TSTP Solution File: SYN266-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN266-1 : 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 : n019.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 03:33:50 EDT 2023
% Result : Unsatisfiable 34.23s 4.93s
% Output : Proof 34.23s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN266-1 : TPTP v8.1.2. Released v1.1.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 20:09:43 EDT 2023
% 0.14/0.34 % CPUTime :
% 34.23/4.93 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 34.23/4.93
% 34.23/4.93 % SZS status Unsatisfiable
% 34.23/4.93
% 34.23/4.94 % SZS output start Proof
% 34.23/4.94 Take the following subset of the input axioms:
% 34.23/4.94 fof(axiom_13, axiom, r0(e)).
% 34.23/4.94 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 34.23/4.94 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 34.23/4.94 fof(axiom_31, axiom, m0(b, b, e)).
% 34.23/4.94 fof(prove_this, negated_conjecture, ~p3(b, e, e)).
% 34.23/4.94 fof(rule_005, axiom, ![C, B]: (m1(B, C, B) | ~m0(C, C, B))).
% 34.23/4.94 fof(rule_057, axiom, ![D]: (n1(D, D, D) | ~r0(D))).
% 34.23/4.94 fof(rule_122, axiom, ![G, H]: (q1(G, G, G) | ~m0(G, H, G))).
% 34.23/4.94 fof(rule_152, axiom, ![E, C2, D2]: (p2(C2, D2, D2) | (~n1(E, D2, E) | (~p0(C2, D2) | ~p2(C2, D2, C2))))).
% 34.23/4.94 fof(rule_154, axiom, ![A2]: (p2(A2, A2, A2) | ~q1(A2, A2, A2))).
% 34.23/4.94 fof(rule_176, axiom, ![D2, E2]: (p2(D2, E2, D2) | ~m1(E2, D2, E2))).
% 34.23/4.94 fof(rule_238, axiom, ![I]: (m3(I, I, I) | ~p2(I, I, I))).
% 34.23/4.94 fof(rule_251, axiom, ![C2, D2, B2, A2_2]: (p3(A2_2, B2, B2) | (~m3(B2, C2, D2) | ~p2(A2_2, B2, D2)))).
% 34.23/4.94
% 34.23/4.94 Now clausify the problem and encode Horn clauses using encoding 3 of
% 34.23/4.94 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 34.23/4.94 We repeatedly replace C & s=t => u=v by the two clauses:
% 34.23/4.94 fresh(y, y, x1...xn) = u
% 34.23/4.94 C => fresh(s, t, x1...xn) = v
% 34.23/4.94 where fresh is a fresh function symbol and x1..xn are the free
% 34.23/4.94 variables of u and v.
% 34.23/4.94 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 34.23/4.94 input problem has no model of domain size 1).
% 34.23/4.94
% 34.23/4.94 The encoding turns the above axioms into the following unit equations and goals:
% 34.23/4.94
% 34.23/4.94 Axiom 1 (axiom_13): r0(e) = true.
% 34.23/4.94 Axiom 2 (axiom_14): p0(b, X) = true.
% 34.23/4.94 Axiom 3 (axiom_19): m0(X, d, Y) = true.
% 34.23/4.94 Axiom 4 (axiom_31): m0(b, b, e) = true.
% 34.23/4.94 Axiom 5 (rule_057): fresh367(X, X, Y) = true.
% 34.23/4.94 Axiom 6 (rule_122): fresh279(X, X, Y) = true.
% 34.23/4.94 Axiom 7 (rule_154): fresh241(X, X, Y) = true.
% 34.23/4.94 Axiom 8 (rule_238): fresh129(X, X, Y) = true.
% 34.23/4.94 Axiom 9 (rule_152): fresh565(X, X, Y, Z) = true.
% 34.23/4.94 Axiom 10 (rule_005): fresh437(X, X, Y, Z) = true.
% 34.23/4.94 Axiom 11 (rule_057): fresh367(r0(X), true, X) = n1(X, X, X).
% 34.23/4.94 Axiom 12 (rule_152): fresh243(X, X, Y, Z) = p2(Y, Z, Z).
% 34.23/4.94 Axiom 13 (rule_176): fresh208(X, X, Y, Z) = true.
% 34.23/4.94 Axiom 14 (rule_251): fresh110(X, X, Y, Z) = true.
% 34.23/4.94 Axiom 15 (rule_251): fresh111(X, X, Y, Z, W) = p3(Y, Z, Z).
% 34.23/4.94 Axiom 16 (rule_152): fresh564(X, X, Y, Z, W) = fresh565(p0(Y, Z), true, Y, Z).
% 34.23/4.94 Axiom 17 (rule_122): fresh279(m0(X, Y, X), true, X) = q1(X, X, X).
% 34.23/4.94 Axiom 18 (rule_154): fresh241(q1(X, X, X), true, X) = p2(X, X, X).
% 34.23/4.94 Axiom 19 (rule_238): fresh129(p2(X, X, X), true, X) = m3(X, X, X).
