TSTP Solution File: SWV594-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV594-1 : 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 : n011.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 23:05:31 EDT 2023
% Result : Unsatisfiable 105.53s 13.86s
% Output : Proof 105.53s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV594-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 10:23:11 EDT 2023
% 0.14/0.35 % CPUTime :
% 105.53/13.86 Command-line arguments: --no-flatten-goal
% 105.53/13.86
% 105.53/13.86 % SZS status Unsatisfiable
% 105.53/13.86
% 105.53/13.86 % SZS output start Proof
% 105.53/13.86 Take the following subset of the input axioms:
% 105.53/13.87 fof(cls_0_0, axiom, c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), v_x, tc_RealDef_Oreal)).
% 105.53/13.87 fof(cls_CHAINED_0, axiom, c_HOL_Oord__class_Oless(v_x, c_Transcendental_Opi, tc_RealDef_Oreal)).
% 105.53/13.87 fof(cls_class__semiring_Omul__0_0, axiom, ![T_a, V_x]: (~class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a), V_x, T_a)=c_HOL_Ozero__class_Ozero(T_a))).
% 105.53/13.87 fof(cls_conjecture_0, negated_conjecture, c_Transcendental_Osin(v_x)=c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 105.53/13.87 fof(cls_not__real__square__gt__zero_1, axiom, ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(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)).
% 105.53/13.87 fof(cls_sin__gt__zero__pi_0, axiom, ![V_x2]: (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Osin(V_x2), tc_RealDef_Oreal) | (~c_HOL_Oord__class_Oless(V_x2, c_Transcendental_Opi, tc_RealDef_Oreal) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), V_x2, tc_RealDef_Oreal)))).
% 105.53/13.87 fof(cls_tan__pi_0, axiom, c_Transcendental_Otan(c_Transcendental_Opi)=c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 105.53/13.87 fof(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1, axiom, class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)).
% 105.53/13.87
% 105.53/13.87 Now clausify the problem and encode Horn clauses using encoding 3 of
% 105.53/13.87 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 105.53/13.87 We repeatedly replace C & s=t => u=v by the two clauses:
% 105.53/13.87 fresh(y, y, x1...xn) = u
% 105.53/13.87 C => fresh(s, t, x1...xn) = v
% 105.53/13.87 where fresh is a fresh function symbol and x1..xn are the free
% 105.53/13.87 variables of u and v.
% 105.53/13.87 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 105.53/13.87 input problem has no model of domain size 1).
% 105.53/13.87
% 105.53/13.87 The encoding turns the above axioms into the following unit equations and goals:
% 105.53/13.87
% 105.53/13.87 Axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1): class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) = true2.
% 105.53/13.87 Axiom 2 (cls_tan__pi_0): c_Transcendental_Otan(c_Transcendental_Opi) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).
% 105.53/13.87 Axiom 3 (cls_conjecture_0): c_Transcendental_Osin(v_x) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).
% 105.53/13.87 Axiom 4 (cls_sin__gt__zero__pi_0): fresh195(X, X, Y) = true2.
% 105.53/13.87 Axiom 5 (cls_CHAINED_0): c_HOL_Oord__class_Oless(v_x, c_Transcendental_Opi, tc_RealDef_Oreal) = true2.
% 105.53/13.87 Axiom 6 (cls_class__semiring_Omul__0_0): fresh876(X, X, Y, Z) = c_HOL_Ozero__class_Ozero(Y).
% 105.53/13.87 Axiom 7 (cls_one__less__inverse__iff_0): fresh1519(X, X, Y, Z) = c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(Y), Z, Y).
% 105.53/13.87 Axiom 8 (cls_0_0): c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), v_x, tc_RealDef_Oreal) = true2.
% 105.53/13.87 Axiom 9 (cls_class__semiring_Omul__0_0): fresh876(class_Ring__and__Field_Ocomm__semiring__1(X), true2, X, Y) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X), Y, X).
% 105.53/13.87 Axiom 10 (cls_sin__gt__zero__pi_0): fresh196(X, X, Y) = c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Osin(Y), tc_RealDef_Oreal).
