TSTP Solution File: SYN162-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN162-1 : 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 03:33:25 EDT 2023
% Result : Unsatisfiable 21.43s 3.11s
% Output : Proof 21.43s
% 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 : SYN162-1 : 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
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 18:46:08 EDT 2023
% 0.14/0.35 % CPUTime :
% 21.43/3.11 Command-line arguments: --no-flatten-goal
% 21.43/3.11
% 21.43/3.11 % SZS status Unsatisfiable
% 21.43/3.11
% 21.43/3.12 % SZS output start Proof
% 21.43/3.12 Take the following subset of the input axioms:
% 21.43/3.12 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 21.43/3.12 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 21.43/3.12 fof(axiom_30, axiom, n0(e, e)).
% 21.43/3.12 fof(axiom_34, axiom, n0(c, d)).
% 21.43/3.12 fof(axiom_5, axiom, s0(b)).
% 21.43/3.12 fof(prove_this, negated_conjecture, ~n5(c, c)).
% 21.43/3.12 fof(rule_001, axiom, ![I, J]: (k1(I) | ~n0(J, I))).
% 21.43/3.12 fof(rule_029, axiom, ![H, I2]: (m1(H, I2, H) | (~p0(H, I2) | ~s0(H)))).
% 21.43/3.12 fof(rule_036, axiom, ![B, A2]: (n1(A2, A2, B) | ~m0(b, B, A2))).
% 21.43/3.12 fof(rule_176, axiom, ![D, E]: (p2(D, E, D) | ~m1(E, D, E))).
% 21.43/3.12 fof(rule_179, axiom, ![J2, A2_2]: (q2(J2, J2, J2) | (~k1(A2_2) | ~n1(J2, J2, A2_2)))).
% 21.43/3.12 fof(rule_240, axiom, ![F, D2, E2]: (n3(D2) | ~p2(E2, F, D2))).
% 21.43/3.12 fof(rule_255, axiom, ![G, I2, H2]: (q3(G, H2) | (~q2(I2, G, H2) | ~n0(I2, G)))).
% 21.43/3.12 fof(rule_298, axiom, ![I2, J2, G2, H2]: (r4(G2) | (~n3(G2) | (~q3(H2, I2) | ~p0(J2, G2))))).
% 21.43/3.12 fof(rule_314, axiom, ![B2]: (n5(B2, B2) | ~r4(B2))).
% 21.43/3.12
% 21.43/3.12 Now clausify the problem and encode Horn clauses using encoding 3 of
% 21.43/3.12 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 21.43/3.12 We repeatedly replace C & s=t => u=v by the two clauses:
% 21.43/3.12 fresh(y, y, x1...xn) = u
% 21.43/3.12 C => fresh(s, t, x1...xn) = v
% 21.43/3.12 where fresh is a fresh function symbol and x1..xn are the free
% 21.43/3.12 variables of u and v.
% 21.43/3.12 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 21.43/3.12 input problem has no model of domain size 1).
% 21.43/3.12
% 21.43/3.12 The encoding turns the above axioms into the following unit equations and goals:
% 21.43/3.12
% 21.43/3.12 Axiom 1 (axiom_5): s0(b) = true.
% 21.43/3.12 Axiom 2 (axiom_34): n0(c, d) = true.
% 21.43/3.12 Axiom 3 (axiom_30): n0(e, e) = true.
% 21.43/3.12 Axiom 4 (axiom_14): p0(b, X) = true.
% 21.43/3.12 Axiom 5 (rule_298): fresh459(X, X, Y) = true.
% 21.43/3.12 Axiom 6 (rule_001): fresh440(X, X, Y) = true.
% 21.43/3.12 Axiom 7 (rule_179): fresh202(X, X, Y) = true.
% 21.43/3.12 Axiom 8 (rule_240): fresh127(X, X, Y) = true.
% 21.43/3.12 Axiom 9 (rule_314): fresh23(X, X, Y) = true.
% 21.43/3.12 Axiom 10 (axiom_19): m0(X, d, Y) = true.
% 21.43/3.12 Axiom 11 (rule_029): fresh404(X, X, Y, Z) = m1(Y, Z, Y).
