TSTP Solution File: SWC002-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC002-1 : 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 : n009.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 20:53:21 EDT 2023
% Result : Unsatisfiable 134.53s 17.28s
% Output : Proof 135.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWC002-1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.32 % Computer : n009.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Aug 28 17:46:35 EDT 2023
% 0.12/0.32 % CPUTime :
% 134.53/17.28 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 134.53/17.28
% 134.53/17.28 % SZS status Unsatisfiable
% 134.53/17.28
% 135.49/17.38 % SZS output start Proof
% 135.49/17.38 Take the following subset of the input axioms:
% 135.49/17.39 fof(clause110, axiom, ![U, V]: (~gt(U, V) | (~gt(V, U) | (~ssItem(U) | ~ssItem(V))))).
% 135.49/17.39 fof(clause111, axiom, ![U2, V2]: (U2!=V2 | (~lt(U2, V2) | (~ssItem(V2) | ~ssItem(U2))))).
% 135.49/17.39 fof(clause114, axiom, ![U2, V2]: (~lt(U2, V2) | (~lt(V2, U2) | (~ssItem(U2) | ~ssItem(V2))))).
% 135.49/17.39 fof(clause115, axiom, ![U2, V2]: (U2!=V2 | (~neq(U2, V2) | (~ssList(V2) | ~ssList(U2))))).
% 135.49/17.39 fof(clause117, axiom, ![U2, V2]: (U2!=V2 | (~neq(U2, V2) | (~ssItem(V2) | ~ssItem(U2))))).
% 135.49/17.39 fof(clause179, axiom, ![W, X, Y, U2, V2]: (app(app(U2, cons(V2, W)), cons(V2, X))!=Y | (~ssList(X) | (~ssList(W) | (~ssList(U2) | (~ssItem(V2) | (~duplicatefreeP(Y) | ~ssList(Y)))))))).
% 135.49/17.39 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))))))))))).
% 135.49/17.39 fof(clause63, axiom, ![U2]: (~lt(U2, U2) | ~ssItem(U2))).
% 135.49/17.39 fof(clause71, axiom, ![U2]: (~memberP(nil, U2) | ~ssItem(U2))).
% 135.49/17.39 fof(clause98, axiom, ![U2, V2]: (cons(U2, V2)!=nil | (~ssItem(U2) | ~ssList(V2)))).
% 135.49/17.39 fof(clause99, axiom, ![U2, V2]: (cons(U2, V2)!=V2 | (~ssItem(U2) | ~ssList(V2)))).
% 135.49/17.39 fof(co1_19, negated_conjecture, ![B, C, A2]: (~ssItem(A2) | (~ssList(B) | (~ssList(C) | (app(app(B, cons(A2, nil)), C)!=sk2 | (app(B, C)!=sk1 | (ssItem(sk5(C, B, A2)) | ~neq(sk4, nil)))))))).
% 135.49/17.39 fof(co1_20, negated_conjecture, ![A2_2, B2, C2]: (~ssItem(A2_2) | (~ssList(B2) | (~ssList(C2) | (app(app(B2, cons(A2_2, nil)), C2)!=sk2 | (app(B2, C2)!=sk1 | (memberP(sk2, sk5(C2, B2, A2_2)) | ~neq(sk4, nil)))))))).
% 135.49/17.39 fof(co1_21, negated_conjecture, ![A2_2, B2, C2]: (~ssItem(A2_2) | (~ssList(B2) | (~ssList(C2) | (app(app(B2, cons(A2_2, nil)), C2)!=sk2 | (app(B2, C2)!=sk1 | (geq(sk5(C2, B2, A2_2), A2_2) | ~neq(sk4, nil)))))))).
% 135.49/17.39 fof(co1_22, negated_conjecture, ![A, B2, C2]: (~ssItem(A) | (~ssList(B2) | (~ssList(C2) | (app(app(B2, cons(A, nil)), C2)!=sk2 | (app(B2, C2)!=sk1 | (A!=sk5(C2, B2, A) | ~neq(sk4, nil)))))))).
% 135.49/17.39 fof(co1_23, negated_conjecture, ssItem(sk6) | ~neq(sk4, nil)).
% 135.49/17.39 fof(co1_24, negated_conjecture, ssList(sk7) | ~neq(sk4, nil)).
% 135.49/17.39 fof(co1_25, negated_conjecture, ssList(sk8) | ~neq(sk4, nil)).
% 135.49/17.39 fof(co1_26, negated_conjecture, app(app(sk7, cons(sk6, nil)), sk8)=sk4 | ~neq(sk4, nil)).
