% 0.40/0.58 (^[A: $i] : refl((multiplication(A, zero) = zero) <=> (multiplication(A, zero) = zero))),
% 0.40/0.58 inference(bind,[status(th)],[])).
% 0.40/0.58 tff(139,plain,
% 0.40/0.58 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 0.40/0.58 inference(quant_intro,[status(thm)],[138])).
% 0.40/0.58 tff(140,plain,
% 0.40/0.58 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(141,axiom,(![A: $i] : (multiplication(A, zero) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','right_annihilation')).
% 0.40/0.58 tff(142,plain,
% 0.40/0.58 (![A: $i] : (multiplication(A, zero) = zero)),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.40/0.58 tff(143,plain,(
% 0.40/0.58 ![A: $i] : (multiplication(A, zero) = zero)),
% 0.40/0.58 inference(skolemize,[status(sab)],[142])).
% 0.40/0.58 tff(144,plain,
% 0.40/0.58 (![A: $i] : (multiplication(A, zero) = zero)),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.40/0.58 tff(145,plain,
% 0.40/0.58 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(antidomain(domain(one)), zero) = zero)),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(146,plain,
% 0.40/0.58 (multiplication(antidomain(domain(one)), zero) = zero),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.40/0.58 tff(147,plain,
% 0.40/0.58 (multiplication(antidomain(domain(one)), antidomain(one)) = multiplication(antidomain(domain(one)), zero)),
% 0.40/0.58 inference(monotonicity,[status(thm)],[29])).
% 0.40/0.58 tff(148,plain,
% 0.40/0.58 (multiplication(antidomain(domain(one)), antidomain(one)) = multiplication(zero, antidomain(antidomain(antidomain(antidomain(antidomain(domain(one)))))))),
% 0.40/0.58 inference(transitivity,[status(thm)],[147, 146, 137])).
% 0.40/0.58 tff(149,plain,
% 0.40/0.58 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, antidomain(domain(antidomain(domain(one))))) = zero)),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(150,plain,
% 0.40/0.58 (multiplication(zero, antidomain(domain(antidomain(domain(one))))) = zero),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[149, 134])).
% 0.40/0.58 tff(151,plain,
% 0.40/0.58 (zero = multiplication(zero, antidomain(domain(antidomain(domain(one)))))),
% 0.40/0.58 inference(symmetry,[status(thm)],[150])).
% 0.40/0.58 tff(152,plain,
% 0.40/0.58 ((~![X0: $i] : (multiplication(antidomain(X0), X0) = zero)) | (multiplication(antidomain(domain(one)), domain(one)) = zero)),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(153,plain,
% 0.40/0.58 (multiplication(antidomain(domain(one)), domain(one)) = zero),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[152, 16])).
% 0.40/0.58 tff(154,plain,
% 0.40/0.58 (multiplication(antidomain(domain(one)), antidomain(antidomain(one))) = multiplication(antidomain(domain(one)), domain(one))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[87])).
% 0.40/0.58 tff(155,plain,
% 0.40/0.58 (multiplication(antidomain(domain(one)), antidomain(antidomain(one))) = multiplication(zero, antidomain(domain(antidomain(domain(one)))))),
% 0.40/0.58 inference(transitivity,[status(thm)],[154, 153, 151])).
% 0.40/0.58 tff(156,plain,
% 0.40/0.58 (addition(multiplication(antidomain(domain(one)), antidomain(antidomain(one))), multiplication(antidomain(domain(one)), antidomain(one))) = addition(multiplication(zero, antidomain(domain(antidomain(domain(one))))), multiplication(zero, antidomain(antidomain(antidomain(antidomain(antidomain(domain(one))))))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[155, 148])).
% 0.40/0.58 tff(157,plain,
% 0.40/0.58 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(antidomain(domain(one)), addition(antidomain(antidomain(one)), antidomain(one))) = addition(multiplication(antidomain(domain(one)), antidomain(antidomain(one))), multiplication(antidomain(domain(one)), antidomain(one))))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(158,plain,
% 0.40/0.58 (multiplication(antidomain(domain(one)), addition(antidomain(antidomain(one)), antidomain(one))) = addition(multiplication(antidomain(domain(one)), antidomain(antidomain(one))), multiplication(antidomain(domain(one)), antidomain(one)))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[157, 124])).
