%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV102+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:31:30 AM UTC 2025
% Result : Theorem 2.24s 2.47s
% Output : Proof 2.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV102+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.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 09:28:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 2.24/2.47 % SZS status Theorem
% 2.24/2.47 % SZS output start Proof
% 2.24/2.47 tff(gt_type, type, (
% 2.24/2.47 gt: ( $i * $i ) > $o)).
% 2.24/2.47 tff(n0_type, type, (
% 2.24/2.47 n0: $i)).
% 2.24/2.47 tff(n1_type, type, (
% 2.24/2.47 n1: $i)).
% 2.24/2.47 tff(succ_type, type, (
% 2.24/2.47 succ: $i > $i)).
% 2.24/2.47 tff(use_type, type, (
% 2.24/2.47 use: $i)).
% 2.24/2.47 tff(a_select2_type, type, (
% 2.24/2.47 a_select2: ( $i * $i ) > $i)).
% 2.24/2.47 tff(tptp_update2_type, type, (
% 2.24/2.47 tptp_update2: ( $i * $i * $i ) > $i)).
% 2.24/2.47 tff(n2_type, type, (
% 2.24/2.47 n2: $i)).
% 2.24/2.47 tff(rho_defuse_type, type, (
% 2.24/2.47 rho_defuse: $i)).
% 2.24/2.47 tff(n5_type, type, (
% 2.24/2.47 n5: $i)).
% 2.24/2.47 tff(xinit_defuse_type, type, (
% 2.24/2.47 xinit_defuse: $i)).
% 2.24/2.47 tff(n4_type, type, (
% 2.24/2.47 n4: $i)).
% 2.24/2.47 tff(n3_type, type, (
% 2.24/2.47 n3: $i)).
% 2.24/2.47 tff(a_select3_type, type, (
% 2.24/2.47 a_select3: ( $i * $i * $i ) > $i)).
% 2.24/2.47 tff(u_defuse_type, type, (
% 2.24/2.47 u_defuse: $i)).
% 2.24/2.47 tff(sigma_defuse_type, type, (
% 2.24/2.47 sigma_defuse: $i)).
% 2.24/2.47 tff(1,plain,
% 2.24/2.47 (![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL) <=> ![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(2,plain,
% 2.24/2.47 (![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL) <=> ![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(3,axiom,(![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','sel2_update_1')).
% 2.24/2.47 tff(4,plain,
% 2.24/2.47 (![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[3, 2])).
% 2.24/2.47 tff(5,plain,(
% 2.24/2.47 ![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)),
% 2.24/2.47 inference(skolemize,[status(sab)],[4])).
% 2.24/2.47 tff(6,plain,
% 2.24/2.47 (![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[5, 1])).
% 2.24/2.47 tff(7,plain,
% 2.24/2.47 ((~![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)) | (a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n1) = use)),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(8,plain,
% 2.24/2.47 (a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n1) = use),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[7, 6])).
% 2.24/2.47 tff(9,assumption,(n2 = n1), introduced(assumption)).
% 2.24/2.47 tff(10,plain,
% 2.24/2.47 (n1 = n2),
% 2.24/2.47 inference(symmetry,[status(thm)],[9])).
% 2.24/2.47 tff(11,plain,
% 2.24/2.47 ((succ(n0) = n1) <=> (succ(n0) = n1)),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(12,axiom,(succ(n0) = n1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','successor_1')).
% 2.24/2.47 tff(13,plain,
% 2.24/2.47 (succ(n0) = n1),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[12, 11])).
% 2.24/2.47 tff(14,plain,
% 2.24/2.47 (n1 = succ(n0)),
% 2.24/2.47 inference(symmetry,[status(thm)],[13])).
% 2.24/2.47 tff(15,plain,
% 2.24/2.47 (succ(n1) = succ(succ(n0))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[14])).
% 2.24/2.47 tff(16,plain,
% 2.24/2.47 (succ(succ(n0)) = succ(n1)),
% 2.24/2.47 inference(symmetry,[status(thm)],[15])).
% 2.24/2.47 tff(17,plain,
% 2.24/2.47 ((succ(succ(n0)) = n2) <=> (succ(succ(n0)) = n2)),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(18,axiom,(succ(succ(n0)) = n2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','successor_2')).
% 2.24/2.47 tff(19,plain,
% 2.24/2.47 (succ(succ(n0)) = n2),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[18, 17])).
% 2.24/2.47 tff(20,plain,
% 2.24/2.47 (n2 = succ(succ(n0))),
% 2.24/2.47 inference(symmetry,[status(thm)],[19])).
% 2.24/2.47 tff(21,plain,
% 2.24/2.47 (n2 = succ(n1)),
% 2.24/2.47 inference(transitivity,[status(thm)],[20, 16])).
% 2.24/2.47 tff(22,plain,
% 2.24/2.47 (gt(n2, n1) <=> gt(succ(n1), n2)),
% 2.24/2.47 inference(monotonicity,[status(thm)],[21, 10])).
