TSTP Solution File: SWC380-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC380-1 : 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 : n020.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 20:55:16 EDT 2023
% Result : Unsatisfiable 18.91s 2.79s
% Output : Proof 18.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWC380-1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 14:57:14 EDT 2023
% 0.14/0.34 % CPUTime :
% 18.91/2.79 Command-line arguments: --flatten
% 18.91/2.79
% 18.91/2.79 % SZS status Unsatisfiable
% 18.91/2.79
% 18.91/2.80 % SZS output start Proof
% 18.91/2.80 Take the following subset of the input axioms:
% 18.91/2.80 fof(clause1, axiom, equalelemsP(nil)).
% 18.91/2.80 fof(clause110, axiom, ![U, V]: (~gt(U, V) | (~gt(V, U) | (~ssItem(U) | ~ssItem(V))))).
% 18.91/2.80 fof(clause111, axiom, ![U2, V2]: (U2!=V2 | (~lt(U2, V2) | (~ssItem(V2) | ~ssItem(U2))))).
% 18.91/2.80 fof(clause114, axiom, ![U2, V2]: (~lt(U2, V2) | (~lt(V2, U2) | (~ssItem(U2) | ~ssItem(V2))))).
% 18.91/2.80 fof(clause115, axiom, ![U2, V2]: (U2!=V2 | (~neq(U2, V2) | (~ssList(V2) | ~ssList(U2))))).
% 18.91/2.80 fof(clause117, axiom, ![U2, V2]: (U2!=V2 | (~neq(U2, V2) | (~ssItem(V2) | ~ssItem(U2))))).
% 18.91/2.80 fof(clause120, axiom, ![U2, V2]: (~ssItem(U2) | (~ssList(V2) | app(cons(U2, nil), V2)=cons(U2, V2)))).
% 18.91/2.80 fof(clause138, axiom, ![W, U2, V2]: (U2!=V2 | (~ssList(W) | (~ssItem(V2) | (~ssItem(U2) | memberP(cons(V2, W), U2)))))).
% 18.91/2.80 fof(clause179, axiom, ![X, Y, U2, V2, W2]: (app(app(U2, cons(V2, W2)), cons(V2, X))!=Y | (~ssList(X) | (~ssList(W2) | (~ssList(U2) | (~ssItem(V2) | (~duplicatefreeP(Y) | ~ssList(Y)))))))).
% 18.91/2.80 fof(clause185, axiom, ![Z, U2, V2, W2, X2, Y2]: (~leq(U2, V2) | (~leq(V2, U2) | (app(app(W2, cons(U2, X2)), cons(V2, Y2))!=Z | (~ssList(Y2) | (~ssList(X2) | (~ssList(W2) | (~ssItem(V2) | (~ssItem(U2) | (~cyclefreeP(Z) | ~ssList(Z))))))))))).
% 18.91/2.80 fof(clause2, axiom, duplicatefreeP(nil)).
% 18.91/2.80 fof(clause63, axiom, ![U2]: (~lt(U2, U2) | ~ssItem(U2))).
% 18.91/2.80 fof(clause71, axiom, ![U2]: (~memberP(nil, U2) | ~ssItem(U2))).
% 18.91/2.80 fof(clause98, axiom, ![U2, V2]: (cons(U2, V2)!=nil | (~ssItem(U2) | ~ssList(V2)))).
% 18.91/2.80 fof(clause99, axiom, ![U2, V2]: (cons(U2, V2)!=V2 | (~ssItem(U2) | ~ssList(V2)))).
% 18.91/2.80 fof(co1_14, negated_conjecture, ![A]: (~ssItem(A) | (cons(A, nil)!=sk1 | (~memberP(sk2, A) | ~neq(sk4, nil))))).
% 18.91/2.80 fof(co1_15, negated_conjecture, ssItem(sk5) | ~neq(sk4, nil)).
% 18.91/2.80 fof(co1_16, negated_conjecture, ssList(sk6) | ~neq(sk4, nil)).
% 18.91/2.80 fof(co1_17, negated_conjecture, cons(sk5, nil)=sk3 | ~neq(sk4, nil)).
% 18.91/2.80 fof(co1_18, negated_conjecture, app(cons(sk5, nil), sk6)=sk4 | ~neq(sk4, nil)).
% 18.91/2.80 fof(co1_5, negated_conjecture, sk2=sk4).
