TSTP Solution File: SYN169-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN169-1 : 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 : n017.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 03:33:27 EDT 2023
% Result : Unsatisfiable 16.59s 2.53s
% Output : Proof 16.59s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15 % Problem : SYN169-1 : TPTP v8.1.2. Released v1.1.0.
% 0.08/0.16 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.17/0.38 % Computer : n017.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Sat Aug 26 21:18:56 EDT 2023
% 0.17/0.38 % CPUTime :
% 16.59/2.53 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 16.59/2.53
% 16.59/2.53 % SZS status Unsatisfiable
% 16.59/2.53
% 16.59/2.53 % SZS output start Proof
% 16.59/2.53 Take the following subset of the input axioms:
% 16.59/2.53 fof(axiom_17, axiom, ![X]: q0(X, d)).
% 16.59/2.53 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 16.59/2.53 fof(prove_this, negated_conjecture, ![X2, Y2]: ~p3(X2, d, Y2)).
% 16.59/2.53 fof(rule_107, axiom, ![A2]: (q1(e, A2, A2) | (~m0(A2, d, A2) | ~m0(e, d, A2)))).
% 16.59/2.53 fof(rule_129, axiom, ![J, A]: (k2(J, J) | ~q1(A, J, J))).
% 16.59/2.53 fof(rule_252, axiom, ![I, H, J2]: (p3(H, H, H) | (~q0(I, H) | ~k2(J2, J2)))).
% 16.59/2.53
% 16.59/2.53 Now clausify the problem and encode Horn clauses using encoding 3 of
% 16.59/2.53 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 16.59/2.53 We repeatedly replace C & s=t => u=v by the two clauses:
% 16.59/2.53 fresh(y, y, x1...xn) = u
% 16.59/2.53 C => fresh(s, t, x1...xn) = v
% 16.59/2.53 where fresh is a fresh function symbol and x1..xn are the free
% 16.59/2.53 variables of u and v.
% 16.59/2.53 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 16.59/2.53 input problem has no model of domain size 1).
% 16.59/2.53
% 16.59/2.53 The encoding turns the above axioms into the following unit equations and goals:
% 16.59/2.53
% 16.59/2.53 Axiom 1 (axiom_17): q0(X, d) = true2.
% 16.59/2.53 Axiom 2 (axiom_19): m0(X, d, Y) = true2.
% 16.59/2.53 Axiom 3 (rule_107): fresh301(X, X, Y) = q1(e, Y, Y).
% 16.59/2.53 Axiom 4 (rule_107): fresh300(X, X, Y) = true2.
% 16.59/2.53 Axiom 5 (rule_129): fresh270(X, X, Y) = true2.
% 16.59/2.53 Axiom 6 (rule_252): fresh108(X, X, Y) = true2.
% 16.59/2.53 Axiom 7 (rule_252): fresh109(X, X, Y, Z) = p3(Y, Y, Y).
% 16.59/2.53 Axiom 8 (rule_107): fresh301(m0(e, d, X), true2, X) = fresh300(m0(X, d, X), true2, X).
% 16.59/2.53 Axiom 9 (rule_129): fresh270(q1(X, Y, Y), true2, Y) = k2(Y, Y).
% 16.59/2.53 Axiom 10 (rule_252): fresh109(k2(X, X), true2, Y, Z) = fresh108(q0(Z, Y), true2, Y).
% 16.59/2.53
% 16.59/2.53 Goal 1 (prove_this): p3(X, d, Y) = true2.
% 16.59/2.53 The goal is true when:
% 16.59/2.53 X = d
% 16.59/2.53 Y = d
% 16.59/2.53
% 16.59/2.53 Proof:
% 16.59/2.53 p3(d, d, d)
% 16.59/2.53 = { by axiom 7 (rule_252) R->L }
% 16.59/2.53 fresh109(true2, true2, d, X)
% 16.59/2.53 = { by axiom 5 (rule_129) R->L }
% 16.59/2.53 fresh109(fresh270(true2, true2, Y), true2, d, X)
% 16.59/2.53 = { by axiom 4 (rule_107) R->L }
% 16.59/2.53 fresh109(fresh270(fresh300(true2, true2, Y), true2, Y), true2, d, X)
% 16.59/2.53 = { by axiom 2 (axiom_19) R->L }
% 16.59/2.53 fresh109(fresh270(fresh300(m0(Y, d, Y), true2, Y), true2, Y), true2, d, X)
% 16.59/2.53 = { by axiom 8 (rule_107) R->L }
% 16.59/2.53 fresh109(fresh270(fresh301(m0(e, d, Y), true2, Y), true2, Y), true2, d, X)
% 16.59/2.53 = { by axiom 2 (axiom_19) }
% 16.59/2.53 fresh109(fresh270(fresh301(true2, true2, Y), true2, Y), true2, d, X)
% 16.59/2.53 = { by axiom 3 (rule_107) }
% 16.59/2.53 fresh109(fresh270(q1(e, Y, Y), true2, Y), true2, d, X)
% 16.59/2.53 = { by axiom 9 (rule_129) }
% 16.59/2.53 fresh109(k2(Y, Y), true2, d, X)
% 16.59/2.53 = { by axiom 10 (rule_252) }
% 16.59/2.53 fresh108(q0(X, d), true2, d)
% 16.59/2.53 = { by axiom 1 (axiom_17) }
% 16.59/2.53 fresh108(true2, true2, d)
% 16.59/2.53 = { by axiom 6 (rule_252) }
% 16.59/2.53 true2
% 16.59/2.53 % SZS output end Proof
% 16.59/2.53
% 16.59/2.53 RESULT: Unsatisfiable (the axioms are contradictory).
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