TSTP Solution File: SYN122-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN122-1 : 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 : n021.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 03:33:15 EDT 2023
% Result : Unsatisfiable 32.05s 4.53s
% Output : Proof 32.74s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN122-1 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 18:23:42 EDT 2023
% 0.13/0.34 % CPUTime :
% 32.05/4.53 Command-line arguments: --no-flatten-goal
% 32.05/4.53
% 32.05/4.53 % SZS status Unsatisfiable
% 32.05/4.53
% 32.74/4.54 % SZS output start Proof
% 32.74/4.54 Take the following subset of the input axioms:
% 32.74/4.54 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 32.74/4.54 fof(axiom_17, axiom, ![X2]: q0(X2, d)).
% 32.74/4.54 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 32.74/4.54 fof(axiom_30, axiom, n0(e, e)).
% 32.74/4.54 fof(prove_this, negated_conjecture, ~l2(b, e)).
% 32.74/4.54 fof(rule_125, axiom, ![I]: (s1(I) | ~p0(I, I))).
% 32.74/4.54 fof(rule_126, axiom, ![G, H, F]: (s1(F) | (~q0(F, G) | ~s1(H)))).
% 32.74/4.54 fof(rule_131, axiom, ![D, E]: (l2(D, E) | (~s1(D) | (~n0(e, E) | ~l2(E, E))))).
% 32.74/4.54 fof(rule_133, axiom, ![J, C, B, A2]: (l2(J, J) | (~p0(A2, A2) | (~s1(B) | ~m0(C, B, J))))).
% 32.74/4.54
% 32.74/4.54 Now clausify the problem and encode Horn clauses using encoding 3 of
% 32.74/4.54 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 32.74/4.54 We repeatedly replace C & s=t => u=v by the two clauses:
% 32.74/4.54 fresh(y, y, x1...xn) = u
% 32.74/4.54 C => fresh(s, t, x1...xn) = v
% 32.74/4.54 where fresh is a fresh function symbol and x1..xn are the free
% 32.74/4.54 variables of u and v.
% 32.74/4.54 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 32.74/4.54 input problem has no model of domain size 1).
% 32.74/4.54
% 32.74/4.54 The encoding turns the above axioms into the following unit equations and goals:
% 32.74/4.54
% 32.74/4.54 Axiom 1 (axiom_30): n0(e, e) = true.
% 32.74/4.54 Axiom 2 (axiom_17): q0(X, d) = true.
% 32.74/4.54 Axiom 3 (axiom_14): p0(b, X) = true.
% 32.74/4.54 Axiom 4 (rule_133): fresh585(X, X, Y) = true.
% 32.74/4.54 Axiom 5 (rule_125): fresh275(X, X, Y) = true.
% 32.74/4.54 Axiom 6 (rule_126): fresh273(X, X, Y) = true.
% 32.74/4.54 Axiom 7 (axiom_19): m0(X, d, Y) = true.
% 32.74/4.54 Axiom 8 (rule_131): fresh587(X, X, Y, Z) = l2(Y, Z).
% 32.74/4.54 Axiom 9 (rule_126): fresh274(X, X, Y, Z) = s1(Y).
% 32.74/4.54 Axiom 10 (rule_131): fresh268(X, X, Y, Z) = true.
% 32.74/4.54 Axiom 11 (rule_131): fresh586(X, X, Y, Z) = fresh587(s1(Y), true, Y, Z).
% 32.74/4.54 Axiom 12 (rule_125): fresh275(p0(X, X), true, X) = s1(X).
% 32.74/4.54 Axiom 13 (rule_126): fresh274(s1(X), true, Y, Z) = fresh273(q0(Y, Z), true, Y).
% 32.74/4.54 Axiom 14 (rule_133): fresh267(X, X, Y, Z, W) = l2(Y, Y).
% 32.74/4.54 Axiom 15 (rule_133): fresh584(X, X, Y, Z, W, V) = fresh585(m0(V, W, Y), true, Y).
% 32.74/4.54 Axiom 16 (rule_131): fresh586(l2(X, X), true, Y, X) = fresh268(n0(e, X), true, Y, X).
% 32.74/4.54 Axiom 17 (rule_133): fresh584(s1(X), true, Y, Z, X, W) = fresh267(p0(Z, Z), true, Y, X, W).
% 32.74/4.54
% 32.74/4.54 Lemma 18: s1(X) = true.
% 32.74/4.54 Proof:
% 32.74/4.54 s1(X)
% 32.74/4.54 = { by axiom 9 (rule_126) R->L }
% 32.74/4.54 fresh274(true, true, X, d)
% 32.74/4.54 = { by axiom 5 (rule_125) R->L }
% 32.74/4.54 fresh274(fresh275(true, true, b), true, X, d)
% 32.74/4.54 = { by axiom 3 (axiom_14) R->L }
% 32.74/4.54 fresh274(fresh275(p0(b, b), true, b), true, X, d)
% 32.74/4.54 = { by axiom 12 (rule_125) }
% 32.74/4.54 fresh274(s1(b), true, X, d)
% 32.74/4.54 = { by axiom 13 (rule_126) }
% 32.74/4.54 fresh273(q0(X, d), true, X)
% 32.74/4.54 = { by axiom 2 (axiom_17) }
% 32.74/4.54 fresh273(true, true, X)
% 32.74/4.54 = { by axiom 6 (rule_126) }
% 32.74/4.54 true
% 32.74/4.54
% 32.74/4.54 Goal 1 (prove_this): l2(b, e) = true.
% 32.74/4.54 Proof:
% 32.74/4.54 l2(b, e)
% 32.74/4.54 = { by axiom 8 (rule_131) R->L }
% 32.74/4.54 fresh587(true, true, b, e)
% 32.74/4.54 = { by lemma 18 R->L }
% 32.74/4.54 fresh587(s1(b), true, b, e)
% 32.74/4.54 = { by axiom 11 (rule_131) R->L }
% 32.74/4.54 fresh586(true, true, b, e)
% 32.74/4.54 = { by axiom 4 (rule_133) R->L }
% 32.74/4.54 fresh586(fresh585(true, true, e), true, b, e)
% 32.74/4.54 = { by axiom 7 (axiom_19) R->L }
% 32.74/4.54 fresh586(fresh585(m0(X, d, e), true, e), true, b, e)
% 32.74/4.54 = { by axiom 15 (rule_133) R->L }
% 32.74/4.54 fresh586(fresh584(true, true, e, b, d, X), true, b, e)
% 32.74/4.54 = { by lemma 18 R->L }
% 32.74/4.54 fresh586(fresh584(s1(d), true, e, b, d, X), true, b, e)
% 32.74/4.54 = { by axiom 17 (rule_133) }
% 32.74/4.54 fresh586(fresh267(p0(b, b), true, e, d, X), true, b, e)
% 32.74/4.54 = { by axiom 3 (axiom_14) }
% 32.74/4.54 fresh586(fresh267(true, true, e, d, X), true, b, e)
% 32.74/4.54 = { by axiom 14 (rule_133) }
% 32.74/4.54 fresh586(l2(e, e), true, b, e)
% 32.74/4.54 = { by axiom 16 (rule_131) }
% 32.74/4.54 fresh268(n0(e, e), true, b, e)
% 32.74/4.54 = { by axiom 1 (axiom_30) }
% 32.74/4.54 fresh268(true, true, b, e)
% 32.74/4.54 = { by axiom 10 (rule_131) }
% 32.74/4.54 true
% 32.74/4.54 % SZS output end Proof
% 32.74/4.54
% 32.74/4.54 RESULT: Unsatisfiable (the axioms are contradictory).
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