% 21.43/3.12 Axiom 12 (rule_029): fresh403(X, X, Y, Z) = true.
% 21.43/3.12 Axiom 13 (rule_036): fresh394(X, X, Y, Z) = true.
% 21.43/3.12 Axiom 14 (rule_176): fresh208(X, X, Y, Z) = true.
% 21.43/3.13 Axiom 15 (rule_179): fresh203(X, X, Y, Z) = q2(Y, Y, Y).
% 21.43/3.13 Axiom 16 (rule_255): fresh103(X, X, Y, Z) = true.
% 21.43/3.13 Axiom 17 (rule_298): fresh47(X, X, Y, Z) = r4(Y).
% 21.43/3.13 Axiom 18 (rule_314): fresh23(r4(X), true, X) = n5(X, X).
% 21.43/3.13 Axiom 19 (rule_298): fresh458(X, X, Y, Z) = fresh459(p0(Z, Y), true, Y).
% 21.43/3.13 Axiom 20 (rule_001): fresh440(n0(X, Y), true, Y) = k1(Y).
% 21.43/3.13 Axiom 21 (rule_255): fresh104(X, X, Y, Z, W) = q3(Y, Z).
% 21.43/3.13 Axiom 22 (rule_298): fresh458(q3(X, Y), true, Z, W) = fresh47(n3(Z), true, Z, W).
% 21.43/3.13 Axiom 23 (rule_029): fresh404(p0(X, Y), true, X, Y) = fresh403(s0(X), true, X, Y).
% 21.43/3.13 Axiom 24 (rule_240): fresh127(p2(X, Y, Z), true, Z) = n3(Z).
% 21.43/3.13 Axiom 25 (rule_036): fresh394(m0(b, X, Y), true, Y, X) = n1(Y, Y, X).
% 21.43/3.13 Axiom 26 (rule_176): fresh208(m1(X, Y, X), true, Y, X) = p2(Y, X, Y).
% 21.43/3.13 Axiom 27 (rule_179): fresh203(n1(X, X, Y), true, X, Y) = fresh202(k1(Y), true, X).
% 21.43/3.13 Axiom 28 (rule_255): fresh104(q2(X, Y, Z), true, Y, Z, X) = fresh103(n0(X, Y), true, Y, Z).
% 21.43/3.13
% 21.43/3.13 Goal 1 (prove_this): n5(c, c) = true.
% 21.43/3.13 Proof:
% 21.43/3.13 n5(c, c)
% 21.43/3.13 = { by axiom 18 (rule_314) R->L }
% 21.43/3.13 fresh23(r4(c), true, c)
% 21.43/3.13 = { by axiom 17 (rule_298) R->L }
% 21.43/3.13 fresh23(fresh47(true, true, c, b), true, c)
% 21.43/3.13 = { by axiom 8 (rule_240) R->L }
% 21.43/3.13 fresh23(fresh47(fresh127(true, true, c), true, c, b), true, c)
% 21.43/3.13 = { by axiom 14 (rule_176) R->L }
% 21.43/3.13 fresh23(fresh47(fresh127(fresh208(true, true, c, b), true, c), true, c, b), true, c)
% 21.43/3.13 = { by axiom 12 (rule_029) R->L }
% 21.43/3.13 fresh23(fresh47(fresh127(fresh208(fresh403(true, true, b, c), true, c, b), true, c), true, c, b), true, c)
% 21.43/3.13 = { by axiom 1 (axiom_5) R->L }
% 21.43/3.13 fresh23(fresh47(fresh127(fresh208(fresh403(s0(b), true, b, c), true, c, b), true, c), true, c, b), true, c)
% 21.43/3.13 = { by axiom 23 (rule_029) R->L }
% 21.43/3.13 fresh23(fresh47(fresh127(fresh208(fresh404(p0(b, c), true, b, c), true, c, b), true, c), true, c, b), true, c)
% 21.43/3.13 = { by axiom 4 (axiom_14) }
% 21.43/3.13 fresh23(fresh47(fresh127(fresh208(fresh404(true, true, b, c), true, c, b), true, c), true, c, b), true, c)
% 21.43/3.13 = { by axiom 11 (rule_029) }
% 21.43/3.13 fresh23(fresh47(fresh127(fresh208(m1(b, c, b), true, c, b), true, c), true, c, b), true, c)
% 21.43/3.13 = { by axiom 26 (rule_176) }
