TSTP Solution File: SET838-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET838-2 : TPTP v8.1.2. Released v3.2.0.
% 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 : n017.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 15:33:27 EDT 2023
% Result : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% 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 : SET838-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 15:52:56 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.37 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.37
% 0.19/0.37 % SZS status Unsatisfiable
% 0.19/0.37
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 Take the following subset of the input axioms:
% 0.19/0.37 fof(cls_conjecture_0, negated_conjecture, v_f(v_g(v_x))=v_x).
% 0.19/0.37 fof(cls_conjecture_1, negated_conjecture, ![V_U]: (V_U=v_x | v_f(v_g(V_U))!=V_U)).
% 0.19/0.37 fof(cls_conjecture_2, negated_conjecture, ![V_U2]: (v_g(v_f(v_xa(V_U2)))=v_xa(V_U2) | v_g(v_f(V_U2))!=V_U2)).
% 0.19/0.37 fof(cls_conjecture_3, negated_conjecture, ![V_U2]: (v_xa(V_U2)!=V_U2 | v_g(v_f(V_U2))!=V_U2)).
% 0.19/0.37
% 0.19/0.37 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.37 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.37 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.37 fresh(y, y, x1...xn) = u
% 0.19/0.37 C => fresh(s, t, x1...xn) = v
% 0.19/0.37 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.37 variables of u and v.
% 0.19/0.37 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.37 input problem has no model of domain size 1).
% 0.19/0.37
% 0.19/0.37 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.37
% 0.19/0.37 Axiom 1 (cls_conjecture_0): v_f(v_g(v_x)) = v_x.
% 0.19/0.37 Axiom 2 (cls_conjecture_1): fresh(X, X, Y) = v_x.
% 0.19/0.37 Axiom 3 (cls_conjecture_2): fresh2(X, X, Y) = v_xa(Y).
% 0.19/0.37 Axiom 4 (cls_conjecture_1): fresh(v_f(v_g(X)), X, X) = X.
% 0.19/0.37 Axiom 5 (cls_conjecture_2): fresh2(v_g(v_f(X)), X, X) = v_g(v_f(v_xa(X))).
% 0.19/0.37
% 0.19/0.37 Lemma 6: v_g(v_f(v_xa(v_g(v_x)))) = v_xa(v_g(v_x)).
% 0.19/0.37 Proof:
% 0.19/0.37 v_g(v_f(v_xa(v_g(v_x))))
% 0.19/0.37 = { by axiom 5 (cls_conjecture_2) R->L }
% 0.19/0.37 fresh2(v_g(v_f(v_g(v_x))), v_g(v_x), v_g(v_x))
% 0.19/0.37 = { by axiom 1 (cls_conjecture_0) }
% 0.19/0.37 fresh2(v_g(v_x), v_g(v_x), v_g(v_x))
% 0.19/0.37 = { by axiom 3 (cls_conjecture_2) }
% 0.19/0.37 v_xa(v_g(v_x))
% 0.19/0.37
% 0.19/0.37 Goal 1 (cls_conjecture_3): tuple(v_g(v_f(X)), v_xa(X)) = tuple(X, X).
% 0.19/0.37 The goal is true when:
% 0.19/0.37 X = v_g(v_x)
% 0.19/0.37
% 0.19/0.37 Proof:
% 0.19/0.37 tuple(v_g(v_f(v_g(v_x))), v_xa(v_g(v_x)))
% 0.19/0.37 = { by lemma 6 R->L }
% 0.19/0.37 tuple(v_g(v_f(v_g(v_x))), v_g(v_f(v_xa(v_g(v_x)))))
% 0.19/0.37 = { by axiom 4 (cls_conjecture_1) R->L }
% 0.19/0.37 tuple(v_g(v_f(v_g(v_x))), v_g(fresh(v_f(v_g(v_f(v_xa(v_g(v_x))))), v_f(v_xa(v_g(v_x))), v_f(v_xa(v_g(v_x))))))
% 0.19/0.37 = { by lemma 6 }
% 0.19/0.37 tuple(v_g(v_f(v_g(v_x))), v_g(fresh(v_f(v_xa(v_g(v_x))), v_f(v_xa(v_g(v_x))), v_f(v_xa(v_g(v_x))))))
% 0.19/0.37 = { by axiom 2 (cls_conjecture_1) }
% 0.19/0.37 tuple(v_g(v_f(v_g(v_x))), v_g(v_x))
% 0.19/0.37 = { by axiom 1 (cls_conjecture_0) }
% 0.19/0.37 tuple(v_g(v_x), v_g(v_x))
% 0.19/0.37 % SZS output end Proof
% 0.19/0.37
% 0.19/0.37 RESULT: Unsatisfiable (the axioms are contradictory).
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