TSTP Solution File: SYN192-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN192-1 : 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 : n008.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 03:33:32 EDT 2023
% Result : Unsatisfiable 24.24s 3.47s
% Output : Proof 24.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN192-1 : 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 : n008.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 18:43:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 24.24/3.47 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 24.24/3.47
% 24.24/3.47 % SZS status Unsatisfiable
% 24.24/3.47
% 24.24/3.48 % SZS output start Proof
% 24.24/3.48 Take the following subset of the input axioms:
% 24.24/3.49 fof(axiom_11, axiom, n0(e, b)).
% 24.24/3.49 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 24.24/3.49 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 24.24/3.49 fof(axiom_28, axiom, k0(e)).
% 24.24/3.49 fof(prove_this, negated_conjecture, ~r4(a)).
% 24.24/3.49 fof(rule_001, axiom, ![I, J]: (k1(I) | ~n0(J, I))).
% 24.24/3.49 fof(rule_040, axiom, ![C, D]: (n1(C, e, e) | (~m0(C, D, e) | ~k1(C)))).
% 24.24/3.49 fof(rule_085, axiom, ![B, C2]: (p1(B, B, B) | ~p0(C2, B))).
% 24.24/3.49 fof(rule_122, axiom, ![G, H]: (q1(G, G, G) | ~m0(G, H, G))).
% 24.24/3.49 fof(rule_154, axiom, ![A2]: (p2(A2, A2, A2) | ~q1(A2, A2, A2))).
% 24.24/3.49 fof(rule_177, axiom, ![E, F]: (q2(E, F, F) | (~k0(F) | ~p1(E, E, E)))).
% 24.24/3.49 fof(rule_182, axiom, ![G2, H2, F2]: (q2(F2, G2, F2) | (~p1(F2, F2, H2) | (~n1(G2, F2, H2) | ~q2(G2, H2, F2))))).
% 24.24/3.49 fof(rule_240, axiom, ![D2, E2, F2]: (n3(D2) | ~p2(E2, F2, D2))).
% 24.24/3.49 fof(rule_255, axiom, ![I2, G2, H2]: (q3(G2, H2) | (~q2(I2, G2, H2) | ~n0(I2, G2)))).
% 24.24/3.49 fof(rule_298, axiom, ![I2, J2, G2, H2]: (r4(G2) | (~n3(G2) | (~q3(H2, I2) | ~p0(J2, G2))))).
% 24.24/3.49
% 24.24/3.49 Now clausify the problem and encode Horn clauses using encoding 3 of
% 24.24/3.49 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 24.24/3.49 We repeatedly replace C & s=t => u=v by the two clauses:
% 24.24/3.49 fresh(y, y, x1...xn) = u
% 24.24/3.49 C => fresh(s, t, x1...xn) = v
% 24.24/3.49 where fresh is a fresh function symbol and x1..xn are the free
% 24.24/3.49 variables of u and v.
% 24.24/3.49 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 24.24/3.49 input problem has no model of domain size 1).
% 24.24/3.49
% 24.24/3.49 The encoding turns the above axioms into the following unit equations and goals:
% 24.24/3.49
% 24.24/3.49 Axiom 1 (axiom_14): p0(b, X) = true.
% 24.24/3.49 Axiom 2 (axiom_11): n0(e, b) = true.
% 24.24/3.49 Axiom 3 (axiom_28): k0(e) = true.
% 24.24/3.49 Axiom 4 (axiom_19): m0(X, d, Y) = true.
% 24.24/3.49 Axiom 5 (rule_298): fresh459(X, X, Y) = true.
% 24.24/3.49 Axiom 6 (rule_001): fresh440(X, X, Y) = true.
% 24.24/3.49 Axiom 7 (rule_040): fresh388(X, X, Y) = true.
% 24.24/3.49 Axiom 8 (rule_085): fresh328(X, X, Y) = true.
% 24.24/3.49 Axiom 9 (rule_122): fresh279(X, X, Y) = true.
% 24.24/3.49 Axiom 10 (rule_154): fresh241(X, X, Y) = true.
% 24.24/3.49 Axiom 11 (rule_240): fresh127(X, X, Y) = true.
% 24.24/3.49 Axiom 12 (rule_182): fresh551(X, X, Y, Z) = true.
% 24.24/3.49 Axiom 13 (rule_298): fresh458(X, X, Y, Z) = fresh459(p0(Z, Y), true, Y).
% 24.24/3.49 Axiom 14 (rule_001): fresh440(n0(X, Y), true, Y) = k1(Y).
% 24.24/3.49 Axiom 15 (rule_040): fresh389(X, X, Y, Z) = n1(Y, e, e).