% 135.49/17.39 fof(co1_27, negated_conjecture, app(sk7, sk8)=sk3 | ~neq(sk4, nil)).
% 135.49/17.39 fof(co1_28, negated_conjecture, ![A2_2]: (~ssItem(A2_2) | (sk6=A2_2 | (~memberP(sk4, A2_2) | (~geq(A2_2, sk6) | ~neq(sk4, nil)))))).
% 135.49/17.39 fof(co1_5, negated_conjecture, sk2=sk4).
% 135.49/17.39 fof(co1_6, negated_conjecture, sk1=sk3).
% 135.49/17.39 fof(co1_7, negated_conjecture, neq(sk2, nil) | neq(sk2, nil)).
% 135.49/17.39
% 135.49/17.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 135.49/17.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 135.49/17.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 135.49/17.39 fresh(y, y, x1...xn) = u
% 135.49/17.39 C => fresh(s, t, x1...xn) = v
% 135.49/17.39 where fresh is a fresh function symbol and x1..xn are the free
% 135.49/17.39 variables of u and v.
% 135.49/17.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 135.49/17.39 input problem has no model of domain size 1).
% 135.49/17.39
% 135.49/17.39 The encoding turns the above axioms into the following unit equations and goals:
% 135.49/17.39
% 135.49/17.39 Axiom 1 (co1_5): sk2 = sk4.
% 135.49/17.39 Axiom 2 (co1_6): sk1 = sk3.
% 135.49/17.39 Axiom 3 (co1_7): neq(sk2, nil) = true2.
% 135.49/17.39 Axiom 4 (co1_23): fresh19(X, X) = true2.
% 135.49/17.39 Axiom 5 (co1_24): fresh18(X, X) = true2.
% 135.49/17.39 Axiom 6 (co1_25): fresh17(X, X) = true2.
% 135.49/17.39 Axiom 7 (co1_26): fresh16(X, X) = sk4.
% 135.49/17.39 Axiom 8 (co1_27): fresh15(X, X) = sk3.
% 135.49/17.39 Axiom 9 (co1_28): fresh93(X, X, Y) = Y.
% 135.49/17.39 Axiom 10 (co1_28): fresh91(X, X, Y) = sk6.
% 135.49/17.39 Axiom 11 (co1_23): fresh19(neq(sk4, nil), true2) = ssItem(sk6).
% 135.49/17.39 Axiom 12 (co1_24): fresh18(neq(sk4, nil), true2) = ssList(sk7).
% 135.49/17.39 Axiom 13 (co1_25): fresh17(neq(sk4, nil), true2) = ssList(sk8).
% 135.49/17.39 Axiom 14 (co1_27): fresh15(neq(sk4, nil), true2) = app(sk7, sk8).
% 135.49/17.39 Axiom 15 (co1_26): fresh16(neq(sk4, nil), true2) = app(app(sk7, cons(sk6, nil)), sk8).
% 135.49/17.39 Axiom 16 (co1_28): fresh92(X, X, Y) = fresh93(ssItem(Y), true2, Y).
% 135.49/17.39 Axiom 17 (co1_28): fresh90(X, X, Y) = fresh91(geq(Y, sk6), true2, Y).
% 135.49/17.39 Axiom 18 (co1_28): fresh90(neq(sk4, nil), true2, X) = fresh92(memberP(sk4, X), true2, X).
% 135.49/17.39 Axiom 19 (co1_19): fresh108(X, X, Y, Z, W) = true2.
% 135.49/17.39 Axiom 20 (co1_20): fresh103(X, X, Y, Z, W) = true2.
% 135.49/17.39 Axiom 21 (co1_21): fresh98(X, X, Y, Z, W) = true2.
% 135.49/17.39 Axiom 22 (co1_19): fresh22(X, X, Y, Z, W) = ssItem(sk5(W, Z, Y)).
% 135.49/17.39 Axiom 23 (co1_20): fresh21(X, X, Y, Z, W) = memberP(sk2, sk5(W, Z, Y)).
% 135.49/17.39 Axiom 24 (co1_21): fresh20(X, X, Y, Z, W) = geq(sk5(W, Z, Y), Y).
% 135.49/17.39 Axiom 25 (co1_19): fresh107(X, X, Y, Z, W) = fresh108(app(Z, W), sk1, Y, Z, W).
% 135.49/17.39 Axiom 26 (co1_19): fresh106(X, X, Y, Z, W) = fresh107(ssList(Z), true2, Y, Z, W).
% 135.49/17.39 Axiom 27 (co1_19): fresh105(X, X, Y, Z, W) = fresh106(ssList(W), true2, Y, Z, W).
