TSTP Solution File: SWC042-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC042-1 : 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 : n010.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 20:53:34 EDT 2023
% Result : Unsatisfiable 4.84s 1.04s
% Output : Proof 4.84s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SWC042-1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 14:55:34 EDT 2023
% 0.14/0.36 % CPUTime :
% 4.84/1.04 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 4.84/1.04
% 4.84/1.04 % SZS status Unsatisfiable
% 4.84/1.04
% 4.84/1.04 % SZS output start Proof
% 4.84/1.04 Take the following subset of the input axioms:
% 4.84/1.04 fof(clause118, axiom, ![U, V]: (app(U, V)!=nil | (~ssList(V) | (~ssList(U) | nil=U)))).
% 4.84/1.04 fof(co1_1, negated_conjecture, ssList(sk1)).
% 4.84/1.04 fof(co1_10, negated_conjecture, app(sk3, sk5)=sk4).
% 4.84/1.04 fof(co1_5, negated_conjecture, nil=sk2).
% 4.84/1.04 fof(co1_6, negated_conjecture, sk2=sk4).
% 4.84/1.04 fof(co1_7, negated_conjecture, sk1=sk3).
% 4.84/1.04 fof(co1_8, negated_conjecture, nil!=sk1).
% 4.84/1.04 fof(co1_9, negated_conjecture, ssList(sk5)).
% 4.84/1.04
% 4.84/1.04 Now clausify the problem and encode Horn clauses using encoding 3 of
% 4.84/1.04 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 4.84/1.04 We repeatedly replace C & s=t => u=v by the two clauses:
% 4.84/1.04 fresh(y, y, x1...xn) = u
% 4.84/1.04 C => fresh(s, t, x1...xn) = v
% 4.84/1.04 where fresh is a fresh function symbol and x1..xn are the free
% 4.84/1.04 variables of u and v.
% 4.84/1.04 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 4.84/1.04 input problem has no model of domain size 1).
% 4.84/1.04
% 4.84/1.04 The encoding turns the above axioms into the following unit equations and goals:
% 4.84/1.04
% 4.84/1.04 Axiom 1 (co1_6): sk2 = sk4.
% 4.84/1.04 Axiom 2 (co1_7): sk1 = sk3.
% 4.84/1.04 Axiom 3 (co1_5): nil = sk2.
% 4.84/1.04 Axiom 4 (co1_1): ssList(sk1) = true2.
% 4.84/1.04 Axiom 5 (co1_9): ssList(sk5) = true2.
% 4.84/1.04 Axiom 6 (co1_10): app(sk3, sk5) = sk4.
% 4.84/1.04 Axiom 7 (clause118): fresh252(X, X, Y) = Y.
% 4.84/1.04 Axiom 8 (clause118): fresh72(X, X, Y, Z) = nil.
% 4.84/1.04 Axiom 9 (clause118): fresh251(X, X, Y, Z) = fresh252(app(Y, Z), nil, Y).
% 4.84/1.04 Axiom 10 (clause118): fresh251(ssList(X), true2, Y, X) = fresh72(ssList(Y), true2, Y, X).
% 4.84/1.04
% 4.84/1.04 Goal 1 (co1_8): nil = sk1.
% 4.84/1.04 Proof:
% 4.84/1.04 nil
% 4.84/1.04 = { by axiom 8 (clause118) R->L }
% 4.84/1.04 fresh72(true2, true2, sk1, sk5)
% 4.84/1.04 = { by axiom 4 (co1_1) R->L }
% 4.84/1.04 fresh72(ssList(sk1), true2, sk1, sk5)
% 4.84/1.04 = { by axiom 10 (clause118) R->L }
% 4.84/1.04 fresh251(ssList(sk5), true2, sk1, sk5)
% 4.84/1.04 = { by axiom 5 (co1_9) }
% 4.84/1.04 fresh251(true2, true2, sk1, sk5)
% 4.84/1.04 = { by axiom 9 (clause118) }
% 4.84/1.04 fresh252(app(sk1, sk5), nil, sk1)
% 4.84/1.04 = { by axiom 3 (co1_5) }
% 4.84/1.04 fresh252(app(sk1, sk5), sk2, sk1)
% 4.84/1.04 = { by axiom 2 (co1_7) }
% 4.84/1.04 fresh252(app(sk3, sk5), sk2, sk1)
% 4.84/1.04 = { by axiom 6 (co1_10) }
% 4.84/1.04 fresh252(sk4, sk2, sk1)
% 4.84/1.04 = { by axiom 1 (co1_6) R->L }
% 4.84/1.04 fresh252(sk2, sk2, sk1)
% 4.84/1.04 = { by axiom 7 (clause118) }
% 4.84/1.04 sk1
% 4.84/1.04 % SZS output end Proof
% 4.84/1.04
% 4.84/1.04 RESULT: Unsatisfiable (the axioms are contradictory).
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