TSTP Solution File: SYN333-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN333-1 : TPTP v8.1.2. Released v1.2.0.
% 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 : n031.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 03:34:08 EDT 2023
% Result : Unsatisfiable 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN333-1 : TPTP v8.1.2. Released v1.2.0.
% 0.13/0.13 % 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 : n031.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 : Sat Aug 26 21:20:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.37 Command-line arguments: --no-flatten-goal
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% 0.20/0.37 % SZS status Unsatisfiable
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% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 Take the following subset of the input axioms:
% 0.20/0.38 fof(clause1, negated_conjecture, ![X, Y]: f(X, Y)).
% 0.20/0.38 fof(clause2, negated_conjecture, ![X2, Y2]: (~f(Y2, z(X2, Y2)) | (~f(z(X2, Y2), z(X2, Y2)) | g(X2, Y2)))).
% 0.20/0.38 fof(clause3, negated_conjecture, ![X2, Y2]: (~f(Y2, z(X2, Y2)) | (~f(z(X2, Y2), z(X2, Y2)) | (~g(X2, z(X2, Y2)) | ~g(z(X2, Y2), z(X2, Y2)))))).
% 0.20/0.38
% 0.20/0.38 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.38 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.38 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.38 fresh(y, y, x1...xn) = u
% 0.20/0.38 C => fresh(s, t, x1...xn) = v
% 0.20/0.38 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.38 variables of u and v.
% 0.20/0.38 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.38 input problem has no model of domain size 1).
% 0.20/0.38
% 0.20/0.38 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.38
% 0.20/0.38 Axiom 1 (clause1): f(X, Y) = true2.
% 0.20/0.38 Axiom 2 (clause2): fresh(X, X, Y, Z) = g(Z, Y).
% 0.20/0.38 Axiom 3 (clause2): fresh2(X, X, Y, Z) = true2.
% 0.20/0.38 Axiom 4 (clause2): fresh(f(z(X, Y), z(X, Y)), true2, Y, X) = fresh2(f(Y, z(X, Y)), true2, Y, X).
% 0.20/0.38
% 0.20/0.38 Lemma 5: g(X, Y) = true2.
% 0.20/0.38 Proof:
% 0.20/0.38 g(X, Y)
% 0.20/0.38 = { by axiom 2 (clause2) R->L }
% 0.20/0.38 fresh(true2, true2, Y, X)
% 0.20/0.38 = { by axiom 1 (clause1) R->L }
% 0.20/0.38 fresh(f(z(X, Y), z(X, Y)), true2, Y, X)
% 0.20/0.38 = { by axiom 4 (clause2) }
% 0.20/0.38 fresh2(f(Y, z(X, Y)), true2, Y, X)
% 0.20/0.38 = { by axiom 1 (clause1) }
% 0.20/0.38 fresh2(true2, true2, Y, X)
% 0.20/0.38 = { by axiom 3 (clause2) }
% 0.20/0.38 true2
% 0.20/0.38
% 0.20/0.38 Goal 1 (clause3): tuple(f(X, z(Y, X)), f(z(Y, X), z(Y, X)), g(Y, z(Y, X)), g(z(Y, X), z(Y, X))) = tuple(true2, true2, true2, true2).
% 0.20/0.38 The goal is true when:
% 0.20/0.38 X = Y
% 0.20/0.38 Y = X
% 0.20/0.38
% 0.20/0.38 Proof:
% 0.20/0.38 tuple(f(Y, z(X, Y)), f(z(X, Y), z(X, Y)), g(X, z(X, Y)), g(z(X, Y), z(X, Y)))
% 0.20/0.38 = { by axiom 1 (clause1) }
% 0.20/0.38 tuple(true2, f(z(X, Y), z(X, Y)), g(X, z(X, Y)), g(z(X, Y), z(X, Y)))
% 0.20/0.38 = { by axiom 1 (clause1) }
% 0.20/0.38 tuple(true2, true2, g(X, z(X, Y)), g(z(X, Y), z(X, Y)))
% 0.20/0.38 = { by lemma 5 }
% 0.20/0.38 tuple(true2, true2, true2, g(z(X, Y), z(X, Y)))
% 0.20/0.38 = { by lemma 5 }
% 0.20/0.38 tuple(true2, true2, true2, true2)
% 0.20/0.38 % SZS output end Proof
% 0.20/0.38
% 0.20/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
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