% 0.40/0.58 tff(159,plain,
% 0.40/0.58 (one = addition(antidomain(antidomain(one)), antidomain(one))),
% 0.40/0.58 inference(symmetry,[status(thm)],[9])).
% 0.40/0.58 tff(160,plain,
% 0.40/0.58 (multiplication(antidomain(domain(one)), one) = multiplication(antidomain(domain(one)), addition(antidomain(antidomain(one)), antidomain(one)))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[159])).
% 0.40/0.58 tff(161,plain,
% 0.40/0.58 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(antidomain(domain(one)), one) = antidomain(domain(one)))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(162,plain,
% 0.40/0.58 (multiplication(antidomain(domain(one)), one) = antidomain(domain(one))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[161, 25])).
% 0.40/0.58 tff(163,plain,
% 0.40/0.58 (antidomain(domain(one)) = multiplication(antidomain(domain(one)), one)),
% 0.40/0.58 inference(symmetry,[status(thm)],[162])).
% 0.40/0.58 tff(164,plain,
% 0.40/0.58 (multiplication(antidomain(domain(one)), domain(one)) = antidomain(one)),
% 0.40/0.58 inference(transitivity,[status(thm)],[153, 95, 27])).
% 0.40/0.58 tff(165,plain,
% 0.40/0.58 (domain(multiplication(antidomain(domain(one)), domain(one))) = domain(antidomain(one))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[164])).
% 0.40/0.58 tff(166,plain,
% 0.40/0.58 (zero = multiplication(antidomain(domain(one)), domain(one))),
% 0.40/0.58 inference(symmetry,[status(thm)],[153])).
% 0.40/0.58 tff(167,plain,
% 0.40/0.58 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(X0!0, zero) = zero)),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(168,plain,
% 0.40/0.58 (multiplication(X0!0, zero) = zero),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[167, 144])).
% 0.40/0.58 tff(169,plain,
% 0.40/0.58 (multiplication(X0!0, antidomain(one)) = multiplication(X0!0, zero)),
% 0.40/0.58 inference(monotonicity,[status(thm)],[29])).
% 0.40/0.58 tff(170,plain,
% 0.40/0.58 (antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one)))))))) = antidomain(antidomain(one))),
% 0.40/0.58 inference(symmetry,[status(thm)],[67])).
% 0.40/0.58 tff(171,plain,
% 0.40/0.58 (antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one)))))))) = domain(one)),
% 0.40/0.58 inference(transitivity,[status(thm)],[170, 87])).
% 0.40/0.58 tff(172,plain,
% 0.40/0.58 (multiplication(antidomain(domain(one)), antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one))))))))) = multiplication(antidomain(domain(one)), domain(one))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[171])).
% 0.40/0.58 tff(173,plain,
% 0.40/0.58 (multiplication(antidomain(domain(one)), antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one))))))))) = antidomain(one)),
% 0.40/0.58 inference(transitivity,[status(thm)],[172, 153, 95, 27])).
% 0.40/0.58 tff(174,plain,
% 0.40/0.58 (multiplication(X0!0, multiplication(antidomain(domain(one)), antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one)))))))))) = multiplication(X0!0, antidomain(one))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[173])).
% 0.40/0.58 tff(175,plain,
% 0.40/0.58 (^[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)))),
% 0.40/0.58 inference(bind,[status(th)],[])).
% 0.40/0.58 tff(176,plain,
% 0.40/0.58 (![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))),
% 0.40/0.58 inference(quant_intro,[status(thm)],[175])).
% 0.40/0.58 tff(177,plain,
% 0.40/0.58 (![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))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(178,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_associativity')).
% 0.40/0.58 tff(179,plain,
% 0.40/0.58 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.40/0.58 tff(180,plain,(
% 0.40/0.58 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.40/0.58 inference(skolemize,[status(sab)],[179])).
% 0.40/0.58 tff(181,plain,
% 0.40/0.58 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[180, 176])).
