TSTP Solution File: SYN229-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN229-1 : 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 : 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 03:33:41 EDT 2023
% Result : Unsatisfiable 13.61s 2.12s
% Output : Proof 13.61s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYN229-1 : TPTP v8.1.2. Released v1.1.0.
% 0.12/0.14 % 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 21:32:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 13.61/2.12 Command-line arguments: --no-flatten-goal
% 13.61/2.12
% 13.61/2.12 % SZS status Unsatisfiable
% 13.61/2.12
% 13.61/2.12 % SZS output start Proof
% 13.61/2.12 Take the following subset of the input axioms:
% 13.61/2.12 fof(axiom_15, axiom, n0(a, b)).
% 13.61/2.12 fof(axiom_18, axiom, p0(c, b)).
% 13.61/2.12 fof(prove_this, negated_conjecture, ![X]: ~l3(c, X)).
% 13.61/2.12 fof(rule_001, axiom, ![I, J]: (k1(I) | ~n0(J, I))).
% 13.61/2.12 fof(rule_069, axiom, ![C, B]: (p1(B, B, C) | ~p0(C, B))).
% 13.61/2.12 fof(rule_136, axiom, m2(b) | ~k1(b)).
% 13.61/2.12 fof(rule_137, axiom, ![A2, C2, B2]: (n2(A2) | ~p1(B2, C2, A2))).
% 13.61/2.12 fof(rule_217, axiom, ![C2]: (l3(C2, C2) | (~n2(C2) | ~m2(b)))).
% 13.61/2.12
% 13.61/2.12 Now clausify the problem and encode Horn clauses using encoding 3 of
% 13.61/2.12 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 13.61/2.12 We repeatedly replace C & s=t => u=v by the two clauses:
% 13.61/2.12 fresh(y, y, x1...xn) = u
% 13.61/2.12 C => fresh(s, t, x1...xn) = v
% 13.61/2.12 where fresh is a fresh function symbol and x1..xn are the free
% 13.61/2.12 variables of u and v.
% 13.61/2.12 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 13.61/2.12 input problem has no model of domain size 1).
% 13.61/2.12
% 13.61/2.12 The encoding turns the above axioms into the following unit equations and goals:
% 13.61/2.12
% 13.61/2.12 Axiom 1 (rule_136): fresh263(X, X) = true2.
% 13.61/2.12 Axiom 2 (axiom_15): n0(a, b) = true2.
% 13.61/2.12 Axiom 3 (axiom_18): p0(c, b) = true2.
% 13.61/2.12 Axiom 4 (rule_001): fresh440(X, X, Y) = true2.
% 13.61/2.12 Axiom 5 (rule_136): fresh263(k1(b), true2) = m2(b).
% 13.61/2.12 Axiom 6 (rule_137): fresh262(X, X, Y) = true2.
% 13.61/2.12 Axiom 7 (rule_217): fresh156(X, X, Y) = l3(Y, Y).
% 13.61/2.12 Axiom 8 (rule_217): fresh155(X, X, Y) = true2.
% 13.61/2.12 Axiom 9 (rule_069): fresh349(X, X, Y, Z) = true2.
% 13.61/2.12 Axiom 10 (rule_217): fresh156(n2(X), true2, X) = fresh155(m2(b), true2, X).
% 13.61/2.12 Axiom 11 (rule_001): fresh440(n0(X, Y), true2, Y) = k1(Y).
% 13.61/2.12 Axiom 12 (rule_069): fresh349(p0(X, Y), true2, Y, X) = p1(Y, Y, X).
% 13.61/2.12 Axiom 13 (rule_137): fresh262(p1(X, Y, Z), true2, Z) = n2(Z).
% 13.61/2.12
% 13.61/2.12 Goal 1 (prove_this): l3(c, X) = true2.
% 13.61/2.12 The goal is true when:
% 13.61/2.12 X = c
% 13.61/2.12
% 13.61/2.12 Proof:
% 13.61/2.12 l3(c, c)
% 13.61/2.12 = { by axiom 7 (rule_217) R->L }
% 13.61/2.12 fresh156(true2, true2, c)
% 13.61/2.12 = { by axiom 6 (rule_137) R->L }
% 13.61/2.12 fresh156(fresh262(true2, true2, c), true2, c)
% 13.61/2.12 = { by axiom 9 (rule_069) R->L }
% 13.61/2.12 fresh156(fresh262(fresh349(true2, true2, b, c), true2, c), true2, c)
% 13.61/2.12 = { by axiom 3 (axiom_18) R->L }
% 13.61/2.12 fresh156(fresh262(fresh349(p0(c, b), true2, b, c), true2, c), true2, c)
% 13.61/2.12 = { by axiom 12 (rule_069) }
% 13.61/2.12 fresh156(fresh262(p1(b, b, c), true2, c), true2, c)
% 13.61/2.12 = { by axiom 13 (rule_137) }
% 13.61/2.12 fresh156(n2(c), true2, c)
% 13.61/2.12 = { by axiom 10 (rule_217) }
% 13.61/2.12 fresh155(m2(b), true2, c)
% 13.61/2.12 = { by axiom 5 (rule_136) R->L }
% 13.61/2.12 fresh155(fresh263(k1(b), true2), true2, c)
% 13.61/2.12 = { by axiom 11 (rule_001) R->L }
% 13.61/2.12 fresh155(fresh263(fresh440(n0(a, b), true2, b), true2), true2, c)
% 13.61/2.12 = { by axiom 2 (axiom_15) }
% 13.61/2.12 fresh155(fresh263(fresh440(true2, true2, b), true2), true2, c)
% 13.61/2.12 = { by axiom 4 (rule_001) }
% 13.61/2.12 fresh155(fresh263(true2, true2), true2, c)
% 13.61/2.12 = { by axiom 1 (rule_136) }
% 13.61/2.12 fresh155(true2, true2, c)
% 13.61/2.12 = { by axiom 8 (rule_217) }
% 13.61/2.12 true2
% 13.61/2.12 % SZS output end Proof
% 13.61/2.12
% 13.61/2.12 RESULT: Unsatisfiable (the axioms are contradictory).
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