TSTP Solution File: SYN208-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN208-1 : 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 : n028.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 03:33:36 EDT 2023
% Result : Unsatisfiable 27.20s 3.91s
% Output : Proof 27.20s
% 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 : SYN208-1 : 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
% 0.16/0.34 % Computer : n028.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Sat Aug 26 21:57:08 EDT 2023
% 0.16/0.35 % CPUTime :
% 27.20/3.91 Command-line arguments: --no-flatten-goal
% 27.20/3.91
% 27.20/3.91 % SZS status Unsatisfiable
% 27.20/3.91
% 27.20/3.92 % SZS output start Proof
% 27.20/3.92 Take the following subset of the input axioms:
% 27.20/3.92 fof(axiom_1, axiom, s0(d)).
% 27.20/3.92 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 27.20/3.92 fof(axiom_17, axiom, ![X2]: q0(X2, d)).
% 27.20/3.92 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 27.20/3.92 fof(axiom_28, axiom, k0(e)).
% 27.20/3.92 fof(axiom_34, axiom, n0(c, d)).
% 27.20/3.92 fof(prove_this, negated_conjecture, ~s3(d, b)).
% 27.20/3.92 fof(rule_001, axiom, ![I, J]: (k1(I) | ~n0(J, I))).
% 27.20/3.92 fof(rule_040, axiom, ![C, D]: (n1(C, e, e) | (~m0(C, D, e) | ~k1(C)))).
% 27.20/3.92 fof(rule_085, axiom, ![B, C2]: (p1(B, B, B) | ~p0(C2, B))).
% 27.20/3.92 fof(rule_125, axiom, ![I2]: (s1(I2) | ~p0(I2, I2))).
% 27.20/3.92 fof(rule_126, axiom, ![G, H, F]: (s1(F) | (~q0(F, G) | ~s1(H)))).
% 27.20/3.92 fof(rule_177, axiom, ![E, F2]: (q2(E, F2, F2) | (~k0(F2) | ~p1(E, E, E)))).
% 27.20/3.92 fof(rule_182, axiom, ![G2, H2, F2]: (q2(F2, G2, F2) | (~p1(F2, F2, H2) | (~n1(G2, F2, H2) | ~q2(G2, H2, F2))))).
% 27.20/3.92 fof(rule_190, axiom, s2(d) | (~s1(a) | ~s0(d))).
% 27.20/3.92 fof(rule_273, axiom, ![A2, I2, J2, B2]: (s3(I2, J2) | (~q2(A2, I2, A2) | (~s2(I2) | ~m0(A2, B2, J2))))).
% 27.20/3.92
% 27.20/3.92 Now clausify the problem and encode Horn clauses using encoding 3 of
% 27.20/3.92 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 27.20/3.92 We repeatedly replace C & s=t => u=v by the two clauses:
% 27.20/3.92 fresh(y, y, x1...xn) = u
% 27.20/3.92 C => fresh(s, t, x1...xn) = v
% 27.20/3.92 where fresh is a fresh function symbol and x1..xn are the free
% 27.20/3.92 variables of u and v.
% 27.20/3.92 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 27.20/3.92 input problem has no model of domain size 1).
% 27.20/3.92
% 27.20/3.92 The encoding turns the above axioms into the following unit equations and goals:
% 27.20/3.92
% 27.20/3.92 Axiom 1 (axiom_28): k0(e) = true.
% 27.20/3.92 Axiom 2 (axiom_1): s0(d) = true.
% 27.20/3.92 Axiom 3 (rule_190): fresh190(X, X) = s2(d).
% 27.20/3.92 Axiom 4 (rule_190): fresh189(X, X) = true.
% 27.20/3.92 Axiom 5 (axiom_34): n0(c, d) = true.
% 27.20/3.92 Axiom 6 (axiom_17): q0(X, d) = true.
% 27.20/3.92 Axiom 7 (axiom_14): p0(b, X) = true.
% 27.20/3.92 Axiom 8 (rule_001): fresh440(X, X, Y) = true.
% 27.20/3.92 Axiom 9 (rule_040): fresh388(X, X, Y) = true.
% 27.20/3.92 Axiom 10 (rule_085): fresh328(X, X, Y) = true.
% 27.20/3.92 Axiom 11 (rule_125): fresh275(X, X, Y) = true.
% 27.20/3.92 Axiom 12 (rule_126): fresh273(X, X, Y) = true.
% 27.20/3.92 Axiom 13 (rule_190): fresh190(s1(a), true) = fresh189(s0(d), true).
% 27.20/3.92 Axiom 14 (rule_073): fresh627(X, X, Y) = p1(Y, Y, Y).
% 27.20/3.92 Axiom 15 (axiom_19): m0(X, d, Y) = true.
% 27.20/3.92 Axiom 16 (rule_182): fresh551(X, X, Y, Z) = true.
% 27.20/3.92 Axiom 17 (rule_273): fresh475(X, X, Y, Z) = true.
