TSTP Solution File: SWC328-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC328-1 : TPTP v8.1.2. Released v2.4.0.
% 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 : n029.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 : Thu Aug 31 20:55:00 EDT 2023
% Result : Unsatisfiable 3.47s 0.84s
% Output : Proof 3.47s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC328-1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13 % 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 : n029.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 : Mon Aug 28 18:12:11 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.47/0.84 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 3.47/0.84
% 3.47/0.84 % SZS status Unsatisfiable
% 3.47/0.84
% 3.47/0.84 % SZS output start Proof
% 3.47/0.84 Take the following subset of the input axioms:
% 3.47/0.84 fof(clause1, axiom, equalelemsP(nil)).
% 3.47/0.84 fof(clause56, axiom, ![U]: (~ssList(U) | segmentP(U, nil))).
% 3.47/0.84 fof(co1_2, negated_conjecture, ssList(sk2)).
% 3.47/0.84 fof(co1_5, negated_conjecture, nil=sk3).
% 3.47/0.84 fof(co1_7, negated_conjecture, sk1=sk3).
% 3.47/0.84 fof(co1_8, negated_conjecture, ~segmentP(sk2, sk1) | ~equalelemsP(sk1)).
% 3.47/0.84
% 3.47/0.84 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.47/0.84 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.47/0.84 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.47/0.84 fresh(y, y, x1...xn) = u
% 3.47/0.84 C => fresh(s, t, x1...xn) = v
% 3.47/0.84 where fresh is a fresh function symbol and x1..xn are the free
% 3.47/0.84 variables of u and v.
% 3.47/0.84 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.47/0.84 input problem has no model of domain size 1).
% 3.47/0.84
% 3.47/0.84 The encoding turns the above axioms into the following unit equations and goals:
% 3.47/0.84
% 3.47/0.84 Axiom 1 (co1_5): nil = sk3.
% 3.47/0.84 Axiom 2 (co1_7): sk1 = sk3.
% 3.47/0.84 Axiom 3 (co1_2): ssList(sk2) = true2.
% 3.47/0.84 Axiom 4 (clause1): equalelemsP(nil) = true2.
% 3.47/0.84 Axiom 5 (clause56): fresh56(X, X, Y) = true2.
% 3.47/0.84 Axiom 6 (clause56): fresh56(ssList(X), true2, X) = segmentP(X, nil).
% 3.47/0.84
% 3.47/0.84 Lemma 7: sk1 = nil.
% 3.47/0.84 Proof:
% 3.47/0.84 sk1
% 3.47/0.84 = { by axiom 2 (co1_7) }
% 3.47/0.84 sk3
% 3.47/0.84 = { by axiom 1 (co1_5) R->L }
% 3.47/0.84 nil
% 3.47/0.84
% 3.47/0.84 Goal 1 (co1_8): tuple2(equalelemsP(sk1), segmentP(sk2, sk1)) = tuple2(true2, true2).
% 3.47/0.84 Proof:
% 3.47/0.84 tuple2(equalelemsP(sk1), segmentP(sk2, sk1))
% 3.47/0.84 = { by lemma 7 }
% 3.47/0.84 tuple2(equalelemsP(sk1), segmentP(sk2, nil))
% 3.47/0.84 = { by lemma 7 }
% 3.47/0.84 tuple2(equalelemsP(nil), segmentP(sk2, nil))
% 3.47/0.84 = { by axiom 4 (clause1) }
% 3.47/0.84 tuple2(true2, segmentP(sk2, nil))
% 3.47/0.84 = { by axiom 6 (clause56) R->L }
% 3.47/0.84 tuple2(true2, fresh56(ssList(sk2), true2, sk2))
% 3.47/0.84 = { by axiom 3 (co1_2) }
% 3.47/0.84 tuple2(true2, fresh56(true2, true2, sk2))
% 3.47/0.84 = { by axiom 5 (clause56) }
% 3.47/0.84 tuple2(true2, true2)
% 3.47/0.84 % SZS output end Proof
% 3.47/0.84
% 3.47/0.84 RESULT: Unsatisfiable (the axioms are contradictory).
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