TSTP Solution File: SYN178-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN178-1 : 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 : n012.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 03:33:29 EDT 2023
% Result : Unsatisfiable 26.51s 3.77s
% Output : Proof 26.63s
% 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 : SYN178-1 : 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 : n012.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 18:44:10 EDT 2023
% 0.19/0.34 % CPUTime :
% 26.51/3.77 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 26.51/3.77
% 26.51/3.77 % SZS status Unsatisfiable
% 26.51/3.77
% 26.63/3.78 % SZS output start Proof
% 26.63/3.78 Take the following subset of the input axioms:
% 26.63/3.78 fof(axiom_1, axiom, s0(d)).
% 26.63/3.78 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 26.63/3.78 fof(axiom_17, axiom, ![X2]: q0(X2, d)).
% 26.63/3.78 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 26.63/3.78 fof(axiom_28, axiom, k0(e)).
% 26.63/3.78 fof(axiom_32, axiom, k0(b)).
% 26.63/3.78 fof(axiom_7, axiom, n0(d, b)).
% 26.63/3.78 fof(prove_this, negated_conjecture, ~q3(b, d)).
% 26.63/3.78 fof(rule_085, axiom, ![C, B]: (p1(B, B, B) | ~p0(C, B))).
% 26.63/3.78 fof(rule_117, axiom, q1(d, d, d) | (~k0(e) | ~s0(d))).
% 26.63/3.78 fof(rule_124, axiom, ![D, E]: (r1(D) | (~q0(D, E) | (~s0(d) | ~q1(d, E, d))))).
% 26.63/3.78 fof(rule_177, axiom, ![F, E2]: (q2(E2, F, F) | (~k0(F) | ~p1(E2, E2, E2)))).
% 26.63/3.78 fof(rule_187, axiom, ![C2, D2, E2, F2]: (q2(C2, D2, C2) | (~r1(D2) | (~m0(E2, F2, C2) | (~k0(D2) | ~q2(D2, D2, D2)))))).
% 26.63/3.78 fof(rule_255, axiom, ![I, G, H]: (q3(G, H) | (~q2(I, G, H) | ~n0(I, G)))).
% 26.63/3.78
% 26.63/3.78 Now clausify the problem and encode Horn clauses using encoding 3 of
% 26.63/3.78 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 26.63/3.78 We repeatedly replace C & s=t => u=v by the two clauses:
% 26.63/3.78 fresh(y, y, x1...xn) = u
% 26.63/3.78 C => fresh(s, t, x1...xn) = v
% 26.63/3.78 where fresh is a fresh function symbol and x1..xn are the free
% 26.63/3.78 variables of u and v.
% 26.63/3.78 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 26.63/3.78 input problem has no model of domain size 1).
% 26.63/3.78
% 26.63/3.78 The encoding turns the above axioms into the following unit equations and goals:
% 26.63/3.78
% 26.63/3.78 Axiom 1 (axiom_14): p0(b, X) = true.
% 26.63/3.78 Axiom 2 (axiom_17): q0(X, d) = true.
% 26.63/3.78 Axiom 3 (axiom_1): s0(d) = true.
% 26.63/3.78 Axiom 4 (axiom_7): n0(d, b) = true.
% 26.63/3.78 Axiom 5 (axiom_32): k0(b) = true.
% 26.63/3.78 Axiom 6 (axiom_28): k0(e) = true.
% 26.63/3.79 Axiom 7 (rule_117): fresh285(X, X) = true.
% 26.63/3.79 Axiom 8 (axiom_19): m0(X, d, Y) = true.
% 26.63/3.79 Axiom 9 (rule_117): fresh286(X, X) = q1(d, d, d).
% 26.63/3.79 Axiom 10 (rule_124): fresh593(X, X, Y) = true.
% 26.63/3.79 Axiom 11 (rule_085): fresh328(X, X, Y) = true.
% 26.63/3.79 Axiom 12 (rule_117): fresh286(k0(e), true) = fresh285(s0(d), true).
% 26.63/3.79 Axiom 13 (rule_124): fresh276(X, X, Y) = r1(Y).
% 26.63/3.79 Axiom 14 (rule_124): fresh592(X, X, Y, Z) = fresh593(s0(d), true, Y).
% 26.63/3.79 Axiom 15 (rule_187): fresh545(X, X, Y, Z) = true.
% 26.63/3.79 Axiom 16 (rule_085): fresh328(p0(X, Y), true, Y) = p1(Y, Y, Y).
% 26.63/3.79 Axiom 17 (rule_177): fresh207(X, X, Y, Z) = q2(Y, Z, Z).
% 26.63/3.79 Axiom 18 (rule_177): fresh206(X, X, Y, Z) = true.
% 26.63/3.79 Axiom 19 (rule_255): fresh103(X, X, Y, Z) = true.
% 26.63/3.79 Axiom 20 (rule_255): fresh104(X, X, Y, Z, W) = q3(Y, Z).
% 26.63/3.79 Axiom 21 (rule_124): fresh592(q1(d, X, d), true, Y, X) = fresh276(q0(Y, X), true, Y).