% 135.49/17.39 Axiom 28 (co1_19): fresh104(X, X, Y, Z, W) = fresh105(ssItem(Y), true2, Y, Z, W).
% 135.49/17.39 Axiom 29 (co1_20): fresh102(X, X, Y, Z, W) = fresh103(app(Z, W), sk1, Y, Z, W).
% 135.49/17.39 Axiom 30 (co1_20): fresh101(X, X, Y, Z, W) = fresh102(ssList(Z), true2, Y, Z, W).
% 135.49/17.39 Axiom 31 (co1_20): fresh100(X, X, Y, Z, W) = fresh101(ssList(W), true2, Y, Z, W).
% 135.49/17.39 Axiom 32 (co1_20): fresh99(X, X, Y, Z, W) = fresh100(ssItem(Y), true2, Y, Z, W).
% 135.49/17.39 Axiom 33 (co1_21): fresh97(X, X, Y, Z, W) = fresh98(app(Z, W), sk1, Y, Z, W).
% 135.49/17.39 Axiom 34 (co1_21): fresh96(X, X, Y, Z, W) = fresh97(ssList(Z), true2, Y, Z, W).
% 135.49/17.39 Axiom 35 (co1_21): fresh95(X, X, Y, Z, W) = fresh96(ssList(W), true2, Y, Z, W).
% 135.49/17.39 Axiom 36 (co1_21): fresh94(X, X, Y, Z, W) = fresh95(ssItem(Y), true2, Y, Z, W).
% 135.49/17.39 Axiom 37 (co1_19): fresh104(neq(sk4, nil), true2, X, Y, Z) = fresh22(app(app(Y, cons(X, nil)), Z), sk2, X, Y, Z).
% 135.49/17.39 Axiom 38 (co1_20): fresh99(neq(sk4, nil), true2, X, Y, Z) = fresh21(app(app(Y, cons(X, nil)), Z), sk2, X, Y, Z).
% 135.49/17.39 Axiom 39 (co1_21): fresh94(neq(sk4, nil), true2, X, Y, Z) = fresh20(app(app(Y, cons(X, nil)), Z), sk2, X, Y, Z).
% 135.49/17.39
% 135.49/17.39 Lemma 40: neq(sk4, nil) = true2.
% 135.49/17.39 Proof:
% 135.49/17.39 neq(sk4, nil)
% 135.49/17.39 = { by axiom 1 (co1_5) R->L }
% 135.49/17.39 neq(sk2, nil)
% 135.49/17.39 = { by axiom 3 (co1_7) }
% 135.49/17.39 true2
% 135.49/17.39
% 135.49/17.39 Lemma 41: ssItem(sk6) = true2.
% 135.49/17.39 Proof:
% 135.49/17.39 ssItem(sk6)
% 135.49/17.39 = { by axiom 11 (co1_23) R->L }
% 135.49/17.39 fresh19(neq(sk4, nil), true2)
% 135.49/17.39 = { by lemma 40 }
% 135.49/17.39 fresh19(true2, true2)
% 135.49/17.39 = { by axiom 4 (co1_23) }
% 135.49/17.39 true2
% 135.49/17.39
% 135.49/17.39 Lemma 42: ssList(sk7) = true2.
% 135.49/17.39 Proof:
% 135.49/17.39 ssList(sk7)
% 135.49/17.39 = { by axiom 12 (co1_24) R->L }
% 135.49/17.39 fresh18(neq(sk4, nil), true2)
% 135.49/17.39 = { by lemma 40 }
% 135.49/17.39 fresh18(true2, true2)
% 135.49/17.39 = { by axiom 5 (co1_24) }
% 135.49/17.39 true2
% 135.49/17.39
% 135.49/17.39 Lemma 43: ssList(sk8) = true2.
% 135.49/17.39 Proof:
% 135.49/17.39 ssList(sk8)
% 135.49/17.39 = { by axiom 13 (co1_25) R->L }
% 135.49/17.39 fresh17(neq(sk4, nil), true2)
% 135.49/17.39 = { by lemma 40 }
% 135.49/17.39 fresh17(true2, true2)
% 135.49/17.39 = { by axiom 6 (co1_25) }
% 135.49/17.39 true2
% 135.49/17.39
% 135.49/17.39 Lemma 44: app(sk7, sk8) = sk1.
% 135.49/17.39 Proof:
% 135.49/17.39 app(sk7, sk8)
% 135.49/17.39 = { by axiom 14 (co1_27) R->L }
% 135.49/17.39 fresh15(neq(sk4, nil), true2)
% 135.49/17.39 = { by lemma 40 }
% 135.49/17.39 fresh15(true2, true2)
% 135.49/17.39 = { by axiom 8 (co1_27) }
% 135.49/17.39 sk3
% 135.49/17.39 = { by axiom 2 (co1_6) R->L }
% 135.49/17.39 sk1
% 135.49/17.39
% 135.49/17.39 Lemma 45: app(app(sk7, cons(sk6, nil)), sk8) = sk4.