% 24.24/3.49 Axiom 16 (rule_085): fresh328(p0(X, Y), true, Y) = p1(Y, Y, Y).
% 24.24/3.49 Axiom 17 (rule_177): fresh207(X, X, Y, Z) = q2(Y, Z, Z).
% 24.24/3.49 Axiom 18 (rule_177): fresh206(X, X, Y, Z) = true.
% 24.24/3.49 Axiom 19 (rule_255): fresh103(X, X, Y, Z) = true.
% 24.24/3.49 Axiom 20 (rule_298): fresh47(X, X, Y, Z) = r4(Y).
% 24.24/3.49 Axiom 21 (rule_040): fresh389(k1(X), true, X, Y) = fresh388(m0(X, Y, e), true, X).
% 24.24/3.49 Axiom 22 (rule_122): fresh279(m0(X, Y, X), true, X) = q1(X, X, X).
% 24.24/3.49 Axiom 23 (rule_154): fresh241(q1(X, X, X), true, X) = p2(X, X, X).
% 24.24/3.49 Axiom 24 (rule_182): fresh199(X, X, Y, Z, W) = q2(Y, Z, Y).
% 24.24/3.49 Axiom 25 (rule_240): fresh127(p2(X, Y, Z), true, Z) = n3(Z).
% 24.24/3.49 Axiom 26 (rule_255): fresh104(X, X, Y, Z, W) = q3(Y, Z).
% 24.24/3.49 Axiom 27 (rule_298): fresh458(q3(X, Y), true, Z, W) = fresh47(n3(Z), true, Z, W).
% 24.24/3.49 Axiom 28 (rule_182): fresh550(X, X, Y, Z, W) = fresh551(n1(Z, Y, W), true, Y, Z).
% 24.24/3.49 Axiom 29 (rule_177): fresh207(p1(X, X, X), true, X, Y) = fresh206(k0(Y), true, X, Y).
% 24.24/3.49 Axiom 30 (rule_182): fresh550(q2(X, Y, Z), true, Z, X, Y) = fresh199(p1(Z, Z, Y), true, Z, X, Y).
% 24.24/3.49 Axiom 31 (rule_255): fresh104(q2(X, Y, Z), true, Y, Z, X) = fresh103(n0(X, Y), true, Y, Z).
% 24.24/3.49
% 24.24/3.49 Lemma 32: p1(X, X, X) = true.
% 24.24/3.49 Proof:
% 24.24/3.49 p1(X, X, X)
% 24.24/3.49 = { by axiom 16 (rule_085) R->L }
% 24.24/3.49 fresh328(p0(b, X), true, X)
% 24.24/3.49 = { by axiom 1 (axiom_14) }
% 24.24/3.49 fresh328(true, true, X)
% 24.24/3.49 = { by axiom 8 (rule_085) }
% 24.24/3.49 true
% 24.24/3.49
% 24.24/3.49 Goal 1 (prove_this): r4(a) = true.
% 24.24/3.49 Proof:
% 24.24/3.49 r4(a)
% 24.24/3.49 = { by axiom 20 (rule_298) R->L }
% 24.24/3.49 fresh47(true, true, a, b)
% 24.24/3.49 = { by axiom 11 (rule_240) R->L }
% 24.24/3.49 fresh47(fresh127(true, true, a), true, a, b)
% 24.24/3.49 = { by axiom 10 (rule_154) R->L }
% 24.24/3.49 fresh47(fresh127(fresh241(true, true, a), true, a), true, a, b)
% 24.24/3.49 = { by axiom 9 (rule_122) R->L }
% 24.24/3.49 fresh47(fresh127(fresh241(fresh279(true, true, a), true, a), true, a), true, a, b)
% 24.24/3.49 = { by axiom 4 (axiom_19) R->L }
% 24.24/3.49 fresh47(fresh127(fresh241(fresh279(m0(a, d, a), true, a), true, a), true, a), true, a, b)
% 24.24/3.49 = { by axiom 22 (rule_122) }
% 24.24/3.49 fresh47(fresh127(fresh241(q1(a, a, a), true, a), true, a), true, a, b)
% 24.24/3.49 = { by axiom 23 (rule_154) }
% 24.24/3.49 fresh47(fresh127(p2(a, a, a), true, a), true, a, b)
% 24.24/3.49 = { by axiom 25 (rule_240) }
% 24.24/3.49 fresh47(n3(a), true, a, b)
% 24.24/3.49 = { by axiom 27 (rule_298) R->L }
% 24.24/3.49 fresh458(q3(b, e), true, a, b)
% 24.24/3.49 = { by axiom 26 (rule_255) R->L }
% 24.24/3.49 fresh458(fresh104(true, true, b, e, e), true, a, b)
% 24.24/3.49 = { by axiom 12 (rule_182) R->L }
% 24.24/3.49 fresh458(fresh104(fresh551(true, true, e, b), true, b, e, e), true, a, b)
% 24.24/3.49 = { by axiom 7 (rule_040) R->L }
