TSTP Solution File: SWV603-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWV603-1 : 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 : n025.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 23:05:34 EDT 2023
% Result : Unsatisfiable 92.71s 12.18s
% Output : Proof 92.71s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWV603-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.09/0.31 % Computer : n025.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Tue Aug 29 03:42:55 EDT 2023
% 0.09/0.31 % CPUTime :
% 92.71/12.18 Command-line arguments: --no-flatten-goal
% 92.71/12.18
% 92.71/12.18 % SZS status Unsatisfiable
% 92.71/12.18
% 92.71/12.18 % SZS output start Proof
% 92.71/12.18 Take the following subset of the input axioms:
% 92.71/12.18 fof(cls_abs__eq__0_1, axiom, ![T_a]: (~class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a), T_a)=c_HOL_Ozero__class_Ozero(T_a))).
% 92.71/12.18 fof(cls_conjecture_0, negated_conjecture, c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal))=c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 92.71/12.18 fof(cls_conjecture_1, negated_conjecture, c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)), tc_RealDef_Oreal)=c_HOL_Oone__class_Oone(tc_RealDef_Oreal)).
% 92.71/12.18 fof(cls_real__zero__not__eq__one_0, axiom, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_HOL_Oone__class_Oone(tc_RealDef_Oreal)).
% 92.71/12.18 fof(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs, axiom, class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)).
% 92.71/12.18
% 92.71/12.18 Now clausify the problem and encode Horn clauses using encoding 3 of
% 92.71/12.18 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 92.71/12.18 We repeatedly replace C & s=t => u=v by the two clauses:
% 92.71/12.18 fresh(y, y, x1...xn) = u
% 92.71/12.18 C => fresh(s, t, x1...xn) = v
% 92.71/12.18 where fresh is a fresh function symbol and x1..xn are the free
% 92.71/12.18 variables of u and v.
% 92.71/12.18 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 92.71/12.18 input problem has no model of domain size 1).
% 92.71/12.18
% 92.71/12.18 The encoding turns the above axioms into the following unit equations and goals:
% 92.71/12.18
% 92.71/12.18 Axiom 1 (clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs): class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) = true2.
% 92.71/12.18 Axiom 2 (cls_abs__eq__0_1): fresh663(X, X, Y) = c_HOL_Ozero__class_Ozero(Y).
% 92.71/12.18 Axiom 3 (cls_abs__eq__0_1): fresh663(class_OrderedGroup_Opordered__ab__group__add__abs(X), true2, X) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X), X).
% 92.71/12.18 Axiom 4 (cls_conjecture_0): c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).
% 92.71/12.18 Axiom 5 (cls_conjecture_1): c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)), tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal).
% 92.71/12.18
% 92.71/12.18 Goal 1 (cls_real__zero__not__eq__one_0): c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal).
% 92.71/12.18 Proof:
% 92.71/12.18 c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
% 92.71/12.18 = { by axiom 2 (cls_abs__eq__0_1) R->L }
% 92.71/12.18 fresh663(true2, true2, tc_RealDef_Oreal)
% 92.71/12.18 = { by axiom 1 (clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) R->L }
% 92.71/12.18 fresh663(class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal), true2, tc_RealDef_Oreal)
% 92.71/12.18 = { by axiom 3 (cls_abs__eq__0_1) }
% 92.71/12.18 c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal)
% 92.71/12.18 = { by axiom 4 (cls_conjecture_0) R->L }
% 92.71/12.18 c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)), tc_RealDef_Oreal)
% 92.71/12.18 = { by axiom 5 (cls_conjecture_1) }
% 92.71/12.18 c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
% 92.71/12.18 % SZS output end Proof
% 92.71/12.18
% 92.71/12.18 RESULT: Unsatisfiable (the axioms are contradictory).
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