TSTP Solution File: SWV602-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV602-1 : 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 : n016.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 86.80s 11.36s
% Output : Proof 87.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV602-1 : TPTP v8.1.2. Released v4.1.0.
% 0.03/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 10:47:45 EDT 2023
% 0.13/0.34 % CPUTime :
% 86.80/11.36 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 86.80/11.36
% 86.80/11.36 % SZS status Unsatisfiable
% 86.80/11.36
% 87.11/11.36 % SZS output start Proof
% 87.11/11.36 Take the following subset of the input axioms:
% 87.11/11.37 fof(cls_class__ringb_Oadd__mul__solve_1, axiom, ![T_a, V_x, V_y, V_z]: (~class_Ring__and__Field_Oidom(T_a) | (~class_Int_Onumber__ring(T_a) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x, V_y, T_a), c_HOL_Otimes__class_Otimes(V_x, V_z, T_a), T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x, V_z, T_a), c_HOL_Otimes__class_Otimes(V_x, V_y, T_a), T_a)))).
% 87.11/11.37 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)).
% 87.11/11.37 fof(cls_conjecture_1, negated_conjecture, c_Transcendental_Osin(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)).
% 87.11/11.37 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)).
% 87.11/11.37 fof(cls_sin__cos__squared__add3_0, axiom, ![V_x2]: c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_x2), c_Transcendental_Ocos(V_x2), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_x2), c_Transcendental_Osin(V_x2), tc_RealDef_Oreal), tc_RealDef_Oreal)=c_HOL_Oone__class_Oone(tc_RealDef_Oreal)).
% 87.11/11.37 fof(cls_sum__squares__eq__zero__iff_2, axiom, ![T_a2]: (~class_Ring__and__Field_Oordered__ring__strict(T_a2) | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2), c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2), T_a2)=c_HOL_Ozero__class_Ozero(T_a2))).
% 87.11/11.37 fof(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict, axiom, class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal)).
% 87.11/11.37
% 87.11/11.37 Now clausify the problem and encode Horn clauses using encoding 3 of
% 87.11/11.37 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 87.11/11.37 We repeatedly replace C & s=t => u=v by the two clauses:
% 87.11/11.37 fresh(y, y, x1...xn) = u
% 87.11/11.37 C => fresh(s, t, x1...xn) = v
% 87.11/11.37 where fresh is a fresh function symbol and x1..xn are the free
% 87.11/11.37 variables of u and v.
% 87.11/11.37 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 87.11/11.37 input problem has no model of domain size 1).
% 87.11/11.37
% 87.11/11.37 The encoding turns the above axioms into the following unit equations and goals:
% 87.11/11.37
% 87.11/11.37 Axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict): class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) = true2.
% 87.11/11.37 Axiom 2 (cls_sum__squares__eq__zero__iff_2): fresh129(X, X, Y) = c_HOL_Ozero__class_Ozero(Y).
% 87.11/11.37 Axiom 3 (cls_class__ringb_Oadd__mul__solve_1): fresh827(class_Ring__and__Field_Oidom(X), true2, X, Y, Z, W) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(Y, Z, X), c_HOL_Otimes__class_Otimes(Y, W, X), X).
% 87.11/11.37 Axiom 4 (cls_class__ringb_Oadd__mul__solve_1): fresh828(X, X, Y, Z, W, V) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(Z, V, Y), c_HOL_Otimes__class_Otimes(Z, W, Y), Y).
% 87.11/11.37 Axiom 5 (cls_sum__squares__eq__zero__iff_2): fresh129(class_Ring__and__Field_Oordered__ring__strict(X), true2, X) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X), c_HOL_Ozero__class_Ozero(X), X), c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X), c_HOL_Ozero__class_Ozero(X), X), X).
% 87.11/11.37 Axiom 6 (cls_sin__cos__squared__add3_0): c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X), c_Transcendental_Ocos(X), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(X), c_Transcendental_Osin(X), tc_RealDef_Oreal), tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal).
% 87.11/11.37 Axiom 7 (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).
% 87.11/11.37 Axiom 8 (cls_conjecture_1): c_Transcendental_Osin(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).
% 87.11/11.37
% 87.11/11.37 Lemma 9: fresh827(class_Ring__and__Field_Oidom(X), true2, X, Y, Z, W) = fresh828(V, V, X, Y, W, Z).
% 87.11/11.37 Proof:
% 87.11/11.37 fresh827(class_Ring__and__Field_Oidom(X), true2, X, Y, Z, W)
% 87.11/11.37 = { by axiom 3 (cls_class__ringb_Oadd__mul__solve_1) }
% 87.11/11.37 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(Y, Z, X), c_HOL_Otimes__class_Otimes(Y, W, X), X)
% 87.11/11.37 = { by axiom 4 (cls_class__ringb_Oadd__mul__solve_1) R->L }
% 87.11/11.37 fresh828(V, V, X, Y, W, Z)
% 87.11/11.37
% 87.11/11.37 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).
% 87.11/11.37 Proof:
% 87.11/11.37 c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
% 87.11/11.37 = { by axiom 2 (cls_sum__squares__eq__zero__iff_2) R->L }
% 87.11/11.37 fresh129(true2, true2, tc_RealDef_Oreal)
% 87.11/11.37 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) R->L }
% 87.11/11.37 fresh129(class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal), true2, tc_RealDef_Oreal)
% 87.11/11.37 = { by axiom 5 (cls_sum__squares__eq__zero__iff_2) }
% 87.11/11.37 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 87.11/11.37 = { by axiom 3 (cls_class__ringb_Oadd__mul__solve_1) R->L }
% 87.11/11.37 fresh827(class_Ring__and__Field_Oidom(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))
% 87.11/11.37 = { by lemma 9 }
% 87.11/11.37 fresh828(X, X, tc_RealDef_Oreal, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))
% 87.11/11.37 = { by axiom 8 (cls_conjecture_1) R->L }
% 87.11/11.37 fresh828(X, X, tc_RealDef_Oreal, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Osin(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))
% 87.11/11.37 = { by lemma 9 R->L }
% 87.11/11.37 fresh827(class_Ring__and__Field_Oidom(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Osin(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)))
% 87.11/11.37 = { by axiom 3 (cls_class__ringb_Oadd__mul__solve_1) }
% 87.11/11.37 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Osin(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), tc_RealDef_Oreal)
% 87.11/11.37 = { by axiom 7 (cls_conjecture_0) R->L }
% 87.11/11.37 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), 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_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Osin(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), tc_RealDef_Oreal)
% 87.11/11.37 = { by axiom 7 (cls_conjecture_0) R->L }
% 87.11/11.37 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(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_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_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Osin(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), tc_RealDef_Oreal)
% 87.11/11.37 = { by axiom 8 (cls_conjecture_1) R->L }
% 87.11/11.37 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(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_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_Otimes__class_Otimes(c_Transcendental_Osin(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_Transcendental_Osin(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), tc_RealDef_Oreal)
% 87.11/11.37 = { by axiom 6 (cls_sin__cos__squared__add3_0) }
% 87.11/11.37 c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
% 87.11/11.37 % SZS output end Proof
% 87.11/11.37
% 87.11/11.37 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------