TSTP Solution File: SWC153-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC153-1 : 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 : n015.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 20:54:10 EDT 2023
% Result : Unsatisfiable 149.51s 19.57s
% Output : Proof 149.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC153-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % 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 : n015.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 19:14:40 EDT 2023
% 0.14/0.34 % CPUTime :
% 149.51/19.57 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 149.51/19.57
% 149.51/19.57 % SZS status Unsatisfiable
% 149.51/19.57
% 149.78/19.60 % SZS output start Proof
% 149.78/19.60 Take the following subset of the input axioms:
% 149.78/19.60 fof(clause130, axiom, ![U, V]: (~leq(U, V) | (~leq(V, U) | (~ssItem(U) | (~ssItem(V) | V=U))))).
% 149.78/19.61 fof(clause62, axiom, ![U2]: (~ssItem(U2) | leq(U2, U2))).
% 149.78/19.61 fof(co1_10, negated_conjecture, ssItem(sk5)).
% 149.78/19.61 fof(co1_11, negated_conjecture, ssItem(sk6)).
% 149.78/19.61 fof(co1_12, negated_conjecture, ssList(sk7)).
% 149.78/19.61 fof(co1_13, negated_conjecture, ssList(sk8)).
% 149.78/19.61 fof(co1_14, negated_conjecture, ssList(sk9)).
% 149.78/19.61 fof(co1_15, negated_conjecture, app(app(app(app(sk7, cons(sk5, nil)), sk8), cons(sk6, nil)), sk9)=sk1).
% 149.78/19.61 fof(co1_16, negated_conjecture, leq(sk6, sk5)).
% 149.78/19.61 fof(co1_17, negated_conjecture, ssItem(sk10) | ~leq(sk5, sk6)).
% 149.78/19.61 fof(co1_18, negated_conjecture, memberP(sk8, sk10) | ~leq(sk5, sk6)).
% 149.78/19.61 fof(co1_19, negated_conjecture, ~leq(sk10, sk6) | (~leq(sk5, sk10) | ~leq(sk5, sk6))).
% 149.78/19.61 fof(co1_6, negated_conjecture, sk3=sk1).
% 149.78/19.61 fof(co1_7, negated_conjecture, ![B, C, D, E, A2]: (~ssItem(A2) | (~ssItem(B) | (~ssList(C) | (~ssList(D) | (~ssList(E) | (app(app(app(app(C, cons(A2, nil)), D), cons(B, nil)), E)!=sk3 | (~leq(B, A2) | leq(A2, B))))))))).
% 149.78/19.61 fof(co1_8, negated_conjecture, ![F, B2, C2, D2, E2, A2_2]: (~ssItem(A2_2) | (~ssItem(B2) | (~ssList(C2) | (~ssList(D2) | (~ssList(E2) | (app(app(app(app(C2, cons(A2_2, nil)), D2), cons(B2, nil)), E2)!=sk3 | (~leq(B2, A2_2) | (~ssItem(F) | (~memberP(D2, F) | leq(A2_2, F))))))))))).
% 149.78/19.61 fof(co1_9, negated_conjecture, ![B2, C2, D2, E2, F2, A2_2]: (~ssItem(A2_2) | (~ssItem(B2) | (~ssList(C2) | (~ssList(D2) | (~ssList(E2) | (app(app(app(app(C2, cons(A2_2, nil)), D2), cons(B2, nil)), E2)!=sk3 | (~leq(B2, A2_2) | (~ssItem(F2) | (~memberP(D2, F2) | leq(F2, B2))))))))))).
% 149.78/19.61
% 149.78/19.61 Now clausify the problem and encode Horn clauses using encoding 3 of
% 149.78/19.61 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 149.78/19.61 We repeatedly replace C & s=t => u=v by the two clauses:
% 149.78/19.61 fresh(y, y, x1...xn) = u
% 149.78/19.61 C => fresh(s, t, x1...xn) = v
% 149.78/19.61 where fresh is a fresh function symbol and x1..xn are the free
% 149.78/19.61 variables of u and v.
% 149.78/19.61 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 149.78/19.61 input problem has no model of domain size 1).
% 149.78/19.61
% 149.78/19.61 The encoding turns the above axioms into the following unit equations and goals:
% 149.78/19.61
% 149.78/19.61 Axiom 1 (co1_6): sk3 = sk1.
% 149.78/19.61 Axiom 2 (co1_13): ssList(sk8) = true2.