% 0.40/0.58 tff(182,plain,
% 0.40/0.58 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X0!0, multiplication(antidomain(domain(one)), antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one)))))))))) = multiplication(multiplication(X0!0, antidomain(domain(one))), antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one))))))))))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(183,plain,
% 0.40/0.58 (multiplication(X0!0, multiplication(antidomain(domain(one)), antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one)))))))))) = multiplication(multiplication(X0!0, antidomain(domain(one))), antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one)))))))))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.40/0.58 tff(184,plain,
% 0.40/0.58 (multiplication(multiplication(X0!0, antidomain(domain(one))), antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one))))))))) = multiplication(X0!0, multiplication(antidomain(domain(one)), antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one))))))))))),
% 0.40/0.58 inference(symmetry,[status(thm)],[183])).
% 0.40/0.58 tff(185,plain,
% 0.40/0.58 (one = antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one))))))))),
% 0.40/0.58 inference(transitivity,[status(thm)],[159, 68, 78])).
% 0.40/0.58 tff(186,plain,
% 0.40/0.58 (multiplication(multiplication(X0!0, antidomain(domain(one))), one) = multiplication(multiplication(X0!0, antidomain(domain(one))), antidomain(multiplication(c(forward_diamond(X0!0, c(one))), antidomain(antidomain(domain(multiplication(X0!0, domain(c(one)))))))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[185])).
% 0.40/0.58 tff(187,plain,
% 0.40/0.58 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X0!0, multiplication(antidomain(domain(one)), one)) = multiplication(multiplication(X0!0, antidomain(domain(one))), one))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(188,plain,
% 0.40/0.58 (multiplication(X0!0, multiplication(antidomain(domain(one)), one)) = multiplication(multiplication(X0!0, antidomain(domain(one))), one)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[187, 181])).
% 0.40/0.58 tff(189,plain,
% 0.40/0.58 (multiplication(X0!0, antidomain(domain(one))) = multiplication(X0!0, multiplication(antidomain(domain(one)), one))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[163])).
% 0.40/0.58 tff(190,plain,
% 0.40/0.58 (multiplication(X0!0, antidomain(domain(one))) = multiplication(antidomain(domain(one)), domain(one))),
% 0.40/0.58 inference(transitivity,[status(thm)],[189, 188, 186, 184, 174, 169, 168, 166])).
% 0.40/0.58 tff(191,plain,
% 0.40/0.58 (domain(multiplication(X0!0, antidomain(domain(one)))) = domain(multiplication(antidomain(domain(one)), domain(one)))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[190])).
% 0.40/0.58 tff(192,plain,
% 0.40/0.58 (multiplication(X0!0, domain(antidomain(one))) = multiplication(X0!0, antidomain(domain(one)))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[91])).
% 0.40/0.58 tff(193,plain,
% 0.40/0.58 (domain(multiplication(X0!0, domain(antidomain(one)))) = domain(multiplication(X0!0, antidomain(domain(one))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[192])).
% 0.40/0.58 tff(194,plain,
% 0.40/0.58 ((~![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))) | (forward_diamond(X0!0, antidomain(one)) = domain(multiplication(X0!0, domain(antidomain(one)))))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(195,plain,
% 0.40/0.58 (forward_diamond(X0!0, antidomain(one)) = domain(multiplication(X0!0, domain(antidomain(one))))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[194, 36])).
% 0.40/0.58 tff(196,plain,
% 0.40/0.58 ((~![X0: $i] : (c(X0) = antidomain(domain(X0)))) | (c(one) = antidomain(domain(one)))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(197,plain,
% 0.40/0.58 (c(one) = antidomain(domain(one))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[196, 58])).
% 0.40/0.58 tff(198,plain,
% 0.40/0.58 (c(one) = antidomain(one)),
% 0.40/0.58 inference(transitivity,[status(thm)],[197, 163, 160, 158, 156, 127, 117, 27])).
% 0.40/0.58 tff(199,plain,
% 0.40/0.58 (forward_diamond(X0!0, c(one)) = forward_diamond(X0!0, antidomain(one))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[198])).
% 0.40/0.58 tff(200,plain,
% 0.40/0.58 (forward_diamond(X0!0, c(one)) = zero),
% 0.40/0.58 inference(transitivity,[status(thm)],[199, 195, 193, 191, 165, 90, 88, 163, 160, 158, 156, 127, 117, 18])).