% 2.24/2.47 tff(23,plain,
% 2.24/2.47 (gt(succ(n1), n2) <=> gt(n2, n1)),
% 2.24/2.47 inference(symmetry,[status(thm)],[22])).
% 2.24/2.47 tff(24,plain,
% 2.24/2.47 ((~gt(succ(n1), n2)) <=> (~gt(n2, n1))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[23])).
% 2.24/2.47 tff(25,plain,
% 2.24/2.47 (gt(n2, n2) <=> gt(succ(n1), n2)),
% 2.24/2.47 inference(monotonicity,[status(thm)],[21])).
% 2.24/2.47 tff(26,plain,
% 2.24/2.47 ((~gt(n2, n2)) <=> (~gt(succ(n1), n2))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[25])).
% 2.24/2.47 tff(27,plain,
% 2.24/2.47 (^[X: $i] : refl((~gt(X, X)) <=> (~gt(X, X)))),
% 2.24/2.47 inference(bind,[status(th)],[])).
% 2.24/2.47 tff(28,plain,
% 2.24/2.47 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 2.24/2.47 inference(quant_intro,[status(thm)],[27])).
% 2.24/2.47 tff(29,plain,
% 2.24/2.47 (![X: $i] : (~gt(X, X)) <=> ![X: $i] : (~gt(X, X))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(30,axiom,(![X: $i] : (~gt(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','irreflexivity_gt')).
% 2.24/2.47 tff(31,plain,
% 2.24/2.47 (![X: $i] : (~gt(X, X))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[30, 29])).
% 2.24/2.47 tff(32,plain,(
% 2.24/2.47 ![X: $i] : (~gt(X, X))),
% 2.24/2.47 inference(skolemize,[status(sab)],[31])).
% 2.24/2.47 tff(33,plain,
% 2.24/2.47 (![X: $i] : (~gt(X, X))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[32, 28])).
% 2.24/2.47 tff(34,plain,
% 2.24/2.47 ((~![X: $i] : (~gt(X, X))) | (~gt(n2, n2))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(35,plain,
% 2.24/2.47 (~gt(n2, n2)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[34, 33])).
% 2.24/2.47 tff(36,plain,
% 2.24/2.47 (~gt(succ(n1), n2)),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[35, 26])).
% 2.24/2.47 tff(37,plain,
% 2.24/2.47 (~gt(n2, n1)),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[36, 24])).
% 2.24/2.47 tff(38,plain,
% 2.24/2.47 (gt(n2, n1) <=> gt(n2, n1)),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(39,axiom,(gt(n2, n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gt_2_1')).
% 2.24/2.47 tff(40,plain,
% 2.24/2.47 (gt(n2, n1)),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[39, 38])).
% 2.24/2.47 tff(41,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[40, 37])).
% 2.24/2.47 tff(42,plain,(~(n2 = n1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(43,plain,
% 2.24/2.47 (![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U)) <=> ![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(44,plain,
% 2.24/2.47 (![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U)) <=> ![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(45,plain,
% 2.24/2.47 (![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U)) <=> ![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 2.24/2.47 inference(elim_unused_vars,[status(thm)],[])).
% 2.24/2.47 tff(46,plain,
% 2.24/2.47 (![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : ((~((~(I = U)) & (a_select2(X, U) = VAL))) | (a_select2(tptp_update2(X, I, VAL2), U) = VAL)) <=> ![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 2.24/2.47 inference(destructive_equality_resolution,[status(thm)],[])).
% 2.24/2.47 tff(47,plain,
% 2.24/2.47 (![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : ((~((~(I = U)) & (a_select2(X, U) = VAL))) | (a_select2(tptp_update2(X, I, VAL2), U) = VAL)) <=> ![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 2.24/2.47 inference(transitivity,[status(thm)],[46, 45])).
% 2.24/2.47 tff(48,plain,
% 2.24/2.47 (^[I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : rewrite((((~(I = U)) & (a_select2(X, U) = VAL)) => (a_select2(tptp_update2(X, I, VAL2), U) = VAL)) <=> ((~((~(I = U)) & (a_select2(X, U) = VAL))) | (a_select2(tptp_update2(X, I, VAL2), U) = VAL)))),
% 2.24/2.47 inference(bind,[status(th)],[])).
% 2.24/2.47 tff(49,plain,
% 2.24/2.47 (![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : (((~(I = U)) & (a_select2(X, U) = VAL)) => (a_select2(tptp_update2(X, I, VAL2), U) = VAL)) <=> ![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : ((~((~(I = U)) & (a_select2(X, U) = VAL))) | (a_select2(tptp_update2(X, I, VAL2), U) = VAL))),
% 2.24/2.47 inference(quant_intro,[status(thm)],[48])).