% 135.49/17.39 Proof:
% 135.49/17.39 app(app(sk7, cons(sk6, nil)), sk8)
% 135.49/17.39 = { by axiom 15 (co1_26) R->L }
% 135.49/17.39 fresh16(neq(sk4, nil), true2)
% 135.49/17.39 = { by lemma 40 }
% 135.49/17.39 fresh16(true2, true2)
% 135.49/17.39 = { by axiom 7 (co1_26) }
% 135.49/17.40 sk4
% 135.49/17.40
% 135.49/17.40 Goal 1 (co1_22): tuple6(X, app(Y, Z), app(app(Y, cons(X, nil)), Z), ssList(Y), ssList(Z), ssItem(X), neq(sk4, nil)) = tuple6(sk5(Z, Y, X), sk1, sk2, true2, true2, true2, true2).
% 135.49/17.40 The goal is true when:
% 135.49/17.40 X = sk6
% 135.49/17.40 Y = sk7
% 135.49/17.40 Z = sk8
% 135.49/17.40
% 135.49/17.40 Proof:
% 135.49/17.40 tuple6(sk6, app(sk7, sk8), app(app(sk7, cons(sk6, nil)), sk8), ssList(sk7), ssList(sk8), ssItem(sk6), neq(sk4, nil))
% 135.49/17.40 = { by lemma 40 }
% 135.49/17.40 tuple6(sk6, app(sk7, sk8), app(app(sk7, cons(sk6, nil)), sk8), ssList(sk7), ssList(sk8), ssItem(sk6), true2)
% 135.49/17.40 = { by lemma 44 }
% 135.49/17.40 tuple6(sk6, sk1, app(app(sk7, cons(sk6, nil)), sk8), ssList(sk7), ssList(sk8), ssItem(sk6), true2)
% 135.49/17.40 = { by lemma 45 }
% 135.49/17.40 tuple6(sk6, sk1, sk4, ssList(sk7), ssList(sk8), ssItem(sk6), true2)
% 135.49/17.40 = { by lemma 42 }
% 135.49/17.40 tuple6(sk6, sk1, sk4, true2, ssList(sk8), ssItem(sk6), true2)
% 135.49/17.40 = { by lemma 43 }
% 135.49/17.40 tuple6(sk6, sk1, sk4, true2, true2, ssItem(sk6), true2)
% 135.49/17.40 = { by lemma 41 }
% 135.49/17.40 tuple6(sk6, sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 10 (co1_28) R->L }
% 135.49/17.40 tuple6(fresh91(true2, true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 21 (co1_21) R->L }
% 135.49/17.40 tuple6(fresh91(fresh98(sk1, sk1, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by lemma 44 R->L }
% 135.49/17.40 tuple6(fresh91(fresh98(app(sk7, sk8), sk1, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 33 (co1_21) R->L }
% 135.49/17.40 tuple6(fresh91(fresh97(true2, true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by lemma 42 R->L }
% 135.49/17.40 tuple6(fresh91(fresh97(ssList(sk7), true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 34 (co1_21) R->L }
% 135.49/17.40 tuple6(fresh91(fresh96(true2, true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by lemma 43 R->L }
% 135.49/17.40 tuple6(fresh91(fresh96(ssList(sk8), true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 35 (co1_21) R->L }
% 135.49/17.40 tuple6(fresh91(fresh95(true2, true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by lemma 41 R->L }
% 135.49/17.40 tuple6(fresh91(fresh95(ssItem(sk6), true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 36 (co1_21) R->L }
% 135.49/17.40 tuple6(fresh91(fresh94(true2, true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by lemma 40 R->L }
% 135.49/17.40 tuple6(fresh91(fresh94(neq(sk4, nil), true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 39 (co1_21) }
% 135.49/17.40 tuple6(fresh91(fresh20(app(app(sk7, cons(sk6, nil)), sk8), sk2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 1 (co1_5) }
% 135.49/17.40 tuple6(fresh91(fresh20(app(app(sk7, cons(sk6, nil)), sk8), sk4, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by lemma 45 }
% 135.49/17.40 tuple6(fresh91(fresh20(sk4, sk4, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 24 (co1_21) }
% 135.49/17.40 tuple6(fresh91(geq(sk5(sk8, sk7, sk6), sk6), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 17 (co1_28) R->L }
% 135.49/17.40 tuple6(fresh90(true2, true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by lemma 40 R->L }
% 135.49/17.40 tuple6(fresh90(neq(sk4, nil), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 18 (co1_28) }
% 135.49/17.40 tuple6(fresh92(memberP(sk4, sk5(sk8, sk7, sk6)), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 1 (co1_5) R->L }
% 135.49/17.40 tuple6(fresh92(memberP(sk2, sk5(sk8, sk7, sk6)), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 23 (co1_20) R->L }
% 135.49/17.40 tuple6(fresh92(fresh21(sk4, sk4, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by lemma 45 R->L }