% 105.53/13.87 Axiom 11 (cls_sin__gt__zero__pi_0): fresh196(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), X, tc_RealDef_Oreal), true2, X) = fresh195(c_HOL_Oord__class_Oless(X, c_Transcendental_Opi, tc_RealDef_Oreal), true2, X).
% 105.53/13.87
% 105.53/13.87 Goal 1 (cls_not__real__square__gt__zero_1): c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(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) = true2.
% 105.53/13.87 Proof:
% 105.53/13.87 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(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)
% 105.53/13.87 = { by axiom 2 (cls_tan__pi_0) R->L }
% 105.53/13.87 c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi), 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)
% 105.53/13.87 = { by axiom 2 (cls_tan__pi_0) R->L }
% 105.53/13.87 c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi), c_HOL_Otimes__class_Otimes(c_Transcendental_Otan(c_Transcendental_Opi), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 105.53/13.87 = { by axiom 2 (cls_tan__pi_0) R->L }
% 105.53/13.87 c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi), c_HOL_Otimes__class_Otimes(c_Transcendental_Otan(c_Transcendental_Opi), c_Transcendental_Otan(c_Transcendental_Opi), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 105.53/13.87 = { by axiom 2 (cls_tan__pi_0) }
% 105.53/13.87 c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi), c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Otan(c_Transcendental_Opi), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 105.53/13.87 = { by axiom 9 (cls_class__semiring_Omul__0_0) R->L }
% 105.53/13.87 c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi), fresh876(class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_Transcendental_Otan(c_Transcendental_Opi)), tc_RealDef_Oreal)
% 105.53/13.87 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) }
% 105.53/13.87 c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi), fresh876(true2, true2, tc_RealDef_Oreal, c_Transcendental_Otan(c_Transcendental_Opi)), tc_RealDef_Oreal)
% 105.53/13.87 = { by axiom 6 (cls_class__semiring_Omul__0_0) }
% 105.53/13.87 c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal)
% 105.53/13.87 = { by axiom 2 (cls_tan__pi_0) R->L }
% 105.53/13.87 c_HOL_Oord__class_Oless(c_Transcendental_Otan(c_Transcendental_Opi), c_Transcendental_Otan(c_Transcendental_Opi), tc_RealDef_Oreal)
% 105.53/13.87 = { by axiom 2 (cls_tan__pi_0) }
% 105.53/13.87 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Otan(c_Transcendental_Opi), tc_RealDef_Oreal)
% 105.53/13.87 = { by axiom 7 (cls_one__less__inverse__iff_0) R->L }
% 105.53/13.87 fresh1519(X, X, tc_RealDef_Oreal, c_Transcendental_Otan(c_Transcendental_Opi))
% 105.53/13.87 = { by axiom 2 (cls_tan__pi_0) }
% 105.53/13.87 fresh1519(X, X, tc_RealDef_Oreal, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))
% 105.53/13.87 = { by axiom 3 (cls_conjecture_0) R->L }
% 105.53/13.87 fresh1519(X, X, tc_RealDef_Oreal, c_Transcendental_Osin(v_x))
% 105.53/13.87 = { by axiom 7 (cls_one__less__inverse__iff_0) }
% 105.53/13.87 c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Osin(v_x), tc_RealDef_Oreal)
% 105.53/13.87 = { by axiom 10 (cls_sin__gt__zero__pi_0) R->L }
% 105.53/13.87 fresh196(true2, true2, v_x)
% 105.53/13.87 = { by axiom 8 (cls_0_0) R->L }
% 105.53/13.87 fresh196(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), v_x, tc_RealDef_Oreal), true2, v_x)
% 105.53/13.87 = { by axiom 11 (cls_sin__gt__zero__pi_0) }
% 105.53/13.87 fresh195(c_HOL_Oord__class_Oless(v_x, c_Transcendental_Opi, tc_RealDef_Oreal), true2, v_x)
% 105.53/13.87 = { by axiom 5 (cls_CHAINED_0) }
% 105.53/13.87 fresh195(true2, true2, v_x)
% 105.53/13.87 = { by axiom 4 (cls_sin__gt__zero__pi_0) }
% 105.53/13.87 true2
% 105.53/13.87 % SZS output end Proof
% 105.53/13.87
% 105.53/13.87 RESULT: Unsatisfiable (the axioms are contradictory).
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