% 21.43/3.13 fresh23(fresh47(fresh127(p2(c, b, c), true, c), true, c, b), true, c)
% 21.43/3.13 = { by axiom 24 (rule_240) }
% 21.43/3.13 fresh23(fresh47(n3(c), true, c, b), true, c)
% 21.43/3.13 = { by axiom 22 (rule_298) R->L }
% 21.43/3.13 fresh23(fresh458(q3(e, e), true, c, b), true, c)
% 21.43/3.13 = { by axiom 21 (rule_255) R->L }
% 21.43/3.13 fresh23(fresh458(fresh104(true, true, e, e, e), true, c, b), true, c)
% 21.43/3.13 = { by axiom 7 (rule_179) R->L }
% 21.43/3.13 fresh23(fresh458(fresh104(fresh202(true, true, e), true, e, e, e), true, c, b), true, c)
% 21.43/3.13 = { by axiom 6 (rule_001) R->L }
% 21.43/3.13 fresh23(fresh458(fresh104(fresh202(fresh440(true, true, d), true, e), true, e, e, e), true, c, b), true, c)
% 21.43/3.13 = { by axiom 2 (axiom_34) R->L }
% 21.43/3.13 fresh23(fresh458(fresh104(fresh202(fresh440(n0(c, d), true, d), true, e), true, e, e, e), true, c, b), true, c)
% 21.43/3.13 = { by axiom 20 (rule_001) }
% 21.43/3.13 fresh23(fresh458(fresh104(fresh202(k1(d), true, e), true, e, e, e), true, c, b), true, c)
% 21.43/3.13 = { by axiom 27 (rule_179) R->L }
% 21.43/3.13 fresh23(fresh458(fresh104(fresh203(n1(e, e, d), true, e, d), true, e, e, e), true, c, b), true, c)
% 21.43/3.13 = { by axiom 25 (rule_036) R->L }
% 21.43/3.13 fresh23(fresh458(fresh104(fresh203(fresh394(m0(b, d, e), true, e, d), true, e, d), true, e, e, e), true, c, b), true, c)
% 21.43/3.13 = { by axiom 10 (axiom_19) }
% 21.43/3.13 fresh23(fresh458(fresh104(fresh203(fresh394(true, true, e, d), true, e, d), true, e, e, e), true, c, b), true, c)
% 21.43/3.13 = { by axiom 13 (rule_036) }
% 21.43/3.13 fresh23(fresh458(fresh104(fresh203(true, true, e, d), true, e, e, e), true, c, b), true, c)
% 21.43/3.13 = { by axiom 15 (rule_179) }
% 21.43/3.13 fresh23(fresh458(fresh104(q2(e, e, e), true, e, e, e), true, c, b), true, c)
% 21.43/3.13 = { by axiom 28 (rule_255) }
% 21.43/3.13 fresh23(fresh458(fresh103(n0(e, e), true, e, e), true, c, b), true, c)
% 21.43/3.13 = { by axiom 3 (axiom_30) }
% 21.43/3.13 fresh23(fresh458(fresh103(true, true, e, e), true, c, b), true, c)
% 21.43/3.13 = { by axiom 16 (rule_255) }
% 21.43/3.13 fresh23(fresh458(true, true, c, b), true, c)
% 21.43/3.13 = { by axiom 19 (rule_298) }
% 21.43/3.13 fresh23(fresh459(p0(b, c), true, c), true, c)
% 21.43/3.13 = { by axiom 4 (axiom_14) }
% 21.43/3.13 fresh23(fresh459(true, true, c), true, c)
% 21.43/3.13 = { by axiom 5 (rule_298) }
% 21.43/3.13 fresh23(true, true, c)
% 21.43/3.13 = { by axiom 9 (rule_314) }
% 21.43/3.13 true
% 21.43/3.13 % SZS output end Proof
% 21.43/3.13
% 21.43/3.13 RESULT: Unsatisfiable (the axioms are contradictory).
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