% 18.91/2.80 fof(co1_6, negated_conjecture, sk1=sk3).
% 18.91/2.80 fof(co1_7, negated_conjecture, neq(sk2, nil) | neq(sk2, nil)).
% 18.91/2.80
% 18.91/2.80 Now clausify the problem and encode Horn clauses using encoding 3 of
% 18.91/2.80 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 18.91/2.80 We repeatedly replace C & s=t => u=v by the two clauses:
% 18.91/2.80 fresh(y, y, x1...xn) = u
% 18.91/2.80 C => fresh(s, t, x1...xn) = v
% 18.91/2.80 where fresh is a fresh function symbol and x1..xn are the free
% 18.91/2.80 variables of u and v.
% 18.91/2.80 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 18.91/2.80 input problem has no model of domain size 1).
% 18.91/2.80
% 18.91/2.80 The encoding turns the above axioms into the following unit equations and goals:
% 18.91/2.80
% 18.91/2.80 Axiom 1 (co1_6): sk1 = sk3.
% 18.91/2.80 Axiom 2 (co1_5): sk2 = sk4.
% 18.91/2.80 Axiom 3 (clause2): duplicatefreeP(nil) = true2.
% 18.91/2.80 Axiom 4 (clause1): equalelemsP(nil) = true2.
% 18.91/2.80 Axiom 5 (co1_15): fresh19(X, X) = true2.
% 18.91/2.80 Axiom 6 (co1_16): fresh18(X, X) = true2.
% 18.91/2.80 Axiom 7 (co1_17): fresh17(X, X) = sk3.
% 18.91/2.80 Axiom 8 (co1_18): fresh16(X, X) = sk4.
% 18.91/2.80 Axiom 9 (co1_7): neq(sk2, nil) = true2.
% 18.91/2.80 Axiom 10 (clause120): fresh75(X, X, Y, Z) = cons(Y, Z).
% 18.91/2.80 Axiom 11 (clause138): fresh70(X, X, Y, Z) = true2.
% 18.91/2.80 Axiom 12 (co1_15): fresh19(neq(sk4, nil), true2) = ssItem(sk5).
% 18.91/2.80 Axiom 13 (co1_16): fresh18(neq(sk4, nil), true2) = ssList(sk6).
% 18.91/2.80 Axiom 14 (co1_17): fresh17(neq(sk4, nil), true2) = cons(sk5, nil).
% 18.91/2.80 Axiom 15 (clause138): fresh71(X, X, Y, Z) = memberP(cons(Y, Z), Y).
% 18.91/2.80 Axiom 16 (clause120): fresh74(X, X, Y, Z) = app(cons(Y, nil), Z).
% 18.91/2.80 Axiom 17 (co1_18): fresh16(neq(sk4, nil), true2) = app(cons(sk5, nil), sk6).
% 18.91/2.80 Axiom 18 (clause120): fresh74(ssItem(X), true2, X, Y) = fresh75(ssList(Y), true2, X, Y).
% 18.91/2.80 Axiom 19 (clause138): fresh71(ssItem(X), true2, X, Y) = fresh70(ssList(Y), true2, X, Y).
% 18.91/2.80
% 18.91/2.80 Lemma 20: equalelemsP(nil) = duplicatefreeP(nil).
% 18.91/2.80 Proof:
% 18.91/2.80 equalelemsP(nil)
% 18.91/2.80 = { by axiom 4 (clause1) }
% 18.91/2.80 true2
% 18.91/2.80 = { by axiom 3 (clause2) R->L }
% 18.91/2.80 duplicatefreeP(nil)
% 18.91/2.80
% 18.91/2.80 Lemma 21: neq(sk2, nil) = equalelemsP(nil).
% 18.91/2.80 Proof:
% 18.91/2.80 neq(sk2, nil)
% 18.91/2.80 = { by axiom 9 (co1_7) }
% 18.91/2.80 true2
% 18.91/2.80 = { by axiom 3 (clause2) R->L }
% 18.91/2.80 duplicatefreeP(nil)
% 18.91/2.80 = { by lemma 20 R->L }
% 18.91/2.80 equalelemsP(nil)
% 18.91/2.80
% 18.91/2.80 Lemma 22: ssItem(sk5) = equalelemsP(nil).
