TSTP Solution File: SWV592-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWV592-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n031.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 : Thu Aug 31 23:05:30 EDT 2023
% Result : Unsatisfiable 62.18s 8.23s
% Output : Proof 62.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.09 % Problem : SWV592-1 : TPTP v8.1.2. Released v4.1.0.
% 0.09/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.09/0.28 % Computer : n031.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Tue Aug 29 08:57:40 EDT 2023
% 0.09/0.28 % CPUTime :
% 62.18/8.23 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 62.18/8.23
% 62.18/8.23 % SZS status Unsatisfiable
% 62.18/8.23
% 62.18/8.24 % SZS output start Proof
% 62.18/8.24 Take the following subset of the input axioms:
% 62.18/8.24 fof(cls_conjecture_0, negated_conjecture, c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x, c_Transcendental_Opi, tc_RealDef_Oreal))!=c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(v_x), tc_RealDef_Oreal)).
% 62.18/8.24 fof(cls_eq__diff__eq_H_0, axiom, ![V_y, V_z]: V_y=c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_y, V_z, tc_RealDef_Oreal), V_z, tc_RealDef_Oreal)).
% 62.18/8.24 fof(cls_minus__equation__iff_1, axiom, ![T_a, V_b]: (~class_OrderedGroup_Ogroup__add(T_a) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b, T_a), T_a)=V_b)).
% 62.18/8.24 fof(cls_sin__periodic__pi_0, axiom, ![V_x]: c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(V_x, c_Transcendental_Opi, tc_RealDef_Oreal))=c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x), tc_RealDef_Oreal)).
% 62.18/8.24 fof(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add, axiom, class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)).
% 62.18/8.24
% 62.18/8.24 Now clausify the problem and encode Horn clauses using encoding 3 of
% 62.18/8.24 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 62.18/8.24 We repeatedly replace C & s=t => u=v by the two clauses:
% 62.18/8.24 fresh(y, y, x1...xn) = u
% 62.18/8.24 C => fresh(s, t, x1...xn) = v
% 62.18/8.24 where fresh is a fresh function symbol and x1..xn are the free
% 62.18/8.24 variables of u and v.
% 62.18/8.24 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 62.18/8.24 input problem has no model of domain size 1).
% 62.18/8.24
% 62.18/8.24 The encoding turns the above axioms into the following unit equations and goals:
% 62.18/8.24
% 62.18/8.24 Axiom 1 (clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add): class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) = true2.
% 62.18/8.24 Axiom 2 (cls_sin__periodic__pi_0): c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(X, c_Transcendental_Opi, tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X), tc_RealDef_Oreal).
% 62.18/8.24 Axiom 3 (cls_minus__equation__iff_1): fresh7(X, X, Y, Z) = Z.
% 62.18/8.24 Axiom 4 (cls_minus__equation__iff_1): fresh7(class_OrderedGroup_Ogroup__add(X), true2, X, Y) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(Y, X), X).
% 62.18/8.24 Axiom 5 (cls_eq__diff__eq_H_0): X = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X, Y, tc_RealDef_Oreal), Y, tc_RealDef_Oreal).
% 62.18/8.24
% 62.18/8.24 Goal 1 (cls_conjecture_0): c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x, c_Transcendental_Opi, tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(v_x), tc_RealDef_Oreal).
% 62.18/8.24 Proof:
% 62.18/8.24 c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x, c_Transcendental_Opi, tc_RealDef_Oreal))
% 62.18/8.24 = { by axiom 3 (cls_minus__equation__iff_1) R->L }
% 62.18/8.24 fresh7(true2, true2, tc_RealDef_Oreal, c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x, c_Transcendental_Opi, tc_RealDef_Oreal)))
% 62.18/8.24 = { by axiom 1 (clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) R->L }
% 62.18/8.24 fresh7(class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x, c_Transcendental_Opi, tc_RealDef_Oreal)))
% 62.18/8.24 = { by axiom 4 (cls_minus__equation__iff_1) }
% 62.18/8.24 c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x, c_Transcendental_Opi, tc_RealDef_Oreal)), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 62.18/8.24 = { by axiom 2 (cls_sin__periodic__pi_0) R->L }
% 62.18/8.24 c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(v_x, c_Transcendental_Opi, tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal)), tc_RealDef_Oreal)
% 62.18/8.24 = { by axiom 5 (cls_eq__diff__eq_H_0) R->L }
% 62.18/8.24 c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(v_x), tc_RealDef_Oreal)
% 62.18/8.24 % SZS output end Proof
% 62.18/8.24
% 62.18/8.24 RESULT: Unsatisfiable (the axioms are contradictory).
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