% 2.24/2.47 tff(50,plain,
% 2.24/2.47 (![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : (((~(I = U)) & (a_select2(X, U) = VAL)) => (a_select2(tptp_update2(X, I, VAL2), U) = VAL)) <=> ![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 2.24/2.47 inference(transitivity,[status(thm)],[49, 47])).
% 2.24/2.47 tff(51,axiom,(![I: $i, U: $i, X: $i, VAL: $i, VAL2: $i] : (((~(I = U)) & (a_select2(X, U) = VAL)) => (a_select2(tptp_update2(X, I, VAL2), U) = VAL))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','sel2_update_2')).
% 2.24/2.47 tff(52,plain,
% 2.24/2.47 (![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[51, 50])).
% 2.24/2.47 tff(53,plain,
% 2.24/2.47 (![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[52, 44])).
% 2.24/2.47 tff(54,plain,(
% 2.24/2.47 ![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 2.24/2.47 inference(skolemize,[status(sab)],[53])).
% 2.24/2.47 tff(55,plain,
% 2.24/2.47 (![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[54, 43])).
% 2.24/2.47 tff(56,plain,
% 2.24/2.47 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n2 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n1)))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n2 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n1)))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(57,plain,
% 2.24/2.47 (((a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n1)) | (n2 = n1)) <=> ((n2 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n1)))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(58,plain,
% 2.24/2.47 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n1)) | (n2 = n1))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n2 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n1))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[57])).
% 2.24/2.47 tff(59,plain,
% 2.24/2.47 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n1)) | (n2 = n1))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n2 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n1)))),
% 2.24/2.47 inference(transitivity,[status(thm)],[58, 56])).
% 2.24/2.47 tff(60,plain,
% 2.24/2.47 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n1)) | (n2 = n1))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(61,plain,
% 2.24/2.47 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n2 = n1) | (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n1))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[60, 59])).
% 2.24/2.47 tff(62,plain,
% 2.24/2.47 (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[61, 55, 42])).
% 2.24/2.47 tff(63,plain,
% 2.24/2.47 (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use),
% 2.24/2.47 inference(transitivity,[status(thm)],[62, 8])).
% 2.24/2.47 tff(64,assumption,(~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use)), introduced(assumption)).
% 2.24/2.47 tff(65,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[64, 63])).
% 2.24/2.47 tff(66,plain,(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(67,assumption,(~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n2) = use)), introduced(assumption)).
% 2.24/2.47 tff(68,plain,
% 2.24/2.47 ((~![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)) | (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n2) = use)),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(69,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[68, 6, 67])).
% 2.24/2.47 tff(70,plain,(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n2) = use), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(71,plain,
% 2.24/2.47 ((a_select2(xinit_defuse, n5) = use) <=> (a_select2(xinit_defuse, n5) = use)),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(72,plain,
% 2.24/2.47 ((~(((((((((((((a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use)) & (a_select2(sigma_defuse, n2) = use)) & (a_select2(sigma_defuse, n3) = use)) & (a_select2(sigma_defuse, n4) = use)) & (a_select2(sigma_defuse, n5) = use)) & (a_select3(u_defuse, n0, n0) = use)) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) => (((((((((((((((a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use)) & (a_select2(sigma_defuse, n2) = use)) & (a_select2(sigma_defuse, n3) = use)) & (a_select2(sigma_defuse, n4) = use)) & (a_select2(sigma_defuse, n5) = use)) & (a_select3(u_defuse, n0, n0) = use)) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use)) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use)) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n2) = use)))) <=> (~((~((a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use))) | ((a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n2) = use))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(73,axiom,(~(((((((((((((a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use)) & (a_select2(sigma_defuse, n2) = use)) & (a_select2(sigma_defuse, n3) = use)) & (a_select2(sigma_defuse, n4) = use)) & (a_select2(sigma_defuse, n5) = use)) & (a_select3(u_defuse, n0, n0) = use)) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) => (((((((((((((((a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use)) & (a_select2(sigma_defuse, n2) = use)) & (a_select2(sigma_defuse, n3) = use)) & (a_select2(sigma_defuse, n4) = use)) & (a_select2(sigma_defuse, n5) = use)) & (a_select3(u_defuse, n0, n0) = use)) & (a_select3(u_defuse, n1, n0) = use)) & (a_select3(u_defuse, n2, n0) = use)) & (a_select2(xinit_defuse, n3) = use)) & (a_select2(xinit_defuse, n4) = use)) & (a_select2(xinit_defuse, n5) = use)) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use)) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use)) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n2) = use)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quaternion_ds1_inuse_0014')).
% 2.24/2.47 tff(74,plain,
% 2.24/2.47 (~((~((a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use))) | ((a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n2) = use)))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[73, 72])).
% 2.24/2.47 tff(75,plain,
% 2.24/2.47 ((a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use)),
% 2.24/2.47 inference(or_elim,[status(thm)],[74])).
% 2.24/2.47 tff(76,plain,
% 2.24/2.47 (a_select2(xinit_defuse, n5) = use),
% 2.24/2.47 inference(and_elim,[status(thm)],[75])).