% 18.91/2.80 Proof:
% 18.91/2.80 ssItem(sk5)
% 18.91/2.80 = { by axiom 12 (co1_15) R->L }
% 18.91/2.80 fresh19(neq(sk4, nil), true2)
% 18.91/2.80 = { by axiom 2 (co1_5) R->L }
% 18.91/2.80 fresh19(neq(sk2, nil), true2)
% 18.91/2.80 = { by lemma 21 }
% 18.91/2.80 fresh19(equalelemsP(nil), true2)
% 18.91/2.80 = { by axiom 3 (clause2) R->L }
% 18.91/2.80 fresh19(equalelemsP(nil), duplicatefreeP(nil))
% 18.91/2.80 = { by lemma 20 R->L }
% 18.91/2.80 fresh19(equalelemsP(nil), equalelemsP(nil))
% 18.91/2.80 = { by axiom 5 (co1_15) }
% 18.91/2.80 true2
% 18.91/2.80 = { by axiom 3 (clause2) R->L }
% 18.91/2.80 duplicatefreeP(nil)
% 18.91/2.80 = { by lemma 20 R->L }
% 18.91/2.80 equalelemsP(nil)
% 18.91/2.80
% 18.91/2.80 Lemma 23: ssList(sk6) = equalelemsP(nil).
% 18.91/2.80 Proof:
% 18.91/2.80 ssList(sk6)
% 18.91/2.80 = { by axiom 13 (co1_16) R->L }
% 18.91/2.80 fresh18(neq(sk4, nil), true2)
% 18.91/2.80 = { by axiom 2 (co1_5) R->L }
% 18.91/2.80 fresh18(neq(sk2, nil), true2)
% 18.91/2.80 = { by lemma 21 }
% 18.91/2.80 fresh18(equalelemsP(nil), true2)
% 18.91/2.80 = { by axiom 3 (clause2) R->L }
% 18.91/2.80 fresh18(equalelemsP(nil), duplicatefreeP(nil))
% 18.91/2.80 = { by lemma 20 R->L }
% 18.91/2.80 fresh18(equalelemsP(nil), equalelemsP(nil))
% 18.91/2.80 = { by axiom 6 (co1_16) }
% 18.91/2.80 true2
% 18.91/2.80 = { by axiom 3 (clause2) R->L }
% 18.91/2.80 duplicatefreeP(nil)
% 18.91/2.80 = { by lemma 20 R->L }
% 18.91/2.80 equalelemsP(nil)
% 18.91/2.80
% 18.91/2.80 Goal 1 (co1_14): tuple5(cons(X, nil), ssItem(X), memberP(sk2, X), neq(sk4, nil)) = tuple5(sk1, true2, true2, true2).
% 18.91/2.80 The goal is true when:
% 18.91/2.80 X = sk5
% 18.91/2.80
% 18.91/2.80 Proof:
% 18.91/2.80 tuple5(cons(sk5, nil), ssItem(sk5), memberP(sk2, sk5), neq(sk4, nil))
% 18.91/2.80 = { by axiom 2 (co1_5) }
% 18.91/2.80 tuple5(cons(sk5, nil), ssItem(sk5), memberP(sk4, sk5), neq(sk4, nil))
% 18.91/2.80 = { by axiom 8 (co1_18) R->L }
% 18.91/2.80 tuple5(cons(sk5, nil), ssItem(sk5), memberP(fresh16(equalelemsP(nil), equalelemsP(nil)), sk5), neq(sk4, nil))
% 18.91/2.80 = { by lemma 20 }
% 18.91/2.80 tuple5(cons(sk5, nil), ssItem(sk5), memberP(fresh16(equalelemsP(nil), duplicatefreeP(nil)), sk5), neq(sk4, nil))
% 18.91/2.80 = { by axiom 3 (clause2) }
% 18.91/2.80 tuple5(cons(sk5, nil), ssItem(sk5), memberP(fresh16(equalelemsP(nil), true2), sk5), neq(sk4, nil))
% 18.91/2.80 = { by lemma 21 R->L }
% 18.91/2.80 tuple5(cons(sk5, nil), ssItem(sk5), memberP(fresh16(neq(sk2, nil), true2), sk5), neq(sk4, nil))
% 18.91/2.80 = { by axiom 2 (co1_5) }
% 18.91/2.80 tuple5(cons(sk5, nil), ssItem(sk5), memberP(fresh16(neq(sk4, nil), true2), sk5), neq(sk4, nil))