% 135.49/17.40 tuple6(fresh92(fresh21(app(app(sk7, cons(sk6, nil)), sk8), sk4, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 1 (co1_5) R->L }
% 135.49/17.40 tuple6(fresh92(fresh21(app(app(sk7, cons(sk6, nil)), sk8), sk2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 38 (co1_20) R->L }
% 135.49/17.40 tuple6(fresh92(fresh99(neq(sk4, nil), true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by lemma 40 }
% 135.49/17.40 tuple6(fresh92(fresh99(true2, true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 32 (co1_20) }
% 135.49/17.40 tuple6(fresh92(fresh100(ssItem(sk6), true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by lemma 41 }
% 135.49/17.40 tuple6(fresh92(fresh100(true2, true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 31 (co1_20) }
% 135.49/17.40 tuple6(fresh92(fresh101(ssList(sk8), true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by lemma 43 }
% 135.49/17.40 tuple6(fresh92(fresh101(true2, true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 30 (co1_20) }
% 135.49/17.40 tuple6(fresh92(fresh102(ssList(sk7), true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by lemma 42 }
% 135.49/17.40 tuple6(fresh92(fresh102(true2, true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 29 (co1_20) }
% 135.49/17.40 tuple6(fresh92(fresh103(app(sk7, sk8), sk1, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by lemma 44 }
% 135.49/17.40 tuple6(fresh92(fresh103(sk1, sk1, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 20 (co1_20) }
% 135.49/17.40 tuple6(fresh92(true2, true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 16 (co1_28) }
% 135.49/17.40 tuple6(fresh93(ssItem(sk5(sk8, sk7, sk6)), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 22 (co1_19) R->L }
% 135.49/17.40 tuple6(fresh93(fresh22(sk4, sk4, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by lemma 45 R->L }
% 135.49/17.40 tuple6(fresh93(fresh22(app(app(sk7, cons(sk6, nil)), sk8), sk4, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 1 (co1_5) R->L }
% 135.49/17.40 tuple6(fresh93(fresh22(app(app(sk7, cons(sk6, nil)), sk8), sk2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 37 (co1_19) R->L }
% 135.49/17.40 tuple6(fresh93(fresh104(neq(sk4, nil), true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by lemma 40 }
% 135.49/17.40 tuple6(fresh93(fresh104(true2, true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 28 (co1_19) }
% 135.49/17.40 tuple6(fresh93(fresh105(ssItem(sk6), true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by lemma 41 }
% 135.49/17.40 tuple6(fresh93(fresh105(true2, true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by axiom 27 (co1_19) }
% 135.49/17.40 tuple6(fresh93(fresh106(ssList(sk8), true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.40 = { by lemma 43 }
% 135.49/17.40 tuple6(fresh93(fresh106(true2, true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.41 = { by axiom 26 (co1_19) }
% 135.49/17.41 tuple6(fresh93(fresh107(ssList(sk7), true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.41 = { by lemma 42 }
% 135.49/17.41 tuple6(fresh93(fresh107(true2, true2, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.41 = { by axiom 25 (co1_19) }
% 135.49/17.41 tuple6(fresh93(fresh108(app(sk7, sk8), sk1, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.41 = { by lemma 44 }
% 135.49/17.41 tuple6(fresh93(fresh108(sk1, sk1, sk6, sk7, sk8), true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.41 = { by axiom 19 (co1_19) }
% 135.49/17.41 tuple6(fresh93(true2, true2, sk5(sk8, sk7, sk6)), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.41 = { by axiom 9 (co1_28) }
% 135.49/17.41 tuple6(sk5(sk8, sk7, sk6), sk1, sk4, true2, true2, true2, true2)
% 135.49/17.41 = { by axiom 1 (co1_5) R->L }
% 135.49/17.41 tuple6(sk5(sk8, sk7, sk6), sk1, sk2, true2, true2, true2, true2)
% 135.49/17.41 % SZS output end Proof
% 135.49/17.41
% 135.49/17.41 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------