TSTP Solution File: SYN216-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN216-1 : 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 : n005.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 03:33:38 EDT 2023
% Result : Unsatisfiable 32.43s 4.50s
% Output : Proof 32.43s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN216-1 : TPTP v8.1.2. Released v1.1.0.
% 0.07/0.14 % 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 : n005.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 18:52:53 EDT 2023
% 0.20/0.35 % CPUTime :
% 32.43/4.50 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 32.43/4.50
% 32.43/4.50 % SZS status Unsatisfiable
% 32.43/4.50
% 32.43/4.51 % SZS output start Proof
% 32.43/4.51 Take the following subset of the input axioms:
% 32.43/4.51 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 32.43/4.51 fof(axiom_17, axiom, ![X2]: q0(X2, d)).
% 32.43/4.51 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 32.43/4.51 fof(prove_this, negated_conjecture, ~l2(a, a)).
% 32.43/4.51 fof(rule_125, axiom, ![I]: (s1(I) | ~p0(I, I))).
% 32.43/4.51 fof(rule_126, axiom, ![G, H, F]: (s1(F) | (~q0(F, G) | ~s1(H)))).
% 32.43/4.51 fof(rule_133, axiom, ![J, C, B, A2]: (l2(J, J) | (~p0(A2, A2) | (~s1(B) | ~m0(C, B, J))))).
% 32.43/4.51
% 32.43/4.51 Now clausify the problem and encode Horn clauses using encoding 3 of
% 32.43/4.51 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 32.43/4.51 We repeatedly replace C & s=t => u=v by the two clauses:
% 32.43/4.51 fresh(y, y, x1...xn) = u
% 32.43/4.51 C => fresh(s, t, x1...xn) = v
% 32.43/4.51 where fresh is a fresh function symbol and x1..xn are the free
% 32.43/4.51 variables of u and v.
% 32.43/4.51 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 32.43/4.51 input problem has no model of domain size 1).
% 32.43/4.51
% 32.43/4.51 The encoding turns the above axioms into the following unit equations and goals:
% 32.43/4.51
% 32.43/4.51 Axiom 1 (axiom_14): p0(b, X) = true.
% 32.43/4.51 Axiom 2 (axiom_17): q0(X, d) = true.
% 32.43/4.51 Axiom 3 (axiom_19): m0(X, d, Y) = true.
% 32.43/4.51 Axiom 4 (rule_133): fresh585(X, X, Y) = true.
% 32.43/4.51 Axiom 5 (rule_125): fresh275(X, X, Y) = true.
% 32.43/4.51 Axiom 6 (rule_126): fresh273(X, X, Y) = true.
% 32.43/4.51 Axiom 7 (rule_126): fresh274(X, X, Y, Z) = s1(Y).
% 32.43/4.51 Axiom 8 (rule_125): fresh275(p0(X, X), true, X) = s1(X).
% 32.43/4.51 Axiom 9 (rule_126): fresh274(s1(X), true, Y, Z) = fresh273(q0(Y, Z), true, Y).
% 32.43/4.51 Axiom 10 (rule_133): fresh267(X, X, Y, Z, W) = l2(Y, Y).
% 32.43/4.51 Axiom 11 (rule_133): fresh584(X, X, Y, Z, W, V) = fresh585(m0(V, W, Y), true, Y).
% 32.43/4.51 Axiom 12 (rule_133): fresh584(s1(X), true, Y, Z, X, W) = fresh267(p0(Z, Z), true, Y, X, W).
% 32.43/4.51
% 32.43/4.51 Goal 1 (prove_this): l2(a, a) = true.
% 32.43/4.51 Proof:
% 32.43/4.51 l2(a, a)
% 32.43/4.51 = { by axiom 10 (rule_133) R->L }
% 32.43/4.51 fresh267(true, true, a, d, X)
% 32.43/4.51 = { by axiom 1 (axiom_14) R->L }
% 32.43/4.51 fresh267(p0(b, b), true, a, d, X)
% 32.43/4.51 = { by axiom 12 (rule_133) R->L }
% 32.43/4.51 fresh584(s1(d), true, a, b, d, X)
% 32.43/4.51 = { by axiom 7 (rule_126) R->L }
% 32.43/4.51 fresh584(fresh274(true, true, d, d), true, a, b, d, X)
% 32.43/4.51 = { by axiom 5 (rule_125) R->L }
% 32.43/4.51 fresh584(fresh274(fresh275(true, true, b), true, d, d), true, a, b, d, X)
% 32.43/4.51 = { by axiom 1 (axiom_14) R->L }
% 32.43/4.51 fresh584(fresh274(fresh275(p0(b, b), true, b), true, d, d), true, a, b, d, X)
% 32.43/4.51 = { by axiom 8 (rule_125) }
% 32.43/4.51 fresh584(fresh274(s1(b), true, d, d), true, a, b, d, X)
% 32.43/4.51 = { by axiom 9 (rule_126) }
% 32.43/4.51 fresh584(fresh273(q0(d, d), true, d), true, a, b, d, X)
% 32.43/4.51 = { by axiom 2 (axiom_17) }
% 32.43/4.51 fresh584(fresh273(true, true, d), true, a, b, d, X)
% 32.43/4.51 = { by axiom 6 (rule_126) }
% 32.43/4.51 fresh584(true, true, a, b, d, X)
% 32.43/4.51 = { by axiom 11 (rule_133) }
% 32.43/4.51 fresh585(m0(X, d, a), true, a)
% 32.43/4.51 = { by axiom 3 (axiom_19) }
% 32.43/4.51 fresh585(true, true, a)
% 32.43/4.51 = { by axiom 4 (rule_133) }
% 32.43/4.51 true
% 32.43/4.51 % SZS output end Proof
% 32.43/4.51
% 32.43/4.51 RESULT: Unsatisfiable (the axioms are contradictory).
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