% 2.24/2.47 tff(77,plain,
% 2.24/2.47 (a_select2(xinit_defuse, n5) = use),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[76, 71])).
% 2.24/2.47 tff(78,plain,
% 2.24/2.47 ((a_select2(xinit_defuse, n4) = use) <=> (a_select2(xinit_defuse, n4) = use)),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(79,plain,
% 2.24/2.47 (a_select2(xinit_defuse, n4) = use),
% 2.24/2.47 inference(and_elim,[status(thm)],[75])).
% 2.24/2.47 tff(80,plain,
% 2.24/2.47 (a_select2(xinit_defuse, n4) = use),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[79, 78])).
% 2.24/2.47 tff(81,plain,
% 2.24/2.47 ((a_select2(xinit_defuse, n3) = use) <=> (a_select2(xinit_defuse, n3) = use)),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(82,plain,
% 2.24/2.47 (a_select2(xinit_defuse, n3) = use),
% 2.24/2.47 inference(and_elim,[status(thm)],[75])).
% 2.24/2.47 tff(83,plain,
% 2.24/2.47 (a_select2(xinit_defuse, n3) = use),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[82, 81])).
% 2.24/2.47 tff(84,plain,
% 2.24/2.47 ((a_select3(u_defuse, n2, n0) = use) <=> (a_select3(u_defuse, n2, n0) = use)),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(85,plain,
% 2.24/2.47 (a_select3(u_defuse, n2, n0) = use),
% 2.24/2.47 inference(and_elim,[status(thm)],[75])).
% 2.24/2.47 tff(86,plain,
% 2.24/2.47 (a_select3(u_defuse, n2, n0) = use),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[85, 84])).
% 2.24/2.47 tff(87,plain,
% 2.24/2.47 ((a_select3(u_defuse, n1, n0) = use) <=> (a_select3(u_defuse, n1, n0) = use)),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(88,plain,
% 2.24/2.47 (a_select3(u_defuse, n1, n0) = use),
% 2.24/2.47 inference(and_elim,[status(thm)],[75])).
% 2.24/2.47 tff(89,plain,
% 2.24/2.47 (a_select3(u_defuse, n1, n0) = use),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[88, 87])).
% 2.24/2.47 tff(90,plain,
% 2.24/2.47 ((a_select3(u_defuse, n0, n0) = use) <=> (a_select3(u_defuse, n0, n0) = use)),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(91,plain,
% 2.24/2.47 (a_select3(u_defuse, n0, n0) = use),
% 2.24/2.47 inference(and_elim,[status(thm)],[75])).
% 2.24/2.47 tff(92,plain,
% 2.24/2.47 (a_select3(u_defuse, n0, n0) = use),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[91, 90])).
% 2.24/2.47 tff(93,plain,
% 2.24/2.47 ((a_select2(sigma_defuse, n5) = use) <=> (a_select2(sigma_defuse, n5) = use)),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(94,plain,
% 2.24/2.47 (a_select2(sigma_defuse, n5) = use),
% 2.24/2.48 inference(and_elim,[status(thm)],[75])).
% 2.24/2.48 tff(95,plain,
% 2.24/2.48 (a_select2(sigma_defuse, n5) = use),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[94, 93])).
% 2.24/2.48 tff(96,plain,
% 2.24/2.48 ((a_select2(sigma_defuse, n4) = use) <=> (a_select2(sigma_defuse, n4) = use)),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(97,plain,
% 2.24/2.48 (a_select2(sigma_defuse, n4) = use),
% 2.24/2.48 inference(and_elim,[status(thm)],[75])).
% 2.24/2.48 tff(98,plain,
% 2.24/2.48 (a_select2(sigma_defuse, n4) = use),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[97, 96])).
% 2.24/2.48 tff(99,plain,
% 2.24/2.48 ((a_select2(sigma_defuse, n3) = use) <=> (a_select2(sigma_defuse, n3) = use)),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(100,plain,
% 2.24/2.48 (a_select2(sigma_defuse, n3) = use),
% 2.24/2.48 inference(and_elim,[status(thm)],[75])).
% 2.24/2.48 tff(101,plain,
% 2.24/2.48 (a_select2(sigma_defuse, n3) = use),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[100, 99])).
% 2.24/2.48 tff(102,plain,
% 2.24/2.48 ((a_select2(sigma_defuse, n2) = use) <=> (a_select2(sigma_defuse, n2) = use)),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(103,plain,
% 2.24/2.48 (a_select2(sigma_defuse, n2) = use),
% 2.24/2.48 inference(and_elim,[status(thm)],[75])).
% 2.24/2.48 tff(104,plain,
% 2.24/2.48 (a_select2(sigma_defuse, n2) = use),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[103, 102])).