% 27.20/3.92 Axiom 18 (rule_040): fresh389(X, X, Y, Z) = n1(Y, e, e).
% 27.20/3.92 Axiom 19 (rule_126): fresh274(X, X, Y, Z) = s1(Y).
% 27.20/3.92 Axiom 20 (rule_177): fresh207(X, X, Y, Z) = q2(Y, Z, Z).
% 27.20/3.92 Axiom 21 (rule_177): fresh206(X, X, Y, Z) = true.
% 27.20/3.92 Axiom 22 (rule_001): fresh440(n0(X, Y), true, Y) = k1(Y).
% 27.20/3.92 Axiom 23 (rule_085): fresh328(p0(X, Y), true, Y) = p1(Y, Y, Y).
% 27.20/3.92 Axiom 24 (rule_125): fresh275(p0(X, X), true, X) = s1(X).
% 27.20/3.92 Axiom 25 (rule_126): fresh274(s1(X), true, Y, Z) = fresh273(q0(Y, Z), true, Y).
% 27.20/3.92 Axiom 26 (rule_182): fresh199(X, X, Y, Z, W) = q2(Y, Z, Y).
% 27.20/3.92 Axiom 27 (rule_040): fresh389(k1(X), true, X, Y) = fresh388(m0(X, Y, e), true, X).
% 27.20/3.92 Axiom 28 (rule_273): fresh82(X, X, Y, Z, W, V) = s3(Y, Z).
% 27.20/3.92 Axiom 29 (rule_182): fresh550(X, X, Y, Z, W) = fresh551(n1(Z, Y, W), true, Y, Z).
% 27.20/3.92 Axiom 30 (rule_273): fresh474(X, X, Y, Z, W, V) = fresh475(m0(W, V, Z), true, Y, Z).
% 27.20/3.92 Axiom 31 (rule_177): fresh207(p1(X, X, X), true, X, Y) = fresh206(k0(Y), true, X, Y).
% 27.20/3.92 Axiom 32 (rule_182): fresh550(q2(X, Y, Z), true, Z, X, Y) = fresh199(p1(Z, Z, Y), true, Z, X, Y).
% 27.20/3.92 Axiom 33 (rule_273): fresh474(s2(X), true, X, Y, Z, W) = fresh82(q2(Z, X, Z), true, X, Y, Z, W).
% 27.20/3.92
% 27.20/3.92 Lemma 34: fresh627(X, X, Y) = true.
% 27.20/3.92 Proof:
% 27.20/3.92 fresh627(X, X, Y)
% 27.20/3.92 = { by axiom 14 (rule_073) }
% 27.20/3.92 p1(Y, Y, Y)
% 27.20/3.92 = { by axiom 23 (rule_085) R->L }
% 27.20/3.92 fresh328(p0(b, Y), true, Y)
% 27.20/3.92 = { by axiom 7 (axiom_14) }
% 27.20/3.92 fresh328(true, true, Y)
% 27.20/3.92 = { by axiom 10 (rule_085) }
% 27.20/3.92 true
% 27.20/3.92
% 27.20/3.92 Goal 1 (prove_this): s3(d, b) = true.
% 27.20/3.92 Proof:
% 27.20/3.92 s3(d, b)
% 27.20/3.92 = { by axiom 28 (rule_273) R->L }
% 27.20/3.92 fresh82(true, true, d, b, e, d)
% 27.20/3.92 = { by axiom 16 (rule_182) R->L }
% 27.20/3.92 fresh82(fresh551(true, true, e, d), true, d, b, e, d)
% 27.20/3.92 = { by axiom 9 (rule_040) R->L }
% 27.20/3.92 fresh82(fresh551(fresh388(true, true, d), true, e, d), true, d, b, e, d)
% 27.20/3.92 = { by axiom 15 (axiom_19) R->L }
% 27.20/3.92 fresh82(fresh551(fresh388(m0(d, d, e), true, d), true, e, d), true, d, b, e, d)
% 27.20/3.92 = { by axiom 27 (rule_040) R->L }
% 27.20/3.92 fresh82(fresh551(fresh389(k1(d), true, d, d), true, e, d), true, d, b, e, d)
% 27.20/3.92 = { by axiom 22 (rule_001) R->L }
% 27.20/3.92 fresh82(fresh551(fresh389(fresh440(n0(c, d), true, d), true, d, d), true, e, d), true, d, b, e, d)
% 27.20/3.92 = { by axiom 5 (axiom_34) }
% 27.20/3.92 fresh82(fresh551(fresh389(fresh440(true, true, d), true, d, d), true, e, d), true, d, b, e, d)
% 27.20/3.92 = { by axiom 8 (rule_001) }
% 27.20/3.92 fresh82(fresh551(fresh389(true, true, d, d), true, e, d), true, d, b, e, d)
% 27.20/3.92 = { by axiom 18 (rule_040) }
% 27.20/3.92 fresh82(fresh551(n1(d, e, e), true, e, d), true, d, b, e, d)
% 27.20/3.92 = { by axiom 29 (rule_182) R->L }
% 27.20/3.92 fresh82(fresh550(true, true, e, d, e), true, d, b, e, d)