% 34.23/4.94 Axiom 20 (rule_005): fresh437(m0(X, X, Y), true, Y, X) = m1(Y, X, Y).
% 34.23/4.94 Axiom 21 (rule_176): fresh208(m1(X, Y, X), true, Y, X) = p2(Y, X, Y).
% 34.23/4.94 Axiom 22 (rule_152): fresh564(p2(X, Y, X), true, X, Y, Z) = fresh243(n1(Z, Y, Z), true, X, Y).
% 34.23/4.94 Axiom 23 (rule_251): fresh111(m3(X, Y, Z), true, W, X, Z) = fresh110(p2(W, X, Z), true, W, X).
% 34.23/4.94
% 34.23/4.94 Goal 1 (prove_this): p3(b, e, e) = true.
% 34.23/4.94 Proof:
% 34.23/4.94 p3(b, e, e)
% 34.23/4.94 = { by axiom 15 (rule_251) R->L }
% 34.23/4.94 fresh111(true, true, b, e, e)
% 34.23/4.94 = { by axiom 8 (rule_238) R->L }
% 34.23/4.94 fresh111(fresh129(true, true, e), true, b, e, e)
% 34.23/4.94 = { by axiom 7 (rule_154) R->L }
% 34.23/4.94 fresh111(fresh129(fresh241(true, true, e), true, e), true, b, e, e)
% 34.23/4.94 = { by axiom 6 (rule_122) R->L }
% 34.23/4.94 fresh111(fresh129(fresh241(fresh279(true, true, e), true, e), true, e), true, b, e, e)
% 34.23/4.94 = { by axiom 3 (axiom_19) R->L }
% 34.23/4.94 fresh111(fresh129(fresh241(fresh279(m0(e, d, e), true, e), true, e), true, e), true, b, e, e)
% 34.23/4.94 = { by axiom 17 (rule_122) }
% 34.23/4.94 fresh111(fresh129(fresh241(q1(e, e, e), true, e), true, e), true, b, e, e)
% 34.23/4.94 = { by axiom 18 (rule_154) }
% 34.23/4.94 fresh111(fresh129(p2(e, e, e), true, e), true, b, e, e)
% 34.23/4.94 = { by axiom 19 (rule_238) }
% 34.23/4.94 fresh111(m3(e, e, e), true, b, e, e)
% 34.23/4.94 = { by axiom 23 (rule_251) }
% 34.23/4.94 fresh110(p2(b, e, e), true, b, e)
% 34.23/4.94 = { by axiom 12 (rule_152) R->L }
% 34.23/4.94 fresh110(fresh243(true, true, b, e), true, b, e)
% 34.23/4.94 = { by axiom 5 (rule_057) R->L }
% 34.23/4.94 fresh110(fresh243(fresh367(true, true, e), true, b, e), true, b, e)
% 34.23/4.94 = { by axiom 1 (axiom_13) R->L }
% 34.23/4.94 fresh110(fresh243(fresh367(r0(e), true, e), true, b, e), true, b, e)
% 34.23/4.94 = { by axiom 11 (rule_057) }
% 34.23/4.94 fresh110(fresh243(n1(e, e, e), true, b, e), true, b, e)
% 34.23/4.95 = { by axiom 22 (rule_152) R->L }
% 34.23/4.95 fresh110(fresh564(p2(b, e, b), true, b, e, e), true, b, e)
% 34.23/4.95 = { by axiom 21 (rule_176) R->L }
% 34.23/4.95 fresh110(fresh564(fresh208(m1(e, b, e), true, b, e), true, b, e, e), true, b, e)
% 34.23/4.95 = { by axiom 20 (rule_005) R->L }
% 34.23/4.95 fresh110(fresh564(fresh208(fresh437(m0(b, b, e), true, e, b), true, b, e), true, b, e, e), true, b, e)
% 34.23/4.95 = { by axiom 4 (axiom_31) }
% 34.23/4.95 fresh110(fresh564(fresh208(fresh437(true, true, e, b), true, b, e), true, b, e, e), true, b, e)
% 34.23/4.95 = { by axiom 10 (rule_005) }
% 34.23/4.95 fresh110(fresh564(fresh208(true, true, b, e), true, b, e, e), true, b, e)
% 34.23/4.95 = { by axiom 13 (rule_176) }
% 34.23/4.95 fresh110(fresh564(true, true, b, e, e), true, b, e)
% 34.23/4.95 = { by axiom 16 (rule_152) }
% 34.23/4.95 fresh110(fresh565(p0(b, e), true, b, e), true, b, e)
% 34.23/4.95 = { by axiom 2 (axiom_14) }
% 34.23/4.95 fresh110(fresh565(true, true, b, e), true, b, e)
% 34.23/4.95 = { by axiom 9 (rule_152) }
% 34.23/4.95 fresh110(true, true, b, e)
% 34.23/4.95 = { by axiom 14 (rule_251) }
% 34.23/4.95 true
% 34.23/4.95 % SZS output end Proof
% 34.23/4.95
% 34.23/4.95 RESULT: Unsatisfiable (the axioms are contradictory).
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