% 2.24/2.48 tff(105,plain,
% 2.24/2.48 ((a_select2(sigma_defuse, n1) = use) <=> (a_select2(sigma_defuse, n1) = use)),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(106,plain,
% 2.24/2.48 (a_select2(sigma_defuse, n1) = use),
% 2.24/2.48 inference(and_elim,[status(thm)],[75])).
% 2.24/2.48 tff(107,plain,
% 2.24/2.48 (a_select2(sigma_defuse, n1) = use),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[106, 105])).
% 2.24/2.48 tff(108,plain,
% 2.24/2.48 ((a_select2(sigma_defuse, n0) = use) <=> (a_select2(sigma_defuse, n0) = use)),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(109,plain,
% 2.24/2.48 (a_select2(sigma_defuse, n0) = use),
% 2.24/2.48 inference(and_elim,[status(thm)],[75])).
% 2.24/2.48 tff(110,plain,
% 2.24/2.48 (a_select2(sigma_defuse, n0) = use),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[109, 108])).
% 2.24/2.48 tff(111,plain,
% 2.24/2.48 ((~(~((~(a_select2(sigma_defuse, n0) = use)) | (~(a_select2(sigma_defuse, n1) = use)) | (~(a_select2(sigma_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n3) = use)) | (~(a_select2(sigma_defuse, n4) = use)) | (~(a_select2(sigma_defuse, n5) = use)) | (~(a_select3(u_defuse, n0, n0) = use)) | (~(a_select3(u_defuse, n1, n0) = use)) | (~(a_select3(u_defuse, n2, n0) = use)) | (~(a_select2(xinit_defuse, n3) = use)) | (~(a_select2(xinit_defuse, n4) = use)) | (~(a_select2(xinit_defuse, n5) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n2) = use))))) <=> ((~(a_select2(sigma_defuse, n0) = use)) | (~(a_select2(sigma_defuse, n1) = use)) | (~(a_select2(sigma_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n3) = use)) | (~(a_select2(sigma_defuse, n4) = use)) | (~(a_select2(sigma_defuse, n5) = use)) | (~(a_select3(u_defuse, n0, n0) = use)) | (~(a_select3(u_defuse, n1, n0) = use)) | (~(a_select3(u_defuse, n2, n0) = use)) | (~(a_select2(xinit_defuse, n3) = use)) | (~(a_select2(xinit_defuse, n4) = use)) | (~(a_select2(xinit_defuse, n5) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n2) = use)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(112,plain,
% 2.24/2.48 (((a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n2) = use)) <=> (~((~(a_select2(sigma_defuse, n0) = use)) | (~(a_select2(sigma_defuse, n1) = use)) | (~(a_select2(sigma_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n3) = use)) | (~(a_select2(sigma_defuse, n4) = use)) | (~(a_select2(sigma_defuse, n5) = use)) | (~(a_select3(u_defuse, n0, n0) = use)) | (~(a_select3(u_defuse, n1, n0) = use)) | (~(a_select3(u_defuse, n2, n0) = use)) | (~(a_select2(xinit_defuse, n3) = use)) | (~(a_select2(xinit_defuse, n4) = use)) | (~(a_select2(xinit_defuse, n5) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n2) = use))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(113,plain,
% 2.24/2.48 ((~((a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n2) = use))) <=> (~(~((~(a_select2(sigma_defuse, n0) = use)) | (~(a_select2(sigma_defuse, n1) = use)) | (~(a_select2(sigma_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n3) = use)) | (~(a_select2(sigma_defuse, n4) = use)) | (~(a_select2(sigma_defuse, n5) = use)) | (~(a_select3(u_defuse, n0, n0) = use)) | (~(a_select3(u_defuse, n1, n0) = use)) | (~(a_select3(u_defuse, n2, n0) = use)) | (~(a_select2(xinit_defuse, n3) = use)) | (~(a_select2(xinit_defuse, n4) = use)) | (~(a_select2(xinit_defuse, n5) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n2) = use)))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[112])).
% 2.24/2.48 tff(114,plain,
% 2.24/2.48 ((~((a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n2) = use))) <=> ((~(a_select2(sigma_defuse, n0) = use)) | (~(a_select2(sigma_defuse, n1) = use)) | (~(a_select2(sigma_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n3) = use)) | (~(a_select2(sigma_defuse, n4) = use)) | (~(a_select2(sigma_defuse, n5) = use)) | (~(a_select3(u_defuse, n0, n0) = use)) | (~(a_select3(u_defuse, n1, n0) = use)) | (~(a_select3(u_defuse, n2, n0) = use)) | (~(a_select2(xinit_defuse, n3) = use)) | (~(a_select2(xinit_defuse, n4) = use)) | (~(a_select2(xinit_defuse, n5) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n2) = use)))),
% 2.24/2.48 inference(transitivity,[status(thm)],[113, 111])).