% 27.20/3.92 = { by axiom 21 (rule_177) R->L }
% 27.20/3.92 fresh82(fresh550(fresh206(true, true, d, e), true, e, d, e), true, d, b, e, d)
% 27.20/3.92 = { by axiom 1 (axiom_28) R->L }
% 27.20/3.92 fresh82(fresh550(fresh206(k0(e), true, d, e), true, e, d, e), true, d, b, e, d)
% 27.20/3.92 = { by axiom 31 (rule_177) R->L }
% 27.20/3.92 fresh82(fresh550(fresh207(p1(d, d, d), true, d, e), true, e, d, e), true, d, b, e, d)
% 27.20/3.92 = { by axiom 14 (rule_073) R->L }
% 27.20/3.92 fresh82(fresh550(fresh207(fresh627(X, X, d), true, d, e), true, e, d, e), true, d, b, e, d)
% 27.20/3.92 = { by lemma 34 }
% 27.20/3.92 fresh82(fresh550(fresh207(true, true, d, e), true, e, d, e), true, d, b, e, d)
% 27.20/3.92 = { by axiom 20 (rule_177) }
% 27.20/3.92 fresh82(fresh550(q2(d, e, e), true, e, d, e), true, d, b, e, d)
% 27.20/3.92 = { by axiom 32 (rule_182) }
% 27.20/3.92 fresh82(fresh199(p1(e, e, e), true, e, d, e), true, d, b, e, d)
% 27.20/3.92 = { by axiom 14 (rule_073) R->L }
% 27.20/3.92 fresh82(fresh199(fresh627(Y, Y, e), true, e, d, e), true, d, b, e, d)
% 27.20/3.92 = { by lemma 34 }
% 27.20/3.92 fresh82(fresh199(true, true, e, d, e), true, d, b, e, d)
% 27.20/3.92 = { by axiom 26 (rule_182) }
% 27.20/3.92 fresh82(q2(e, d, e), true, d, b, e, d)
% 27.20/3.92 = { by axiom 33 (rule_273) R->L }
% 27.20/3.92 fresh474(s2(d), true, d, b, e, d)
% 27.20/3.92 = { by axiom 3 (rule_190) R->L }
% 27.20/3.92 fresh474(fresh190(true, true), true, d, b, e, d)
% 27.20/3.93 = { by axiom 12 (rule_126) R->L }
% 27.20/3.93 fresh474(fresh190(fresh273(true, true, a), true), true, d, b, e, d)
% 27.20/3.93 = { by axiom 6 (axiom_17) R->L }
% 27.20/3.93 fresh474(fresh190(fresh273(q0(a, d), true, a), true), true, d, b, e, d)
% 27.20/3.93 = { by axiom 25 (rule_126) R->L }
% 27.20/3.93 fresh474(fresh190(fresh274(s1(b), true, a, d), true), true, d, b, e, d)
% 27.20/3.93 = { by axiom 24 (rule_125) R->L }
% 27.20/3.93 fresh474(fresh190(fresh274(fresh275(p0(b, b), true, b), true, a, d), true), true, d, b, e, d)
% 27.20/3.93 = { by axiom 7 (axiom_14) }
% 27.20/3.93 fresh474(fresh190(fresh274(fresh275(true, true, b), true, a, d), true), true, d, b, e, d)
% 27.20/3.93 = { by axiom 11 (rule_125) }
% 27.20/3.93 fresh474(fresh190(fresh274(true, true, a, d), true), true, d, b, e, d)
% 27.20/3.93 = { by axiom 19 (rule_126) }
% 27.20/3.93 fresh474(fresh190(s1(a), true), true, d, b, e, d)
% 27.20/3.93 = { by axiom 13 (rule_190) }
% 27.20/3.93 fresh474(fresh189(s0(d), true), true, d, b, e, d)
% 27.20/3.93 = { by axiom 2 (axiom_1) }
% 27.20/3.93 fresh474(fresh189(true, true), true, d, b, e, d)
% 27.20/3.93 = { by axiom 4 (rule_190) }
% 27.20/3.93 fresh474(true, true, d, b, e, d)
% 27.20/3.93 = { by axiom 30 (rule_273) }
% 27.20/3.93 fresh475(m0(e, d, b), true, d, b)
% 27.20/3.93 = { by axiom 15 (axiom_19) }
% 27.20/3.93 fresh475(true, true, d, b)
% 27.20/3.93 = { by axiom 17 (rule_273) }
% 27.20/3.93 true
% 27.20/3.93 % SZS output end Proof
% 27.20/3.93
% 27.20/3.93 RESULT: Unsatisfiable (the axioms are contradictory).
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