% 149.78/19.61 Axiom 3 (co1_12): ssList(sk7) = true2.
% 149.78/19.61 Axiom 4 (co1_14): ssList(sk9) = true2.
% 149.78/19.61 Axiom 5 (co1_10): ssItem(sk5) = true2.
% 149.78/19.61 Axiom 6 (co1_11): ssItem(sk6) = true2.
% 149.78/19.61 Axiom 7 (co1_16): leq(sk6, sk5) = true2.
% 149.78/19.61 Axiom 8 (co1_17): fresh18(X, X) = true2.
% 149.78/19.61 Axiom 9 (co1_18): fresh17(X, X) = true2.
% 149.78/19.61 Axiom 10 (clause62): fresh55(X, X, Y) = true2.
% 149.78/19.61 Axiom 11 (co1_17): fresh18(leq(sk5, sk6), true2) = ssItem(sk10).
% 149.78/19.61 Axiom 12 (co1_18): fresh17(leq(sk5, sk6), true2) = memberP(sk8, sk10).
% 149.78/19.61 Axiom 13 (clause130): fresh258(X, X, Y, Z) = Y.
% 149.78/19.61 Axiom 14 (clause130): fresh256(X, X, Y, Z) = Z.
% 149.78/19.61 Axiom 15 (clause62): fresh55(ssItem(X), true2, X) = leq(X, X).
% 149.78/19.61 Axiom 16 (co1_7): fresh16(X, X, Y, Z) = true2.
% 149.78/19.61 Axiom 17 (co1_8): fresh15(X, X, Y, Z) = true2.
% 149.78/19.61 Axiom 18 (co1_9): fresh14(X, X, Y, Z) = true2.
% 149.78/19.61 Axiom 19 (clause130): fresh257(X, X, Y, Z) = fresh258(ssItem(Y), true2, Y, Z).
% 149.78/19.61 Axiom 20 (clause130): fresh255(X, X, Y, Z) = fresh256(ssItem(Z), true2, Y, Z).
% 149.78/19.61 Axiom 21 (clause130): fresh255(leq(X, Y), true2, Y, X) = fresh257(leq(Y, X), true2, Y, X).
% 149.78/19.61 Axiom 22 (co1_15): app(app(app(app(sk7, cons(sk5, nil)), sk8), cons(sk6, nil)), sk9) = sk1.
% 149.78/19.61 Axiom 23 (co1_7): fresh107(X, X, Y, Z, W, V, U) = leq(Y, Z).
% 149.78/19.61 Axiom 24 (co1_7): fresh106(X, X, Y, Z, W, V, U) = fresh107(ssList(W), true2, Y, Z, W, V, U).
% 149.78/19.61 Axiom 25 (co1_7): fresh105(X, X, Y, Z, W, V, U) = fresh106(ssList(V), true2, Y, Z, W, V, U).
% 149.78/19.61 Axiom 26 (co1_7): fresh104(X, X, Y, Z, W, V, U) = fresh105(ssList(U), true2, Y, Z, W, V, U).
% 149.78/19.61 Axiom 27 (co1_7): fresh103(X, X, Y, Z, W, V, U) = fresh104(ssItem(Y), true2, Y, Z, W, V, U).
% 149.78/19.61 Axiom 28 (co1_7): fresh102(X, X, Y, Z, W, V, U) = fresh103(ssItem(Z), true2, Y, Z, W, V, U).
% 149.78/19.61 Axiom 29 (co1_8): fresh101(X, X, Y, Z, W, V, U, T) = leq(Y, T).
% 149.78/19.61 Axiom 30 (co1_9): fresh93(X, X, Y, Z, W, V, U, T) = leq(T, Z).
% 149.78/19.61 Axiom 31 (co1_8): fresh100(X, X, Y, Z, W, V, U, T) = fresh101(ssList(W), true2, Y, Z, W, V, U, T).
% 149.78/19.61 Axiom 32 (co1_8): fresh99(X, X, Y, Z, W, V, U, T) = fresh100(ssList(V), true2, Y, Z, W, V, U, T).
% 149.78/19.61 Axiom 33 (co1_8): fresh98(X, X, Y, Z, W, V, U, T) = fresh99(ssList(U), true2, Y, Z, W, V, U, T).
% 149.78/19.61 Axiom 34 (co1_8): fresh97(X, X, Y, Z, W, V, U, T) = fresh98(ssItem(Y), true2, Y, Z, W, V, U, T).