% 24.24/3.49 fresh458(fresh104(fresh551(fresh388(true, true, b), true, e, b), true, b, e, e), true, a, b)
% 24.24/3.49 = { by axiom 4 (axiom_19) R->L }
% 24.24/3.49 fresh458(fresh104(fresh551(fresh388(m0(b, d, e), true, b), true, e, b), true, b, e, e), true, a, b)
% 24.24/3.49 = { by axiom 21 (rule_040) R->L }
% 24.24/3.49 fresh458(fresh104(fresh551(fresh389(k1(b), true, b, d), true, e, b), true, b, e, e), true, a, b)
% 24.24/3.49 = { by axiom 14 (rule_001) R->L }
% 24.24/3.49 fresh458(fresh104(fresh551(fresh389(fresh440(n0(e, b), true, b), true, b, d), true, e, b), true, b, e, e), true, a, b)
% 24.24/3.49 = { by axiom 2 (axiom_11) }
% 24.24/3.49 fresh458(fresh104(fresh551(fresh389(fresh440(true, true, b), true, b, d), true, e, b), true, b, e, e), true, a, b)
% 24.24/3.49 = { by axiom 6 (rule_001) }
% 24.24/3.49 fresh458(fresh104(fresh551(fresh389(true, true, b, d), true, e, b), true, b, e, e), true, a, b)
% 24.24/3.49 = { by axiom 15 (rule_040) }
% 24.24/3.49 fresh458(fresh104(fresh551(n1(b, e, e), true, e, b), true, b, e, e), true, a, b)
% 24.24/3.49 = { by axiom 28 (rule_182) R->L }
% 24.24/3.49 fresh458(fresh104(fresh550(true, true, e, b, e), true, b, e, e), true, a, b)
% 24.24/3.49 = { by axiom 18 (rule_177) R->L }
% 24.24/3.49 fresh458(fresh104(fresh550(fresh206(true, true, b, e), true, e, b, e), true, b, e, e), true, a, b)
% 24.24/3.49 = { by axiom 3 (axiom_28) R->L }
% 24.24/3.49 fresh458(fresh104(fresh550(fresh206(k0(e), true, b, e), true, e, b, e), true, b, e, e), true, a, b)
% 24.24/3.49 = { by axiom 29 (rule_177) R->L }
% 24.24/3.49 fresh458(fresh104(fresh550(fresh207(p1(b, b, b), true, b, e), true, e, b, e), true, b, e, e), true, a, b)
% 24.24/3.49 = { by lemma 32 }
% 24.24/3.49 fresh458(fresh104(fresh550(fresh207(true, true, b, e), true, e, b, e), true, b, e, e), true, a, b)
% 24.24/3.49 = { by axiom 17 (rule_177) }
% 24.24/3.49 fresh458(fresh104(fresh550(q2(b, e, e), true, e, b, e), true, b, e, e), true, a, b)
% 24.24/3.49 = { by axiom 30 (rule_182) }
% 24.24/3.49 fresh458(fresh104(fresh199(p1(e, e, e), true, e, b, e), true, b, e, e), true, a, b)
% 24.24/3.49 = { by lemma 32 }
% 24.24/3.49 fresh458(fresh104(fresh199(true, true, e, b, e), true, b, e, e), true, a, b)
% 24.24/3.49 = { by axiom 24 (rule_182) }
% 24.24/3.49 fresh458(fresh104(q2(e, b, e), true, b, e, e), true, a, b)
% 24.24/3.49 = { by axiom 31 (rule_255) }
% 24.24/3.49 fresh458(fresh103(n0(e, b), true, b, e), true, a, b)
% 24.24/3.49 = { by axiom 2 (axiom_11) }
% 24.24/3.49 fresh458(fresh103(true, true, b, e), true, a, b)
% 24.24/3.49 = { by axiom 19 (rule_255) }
% 24.24/3.49 fresh458(true, true, a, b)
% 24.24/3.49 = { by axiom 13 (rule_298) }
% 24.24/3.49 fresh459(p0(b, a), true, a)
% 24.24/3.49 = { by axiom 1 (axiom_14) }
% 24.24/3.49 fresh459(true, true, a)
% 24.24/3.49 = { by axiom 5 (rule_298) }
% 24.24/3.49 true
% 24.24/3.49 % SZS output end Proof
% 24.24/3.49
% 24.24/3.49 RESULT: Unsatisfiable (the axioms are contradictory).
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