%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ROB021-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:24:19 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ROB021-1 : TPTP v9.0.0. Released v1.0.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 03:29:50 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Unsatisfiable
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(b_type, type, (
% 0.11/0.36 b: $i)).
% 0.11/0.36 tff(add_type, type, (
% 0.11/0.36 add: ( $i * $i ) > $i)).
% 0.11/0.36 tff(negate_type, type, (
% 0.11/0.36 negate: $i > $i)).
% 0.11/0.36 tff(a_type, type, (
% 0.11/0.36 a: $i)).
% 0.11/0.36 tff(inj_0_type, type, (
% 0.11/0.36 inj_0: $i > $i)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 (![Xk!0: $i] : (inj_0(negate(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(negate(Xk!0)) = Xk!0)),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 (![Y: $i, X: $i] : ((~(negate(X) = negate(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(negate(Xk!0)) = Xk!0)),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (![Y: $i, X: $i] : ((~(negate(X) = negate(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(negate(X) = negate(Y))) | (X = Y))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(4,axiom,(![Y: $i, X: $i] : ((~(negate(X) = negate(Y))) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','negative_equality_implies_positive_equality')).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 (![Y: $i, X: $i] : ((~(negate(X) = negate(Y))) | (X = Y))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.36 tff(6,plain,(
% 0.11/0.36 ![Y: $i, X: $i] : ((~(negate(X) = negate(Y))) | (X = Y))),
% 0.11/0.36 inference(skolemize,[status(sab)],[5])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (![Xk!0: $i] : (inj_0(negate(Xk!0)) = Xk!0)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (![Xk!0: $i] : (inj_0(negate(Xk!0)) = Xk!0)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 ((~![Xk!0: $i] : (inj_0(negate(Xk!0)) = Xk!0)) | (inj_0(negate(b)) = b)),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (inj_0(negate(b)) = b),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (^[Y: $i, X: $i] : refl((add(X, Y) = add(Y, X)) <=> (add(X, Y) = add(Y, X)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (add(X, Y) = add(Y, X)) <=> ![Y: $i, X: $i] : (add(X, Y) = add(Y, X))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[11])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (add(X, Y) = add(Y, X)) <=> ![Y: $i, X: $i] : (add(X, Y) = add(Y, X))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(14,axiom,(![Y: $i, X: $i] : (add(X, Y) = add(Y, X))), file('/export/starexec/sandbox/benchmark/Axioms/ROB001-0.ax','commutativity_of_add')).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (add(X, Y) = add(Y, X))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.11/0.36 tff(16,plain,(
% 0.11/0.36 ![Y: $i, X: $i] : (add(X, Y) = add(Y, X))),
% 0.11/0.36 inference(skolemize,[status(sab)],[15])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (add(X, Y) = add(Y, X))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 ((~![Y: $i, X: $i] : (add(X, Y) = add(Y, X))) | (add(negate(a), negate(b)) = add(negate(b), negate(a)))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(19,plain,
% 0.11/0.36 (add(negate(a), negate(b)) = add(negate(b), negate(a))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 (add(negate(b), negate(a)) = add(negate(a), negate(b))),
% 0.11/0.36 inference(symmetry,[status(thm)],[19])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 (negate(add(negate(b), negate(a))) = negate(add(negate(a), negate(b)))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[20])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 ((~![Y: $i, X: $i] : (add(X, Y) = add(Y, X))) | (add(a, negate(b)) = add(negate(b), a))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (add(a, negate(b)) = add(negate(b), a)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[22, 17])).
% 0.11/0.36 tff(24,plain,
% 0.11/0.36 (add(negate(b), a) = add(a, negate(b))),
% 0.11/0.36 inference(symmetry,[status(thm)],[23])).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 (negate(add(negate(b), a)) = negate(add(a, negate(b)))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[24])).
% 0.11/0.36 tff(26,plain,
% 0.11/0.36 (add(negate(add(negate(b), a)), negate(add(negate(b), negate(a)))) = add(negate(add(a, negate(b))), negate(add(negate(a), negate(b))))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[25, 21])).
% 0.11/0.36 tff(27,plain,
% 0.11/0.36 (add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))) = add(negate(add(negate(b), a)), negate(add(negate(b), negate(a))))),
% 0.11/0.36 inference(symmetry,[status(thm)],[26])).
% 0.11/0.36 tff(28,plain,
% 0.11/0.36 ((~![Y: $i, X: $i] : (add(X, Y) = add(Y, X))) | (add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))) = add(negate(add(negate(a), negate(b))), negate(add(a, negate(b)))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(29,plain,
% 0.11/0.36 (add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))) = add(negate(add(negate(a), negate(b))), negate(add(a, negate(b))))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[28, 17])).
% 0.11/0.36 tff(30,plain,
% 0.11/0.36 (add(negate(add(negate(a), negate(b))), negate(add(a, negate(b)))) = add(negate(add(a, negate(b))), negate(add(negate(a), negate(b))))),
% 0.11/0.36 inference(symmetry,[status(thm)],[29])).
