TSTP Solution File: SYN729-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN729-1 : 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 : n032.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 03:35:52 EDT 2023
% Result : Unsatisfiable 0.13s 0.34s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYN729-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.31 % Computer : n032.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Sat Aug 26 20:59:14 EDT 2023
% 0.13/0.31 % CPUTime :
% 0.13/0.34 Command-line arguments: --no-flatten-goal
% 0.13/0.34
% 0.13/0.34 % SZS status Unsatisfiable
% 0.13/0.34
% 0.13/0.34 % SZS output start Proof
% 0.13/0.34 Take the following subset of the input axioms:
% 0.13/0.34 fof(thm72_1, negated_conjecture, ![A2]: (l(A2, g(h(sk1(A2)))) | ~p(A2))).
% 0.13/0.34 fof(thm72_2, negated_conjecture, ![A2_2]: (p(sk1(A2_2)) | ~p(A2_2))).
% 0.13/0.34 fof(thm72_3, negated_conjecture, ![A2_2]: (p(g(A2_2)) | ~p(A2_2))).
% 0.13/0.34 fof(thm72_4, negated_conjecture, ![A2_2]: (p(h(A2_2)) | ~p(A2_2))).
% 0.13/0.34 fof(thm72_5, negated_conjecture, p(sk2)).
% 0.13/0.34 fof(thm72_6, negated_conjecture, ![A]: (~p(A) | ~l(sk2, A))).
% 0.13/0.34
% 0.13/0.34 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.13/0.34 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.13/0.34 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.13/0.34 fresh(y, y, x1...xn) = u
% 0.13/0.34 C => fresh(s, t, x1...xn) = v
% 0.13/0.34 where fresh is a fresh function symbol and x1..xn are the free
% 0.13/0.34 variables of u and v.
% 0.13/0.34 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.13/0.34 input problem has no model of domain size 1).
% 0.13/0.34
% 0.13/0.34 The encoding turns the above axioms into the following unit equations and goals:
% 0.13/0.34
% 0.13/0.34 Axiom 1 (thm72_5): p(sk2) = true2.
% 0.13/0.34 Axiom 2 (thm72_4): fresh(X, X, Y) = true2.
% 0.13/0.34 Axiom 3 (thm72_2): fresh4(X, X, Y) = true2.
% 0.13/0.34 Axiom 4 (thm72_1): fresh3(X, X, Y) = true2.
% 0.13/0.34 Axiom 5 (thm72_3): fresh2(X, X, Y) = true2.
% 0.13/0.34 Axiom 6 (thm72_4): fresh(p(X), true2, X) = p(h(X)).
% 0.13/0.34 Axiom 7 (thm72_2): fresh4(p(X), true2, X) = p(sk1(X)).
% 0.13/0.34 Axiom 8 (thm72_3): fresh2(p(X), true2, X) = p(g(X)).
% 0.13/0.34 Axiom 9 (thm72_1): fresh3(p(X), true2, X) = l(X, g(h(sk1(X)))).
% 0.13/0.34
% 0.13/0.34 Goal 1 (thm72_6): tuple(l(sk2, X), p(X)) = tuple(true2, true2).
% 0.13/0.34 The goal is true when:
% 0.13/0.34 X = g(h(sk1(sk2)))
% 0.13/0.34
% 0.13/0.34 Proof:
% 0.13/0.34 tuple(l(sk2, g(h(sk1(sk2)))), p(g(h(sk1(sk2)))))
% 0.13/0.34 = { by axiom 8 (thm72_3) R->L }
% 0.13/0.34 tuple(l(sk2, g(h(sk1(sk2)))), fresh2(p(h(sk1(sk2))), true2, h(sk1(sk2))))
% 0.13/0.34 = { by axiom 6 (thm72_4) R->L }
% 0.13/0.34 tuple(l(sk2, g(h(sk1(sk2)))), fresh2(fresh(p(sk1(sk2)), true2, sk1(sk2)), true2, h(sk1(sk2))))
% 0.13/0.34 = { by axiom 7 (thm72_2) R->L }
% 0.13/0.34 tuple(l(sk2, g(h(sk1(sk2)))), fresh2(fresh(fresh4(p(sk2), true2, sk2), true2, sk1(sk2)), true2, h(sk1(sk2))))
% 0.13/0.34 = { by axiom 1 (thm72_5) }
% 0.13/0.34 tuple(l(sk2, g(h(sk1(sk2)))), fresh2(fresh(fresh4(true2, true2, sk2), true2, sk1(sk2)), true2, h(sk1(sk2))))
% 0.13/0.34 = { by axiom 3 (thm72_2) }
% 0.13/0.34 tuple(l(sk2, g(h(sk1(sk2)))), fresh2(fresh(true2, true2, sk1(sk2)), true2, h(sk1(sk2))))
% 0.13/0.34 = { by axiom 2 (thm72_4) }
% 0.13/0.34 tuple(l(sk2, g(h(sk1(sk2)))), fresh2(true2, true2, h(sk1(sk2))))
% 0.13/0.34 = { by axiom 5 (thm72_3) }
% 0.13/0.34 tuple(l(sk2, g(h(sk1(sk2)))), true2)
% 0.13/0.34 = { by axiom 9 (thm72_1) R->L }
% 0.13/0.34 tuple(fresh3(p(sk2), true2, sk2), true2)
% 0.13/0.34 = { by axiom 1 (thm72_5) }
% 0.13/0.34 tuple(fresh3(true2, true2, sk2), true2)
% 0.13/0.34 = { by axiom 4 (thm72_1) }
% 0.13/0.34 tuple(true2, true2)
% 0.13/0.34 % SZS output end Proof
% 0.13/0.34
% 0.13/0.34 RESULT: Unsatisfiable (the axioms are contradictory).
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