TSTP Solution File: SYN110-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN110-1 : 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 : n006.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 03:33:12 EDT 2023
% Result : Unsatisfiable 39.08s 5.34s
% Output : Proof 39.08s
% 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 : SYN110-1 : 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 : n006.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 17:12:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 39.08/5.34 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 39.08/5.34
% 39.08/5.34 % SZS status Unsatisfiable
% 39.08/5.34
% 39.08/5.35 % SZS output start Proof
% 39.08/5.35 Take the following subset of the input axioms:
% 39.08/5.35 fof(axiom_12, axiom, ![X]: m0(a, X, a)).
% 39.08/5.35 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 39.08/5.35 fof(axiom_24, axiom, l0(c)).
% 39.08/5.35 fof(axiom_33, axiom, q0(d, c)).
% 39.08/5.35 fof(axiom_37, axiom, n0(b, a)).
% 39.08/5.35 fof(prove_this, negated_conjecture, ~k2(c, a)).
% 39.08/5.35 fof(rule_001, axiom, ![I, J]: (k1(I) | ~n0(J, I))).
% 39.08/5.35 fof(rule_020, axiom, m1(c, c, c) | ~l0(c)).
% 39.08/5.35 fof(rule_024, axiom, ![G, H, F]: (m1(F, a, G) | (~m0(a, H, a) | (~q0(F, G) | ~m1(G, c, G))))).
% 39.08/5.35 fof(rule_107, axiom, ![A2]: (q1(e, A2, A2) | (~m0(A2, d, A2) | ~m0(e, d, A2)))).
% 39.08/5.35 fof(rule_127, axiom, ![C, D, E, F2]: (k2(C, D) | (~m1(E, D, C) | (~k1(F2) | ~k2(F2, D))))).
% 39.08/5.35 fof(rule_129, axiom, ![A, J2]: (k2(J2, J2) | ~q1(A, J2, J2))).
% 39.08/5.35
% 39.08/5.35 Now clausify the problem and encode Horn clauses using encoding 3 of
% 39.08/5.35 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 39.08/5.35 We repeatedly replace C & s=t => u=v by the two clauses:
% 39.08/5.35 fresh(y, y, x1...xn) = u
% 39.08/5.35 C => fresh(s, t, x1...xn) = v
% 39.08/5.35 where fresh is a fresh function symbol and x1..xn are the free
% 39.08/5.35 variables of u and v.
% 39.08/5.35 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 39.08/5.35 input problem has no model of domain size 1).
% 39.08/5.35
% 39.08/5.35 The encoding turns the above axioms into the following unit equations and goals:
% 39.08/5.35
% 39.08/5.35 Axiom 1 (axiom_33): q0(d, c) = true.
% 39.08/5.35 Axiom 2 (axiom_24): l0(c) = true.
% 39.08/5.35 Axiom 3 (axiom_37): n0(b, a) = true.
% 39.08/5.35 Axiom 4 (rule_020): fresh416(X, X) = true.
% 39.08/5.35 Axiom 5 (axiom_19): m0(X, d, Y) = true.
% 39.08/5.35 Axiom 6 (axiom_12): m0(a, X, a) = true.
% 39.08/5.35 Axiom 7 (rule_001): fresh440(X, X, Y) = true.
% 39.08/5.35 Axiom 8 (rule_020): fresh416(l0(c), true) = m1(c, c, c).
% 39.08/5.35 Axiom 9 (rule_107): fresh301(X, X, Y) = q1(e, Y, Y).
% 39.08/5.35 Axiom 10 (rule_107): fresh300(X, X, Y) = true.
% 39.08/5.35 Axiom 11 (rule_129): fresh270(X, X, Y) = true.
% 39.08/5.35 Axiom 12 (rule_024): fresh662(X, X, Y, Z) = true.
% 39.08/5.35 Axiom 13 (rule_127): fresh591(X, X, Y, Z) = true.
% 39.08/5.35 Axiom 14 (rule_001): fresh440(n0(X, Y), true, Y) = k1(Y).
% 39.08/5.35 Axiom 15 (rule_024): fresh410(X, X, Y, Z) = m1(Y, a, Z).
% 39.08/5.35 Axiom 16 (rule_024): fresh661(X, X, Y, Z, W) = fresh662(q0(Y, Z), true, Y, Z).
% 39.08/5.35 Axiom 17 (rule_107): fresh301(m0(e, d, X), true, X) = fresh300(m0(X, d, X), true, X).
% 39.08/5.35 Axiom 18 (rule_127): fresh272(X, X, Y, Z, W) = k2(Y, Z).
% 39.08/5.35 Axiom 19 (rule_129): fresh270(q1(X, Y, Y), true, Y) = k2(Y, Y).
