TSTP Solution File: SWC362-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC362-1 : 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 : n018.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 20:55:10 EDT 2023
% Result : Unsatisfiable 3.23s 0.87s
% Output : Proof 3.23s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : SWC362-1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.16 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.37 % Computer : n018.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Mon Aug 28 19:05:02 EDT 2023
% 0.14/0.37 % CPUTime :
% 3.23/0.87 Command-line arguments: --no-flatten-goal
% 3.23/0.87
% 3.23/0.87 % SZS status Unsatisfiable
% 3.23/0.87
% 3.23/0.88 % SZS output start Proof
% 3.23/0.88 Take the following subset of the input axioms:
% 3.23/0.88 fof(co1_11, negated_conjecture, segmentP(sk4, sk3) | ~neq(sk4, nil)).
% 3.23/0.88 fof(co1_12, negated_conjecture, ~segmentP(sk2, sk1) | ~neq(sk4, nil)).
% 3.23/0.88 fof(co1_5, negated_conjecture, sk2=sk4).
% 3.23/0.88 fof(co1_6, negated_conjecture, sk1=sk3).
% 3.23/0.88 fof(co1_7, negated_conjecture, neq(sk2, nil) | neq(sk2, nil)).
% 3.23/0.88
% 3.23/0.88 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.23/0.88 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.23/0.88 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.23/0.88 fresh(y, y, x1...xn) = u
% 3.23/0.88 C => fresh(s, t, x1...xn) = v
% 3.23/0.88 where fresh is a fresh function symbol and x1..xn are the free
% 3.23/0.88 variables of u and v.
% 3.23/0.88 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.23/0.88 input problem has no model of domain size 1).
% 3.23/0.88
% 3.23/0.88 The encoding turns the above axioms into the following unit equations and goals:
% 3.23/0.88
% 3.23/0.88 Axiom 1 (co1_6): sk1 = sk3.
% 3.23/0.88 Axiom 2 (co1_5): sk2 = sk4.
% 3.23/0.88 Axiom 3 (co1_11): fresh15(X, X) = true2.
% 3.23/0.88 Axiom 4 (co1_7): neq(sk2, nil) = true2.
% 3.23/0.88 Axiom 5 (co1_11): fresh15(neq(sk4, nil), true2) = segmentP(sk4, sk3).
% 3.23/0.88
% 3.23/0.88 Lemma 6: neq(sk4, nil) = true2.
% 3.23/0.88 Proof:
% 3.23/0.88 neq(sk4, nil)
% 3.23/0.88 = { by axiom 2 (co1_5) R->L }
% 3.23/0.88 neq(sk2, nil)
% 3.23/0.88 = { by axiom 4 (co1_7) }
% 3.23/0.88 true2
% 3.23/0.88
% 3.23/0.88 Goal 1 (co1_12): tuple2(segmentP(sk2, sk1), neq(sk4, nil)) = tuple2(true2, true2).
% 3.23/0.88 Proof:
% 3.23/0.88 tuple2(segmentP(sk2, sk1), neq(sk4, nil))
% 3.23/0.88 = { by axiom 1 (co1_6) }
% 3.23/0.88 tuple2(segmentP(sk2, sk3), neq(sk4, nil))
% 3.23/0.88 = { by axiom 2 (co1_5) }
% 3.23/0.88 tuple2(segmentP(sk4, sk3), neq(sk4, nil))
% 3.23/0.88 = { by lemma 6 }
% 3.23/0.88 tuple2(segmentP(sk4, sk3), true2)
% 3.23/0.88 = { by axiom 5 (co1_11) R->L }
% 3.23/0.88 tuple2(fresh15(neq(sk4, nil), true2), true2)
% 3.23/0.88 = { by lemma 6 }
% 3.23/0.88 tuple2(fresh15(true2, true2), true2)
% 3.23/0.88 = { by axiom 3 (co1_11) }
% 3.23/0.88 tuple2(true2, true2)
% 3.23/0.88 % SZS output end Proof
% 3.23/0.88
% 3.23/0.88 RESULT: Unsatisfiable (the axioms are contradictory).
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