% 0.11/0.36 tff(31,plain,
% 0.11/0.36 (add(negate(add(negate(a), negate(b))), negate(add(a, negate(b)))) = add(negate(add(negate(b), a)), negate(add(negate(b), negate(a))))),
% 0.11/0.36 inference(transitivity,[status(thm)],[30, 27])).
% 0.11/0.36 tff(32,plain,
% 0.11/0.36 (negate(add(negate(add(negate(a), negate(b))), negate(add(a, negate(b))))) = negate(add(negate(add(negate(b), a)), negate(add(negate(b), negate(a)))))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[31])).
% 0.11/0.36 tff(33,plain,
% 0.11/0.36 (negate(add(negate(add(negate(b), a)), negate(add(negate(b), negate(a))))) = negate(add(negate(add(negate(a), negate(b))), negate(add(a, negate(b)))))),
% 0.11/0.36 inference(symmetry,[status(thm)],[32])).
% 0.11/0.36 tff(34,plain,
% 0.11/0.36 (^[Y: $i, X: $i] : refl((negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X) <=> (negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(35,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X) <=> ![Y: $i, X: $i] : (negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X)),
% 0.11/0.36 inference(quant_intro,[status(thm)],[34])).
% 0.11/0.36 tff(36,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X) <=> ![Y: $i, X: $i] : (negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X)),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(37,axiom,(![Y: $i, X: $i] : (negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X)), file('/export/starexec/sandbox/benchmark/Axioms/ROB001-0.ax','robbins_axiom')).
% 0.11/0.36 tff(38,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.11/0.36 tff(39,plain,(
% 0.11/0.36 ![Y: $i, X: $i] : (negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X)),
% 0.11/0.36 inference(skolemize,[status(sab)],[38])).
% 0.11/0.36 tff(40,plain,
% 0.11/0.36 (![Y: $i, X: $i] : (negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.11/0.36 tff(41,plain,
% 0.11/0.36 ((~![Y: $i, X: $i] : (negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X)) | (negate(add(negate(add(negate(b), a)), negate(add(negate(b), negate(a))))) = negate(b))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(42,plain,
% 0.11/0.36 (negate(add(negate(add(negate(b), a)), negate(add(negate(b), negate(a))))) = negate(b)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.11/0.36 tff(43,plain,
% 0.11/0.36 (negate(b) = negate(add(negate(add(negate(b), a)), negate(add(negate(b), negate(a)))))),
% 0.11/0.36 inference(symmetry,[status(thm)],[42])).
% 0.11/0.36 tff(44,plain,
% 0.11/0.36 (negate(b) = negate(add(negate(add(negate(a), negate(b))), negate(add(a, negate(b)))))),
% 0.11/0.36 inference(transitivity,[status(thm)],[43, 33])).
% 0.11/0.36 tff(45,plain,
% 0.11/0.36 (inj_0(negate(b)) = inj_0(negate(add(negate(add(negate(a), negate(b))), negate(add(a, negate(b))))))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[44])).
% 0.11/0.36 tff(46,plain,
% 0.11/0.36 (inj_0(negate(add(negate(add(negate(a), negate(b))), negate(add(a, negate(b)))))) = inj_0(negate(b))),
% 0.11/0.36 inference(symmetry,[status(thm)],[45])).
% 0.11/0.36 tff(47,plain,
% 0.11/0.36 ((~![Xk!0: $i] : (inj_0(negate(Xk!0)) = Xk!0)) | (inj_0(negate(add(negate(add(negate(a), negate(b))), negate(add(a, negate(b)))))) = add(negate(add(negate(a), negate(b))), negate(add(a, negate(b)))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(48,plain,
% 0.11/0.36 (inj_0(negate(add(negate(add(negate(a), negate(b))), negate(add(a, negate(b)))))) = add(negate(add(negate(a), negate(b))), negate(add(a, negate(b))))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[47, 8])).
% 0.11/0.36 tff(49,plain,
% 0.11/0.36 (add(negate(add(negate(a), negate(b))), negate(add(a, negate(b)))) = inj_0(negate(add(negate(add(negate(a), negate(b))), negate(add(a, negate(b))))))),
% 0.11/0.36 inference(symmetry,[status(thm)],[48])).
% 0.11/0.36 tff(50,plain,
% 0.11/0.36 (add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))) = b),
% 0.11/0.36 inference(transitivity,[status(thm)],[29, 49, 46, 10])).
% 0.11/0.36 tff(51,plain,
% 0.11/0.36 ((~(add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))) = b)) <=> (~(add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))) = b))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(52,axiom,(~(add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))) = b)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_huntingtons_axiom')).
% 0.11/0.36 tff(53,plain,
% 0.11/0.36 (~(add(negate(add(a, negate(b))), negate(add(negate(a), negate(b)))) = b)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.11/0.36 tff(54,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[53, 50])).
% 0.11/0.36 % SZS output end Proof
% 0.11/0.36 % E exiting
%------------------------------------------------------------------------------