TSTP Solution File: ALG369-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : ALG369-1 : 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 : Wed Aug 30 16:43:05 EDT 2023
% Result : Unsatisfiable 30.45s 4.34s
% Output : Proof 30.45s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG369-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 04:59:29 EDT 2023
% 0.13/0.35 % CPUTime :
% 30.45/4.34 Command-line arguments: --no-flatten-goal
% 30.45/4.34
% 30.45/4.34 % SZS status Unsatisfiable
% 30.45/4.34
% 30.45/4.34 % SZS output start Proof
% 30.45/4.34 Take the following subset of the input axioms:
% 30.45/4.34 fof(cls_CHAINED_0, axiom, c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), v_sko__CHAINED__1(v_e, v_m____), tc_RealDef_Oreal)).
% 30.45/4.34 fof(cls_CHAINED_1, axiom, c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e, v_m____), c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 30.45/4.34 fof(cls_CHAINED_2, axiom, c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e, v_m____), c_HOL_Oinverse__class_Odivide(v_e, v_m____, tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 30.45/4.34 fof(cls_conjecture_0, negated_conjecture, ~v_thesis____).
% 30.45/4.34 fof(cls_that_0, axiom, ![V_d]: (v_thesis____ | (~c_HOL_Oord__class_Oless(V_d, c_HOL_Oinverse__class_Odivide(v_e, v_m____, tc_RealDef_Oreal), tc_RealDef_Oreal) | (~c_HOL_Oord__class_Oless(V_d, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), V_d, tc_RealDef_Oreal))))).
% 30.45/4.34
% 30.45/4.34 Now clausify the problem and encode Horn clauses using encoding 3 of
% 30.45/4.34 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 30.45/4.34 We repeatedly replace C & s=t => u=v by the two clauses:
% 30.45/4.34 fresh(y, y, x1...xn) = u
% 30.45/4.34 C => fresh(s, t, x1...xn) = v
% 30.45/4.34 where fresh is a fresh function symbol and x1..xn are the free
% 30.45/4.34 variables of u and v.
% 30.45/4.34 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 30.45/4.34 input problem has no model of domain size 1).
% 30.45/4.34
% 30.45/4.34 The encoding turns the above axioms into the following unit equations and goals:
% 30.45/4.34
% 30.45/4.34 Axiom 1 (cls_that_0): fresh473(X, X) = true2.
% 30.45/4.34 Axiom 2 (cls_that_0): fresh84(X, X, Y) = v_thesis____.
% 30.45/4.34 Axiom 3 (cls_that_0): fresh472(X, X, Y) = fresh473(c_HOL_Oord__class_Oless(Y, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), true2).
% 30.45/4.34 Axiom 4 (cls_CHAINED_0): c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), v_sko__CHAINED__1(v_e, v_m____), tc_RealDef_Oreal) = true2.
% 30.45/4.34 Axiom 5 (cls_CHAINED_1): c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e, v_m____), c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal) = true2.
% 30.45/4.34 Axiom 6 (cls_CHAINED_2): c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e, v_m____), c_HOL_Oinverse__class_Odivide(v_e, v_m____, tc_RealDef_Oreal), tc_RealDef_Oreal) = true2.
% 30.45/4.34 Axiom 7 (cls_that_0): fresh472(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), X, tc_RealDef_Oreal), true2, X) = fresh84(c_HOL_Oord__class_Oless(X, c_HOL_Oinverse__class_Odivide(v_e, v_m____, tc_RealDef_Oreal), tc_RealDef_Oreal), true2, X).
% 30.45/4.34
% 30.45/4.34 Goal 1 (cls_conjecture_0): v_thesis____ = true2.
% 30.45/4.34 Proof:
% 30.45/4.34 v_thesis____
% 30.45/4.34 = { by axiom 2 (cls_that_0) R->L }
% 30.45/4.34 fresh84(true2, true2, v_sko__CHAINED__1(v_e, v_m____))
% 30.45/4.34 = { by axiom 6 (cls_CHAINED_2) R->L }
% 30.45/4.34 fresh84(c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e, v_m____), c_HOL_Oinverse__class_Odivide(v_e, v_m____, tc_RealDef_Oreal), tc_RealDef_Oreal), true2, v_sko__CHAINED__1(v_e, v_m____))
% 30.45/4.34 = { by axiom 7 (cls_that_0) R->L }
% 30.45/4.34 fresh472(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), v_sko__CHAINED__1(v_e, v_m____), tc_RealDef_Oreal), true2, v_sko__CHAINED__1(v_e, v_m____))
% 30.45/4.34 = { by axiom 4 (cls_CHAINED_0) }
% 30.45/4.34 fresh472(true2, true2, v_sko__CHAINED__1(v_e, v_m____))
% 30.45/4.34 = { by axiom 3 (cls_that_0) }
% 30.45/4.34 fresh473(c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e, v_m____), c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), true2)
% 30.45/4.34 = { by axiom 5 (cls_CHAINED_1) }
% 30.45/4.34 fresh473(true2, true2)
% 30.45/4.34 = { by axiom 1 (cls_that_0) }
% 30.45/4.34 true2
% 30.45/4.34 % SZS output end Proof
% 30.45/4.34
% 30.45/4.34 RESULT: Unsatisfiable (the axioms are contradictory).
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