TSTP Solution File: SYN137-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN137-1 : 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 : n001.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 03:33:19 EDT 2023
% Result : Unsatisfiable 34.21s 4.79s
% Output : Proof 34.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN137-1 : 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 : n001.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 19:43:01 EDT 2023
% 0.13/0.34 % CPUTime :
% 34.21/4.79 Command-line arguments: --no-flatten-goal
% 34.21/4.79
% 34.21/4.79 % SZS status Unsatisfiable
% 34.21/4.79
% 34.21/4.81 % SZS output start Proof
% 34.21/4.81 Take the following subset of the input axioms:
% 34.21/4.81 fof(axiom_11, axiom, n0(e, b)).
% 34.21/4.81 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 34.21/4.81 fof(axiom_15, axiom, n0(a, b)).
% 34.21/4.81 fof(axiom_17, axiom, ![X2]: q0(X2, d)).
% 34.21/4.81 fof(axiom_20, axiom, l0(a)).
% 34.21/4.81 fof(axiom_24, axiom, l0(c)).
% 34.21/4.81 fof(axiom_26, axiom, n0(d, c)).
% 34.21/4.81 fof(axiom_31, axiom, m0(b, b, e)).
% 34.21/4.81 fof(prove_this, negated_conjecture, ~m3(b, c, b)).
% 34.21/4.81 fof(rule_001, axiom, ![I, J]: (k1(I) | ~n0(J, I))).
% 34.21/4.81 fof(rule_015, axiom, ![C, D, B]: (m1(B, C, C) | (~l0(D) | ~m0(C, C, B)))).
% 34.21/4.81 fof(rule_125, axiom, ![I2]: (s1(I2) | ~p0(I2, I2))).
% 34.21/4.81 fof(rule_126, axiom, ![G, H, F]: (s1(F) | (~q0(F, G) | ~s1(H)))).
% 34.21/4.81 fof(rule_131, axiom, ![E, D2]: (l2(D2, E) | (~s1(D2) | (~n0(e, E) | ~l2(E, E))))).
% 34.21/4.81 fof(rule_134, axiom, ![H2, I2, G2]: (l2(G2, G2) | (~m0(H2, G2, I2) | (~m1(I2, H2, H2) | ~p0(H2, G2))))).
% 34.21/4.81 fof(rule_183, axiom, ![D2, E2]: (q2(D2, c, E2) | (~k1(E2) | (~l0(c) | ~l2(E2, D2))))).
% 34.21/4.81 fof(rule_189, axiom, ![H2]: (s2(H2) | (~q2(b, H2, b) | ~s1(b)))).
% 34.21/4.81 fof(rule_237, axiom, ![J2]: (m3(J2, c, J2) | (~s2(c) | ~q2(J2, c, c)))).
% 34.21/4.81
% 34.21/4.81 Now clausify the problem and encode Horn clauses using encoding 3 of
% 34.21/4.81 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 34.21/4.81 We repeatedly replace C & s=t => u=v by the two clauses:
% 34.21/4.81 fresh(y, y, x1...xn) = u
% 34.21/4.81 C => fresh(s, t, x1...xn) = v
% 34.21/4.81 where fresh is a fresh function symbol and x1..xn are the free
% 34.21/4.81 variables of u and v.
% 34.21/4.81 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 34.21/4.81 input problem has no model of domain size 1).
% 34.21/4.81
% 34.21/4.81 The encoding turns the above axioms into the following unit equations and goals:
% 34.21/4.81
% 34.21/4.81 Axiom 1 (axiom_20): l0(a) = true.
% 34.21/4.81 Axiom 2 (axiom_24): l0(c) = true.
% 34.21/4.81 Axiom 3 (axiom_15): n0(a, b) = true.
% 34.21/4.81 Axiom 4 (axiom_26): n0(d, c) = true.
% 34.21/4.81 Axiom 5 (axiom_11): n0(e, b) = true.
% 34.21/4.81 Axiom 6 (axiom_17): q0(X, d) = true.