% 39.08/5.35 Axiom 20 (rule_127): fresh590(X, X, Y, Z, W, V) = fresh591(k1(W), true, Y, Z).
% 39.08/5.35 Axiom 21 (rule_024): fresh661(m1(X, c, X), true, Y, X, Z) = fresh410(m0(a, Z, a), true, Y, X).
% 39.08/5.35 Axiom 22 (rule_127): fresh590(k2(X, Y), true, Z, Y, X, W) = fresh272(m1(W, Y, Z), true, Z, Y, X).
% 39.08/5.35
% 39.08/5.35 Goal 1 (prove_this): k2(c, a) = true.
% 39.08/5.35 Proof:
% 39.08/5.35 k2(c, a)
% 39.08/5.35 = { by axiom 18 (rule_127) R->L }
% 39.08/5.35 fresh272(true, true, c, a, a)
% 39.08/5.35 = { by axiom 12 (rule_024) R->L }
% 39.08/5.35 fresh272(fresh662(true, true, d, c), true, c, a, a)
% 39.08/5.35 = { by axiom 1 (axiom_33) R->L }
% 39.08/5.35 fresh272(fresh662(q0(d, c), true, d, c), true, c, a, a)
% 39.08/5.35 = { by axiom 16 (rule_024) R->L }
% 39.08/5.35 fresh272(fresh661(true, true, d, c, X), true, c, a, a)
% 39.08/5.35 = { by axiom 4 (rule_020) R->L }
% 39.08/5.35 fresh272(fresh661(fresh416(true, true), true, d, c, X), true, c, a, a)
% 39.08/5.35 = { by axiom 2 (axiom_24) R->L }
% 39.08/5.35 fresh272(fresh661(fresh416(l0(c), true), true, d, c, X), true, c, a, a)
% 39.08/5.35 = { by axiom 8 (rule_020) }
% 39.08/5.35 fresh272(fresh661(m1(c, c, c), true, d, c, X), true, c, a, a)
% 39.08/5.35 = { by axiom 21 (rule_024) }
% 39.08/5.35 fresh272(fresh410(m0(a, X, a), true, d, c), true, c, a, a)
% 39.08/5.35 = { by axiom 6 (axiom_12) }
% 39.08/5.35 fresh272(fresh410(true, true, d, c), true, c, a, a)
% 39.08/5.35 = { by axiom 15 (rule_024) }
% 39.08/5.35 fresh272(m1(d, a, c), true, c, a, a)
% 39.08/5.35 = { by axiom 22 (rule_127) R->L }
% 39.08/5.35 fresh590(k2(a, a), true, c, a, a, d)
% 39.08/5.35 = { by axiom 19 (rule_129) R->L }
% 39.08/5.35 fresh590(fresh270(q1(e, a, a), true, a), true, c, a, a, d)
% 39.08/5.35 = { by axiom 9 (rule_107) R->L }
% 39.08/5.35 fresh590(fresh270(fresh301(true, true, a), true, a), true, c, a, a, d)
% 39.08/5.35 = { by axiom 5 (axiom_19) R->L }
% 39.08/5.35 fresh590(fresh270(fresh301(m0(e, d, a), true, a), true, a), true, c, a, a, d)
% 39.08/5.35 = { by axiom 17 (rule_107) }
% 39.08/5.35 fresh590(fresh270(fresh300(m0(a, d, a), true, a), true, a), true, c, a, a, d)
% 39.08/5.35 = { by axiom 5 (axiom_19) }
% 39.08/5.35 fresh590(fresh270(fresh300(true, true, a), true, a), true, c, a, a, d)
% 39.08/5.35 = { by axiom 10 (rule_107) }
% 39.08/5.35 fresh590(fresh270(true, true, a), true, c, a, a, d)
% 39.08/5.35 = { by axiom 11 (rule_129) }
% 39.08/5.35 fresh590(true, true, c, a, a, d)
% 39.08/5.35 = { by axiom 20 (rule_127) }
% 39.08/5.35 fresh591(k1(a), true, c, a)
% 39.08/5.35 = { by axiom 14 (rule_001) R->L }
% 39.08/5.35 fresh591(fresh440(n0(b, a), true, a), true, c, a)
% 39.08/5.35 = { by axiom 3 (axiom_37) }
% 39.08/5.35 fresh591(fresh440(true, true, a), true, c, a)
% 39.08/5.35 = { by axiom 7 (rule_001) }
% 39.08/5.35 fresh591(true, true, c, a)
% 39.08/5.35 = { by axiom 13 (rule_127) }
% 39.08/5.35 true
% 39.08/5.35 % SZS output end Proof
% 39.08/5.35
% 39.08/5.35 RESULT: Unsatisfiable (the axioms are contradictory).
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