% 0.40/0.58 tff(201,plain,
% 0.40/0.58 (c(forward_diamond(X0!0, c(one))) = c(zero)),
% 0.40/0.58 inference(monotonicity,[status(thm)],[200])).
% 0.40/0.58 tff(202,plain,
% 0.40/0.58 (^[X0: $i, X1: $i] : refl((forward_box(X0, X1) = c(forward_diamond(X0, c(X1)))) <=> (forward_box(X0, X1) = c(forward_diamond(X0, c(X1)))))),
% 0.40/0.58 inference(bind,[status(th)],[])).
% 0.40/0.58 tff(203,plain,
% 0.40/0.58 (![X0: $i, X1: $i] : (forward_box(X0, X1) = c(forward_diamond(X0, c(X1)))) <=> ![X0: $i, X1: $i] : (forward_box(X0, X1) = c(forward_diamond(X0, c(X1))))),
% 0.40/0.58 inference(quant_intro,[status(thm)],[202])).
% 0.40/0.58 tff(204,plain,
% 0.40/0.58 (![X0: $i, X1: $i] : (forward_box(X0, X1) = c(forward_diamond(X0, c(X1)))) <=> ![X0: $i, X1: $i] : (forward_box(X0, X1) = c(forward_diamond(X0, c(X1))))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(205,axiom,(![X0: $i, X1: $i] : (forward_box(X0, X1) = c(forward_diamond(X0, c(X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax','forward_box')).
% 0.40/0.58 tff(206,plain,
% 0.40/0.58 (![X0: $i, X1: $i] : (forward_box(X0, X1) = c(forward_diamond(X0, c(X1))))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.40/0.58 tff(207,plain,(
% 0.40/0.58 ![X0: $i, X1: $i] : (forward_box(X0, X1) = c(forward_diamond(X0, c(X1))))),
% 0.40/0.58 inference(skolemize,[status(sab)],[206])).
% 0.40/0.58 tff(208,plain,
% 0.40/0.58 (![X0: $i, X1: $i] : (forward_box(X0, X1) = c(forward_diamond(X0, c(X1))))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[207, 203])).
% 0.40/0.58 tff(209,plain,
% 0.40/0.58 ((~![X0: $i, X1: $i] : (forward_box(X0, X1) = c(forward_diamond(X0, c(X1))))) | (forward_box(X0!0, one) = c(forward_diamond(X0!0, c(one))))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(210,plain,
% 0.40/0.58 (forward_box(X0!0, one) = c(forward_diamond(X0!0, c(one)))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[209, 208])).
% 0.40/0.58 tff(211,plain,
% 0.40/0.58 (forward_box(X0!0, one) = one),
% 0.40/0.58 inference(transitivity,[status(thm)],[210, 201, 97, 94, 92, 86, 83, 81, 67, 79, 69, 9])).
% 0.40/0.58 tff(212,plain,
% 0.40/0.58 ((~![X0: $i] : (forward_box(X0, one) = one)) <=> (~![X0: $i] : (forward_box(X0, one) = one))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(213,axiom,(~![X0: $i] : (forward_box(X0, one) = one)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.40/0.58 tff(214,plain,
% 0.40/0.58 (~![X0: $i] : (forward_box(X0, one) = one)),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.40/0.58 tff(215,plain,
% 0.40/0.58 (~![X0: $i] : (forward_box(X0, one) = one)),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[214, 212])).
% 0.40/0.58 tff(216,plain,
% 0.40/0.58 (~![X0: $i] : (forward_box(X0, one) = one)),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[215, 212])).
% 0.40/0.58 tff(217,plain,
% 0.40/0.58 (~![X0: $i] : (forward_box(X0, one) = one)),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[216, 212])).
% 0.40/0.58 tff(218,plain,(
% 0.40/0.58 ~(forward_box(X0!0, one) = one)),
% 0.40/0.58 inference(skolemize,[status(sab)],[217])).
% 0.40/0.58 tff(219,plain,
% 0.40/0.58 ($false),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[218, 211])).
% 0.40/0.58 % SZS output end Proof
% 0.40/0.59 % E exiting
%------------------------------------------------------------------------------