% 18.91/2.80 = { by axiom 17 (co1_18) }
% 18.91/2.80 tuple5(cons(sk5, nil), ssItem(sk5), memberP(app(cons(sk5, nil), sk6), sk5), neq(sk4, nil))
% 18.91/2.80 = { by axiom 2 (co1_5) R->L }
% 18.91/2.80 tuple5(cons(sk5, nil), ssItem(sk5), memberP(app(cons(sk5, nil), sk6), sk5), neq(sk2, nil))
% 18.91/2.80 = { by lemma 21 }
% 18.91/2.80 tuple5(cons(sk5, nil), ssItem(sk5), memberP(app(cons(sk5, nil), sk6), sk5), equalelemsP(nil))
% 18.91/2.80 = { by axiom 16 (clause120) R->L }
% 18.91/2.80 tuple5(cons(sk5, nil), ssItem(sk5), memberP(fresh74(equalelemsP(nil), equalelemsP(nil), sk5, sk6), sk5), equalelemsP(nil))
% 18.91/2.80 = { by lemma 22 R->L }
% 18.91/2.80 tuple5(cons(sk5, nil), ssItem(sk5), memberP(fresh74(ssItem(sk5), equalelemsP(nil), sk5, sk6), sk5), equalelemsP(nil))
% 18.91/2.80 = { by lemma 20 }
% 18.91/2.80 tuple5(cons(sk5, nil), ssItem(sk5), memberP(fresh74(ssItem(sk5), duplicatefreeP(nil), sk5, sk6), sk5), equalelemsP(nil))
% 18.91/2.80 = { by axiom 3 (clause2) }
% 18.91/2.80 tuple5(cons(sk5, nil), ssItem(sk5), memberP(fresh74(ssItem(sk5), true2, sk5, sk6), sk5), equalelemsP(nil))
% 18.91/2.81 = { by axiom 18 (clause120) }
% 18.91/2.81 tuple5(cons(sk5, nil), ssItem(sk5), memberP(fresh75(ssList(sk6), true2, sk5, sk6), sk5), equalelemsP(nil))
% 18.91/2.81 = { by axiom 3 (clause2) R->L }
% 18.91/2.81 tuple5(cons(sk5, nil), ssItem(sk5), memberP(fresh75(ssList(sk6), duplicatefreeP(nil), sk5, sk6), sk5), equalelemsP(nil))
% 18.91/2.81 = { by lemma 20 R->L }
% 18.91/2.81 tuple5(cons(sk5, nil), ssItem(sk5), memberP(fresh75(ssList(sk6), equalelemsP(nil), sk5, sk6), sk5), equalelemsP(nil))
% 18.91/2.81 = { by lemma 23 }
% 18.91/2.81 tuple5(cons(sk5, nil), ssItem(sk5), memberP(fresh75(equalelemsP(nil), equalelemsP(nil), sk5, sk6), sk5), equalelemsP(nil))
% 18.91/2.81 = { by axiom 10 (clause120) }
% 18.91/2.81 tuple5(cons(sk5, nil), ssItem(sk5), memberP(cons(sk5, sk6), sk5), equalelemsP(nil))
% 18.91/2.81 = { by axiom 15 (clause138) R->L }
% 18.91/2.81 tuple5(cons(sk5, nil), ssItem(sk5), fresh71(equalelemsP(nil), equalelemsP(nil), sk5, sk6), equalelemsP(nil))
% 18.91/2.81 = { by lemma 22 R->L }
% 18.91/2.81 tuple5(cons(sk5, nil), ssItem(sk5), fresh71(ssItem(sk5), equalelemsP(nil), sk5, sk6), equalelemsP(nil))
% 18.91/2.81 = { by lemma 20 }
% 18.91/2.81 tuple5(cons(sk5, nil), ssItem(sk5), fresh71(ssItem(sk5), duplicatefreeP(nil), sk5, sk6), equalelemsP(nil))
% 18.91/2.81 = { by axiom 3 (clause2) }
% 18.91/2.81 tuple5(cons(sk5, nil), ssItem(sk5), fresh71(ssItem(sk5), true2, sk5, sk6), equalelemsP(nil))
% 18.91/2.81 = { by axiom 19 (clause138) }
% 18.91/2.81 tuple5(cons(sk5, nil), ssItem(sk5), fresh70(ssList(sk6), true2, sk5, sk6), equalelemsP(nil))