% 149.78/19.61 Axiom 35 (co1_8): fresh96(X, X, Y, Z, W, V, U, T) = fresh97(ssItem(Z), true2, Y, Z, W, V, U, T).
% 149.78/19.61 Axiom 36 (co1_8): fresh95(X, X, Y, Z, W, V, U, T) = fresh96(ssItem(T), true2, Y, Z, W, V, U, T).
% 149.78/19.61 Axiom 37 (co1_8): fresh94(X, X, Y, Z, W, V, U, T) = fresh95(leq(Z, Y), true2, Y, Z, W, V, U, T).
% 149.78/19.61 Axiom 38 (co1_9): fresh92(X, X, Y, Z, W, V, U, T) = fresh93(ssList(W), true2, Y, Z, W, V, U, T).
% 149.78/19.61 Axiom 39 (co1_9): fresh91(X, X, Y, Z, W, V, U, T) = fresh92(ssList(V), true2, Y, Z, W, V, U, T).
% 149.78/19.61 Axiom 40 (co1_9): fresh90(X, X, Y, Z, W, V, U, T) = fresh91(ssList(U), true2, Y, Z, W, V, U, T).
% 149.78/19.61 Axiom 41 (co1_9): fresh89(X, X, Y, Z, W, V, U, T) = fresh90(ssItem(Y), true2, Y, Z, W, V, U, T).
% 149.78/19.61 Axiom 42 (co1_9): fresh88(X, X, Y, Z, W, V, U, T) = fresh89(ssItem(Z), true2, Y, Z, W, V, U, T).
% 149.78/19.61 Axiom 43 (co1_9): fresh87(X, X, Y, Z, W, V, U, T) = fresh88(ssItem(T), true2, Y, Z, W, V, U, T).
% 149.78/19.61 Axiom 44 (co1_9): fresh86(X, X, Y, Z, W, V, U, T) = fresh87(leq(Z, Y), true2, Y, Z, W, V, U, T).
% 149.78/19.61 Axiom 45 (co1_7): fresh102(leq(X, Y), true2, Y, X, Z, W, V) = fresh16(app(app(app(app(Z, cons(Y, nil)), W), cons(X, nil)), V), sk3, Y, X).
% 149.78/19.61 Axiom 46 (co1_8): fresh94(memberP(X, Y), true2, Z, W, V, X, U, Y) = fresh15(app(app(app(app(V, cons(Z, nil)), X), cons(W, nil)), U), sk3, Z, Y).
% 149.78/19.61 Axiom 47 (co1_9): fresh86(memberP(X, Y), true2, Z, W, V, X, U, Y) = fresh14(app(app(app(app(V, cons(Z, nil)), X), cons(W, nil)), U), sk3, W, Y).
% 149.78/19.61
% 149.78/19.61 Lemma 48: leq(sk5, sk6) = true2.
% 149.78/19.61 Proof:
% 149.78/19.61 leq(sk5, sk6)
% 149.78/19.61 = { by axiom 23 (co1_7) R->L }
% 149.78/19.61 fresh107(true2, true2, sk5, sk6, sk7, sk8, sk9)
% 149.78/19.61 = { by axiom 3 (co1_12) R->L }
% 149.78/19.61 fresh107(ssList(sk7), true2, sk5, sk6, sk7, sk8, sk9)
% 149.78/19.61 = { by axiom 24 (co1_7) R->L }
% 149.78/19.61 fresh106(true2, true2, sk5, sk6, sk7, sk8, sk9)
% 149.78/19.61 = { by axiom 2 (co1_13) R->L }
% 149.78/19.61 fresh106(ssList(sk8), true2, sk5, sk6, sk7, sk8, sk9)
% 149.78/19.61 = { by axiom 25 (co1_7) R->L }
% 149.78/19.61 fresh105(true2, true2, sk5, sk6, sk7, sk8, sk9)
% 149.78/19.61 = { by axiom 4 (co1_14) R->L }
% 149.78/19.61 fresh105(ssList(sk9), true2, sk5, sk6, sk7, sk8, sk9)
% 149.78/19.61 = { by axiom 26 (co1_7) R->L }
% 149.78/19.61 fresh104(true2, true2, sk5, sk6, sk7, sk8, sk9)
% 149.78/19.61 = { by axiom 5 (co1_10) R->L }