% 2.24/2.48 tff(115,plain,
% 2.24/2.48 ((~((a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n2) = use))) <=> (~((a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n2) = use)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(116,plain,
% 2.24/2.48 (~((a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n2) = use))),
% 2.24/2.48 inference(or_elim,[status(thm)],[74])).
% 2.24/2.48 tff(117,plain,
% 2.24/2.48 (~((a_select2(sigma_defuse, n0) = use) & (a_select2(sigma_defuse, n1) = use) & (a_select2(sigma_defuse, n2) = use) & (a_select2(sigma_defuse, n3) = use) & (a_select2(sigma_defuse, n4) = use) & (a_select2(sigma_defuse, n5) = use) & (a_select3(u_defuse, n0, n0) = use) & (a_select3(u_defuse, n1, n0) = use) & (a_select3(u_defuse, n2, n0) = use) & (a_select2(xinit_defuse, n3) = use) & (a_select2(xinit_defuse, n4) = use) & (a_select2(xinit_defuse, n5) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use) & (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n2) = use))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[116, 115])).
% 2.24/2.48 tff(118,plain,
% 2.24/2.48 ((~(a_select2(sigma_defuse, n0) = use)) | (~(a_select2(sigma_defuse, n1) = use)) | (~(a_select2(sigma_defuse, n2) = use)) | (~(a_select2(sigma_defuse, n3) = use)) | (~(a_select2(sigma_defuse, n4) = use)) | (~(a_select2(sigma_defuse, n5) = use)) | (~(a_select3(u_defuse, n0, n0) = use)) | (~(a_select3(u_defuse, n1, n0) = use)) | (~(a_select3(u_defuse, n2, n0) = use)) | (~(a_select2(xinit_defuse, n3) = use)) | (~(a_select2(xinit_defuse, n4) = use)) | (~(a_select2(xinit_defuse, n5) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n2) = use))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[117, 114])).
% 2.24/2.48 tff(119,plain,
% 2.24/2.48 ((~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n2) = use))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[118, 110, 107, 104, 101, 98, 95, 92, 89, 86, 83, 80, 77])).
% 2.24/2.48 tff(120,plain,
% 2.24/2.48 ((~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use)) | (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n1) = use))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[119, 70])).
% 2.24/2.48 tff(121,plain,
% 2.24/2.48 (~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[120, 66])).
% 2.24/2.48 tff(122,assumption,(~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0))), introduced(assumption)).
% 2.24/2.48 tff(123,assumption,(n2 = n0), introduced(assumption)).
% 2.24/2.48 tff(124,plain,
% 2.24/2.48 (gt(succ(n0), n2) <=> gt(n1, n0)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[13, 123])).
% 2.24/2.48 tff(125,plain,
% 2.24/2.48 (gt(n1, n0) <=> gt(succ(n0), n2)),
% 2.24/2.48 inference(symmetry,[status(thm)],[124])).
% 2.24/2.48 tff(126,plain,
% 2.24/2.48 (gt(n1, n0) <=> gt(n1, n0)),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(127,axiom,(gt(n1, n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gt_1_0')).
% 2.24/2.48 tff(128,plain,
% 2.24/2.48 (gt(n1, n0)),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[127, 126])).
% 2.24/2.48 tff(129,plain,
% 2.24/2.48 (gt(succ(n0), n2)),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[128, 125])).
% 2.24/2.48 tff(130,plain,
% 2.24/2.48 (gt(n1, n2) <=> gt(succ(n0), n2)),
% 2.24/2.48 inference(monotonicity,[status(thm)],[14])).
% 2.24/2.48 tff(131,plain,
% 2.24/2.48 ((~gt(n1, n2)) <=> (~gt(succ(n0), n2))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[130])).
% 2.24/2.48 tff(132,plain,
% 2.24/2.48 ((~![X: $i] : (~gt(X, X))) | (~gt(n1, n1))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(133,plain,
% 2.24/2.48 (~gt(n1, n1)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[132, 33])).
% 2.24/2.48 tff(134,plain,
% 2.24/2.48 (![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(135,plain,
% 2.24/2.48 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((gt(X, Y) & gt(Y, Z)) <=> (~((~gt(X, Y)) | (~gt(Y, Z))))), ((~(gt(X, Y) & gt(Y, Z))) <=> (~(~((~gt(X, Y)) | (~gt(Y, Z))))))), rewrite((~(~((~gt(X, Y)) | (~gt(Y, Z))))) <=> ((~gt(X, Y)) | (~gt(Y, Z)))), ((~(gt(X, Y) & gt(Y, Z))) <=> ((~gt(X, Y)) | (~gt(Y, Z))))), (((~(gt(X, Y) & gt(Y, Z))) | gt(X, Z)) <=> (((~gt(X, Y)) | (~gt(Y, Z))) | gt(X, Z)))), rewrite((((~gt(X, Y)) | (~gt(Y, Z))) | gt(X, Z)) <=> (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))), (((~(gt(X, Y) & gt(Y, Z))) | gt(X, Z)) <=> (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))))),
% 2.24/2.48 inference(bind,[status(th)],[])).
