TSTP Solution File: SWV573-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV573-1 : 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 : n029.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 23:05:26 EDT 2023
% Result : Unsatisfiable 101.98s 13.27s
% Output : Proof 101.98s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SWV573-1 : TPTP v8.1.2. Released v4.1.0.
% 0.04/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 10:54:41 EDT 2023
% 0.12/0.33 % CPUTime :
% 101.98/13.27 Command-line arguments: --no-flatten-goal
% 101.98/13.27
% 101.98/13.27 % SZS status Unsatisfiable
% 101.98/13.27
% 101.98/13.27 % SZS output start Proof
% 101.98/13.27 Take the following subset of the input axioms:
% 101.98/13.27 fof(cls_complex__Im__of__nat_0, axiom, ![V_n]: c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(V_n, tc_Complex_Ocomplex))=c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 101.98/13.27 fof(cls_complex__Re__of__nat_0, axiom, ![V_n2]: c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n2, tc_Complex_Ocomplex))=c_Nat_Osemiring__1__class_Oof__nat(V_n2, tc_RealDef_Oreal)).
% 101.98/13.27 fof(cls_complex__eq__cancel__iff2_2, axiom, ![V_x]: c_Complex_Ocomplex_OComplex(V_x, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))=c_RealVector_Oof__real(V_x, tc_Complex_Ocomplex)).
% 101.98/13.27 fof(cls_complex__surj_0, axiom, ![V_z]: c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z), c_Complex_OIm(V_z))=V_z).
% 101.98/13.27 fof(cls_conjecture_0, negated_conjecture, c_Nat_Osemiring__1__class_Oof__nat(v_n, tc_Complex_Ocomplex)!=c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n, tc_RealDef_Oreal), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 101.98/13.27 fof(cls_tan__pi_0, axiom, c_Transcendental_Otan(c_Transcendental_Opi)=c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 101.98/13.27
% 101.98/13.27 Now clausify the problem and encode Horn clauses using encoding 3 of
% 101.98/13.27 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 101.98/13.27 We repeatedly replace C & s=t => u=v by the two clauses:
% 101.98/13.27 fresh(y, y, x1...xn) = u
% 101.98/13.27 C => fresh(s, t, x1...xn) = v
% 101.98/13.27 where fresh is a fresh function symbol and x1..xn are the free
% 101.98/13.27 variables of u and v.
% 101.98/13.27 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 101.98/13.27 input problem has no model of domain size 1).
% 101.98/13.27
% 101.98/13.27 The encoding turns the above axioms into the following unit equations and goals:
% 101.98/13.27
% 101.98/13.27 Axiom 1 (cls_tan__pi_0): c_Transcendental_Otan(c_Transcendental_Opi) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).
% 101.98/13.27 Axiom 2 (cls_complex__Im__of__nat_0): c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(X, tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).
% 101.98/13.27 Axiom 3 (cls_complex__Re__of__nat_0): c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(X, tc_Complex_Ocomplex)) = c_Nat_Osemiring__1__class_Oof__nat(X, tc_RealDef_Oreal).
% 101.98/13.27 Axiom 4 (cls_complex__eq__cancel__iff2_2): c_Complex_Ocomplex_OComplex(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(X, tc_Complex_Ocomplex).
% 101.98/13.27 Axiom 5 (cls_complex__surj_0): c_Complex_Ocomplex_OComplex(c_Complex_ORe(X), c_Complex_OIm(X)) = X.
% 101.98/13.27
% 101.98/13.27 Lemma 6: c_Complex_Ocomplex_OComplex(X, c_Transcendental_Otan(c_Transcendental_Opi)) = c_RealVector_Oof__real(X, tc_Complex_Ocomplex).
% 101.98/13.27 Proof:
% 101.98/13.27 c_Complex_Ocomplex_OComplex(X, c_Transcendental_Otan(c_Transcendental_Opi))
% 101.98/13.27 = { by axiom 1 (cls_tan__pi_0) }
% 101.98/13.27 c_Complex_Ocomplex_OComplex(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))
% 101.98/13.27 = { by axiom 4 (cls_complex__eq__cancel__iff2_2) }
% 101.98/13.27 c_RealVector_Oof__real(X, tc_Complex_Ocomplex)
% 101.98/13.27
% 101.98/13.27 Goal 1 (cls_conjecture_0): c_Nat_Osemiring__1__class_Oof__nat(v_n, tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n, tc_RealDef_Oreal), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 101.98/13.27 Proof:
% 101.98/13.27 c_Nat_Osemiring__1__class_Oof__nat(v_n, tc_Complex_Ocomplex)
% 101.98/13.27 = { by axiom 5 (cls_complex__surj_0) R->L }
% 101.98/13.27 c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(v_n, tc_Complex_Ocomplex)), c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(v_n, tc_Complex_Ocomplex)))
% 101.98/13.27 = { by axiom 2 (cls_complex__Im__of__nat_0) }
% 101.98/13.27 c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(v_n, tc_Complex_Ocomplex)), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))
% 101.98/13.27 = { by axiom 1 (cls_tan__pi_0) R->L }
% 101.98/13.27 c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(v_n, tc_Complex_Ocomplex)), c_Transcendental_Otan(c_Transcendental_Opi))
% 101.98/13.27 = { by lemma 6 }
% 101.98/13.27 c_RealVector_Oof__real(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(v_n, tc_Complex_Ocomplex)), tc_Complex_Ocomplex)
% 101.98/13.27 = { by axiom 3 (cls_complex__Re__of__nat_0) }
% 101.98/13.27 c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n, tc_RealDef_Oreal), tc_Complex_Ocomplex)
% 101.98/13.27 = { by lemma 6 R->L }
% 101.98/13.27 c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n, tc_RealDef_Oreal), c_Transcendental_Otan(c_Transcendental_Opi))
% 101.98/13.27 = { by axiom 1 (cls_tan__pi_0) }
% 101.98/13.27 c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n, tc_RealDef_Oreal), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))
% 101.98/13.27 % SZS output end Proof
% 101.98/13.27
% 101.98/13.27 RESULT: Unsatisfiable (the axioms are contradictory).
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