% 18.91/2.81 = { by axiom 3 (clause2) R->L }
% 18.91/2.81 tuple5(cons(sk5, nil), ssItem(sk5), fresh70(ssList(sk6), duplicatefreeP(nil), sk5, sk6), equalelemsP(nil))
% 18.91/2.81 = { by lemma 20 R->L }
% 18.91/2.81 tuple5(cons(sk5, nil), ssItem(sk5), fresh70(ssList(sk6), equalelemsP(nil), sk5, sk6), equalelemsP(nil))
% 18.91/2.81 = { by lemma 23 }
% 18.91/2.81 tuple5(cons(sk5, nil), ssItem(sk5), fresh70(equalelemsP(nil), equalelemsP(nil), sk5, sk6), equalelemsP(nil))
% 18.91/2.81 = { by axiom 11 (clause138) }
% 18.91/2.81 tuple5(cons(sk5, nil), ssItem(sk5), true2, equalelemsP(nil))
% 18.91/2.81 = { by axiom 3 (clause2) R->L }
% 18.91/2.81 tuple5(cons(sk5, nil), ssItem(sk5), duplicatefreeP(nil), equalelemsP(nil))
% 18.91/2.81 = { by lemma 20 R->L }
% 18.91/2.81 tuple5(cons(sk5, nil), ssItem(sk5), equalelemsP(nil), equalelemsP(nil))
% 18.91/2.81 = { by lemma 22 }
% 18.91/2.81 tuple5(cons(sk5, nil), equalelemsP(nil), equalelemsP(nil), equalelemsP(nil))
% 18.91/2.81 = { by axiom 14 (co1_17) R->L }
% 18.91/2.81 tuple5(fresh17(neq(sk4, nil), true2), equalelemsP(nil), equalelemsP(nil), equalelemsP(nil))
% 18.91/2.81 = { by axiom 2 (co1_5) R->L }
% 18.91/2.81 tuple5(fresh17(neq(sk2, nil), true2), equalelemsP(nil), equalelemsP(nil), equalelemsP(nil))
% 18.91/2.81 = { by lemma 21 }
% 18.91/2.81 tuple5(fresh17(equalelemsP(nil), true2), equalelemsP(nil), equalelemsP(nil), equalelemsP(nil))
% 18.91/2.81 = { by axiom 3 (clause2) R->L }
% 18.91/2.81 tuple5(fresh17(equalelemsP(nil), duplicatefreeP(nil)), equalelemsP(nil), equalelemsP(nil), equalelemsP(nil))
% 18.91/2.81 = { by lemma 20 R->L }
% 18.91/2.81 tuple5(fresh17(equalelemsP(nil), equalelemsP(nil)), equalelemsP(nil), equalelemsP(nil), equalelemsP(nil))
% 18.91/2.81 = { by axiom 7 (co1_17) }
% 18.91/2.81 tuple5(sk3, equalelemsP(nil), equalelemsP(nil), equalelemsP(nil))
% 18.91/2.81 = { by lemma 20 }
% 18.91/2.81 tuple5(sk3, duplicatefreeP(nil), equalelemsP(nil), equalelemsP(nil))
% 18.91/2.81 = { by lemma 20 }
% 18.91/2.81 tuple5(sk3, duplicatefreeP(nil), duplicatefreeP(nil), equalelemsP(nil))
% 18.91/2.81 = { by lemma 20 }
% 18.91/2.81 tuple5(sk3, duplicatefreeP(nil), duplicatefreeP(nil), duplicatefreeP(nil))
% 18.91/2.81 = { by axiom 3 (clause2) }
% 18.91/2.81 tuple5(sk3, true2, duplicatefreeP(nil), duplicatefreeP(nil))
% 18.91/2.81 = { by axiom 3 (clause2) }
% 18.91/2.81 tuple5(sk3, true2, true2, duplicatefreeP(nil))
% 18.91/2.81 = { by axiom 3 (clause2) }
% 18.91/2.81 tuple5(sk3, true2, true2, true2)
% 18.91/2.81 = { by axiom 1 (co1_6) R->L }
% 18.91/2.81 tuple5(sk1, true2, true2, true2)
% 18.91/2.81 % SZS output end Proof
% 18.91/2.81
% 18.91/2.81 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------