% 2.24/2.48 tff(136,plain,
% 2.24/2.48 (![X: $i, Y: $i, Z: $i] : ((~(gt(X, Y) & gt(Y, Z))) | gt(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))),
% 2.24/2.48 inference(quant_intro,[status(thm)],[135])).
% 2.24/2.48 tff(137,plain,
% 2.24/2.48 (![X: $i, Y: $i, Z: $i] : ((~(gt(X, Y) & gt(Y, Z))) | gt(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(gt(X, Y) & gt(Y, Z))) | gt(X, Z))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(138,plain,
% 2.24/2.48 (^[X: $i, Y: $i, Z: $i] : rewrite(((gt(X, Y) & gt(Y, Z)) => gt(X, Z)) <=> ((~(gt(X, Y) & gt(Y, Z))) | gt(X, Z)))),
% 2.24/2.48 inference(bind,[status(th)],[])).
% 2.24/2.48 tff(139,plain,
% 2.24/2.48 (![X: $i, Y: $i, Z: $i] : ((gt(X, Y) & gt(Y, Z)) => gt(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(gt(X, Y) & gt(Y, Z))) | gt(X, Z))),
% 2.24/2.48 inference(quant_intro,[status(thm)],[138])).
% 2.24/2.48 tff(140,axiom,(![X: $i, Y: $i, Z: $i] : ((gt(X, Y) & gt(Y, Z)) => gt(X, Z))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax','transitivity_gt')).
% 2.24/2.48 tff(141,plain,
% 2.24/2.48 (![X: $i, Y: $i, Z: $i] : ((~(gt(X, Y) & gt(Y, Z))) | gt(X, Z))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[140, 139])).
% 2.24/2.48 tff(142,plain,
% 2.24/2.48 (![X: $i, Y: $i, Z: $i] : ((~(gt(X, Y) & gt(Y, Z))) | gt(X, Z))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[141, 137])).
% 2.24/2.48 tff(143,plain,(
% 2.24/2.48 ![X: $i, Y: $i, Z: $i] : ((~(gt(X, Y) & gt(Y, Z))) | gt(X, Z))),
% 2.24/2.48 inference(skolemize,[status(sab)],[142])).
% 2.24/2.48 tff(144,plain,
% 2.24/2.48 (![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[143, 136])).
% 2.24/2.48 tff(145,plain,
% 2.24/2.48 (![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[144, 134])).
% 2.24/2.48 tff(146,plain,
% 2.24/2.48 (((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | ((~gt(n2, n1)) | gt(n1, n1) | (~gt(n1, n2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (~gt(n2, n1)) | gt(n1, n1) | (~gt(n1, n2)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(147,plain,
% 2.24/2.48 ((gt(n1, n1) | (~gt(n1, n2)) | (~gt(n2, n1))) <=> ((~gt(n2, n1)) | gt(n1, n1) | (~gt(n1, n2)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(148,plain,
% 2.24/2.48 (((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (gt(n1, n1) | (~gt(n1, n2)) | (~gt(n2, n1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | ((~gt(n2, n1)) | gt(n1, n1) | (~gt(n1, n2))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[147])).
% 2.24/2.48 tff(149,plain,
% 2.24/2.48 (((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (gt(n1, n1) | (~gt(n1, n2)) | (~gt(n2, n1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (~gt(n2, n1)) | gt(n1, n1) | (~gt(n1, n2)))),
% 2.24/2.48 inference(transitivity,[status(thm)],[148, 146])).
% 2.24/2.48 tff(150,plain,
% 2.24/2.48 ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (gt(n1, n1) | (~gt(n1, n2)) | (~gt(n2, n1)))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(151,plain,
% 2.24/2.48 ((~![X: $i, Y: $i, Z: $i] : (gt(X, Z) | (~gt(X, Y)) | (~gt(Y, Z)))) | (~gt(n2, n1)) | gt(n1, n1) | (~gt(n1, n2))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[150, 149])).
% 2.24/2.48 tff(152,plain,
% 2.24/2.48 (~gt(n1, n2)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[151, 145, 40, 133])).
% 2.24/2.48 tff(153,plain,
% 2.24/2.48 (~gt(succ(n0), n2)),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[152, 131])).
% 2.24/2.48 tff(154,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[153, 129])).
% 2.24/2.48 tff(155,plain,(~(n2 = n0)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(156,plain,
% 2.24/2.48 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n2 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0)))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n2 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(157,plain,
% 2.24/2.48 (((a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0)) | (n2 = n0)) <=> ((n2 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(158,plain,
% 2.24/2.48 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0)) | (n2 = n0))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n2 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[157])).
% 2.24/2.48 tff(159,plain,
% 2.24/2.48 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0)) | (n2 = n0))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n2 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0)))),
% 2.24/2.48 inference(transitivity,[status(thm)],[158, 156])).
