TSTP Solution File: SYN562-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN562-1 : TPTP v8.1.2. Released v2.5.0.
% 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 : Fri Sep 1 03:35:15 EDT 2023
% Result : Unsatisfiable 0.22s 0.51s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SYN562-1 : TPTP v8.1.2. Released v2.5.0.
% 0.09/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.37 % Computer : n011.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sat Aug 26 17:48:09 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.51 Command-line arguments: --flatten
% 0.22/0.51
% 0.22/0.51 % SZS status Unsatisfiable
% 0.22/0.51
% 0.22/0.52 % SZS output start Proof
% 0.22/0.52 Take the following subset of the input axioms:
% 0.22/0.52 fof(not_p10_3, negated_conjecture, ![X22]: ~p10(X22, X22)).
% 0.22/0.52 fof(p10_14, negated_conjecture, ![X0, X1, X2, X3]: (p10(X0, X1) | (~p2(X2, X0) | (~p2(X3, X1) | ~p10(X2, X3))))).
% 0.22/0.52 fof(p10_16, negated_conjecture, p10(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))).
% 0.22/0.52 fof(p2_1, negated_conjecture, ![X4]: p2(X4, X4)).
% 0.22/0.52 fof(p2_15, negated_conjecture, p2(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))).
% 0.22/0.52 fof(p2_4, negated_conjecture, p2(f9(c11), f3(c12))).
% 0.22/0.52
% 0.22/0.52 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.52 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.52 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.52 fresh(y, y, x1...xn) = u
% 0.22/0.52 C => fresh(s, t, x1...xn) = v
% 0.22/0.52 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.52 variables of u and v.
% 0.22/0.52 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.52 input problem has no model of domain size 1).
% 0.22/0.52
% 0.22/0.52 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.52
% 0.22/0.52 Axiom 1 (p2_1): p2(X, X) = true2.
% 0.22/0.52 Axiom 2 (p10_14): fresh13(X, X, Y, Z) = true2.
% 0.22/0.52 Axiom 3 (p2_4): p2(f9(c11), f3(c12)) = true2.
% 0.22/0.52 Axiom 4 (p10_14): fresh11(X, X, Y, Z, W) = p10(Y, Z).
% 0.22/0.52 Axiom 5 (p10_14): fresh12(X, X, Y, Z, W, V) = fresh13(p2(W, Y), true2, Y, Z).
% 0.22/0.52 Axiom 6 (p10_14): fresh12(p10(X, Y), true2, Z, W, X, Y) = fresh11(p2(Y, W), true2, Z, W, X).
% 0.22/0.52 Axiom 7 (p10_16): p10(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) = true2.
% 0.22/0.52 Axiom 8 (p2_15): p2(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) = true2.
% 0.22/0.52
% 0.22/0.52 Goal 1 (not_p10_3): p10(X, X) = true2.
% 0.22/0.52 The goal is true when:
% 0.22/0.52 X = f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))
% 0.22/0.52
% 0.22/0.52 Proof:
% 0.22/0.52 p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
% 0.22/0.52 = { by axiom 4 (p10_14) R->L }
% 0.22/0.52 fresh11(p2(f9(c11), f3(c12)), p2(f9(c11), f3(c12)), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f7(c11))
% 0.22/0.52 = { by axiom 3 (p2_4) }
% 0.22/0.52 fresh11(true2, p2(f9(c11), f3(c12)), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f7(c11))
% 0.22/0.52 = { by axiom 1 (p2_1) R->L }
% 0.22/0.52 fresh11(p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12)), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f7(c11))
% 0.22/0.52 = { by axiom 3 (p2_4) }
% 0.22/0.53 fresh11(p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), true2, f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f7(c11))
% 0.22/0.53 = { by axiom 6 (p10_14) R->L }
% 0.22/0.53 fresh12(p10(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), true2, f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
% 0.22/0.53 = { by axiom 3 (p2_4) R->L }
% 0.22/0.53 fresh12(p10(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12)), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
% 0.22/0.53 = { by axiom 7 (p10_16) }
% 0.22/0.53 fresh12(true2, p2(f9(c11), f3(c12)), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
% 0.22/0.53 = { by axiom 3 (p2_4) R->L }
% 0.22/0.53 fresh12(p2(f9(c11), f3(c12)), p2(f9(c11), f3(c12)), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
% 0.22/0.53 = { by axiom 5 (p10_14) }
% 0.22/0.53 fresh13(p2(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), true2, f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
% 0.22/0.53 = { by axiom 3 (p2_4) R->L }
% 0.22/0.53 fresh13(p2(f7(c11), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))), p2(f9(c11), f3(c12)), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
% 0.22/0.53 = { by axiom 8 (p2_15) }
% 0.22/0.53 fresh13(true2, p2(f9(c11), f3(c12)), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
% 0.22/0.53 = { by axiom 3 (p2_4) R->L }
% 0.22/0.53 fresh13(p2(f9(c11), f3(c12)), p2(f9(c11), f3(c12)), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))), f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
% 0.22/0.53 = { by axiom 2 (p10_14) }
% 0.22/0.53 true2
% 0.22/0.53 = { by axiom 3 (p2_4) R->L }
% 0.22/0.53 p2(f9(c11), f3(c12))
% 0.22/0.53 = { by axiom 3 (p2_4) }
% 0.22/0.53 true2
% 0.22/0.53 % SZS output end Proof
% 0.22/0.53
% 0.22/0.53 RESULT: Unsatisfiable (the axioms are contradictory).
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