TSTP Solution File: SYN264-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN264-1 : TPTP v8.1.2. Released v1.1.0.
% 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 : n027.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 03:33:50 EDT 2023
% Result : Unsatisfiable 22.20s 3.30s
% Output : Proof 22.87s
% 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 : SYN264-1 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 19:12:50 EDT 2023
% 0.14/0.36 % CPUTime :
% 22.20/3.30 Command-line arguments: --no-flatten-goal
% 22.20/3.30
% 22.20/3.30 % SZS status Unsatisfiable
% 22.20/3.30
% 22.20/3.31 % SZS output start Proof
% 22.20/3.31 Take the following subset of the input axioms:
% 22.87/3.31 fof(axiom_20, axiom, l0(a)).
% 22.87/3.31 fof(axiom_26, axiom, n0(d, c)).
% 22.87/3.31 fof(axiom_28, axiom, k0(e)).
% 22.87/3.31 fof(axiom_5, axiom, s0(b)).
% 22.87/3.31 fof(prove_this, negated_conjecture, ~p1(e, c, e)).
% 22.87/3.31 fof(rule_063, axiom, ![D, E]: (p1(D, D, E) | (~n0(d, D) | ~k0(E)))).
% 22.87/3.31 fof(rule_071, axiom, ![I, J, H, A]: (p1(H, I, H) | (~l0(J) | (~p1(I, A, H) | ~s0(b))))).
% 22.87/3.31
% 22.87/3.31 Now clausify the problem and encode Horn clauses using encoding 3 of
% 22.87/3.31 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 22.87/3.31 We repeatedly replace C & s=t => u=v by the two clauses:
% 22.87/3.31 fresh(y, y, x1...xn) = u
% 22.87/3.31 C => fresh(s, t, x1...xn) = v
% 22.87/3.31 where fresh is a fresh function symbol and x1..xn are the free
% 22.87/3.31 variables of u and v.
% 22.87/3.31 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 22.87/3.31 input problem has no model of domain size 1).
% 22.87/3.31
% 22.87/3.31 The encoding turns the above axioms into the following unit equations and goals:
% 22.87/3.31
% 22.87/3.31 Axiom 1 (axiom_28): k0(e) = true.
% 22.87/3.31 Axiom 2 (axiom_20): l0(a) = true.
% 22.87/3.31 Axiom 3 (axiom_5): s0(b) = true.
% 22.87/3.31 Axiom 4 (axiom_26): n0(d, c) = true.
% 22.87/3.31 Axiom 5 (rule_071): fresh629(X, X, Y, Z) = true.
% 22.87/3.31 Axiom 6 (rule_063): fresh357(X, X, Y, Z) = p1(Y, Y, Z).
% 22.87/3.31 Axiom 7 (rule_063): fresh356(X, X, Y, Z) = true.
% 22.87/3.31 Axiom 8 (rule_071): fresh347(X, X, Y, Z) = p1(Y, Z, Y).
% 22.87/3.31 Axiom 9 (rule_071): fresh628(X, X, Y, Z, W) = fresh629(s0(b), true, Y, W).
% 22.87/3.31 Axiom 10 (rule_063): fresh357(k0(X), true, Y, X) = fresh356(n0(d, Y), true, Y, X).
% 22.87/3.31 Axiom 11 (rule_071): fresh628(p1(X, Y, Z), true, Z, W, X) = fresh347(l0(W), true, Z, X).
% 22.87/3.31
% 22.87/3.31 Goal 1 (prove_this): p1(e, c, e) = true.
% 22.87/3.31 Proof:
% 22.87/3.31 p1(e, c, e)
% 22.87/3.31 = { by axiom 8 (rule_071) R->L }
% 22.87/3.31 fresh347(true, true, e, c)
% 22.87/3.31 = { by axiom 2 (axiom_20) R->L }
% 22.87/3.31 fresh347(l0(a), true, e, c)
% 22.87/3.31 = { by axiom 11 (rule_071) R->L }
% 22.87/3.31 fresh628(p1(c, c, e), true, e, a, c)
% 22.87/3.31 = { by axiom 6 (rule_063) R->L }
% 22.87/3.31 fresh628(fresh357(true, true, c, e), true, e, a, c)
% 22.87/3.31 = { by axiom 1 (axiom_28) R->L }
% 22.87/3.31 fresh628(fresh357(k0(e), true, c, e), true, e, a, c)
% 22.87/3.31 = { by axiom 10 (rule_063) }
% 22.87/3.31 fresh628(fresh356(n0(d, c), true, c, e), true, e, a, c)
% 22.87/3.31 = { by axiom 4 (axiom_26) }
% 22.87/3.31 fresh628(fresh356(true, true, c, e), true, e, a, c)
% 22.87/3.31 = { by axiom 7 (rule_063) }
% 22.87/3.31 fresh628(true, true, e, a, c)
% 22.87/3.31 = { by axiom 9 (rule_071) }
% 22.87/3.31 fresh629(s0(b), true, e, c)
% 22.87/3.31 = { by axiom 3 (axiom_5) }
% 22.87/3.31 fresh629(true, true, e, c)
% 22.87/3.31 = { by axiom 5 (rule_071) }
% 22.87/3.31 true
% 22.87/3.31 % SZS output end Proof
% 22.87/3.31
% 22.87/3.31 RESULT: Unsatisfiable (the axioms are contradictory).
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