% 26.63/3.79 Axiom 22 (rule_187): fresh544(X, X, Y, Z, W, V) = fresh545(m0(W, V, Y), true, Y, Z).
% 26.63/3.79 Axiom 23 (rule_187): fresh543(X, X, Y, Z, W, V) = q2(Y, Z, Y).
% 26.63/3.79 Axiom 24 (rule_177): fresh207(p1(X, X, X), true, X, Y) = fresh206(k0(Y), true, X, Y).
% 26.63/3.79 Axiom 25 (rule_187): fresh542(X, X, Y, Z, W, V) = fresh543(k0(Z), true, Y, Z, W, V).
% 26.63/3.79 Axiom 26 (rule_255): fresh104(q2(X, Y, Z), true, Y, Z, X) = fresh103(n0(X, Y), true, Y, Z).
% 26.63/3.79 Axiom 27 (rule_187): fresh542(q2(X, X, X), true, Y, X, Z, W) = fresh544(r1(X), true, Y, X, Z, W).
% 26.63/3.79
% 26.63/3.79 Goal 1 (prove_this): q3(b, d) = true.
% 26.63/3.79 Proof:
% 26.63/3.79 q3(b, d)
% 26.63/3.79 = { by axiom 20 (rule_255) R->L }
% 26.63/3.79 fresh104(true, true, b, d, d)
% 26.63/3.79 = { by axiom 15 (rule_187) R->L }
% 26.63/3.79 fresh104(fresh545(true, true, d, b), true, b, d, d)
% 26.63/3.79 = { by axiom 8 (axiom_19) R->L }
% 26.63/3.79 fresh104(fresh545(m0(X, d, d), true, d, b), true, b, d, d)
% 26.63/3.79 = { by axiom 22 (rule_187) R->L }
% 26.63/3.79 fresh104(fresh544(true, true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 10 (rule_124) R->L }
% 26.63/3.79 fresh104(fresh544(fresh593(true, true, b), true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 3 (axiom_1) R->L }
% 26.63/3.79 fresh104(fresh544(fresh593(s0(d), true, b), true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 14 (rule_124) R->L }
% 26.63/3.79 fresh104(fresh544(fresh592(true, true, b, d), true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 7 (rule_117) R->L }
% 26.63/3.79 fresh104(fresh544(fresh592(fresh285(true, true), true, b, d), true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 3 (axiom_1) R->L }
% 26.63/3.79 fresh104(fresh544(fresh592(fresh285(s0(d), true), true, b, d), true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 12 (rule_117) R->L }
% 26.63/3.79 fresh104(fresh544(fresh592(fresh286(k0(e), true), true, b, d), true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 6 (axiom_28) }
% 26.63/3.79 fresh104(fresh544(fresh592(fresh286(true, true), true, b, d), true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 9 (rule_117) }
% 26.63/3.79 fresh104(fresh544(fresh592(q1(d, d, d), true, b, d), true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 21 (rule_124) }
% 26.63/3.79 fresh104(fresh544(fresh276(q0(b, d), true, b), true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 2 (axiom_17) }
% 26.63/3.79 fresh104(fresh544(fresh276(true, true, b), true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 13 (rule_124) }
% 26.63/3.79 fresh104(fresh544(r1(b), true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 27 (rule_187) R->L }
% 26.63/3.79 fresh104(fresh542(q2(b, b, b), true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 17 (rule_177) R->L }
% 26.63/3.79 fresh104(fresh542(fresh207(true, true, b, b), true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 11 (rule_085) R->L }
% 26.63/3.79 fresh104(fresh542(fresh207(fresh328(true, true, b), true, b, b), true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 1 (axiom_14) R->L }
% 26.63/3.79 fresh104(fresh542(fresh207(fresh328(p0(b, b), true, b), true, b, b), true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 16 (rule_085) }
% 26.63/3.79 fresh104(fresh542(fresh207(p1(b, b, b), true, b, b), true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 24 (rule_177) }
% 26.63/3.79 fresh104(fresh542(fresh206(k0(b), true, b, b), true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 5 (axiom_32) }
% 26.63/3.79 fresh104(fresh542(fresh206(true, true, b, b), true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 18 (rule_177) }
% 26.63/3.79 fresh104(fresh542(true, true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 25 (rule_187) }
% 26.63/3.79 fresh104(fresh543(k0(b), true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 5 (axiom_32) }
% 26.63/3.79 fresh104(fresh543(true, true, d, b, X, d), true, b, d, d)
% 26.63/3.79 = { by axiom 23 (rule_187) }
% 26.63/3.79 fresh104(q2(d, b, d), true, b, d, d)
% 26.63/3.79 = { by axiom 26 (rule_255) }
% 26.63/3.79 fresh103(n0(d, b), true, b, d)
% 26.63/3.79 = { by axiom 4 (axiom_7) }
% 26.63/3.79 fresh103(true, true, b, d)
% 26.63/3.79 = { by axiom 19 (rule_255) }
% 26.63/3.79 true
% 26.63/3.79 % SZS output end Proof
% 26.63/3.79
% 26.63/3.79 RESULT: Unsatisfiable (the axioms are contradictory).
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