% 34.21/4.81 Axiom 7 (axiom_14): p0(b, X) = true.
% 34.21/4.81 Axiom 8 (rule_134): fresh583(X, X, Y) = true.
% 34.21/4.81 Axiom 9 (rule_001): fresh440(X, X, Y) = true.
% 34.21/4.81 Axiom 10 (rule_125): fresh275(X, X, Y) = true.
% 34.21/4.81 Axiom 11 (rule_126): fresh273(X, X, Y) = true.
% 34.21/4.81 Axiom 12 (rule_189): fresh192(X, X, Y) = s2(Y).
% 34.21/4.81 Axiom 13 (rule_189): fresh191(X, X, Y) = true.
% 34.21/4.81 Axiom 14 (rule_237): fresh130(X, X, Y) = true.
% 34.21/4.81 Axiom 15 (rule_237): fresh131(X, X, Y) = m3(Y, c, Y).
% 34.21/4.81 Axiom 16 (axiom_31): m0(b, b, e) = true.
% 34.21/4.81 Axiom 17 (rule_131): fresh587(X, X, Y, Z) = l2(Y, Z).
% 34.21/4.81 Axiom 18 (rule_183): fresh549(X, X, Y, Z) = true.
% 34.21/4.81 Axiom 19 (rule_015): fresh425(X, X, Y, Z) = m1(Y, Z, Z).
% 34.21/4.81 Axiom 20 (rule_015): fresh424(X, X, Y, Z) = true.
% 34.21/4.81 Axiom 21 (rule_126): fresh274(X, X, Y, Z) = s1(Y).
% 34.21/4.81 Axiom 22 (rule_131): fresh268(X, X, Y, Z) = true.
% 34.21/4.81 Axiom 23 (rule_183): fresh198(X, X, Y, Z) = q2(Y, c, Z).
% 34.21/4.81 Axiom 24 (rule_131): fresh586(X, X, Y, Z) = fresh587(s1(Y), true, Y, Z).
% 34.21/4.81 Axiom 25 (rule_183): fresh548(X, X, Y, Z) = fresh549(l0(c), true, Y, Z).
% 34.21/4.81 Axiom 26 (rule_001): fresh440(n0(X, Y), true, Y) = k1(Y).
% 34.21/4.81 Axiom 27 (rule_125): fresh275(p0(X, X), true, X) = s1(X).
% 34.21/4.81 Axiom 28 (rule_126): fresh274(s1(X), true, Y, Z) = fresh273(q0(Y, Z), true, Y).
% 34.21/4.81 Axiom 29 (rule_134): fresh266(X, X, Y, Z, W) = l2(Y, Y).
% 34.21/4.81 Axiom 30 (rule_134): fresh582(X, X, Y, Z, W) = fresh583(m0(Z, Y, W), true, Y).
% 34.21/4.81 Axiom 31 (rule_183): fresh548(l2(X, Y), true, Y, X) = fresh198(k1(X), true, Y, X).
% 34.21/4.81 Axiom 32 (rule_131): fresh586(l2(X, X), true, Y, X) = fresh268(n0(e, X), true, Y, X).
% 34.21/4.81 Axiom 33 (rule_189): fresh192(q2(b, X, b), true, X) = fresh191(s1(b), true, X).
% 34.21/4.81 Axiom 34 (rule_237): fresh131(s2(c), true, X) = fresh130(q2(X, c, c), true, X).
% 34.21/4.81 Axiom 35 (rule_015): fresh425(l0(X), true, Y, Z) = fresh424(m0(Z, Z, Y), true, Y, Z).
% 34.21/4.81 Axiom 36 (rule_134): fresh582(m1(X, Y, Y), true, Z, Y, X) = fresh266(p0(Y, Z), true, Z, Y, X).
% 34.21/4.81
% 34.21/4.81 Lemma 37: s1(b) = true.
