TSTP Solution File: SWV861-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWV861-1 : 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 : n003.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 23:06:33 EDT 2023
% Result : Unsatisfiable 43.31s 5.94s
% Output : Proof 43.31s
% 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 : SWV861-1 : 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
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 03:40:25 EDT 2023
% 0.13/0.34 % CPUTime :
% 43.31/5.94 Command-line arguments: --no-flatten-goal
% 43.31/5.94
% 43.31/5.94 % SZS status Unsatisfiable
% 43.31/5.94
% 43.31/5.94 % SZS output start Proof
% 43.31/5.94 Take the following subset of the input axioms:
% 43.31/5.94 fof(cls_conjecture_0, negated_conjecture, hBOOL(hAPP(hAPP(v_P, v_Z), v_s))).
% 43.31/5.94 fof(cls_conjecture_1, negated_conjecture, c_Natural_Oevaln(v_c, v_s, v_n, v_s1)).
% 43.31/5.94 fof(cls_conjecture_2, negated_conjecture, c_Natural_Oevaln(v_d, v_s1, v_n, v_s_H)).
% 43.31/5.94 fof(cls_conjecture_3, negated_conjecture, ~hBOOL(hAPP(hAPP(v_R, v_Z), v_s_H))).
% 43.31/5.94 fof(cls_conjecture_5, negated_conjecture, ![V_s, V_s_H, V_Z]: (hBOOL(hAPP(hAPP(v_Q, V_Z), V_s_H)) | (~c_Natural_Oevaln(v_c, V_s, v_n, V_s_H) | ~hBOOL(hAPP(hAPP(v_P, V_Z), V_s))))).
% 43.31/5.94 fof(cls_conjecture_6, negated_conjecture, ![V_s2, V_s_H2, V_Z2]: (hBOOL(hAPP(hAPP(v_R, V_Z2), V_s_H2)) | (~c_Natural_Oevaln(v_d, V_s2, v_n, V_s_H2) | ~hBOOL(hAPP(hAPP(v_Q, V_Z2), V_s2))))).
% 43.31/5.94
% 43.31/5.94 Now clausify the problem and encode Horn clauses using encoding 3 of
% 43.31/5.94 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 43.31/5.94 We repeatedly replace C & s=t => u=v by the two clauses:
% 43.31/5.94 fresh(y, y, x1...xn) = u
% 43.31/5.94 C => fresh(s, t, x1...xn) = v
% 43.31/5.94 where fresh is a fresh function symbol and x1..xn are the free
% 43.31/5.94 variables of u and v.
% 43.31/5.94 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 43.31/5.94 input problem has no model of domain size 1).
% 43.31/5.94
% 43.31/5.94 The encoding turns the above axioms into the following unit equations and goals:
% 43.31/5.94
% 43.31/5.94 Axiom 1 (cls_conjecture_5): fresh327(X, X, Y, Z) = true2.
% 43.31/5.94 Axiom 2 (cls_conjecture_6): fresh325(X, X, Y, Z) = true2.
% 43.31/5.94 Axiom 3 (cls_conjecture_1): c_Natural_Oevaln(v_c, v_s, v_n, v_s1) = true2.
% 43.31/5.94 Axiom 4 (cls_conjecture_2): c_Natural_Oevaln(v_d, v_s1, v_n, v_s_H) = true2.
% 43.31/5.94 Axiom 5 (cls_conjecture_5): fresh328(X, X, Y, Z, W) = hBOOL(hAPP(hAPP(v_Q, Y), Z)).
% 43.31/5.94 Axiom 6 (cls_conjecture_6): fresh326(X, X, Y, Z, W) = hBOOL(hAPP(hAPP(v_R, Y), Z)).
% 43.31/5.94 Axiom 7 (cls_conjecture_0): hBOOL(hAPP(hAPP(v_P, v_Z), v_s)) = true2.
% 43.31/5.94 Axiom 8 (cls_conjecture_5): fresh328(c_Natural_Oevaln(v_c, X, v_n, Y), true2, Z, Y, X) = fresh327(hBOOL(hAPP(hAPP(v_P, Z), X)), true2, Z, Y).
% 43.31/5.94 Axiom 9 (cls_conjecture_6): fresh326(c_Natural_Oevaln(v_d, X, v_n, Y), true2, Z, Y, X) = fresh325(hBOOL(hAPP(hAPP(v_Q, Z), X)), true2, Z, Y).
% 43.31/5.94
% 43.31/5.94 Goal 1 (cls_conjecture_3): hBOOL(hAPP(hAPP(v_R, v_Z), v_s_H)) = true2.
% 43.31/5.94 Proof:
% 43.31/5.94 hBOOL(hAPP(hAPP(v_R, v_Z), v_s_H))
% 43.31/5.94 = { by axiom 6 (cls_conjecture_6) R->L }
% 43.31/5.94 fresh326(true2, true2, v_Z, v_s_H, v_s1)
% 43.31/5.94 = { by axiom 4 (cls_conjecture_2) R->L }
% 43.31/5.94 fresh326(c_Natural_Oevaln(v_d, v_s1, v_n, v_s_H), true2, v_Z, v_s_H, v_s1)
% 43.31/5.94 = { by axiom 9 (cls_conjecture_6) }
% 43.31/5.94 fresh325(hBOOL(hAPP(hAPP(v_Q, v_Z), v_s1)), true2, v_Z, v_s_H)
% 43.31/5.94 = { by axiom 5 (cls_conjecture_5) R->L }
% 43.31/5.94 fresh325(fresh328(true2, true2, v_Z, v_s1, v_s), true2, v_Z, v_s_H)
% 43.31/5.94 = { by axiom 3 (cls_conjecture_1) R->L }
% 43.31/5.94 fresh325(fresh328(c_Natural_Oevaln(v_c, v_s, v_n, v_s1), true2, v_Z, v_s1, v_s), true2, v_Z, v_s_H)
% 43.31/5.94 = { by axiom 8 (cls_conjecture_5) }
% 43.31/5.94 fresh325(fresh327(hBOOL(hAPP(hAPP(v_P, v_Z), v_s)), true2, v_Z, v_s1), true2, v_Z, v_s_H)
% 43.31/5.94 = { by axiom 7 (cls_conjecture_0) }
% 43.31/5.94 fresh325(fresh327(true2, true2, v_Z, v_s1), true2, v_Z, v_s_H)
% 43.31/5.94 = { by axiom 1 (cls_conjecture_5) }
% 43.31/5.94 fresh325(true2, true2, v_Z, v_s_H)
% 43.31/5.94 = { by axiom 2 (cls_conjecture_6) }
% 43.31/5.94 true2
% 43.31/5.94 % SZS output end Proof
% 43.31/5.94
% 43.31/5.94 RESULT: Unsatisfiable (the axioms are contradictory).
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