% 149.78/19.61 fresh104(ssItem(sk5), true2, sk5, sk6, sk7, sk8, sk9)
% 149.78/19.61 = { by axiom 27 (co1_7) R->L }
% 149.78/19.61 fresh103(true2, true2, sk5, sk6, sk7, sk8, sk9)
% 149.78/19.61 = { by axiom 6 (co1_11) R->L }
% 149.78/19.61 fresh103(ssItem(sk6), true2, sk5, sk6, sk7, sk8, sk9)
% 149.78/19.61 = { by axiom 28 (co1_7) R->L }
% 149.78/19.61 fresh102(true2, true2, sk5, sk6, sk7, sk8, sk9)
% 149.78/19.61 = { by axiom 7 (co1_16) R->L }
% 149.78/19.61 fresh102(leq(sk6, sk5), true2, sk5, sk6, sk7, sk8, sk9)
% 149.78/19.61 = { by axiom 45 (co1_7) }
% 149.78/19.61 fresh16(app(app(app(app(sk7, cons(sk5, nil)), sk8), cons(sk6, nil)), sk9), sk3, sk5, sk6)
% 149.78/19.61 = { by axiom 22 (co1_15) }
% 149.78/19.61 fresh16(sk1, sk3, sk5, sk6)
% 149.78/19.61 = { by axiom 1 (co1_6) R->L }
% 149.78/19.61 fresh16(sk3, sk3, sk5, sk6)
% 149.78/19.61 = { by axiom 16 (co1_7) }
% 149.78/19.61 true2
% 149.78/19.61
% 149.78/19.61 Lemma 49: sk6 = sk5.
% 149.78/19.61 Proof:
% 149.78/19.61 sk6
% 149.78/19.61 = { by axiom 13 (clause130) R->L }
% 149.78/19.61 fresh258(true2, true2, sk6, sk5)
% 149.78/19.61 = { by axiom 6 (co1_11) R->L }
% 149.78/19.61 fresh258(ssItem(sk6), true2, sk6, sk5)
% 149.78/19.61 = { by axiom 19 (clause130) R->L }
% 149.78/19.61 fresh257(true2, true2, sk6, sk5)
% 149.78/19.61 = { by axiom 7 (co1_16) R->L }
% 149.78/19.61 fresh257(leq(sk6, sk5), true2, sk6, sk5)
% 149.78/19.61 = { by axiom 21 (clause130) R->L }
% 149.78/19.61 fresh255(leq(sk5, sk6), true2, sk6, sk5)
% 149.78/19.61 = { by lemma 48 }
% 149.78/19.61 fresh255(true2, true2, sk6, sk5)
% 149.78/19.61 = { by axiom 20 (clause130) }
% 149.78/19.61 fresh256(ssItem(sk5), true2, sk6, sk5)
% 149.78/19.61 = { by axiom 5 (co1_10) }
% 149.78/19.61 fresh256(true2, true2, sk6, sk5)
% 149.78/19.61 = { by axiom 14 (clause130) }
% 149.78/19.61 sk5
% 149.78/19.61
% 149.78/19.61 Lemma 50: ssItem(sk10) = true2.
% 149.78/19.61 Proof:
% 149.78/19.61 ssItem(sk10)
% 149.78/19.61 = { by axiom 11 (co1_17) R->L }
% 149.78/19.61 fresh18(leq(sk5, sk6), true2)
% 149.78/19.61 = { by lemma 48 }
% 149.78/19.61 fresh18(true2, true2)
% 149.78/19.61 = { by axiom 8 (co1_17) }
% 149.78/19.61 true2
% 149.78/19.61
% 149.78/19.61 Lemma 51: leq(sk5, sk5) = true2.
% 149.78/19.61 Proof:
% 149.78/19.61 leq(sk5, sk5)
% 149.78/19.61 = { by axiom 15 (clause62) R->L }
% 149.78/19.61 fresh55(ssItem(sk5), true2, sk5)
% 149.78/19.61 = { by axiom 5 (co1_10) }
% 149.78/19.61 fresh55(true2, true2, sk5)
% 149.78/19.61 = { by axiom 10 (clause62) }
% 149.78/19.61 true2
% 149.78/19.61
% 149.78/19.61 Lemma 52: memberP(sk8, sk10) = true2.