% 34.21/4.81 Proof:
% 34.21/4.81 s1(b)
% 34.21/4.81 = { by axiom 27 (rule_125) R->L }
% 34.21/4.81 fresh275(p0(b, b), true, b)
% 34.21/4.81 = { by axiom 7 (axiom_14) }
% 34.21/4.81 fresh275(true, true, b)
% 34.21/4.81 = { by axiom 10 (rule_125) }
% 34.21/4.81 true
% 34.21/4.81
% 34.21/4.81 Lemma 38: fresh198(k1(X), true, b, X) = true.
% 34.21/4.81 Proof:
% 34.21/4.81 fresh198(k1(X), true, b, X)
% 34.21/4.81 = { by axiom 31 (rule_183) R->L }
% 34.21/4.81 fresh548(l2(X, b), true, b, X)
% 34.21/4.81 = { by axiom 17 (rule_131) R->L }
% 34.21/4.81 fresh548(fresh587(true, true, X, b), true, b, X)
% 34.21/4.81 = { by axiom 11 (rule_126) R->L }
% 34.21/4.81 fresh548(fresh587(fresh273(true, true, X), true, X, b), true, b, X)
% 34.21/4.81 = { by axiom 6 (axiom_17) R->L }
% 34.21/4.81 fresh548(fresh587(fresh273(q0(X, d), true, X), true, X, b), true, b, X)
% 34.21/4.81 = { by axiom 28 (rule_126) R->L }
% 34.21/4.81 fresh548(fresh587(fresh274(s1(b), true, X, d), true, X, b), true, b, X)
% 34.21/4.81 = { by lemma 37 }
% 34.21/4.81 fresh548(fresh587(fresh274(true, true, X, d), true, X, b), true, b, X)
% 34.21/4.81 = { by axiom 21 (rule_126) }
% 34.21/4.81 fresh548(fresh587(s1(X), true, X, b), true, b, X)
% 34.21/4.81 = { by axiom 24 (rule_131) R->L }
% 34.21/4.81 fresh548(fresh586(true, true, X, b), true, b, X)
% 34.21/4.81 = { by axiom 8 (rule_134) R->L }
% 34.21/4.81 fresh548(fresh586(fresh583(true, true, b), true, X, b), true, b, X)
% 34.21/4.81 = { by axiom 16 (axiom_31) R->L }
% 34.21/4.81 fresh548(fresh586(fresh583(m0(b, b, e), true, b), true, X, b), true, b, X)
% 34.21/4.81 = { by axiom 30 (rule_134) R->L }
% 34.21/4.81 fresh548(fresh586(fresh582(true, true, b, b, e), true, X, b), true, b, X)
% 34.21/4.81 = { by axiom 20 (rule_015) R->L }
% 34.21/4.81 fresh548(fresh586(fresh582(fresh424(true, true, e, b), true, b, b, e), true, X, b), true, b, X)
% 34.21/4.81 = { by axiom 16 (axiom_31) R->L }
% 34.21/4.81 fresh548(fresh586(fresh582(fresh424(m0(b, b, e), true, e, b), true, b, b, e), true, X, b), true, b, X)
% 34.21/4.81 = { by axiom 35 (rule_015) R->L }
% 34.21/4.81 fresh548(fresh586(fresh582(fresh425(l0(a), true, e, b), true, b, b, e), true, X, b), true, b, X)
% 34.21/4.81 = { by axiom 1 (axiom_20) }
% 34.21/4.81 fresh548(fresh586(fresh582(fresh425(true, true, e, b), true, b, b, e), true, X, b), true, b, X)
% 34.21/4.81 = { by axiom 19 (rule_015) }
% 34.21/4.81 fresh548(fresh586(fresh582(m1(e, b, b), true, b, b, e), true, X, b), true, b, X)
% 34.21/4.81 = { by axiom 36 (rule_134) }
% 34.21/4.81 fresh548(fresh586(fresh266(p0(b, b), true, b, b, e), true, X, b), true, b, X)
% 34.21/4.81 = { by axiom 7 (axiom_14) }
% 34.21/4.81 fresh548(fresh586(fresh266(true, true, b, b, e), true, X, b), true, b, X)
% 34.21/4.81 = { by axiom 29 (rule_134) }
% 34.21/4.81 fresh548(fresh586(l2(b, b), true, X, b), true, b, X)
% 34.21/4.81 = { by axiom 32 (rule_131) }
% 34.21/4.81 fresh548(fresh268(n0(e, b), true, X, b), true, b, X)
% 34.21/4.81 = { by axiom 5 (axiom_11) }
% 34.21/4.81 fresh548(fresh268(true, true, X, b), true, b, X)
% 34.21/4.81 = { by axiom 22 (rule_131) }
% 34.21/4.81 fresh548(true, true, b, X)
% 34.21/4.81 = { by axiom 25 (rule_183) }
% 34.21/4.81 fresh549(l0(c), true, b, X)
% 34.21/4.81 = { by axiom 2 (axiom_24) }
% 34.21/4.81 fresh549(true, true, b, X)
% 34.21/4.81 = { by axiom 18 (rule_183) }
% 34.21/4.81 true
% 34.21/4.81
% 34.21/4.81 Goal 1 (prove_this): m3(b, c, b) = true.