% 2.24/2.48 tff(160,plain,
% 2.24/2.48 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0)) | (n2 = n0))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(161,plain,
% 2.24/2.48 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n2 = n0) | (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[160, 159])).
% 2.24/2.48 tff(162,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[161, 55, 155, 122])).
% 2.24/2.48 tff(163,plain,(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(164,plain,
% 2.24/2.48 ((~![X: $i, U: $i, VAL: $i] : (a_select2(tptp_update2(X, U, VAL), U) = VAL)) | (a_select2(tptp_update2(rho_defuse, n0, use), n0) = use)),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(165,plain,
% 2.24/2.48 (a_select2(tptp_update2(rho_defuse, n0, use), n0) = use),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[164, 6])).
% 2.24/2.48 tff(166,assumption,(~(n1 = n0)), introduced(assumption)).
% 2.24/2.48 tff(167,plain,
% 2.24/2.48 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n1 = n0) | (a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(rho_defuse, n0, use), n0)))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n1 = n0) | (a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(rho_defuse, n0, use), n0)))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(168,plain,
% 2.24/2.49 (((a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(rho_defuse, n0, use), n0)) | (n1 = n0)) <=> ((n1 = n0) | (a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(rho_defuse, n0, use), n0)))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(169,plain,
% 2.24/2.49 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(rho_defuse, n0, use), n0)) | (n1 = n0))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((n1 = n0) | (a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(rho_defuse, n0, use), n0))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[168])).
% 2.24/2.49 tff(170,plain,
% 2.24/2.49 (((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(rho_defuse, n0, use), n0)) | (n1 = n0))) <=> ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n1 = n0) | (a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(rho_defuse, n0, use), n0)))),
% 2.24/2.49 inference(transitivity,[status(thm)],[169, 167])).
% 2.24/2.49 tff(171,plain,
% 2.24/2.49 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | ((a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(rho_defuse, n0, use), n0)) | (n1 = n0))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(172,plain,
% 2.24/2.49 ((~![I: $i, U: $i, X: $i, VAL2: $i] : ((a_select2(tptp_update2(X, I, VAL2), U) = a_select2(X, U)) | (I = U))) | (n1 = n0) | (a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(rho_defuse, n0, use), n0))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[171, 170])).
% 2.24/2.49 tff(173,plain,
% 2.24/2.49 (a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0) = a_select2(tptp_update2(rho_defuse, n0, use), n0)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[172, 55, 166])).
% 2.24/2.49 tff(174,assumption,(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0)), introduced(assumption)).
% 2.24/2.49 tff(175,plain,
% 2.24/2.49 (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use),
% 2.24/2.49 inference(transitivity,[status(thm)],[174, 173, 165])).
% 2.24/2.49 tff(176,assumption,(~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use)), introduced(assumption)).
% 2.24/2.49 tff(177,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[176, 175])).
% 2.24/2.49 tff(178,plain,((~(a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = a_select2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n0))) | (a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use) | (n1 = n0)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(179,plain,
% 2.24/2.49 ((a_select2(tptp_update2(tptp_update2(tptp_update2(rho_defuse, n0, use), n1, use), n2, use), n0) = use) | (n1 = n0)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[178, 163])).
% 2.24/2.49 tff(180,plain,
% 2.24/2.49 (n1 = n0),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[179, 121])).
% 2.24/2.49 tff(181,plain,
% 2.24/2.49 (n0 = n1),
% 2.24/2.49 inference(symmetry,[status(thm)],[180])).
% 2.24/2.49 tff(182,plain,
% 2.24/2.49 (gt(n1, n0) <=> gt(succ(n0), n1)),
% 2.24/2.49 inference(monotonicity,[status(thm)],[14, 181])).
% 2.24/2.49 tff(183,plain,
% 2.24/2.49 (gt(succ(n0), n1) <=> gt(n1, n0)),
% 2.24/2.49 inference(symmetry,[status(thm)],[182])).
% 2.24/2.49 tff(184,plain,
% 2.24/2.49 ((~gt(succ(n0), n1)) <=> (~gt(n1, n0))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[183])).
% 2.24/2.49 tff(185,plain,
% 2.24/2.49 (gt(n1, n1) <=> gt(succ(n0), n1)),
% 2.24/2.49 inference(monotonicity,[status(thm)],[14])).
% 2.24/2.49 tff(186,plain,
% 2.24/2.49 ((~gt(n1, n1)) <=> (~gt(succ(n0), n1))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[185])).
% 2.24/2.49 tff(187,plain,
% 2.24/2.49 (~gt(succ(n0), n1)),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[133, 186])).
% 2.24/2.49 tff(188,plain,
% 2.24/2.49 (~gt(n1, n0)),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[187, 184])).
% 2.24/2.49 tff(189,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[128, 188])).
% 2.24/2.49 % SZS output end Proof
% 2.34/2.50 % E exiting
%------------------------------------------------------------------------------