% 34.21/4.81 Proof:
% 34.21/4.81 m3(b, c, b)
% 34.21/4.81 = { by axiom 15 (rule_237) R->L }
% 34.21/4.81 fresh131(true, true, b)
% 34.21/4.81 = { by axiom 13 (rule_189) R->L }
% 34.21/4.81 fresh131(fresh191(true, true, c), true, b)
% 34.21/4.81 = { by lemma 37 R->L }
% 34.21/4.81 fresh131(fresh191(s1(b), true, c), true, b)
% 34.21/4.81 = { by axiom 33 (rule_189) R->L }
% 34.21/4.81 fresh131(fresh192(q2(b, c, b), true, c), true, b)
% 34.21/4.81 = { by axiom 23 (rule_183) R->L }
% 34.21/4.81 fresh131(fresh192(fresh198(true, true, b, b), true, c), true, b)
% 34.21/4.81 = { by axiom 9 (rule_001) R->L }
% 34.21/4.81 fresh131(fresh192(fresh198(fresh440(true, true, b), true, b, b), true, c), true, b)
% 34.21/4.81 = { by axiom 3 (axiom_15) R->L }
% 34.21/4.81 fresh131(fresh192(fresh198(fresh440(n0(a, b), true, b), true, b, b), true, c), true, b)
% 34.21/4.81 = { by axiom 26 (rule_001) }
% 34.21/4.81 fresh131(fresh192(fresh198(k1(b), true, b, b), true, c), true, b)
% 34.21/4.81 = { by lemma 38 }
% 34.21/4.81 fresh131(fresh192(true, true, c), true, b)
% 34.21/4.81 = { by axiom 12 (rule_189) }
% 34.21/4.81 fresh131(s2(c), true, b)
% 34.21/4.81 = { by axiom 34 (rule_237) }
% 34.21/4.81 fresh130(q2(b, c, c), true, b)
% 34.21/4.81 = { by axiom 23 (rule_183) R->L }
% 34.21/4.81 fresh130(fresh198(true, true, b, c), true, b)
% 34.21/4.81 = { by axiom 9 (rule_001) R->L }
% 34.21/4.81 fresh130(fresh198(fresh440(true, true, c), true, b, c), true, b)
% 34.21/4.81 = { by axiom 4 (axiom_26) R->L }
% 34.21/4.81 fresh130(fresh198(fresh440(n0(d, c), true, c), true, b, c), true, b)
% 34.21/4.81 = { by axiom 26 (rule_001) }
% 34.21/4.81 fresh130(fresh198(k1(c), true, b, c), true, b)
% 34.21/4.81 = { by lemma 38 }
% 34.21/4.81 fresh130(true, true, b)
% 34.21/4.81 = { by axiom 14 (rule_237) }
% 34.21/4.81 true
% 34.21/4.81 % SZS output end Proof
% 34.21/4.81
% 34.21/4.81 RESULT: Unsatisfiable (the axioms are contradictory).
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