% 149.78/19.61 Proof:
% 149.78/19.61 memberP(sk8, sk10)
% 149.78/19.61 = { by axiom 12 (co1_18) R->L }
% 149.78/19.61 fresh17(leq(sk5, sk6), true2)
% 149.78/19.61 = { by lemma 48 }
% 149.78/19.61 fresh17(true2, true2)
% 149.78/19.61 = { by axiom 9 (co1_18) }
% 149.78/19.61 true2
% 149.78/19.61
% 149.78/19.61 Lemma 53: app(app(app(app(sk7, cons(sk5, nil)), sk8), cons(sk5, nil)), sk9) = sk3.
% 149.78/19.61 Proof:
% 149.78/19.61 app(app(app(app(sk7, cons(sk5, nil)), sk8), cons(sk5, nil)), sk9)
% 149.78/19.61 = { by lemma 49 R->L }
% 149.78/19.61 app(app(app(app(sk7, cons(sk5, nil)), sk8), cons(sk6, nil)), sk9)
% 149.78/19.61 = { by axiom 22 (co1_15) }
% 149.78/19.61 sk1
% 149.78/19.61 = { by axiom 1 (co1_6) R->L }
% 149.78/19.61 sk3
% 149.78/19.61
% 149.78/19.61 Goal 1 (co1_19): tuple2(leq(sk5, sk6), leq(sk5, sk10), leq(sk10, sk6)) = tuple2(true2, true2, true2).
% 149.78/19.61 Proof:
% 149.78/19.61 tuple2(leq(sk5, sk6), leq(sk5, sk10), leq(sk10, sk6))
% 149.78/19.61 = { by lemma 48 }
% 149.78/19.61 tuple2(true2, leq(sk5, sk10), leq(sk10, sk6))
% 149.78/19.61 = { by lemma 49 }
% 149.78/19.61 tuple2(true2, leq(sk5, sk10), leq(sk10, sk5))
% 149.78/19.61 = { by axiom 30 (co1_9) R->L }
% 149.78/19.61 tuple2(true2, leq(sk5, sk10), fresh93(true2, true2, sk5, sk5, sk7, sk8, sk9, sk10))
% 149.78/19.61 = { by axiom 3 (co1_12) R->L }
% 149.78/19.61 tuple2(true2, leq(sk5, sk10), fresh93(ssList(sk7), true2, sk5, sk5, sk7, sk8, sk9, sk10))
% 149.78/19.61 = { by axiom 38 (co1_9) R->L }
% 149.78/19.61 tuple2(true2, leq(sk5, sk10), fresh92(true2, true2, sk5, sk5, sk7, sk8, sk9, sk10))
% 149.78/19.61 = { by axiom 2 (co1_13) R->L }
% 149.78/19.61 tuple2(true2, leq(sk5, sk10), fresh92(ssList(sk8), true2, sk5, sk5, sk7, sk8, sk9, sk10))
% 149.78/19.61 = { by axiom 39 (co1_9) R->L }
% 149.78/19.61 tuple2(true2, leq(sk5, sk10), fresh91(true2, true2, sk5, sk5, sk7, sk8, sk9, sk10))
% 149.78/19.61 = { by axiom 4 (co1_14) R->L }
% 149.78/19.61 tuple2(true2, leq(sk5, sk10), fresh91(ssList(sk9), true2, sk5, sk5, sk7, sk8, sk9, sk10))
% 149.78/19.61 = { by axiom 40 (co1_9) R->L }
% 149.78/19.61 tuple2(true2, leq(sk5, sk10), fresh90(true2, true2, sk5, sk5, sk7, sk8, sk9, sk10))
% 149.78/19.61 = { by axiom 5 (co1_10) R->L }
% 149.78/19.61 tuple2(true2, leq(sk5, sk10), fresh90(ssItem(sk5), true2, sk5, sk5, sk7, sk8, sk9, sk10))
% 149.78/19.61 = { by axiom 41 (co1_9) R->L }
% 149.78/19.61 tuple2(true2, leq(sk5, sk10), fresh89(true2, true2, sk5, sk5, sk7, sk8, sk9, sk10))
% 149.78/19.61 = { by axiom 5 (co1_10) R->L }
% 149.78/19.61 tuple2(true2, leq(sk5, sk10), fresh89(ssItem(sk5), true2, sk5, sk5, sk7, sk8, sk9, sk10))
% 149.78/19.61 = { by axiom 42 (co1_9) R->L }
% 149.78/19.61 tuple2(true2, leq(sk5, sk10), fresh88(true2, true2, sk5, sk5, sk7, sk8, sk9, sk10))
% 149.78/19.61 = { by lemma 50 R->L }
% 149.78/19.61 tuple2(true2, leq(sk5, sk10), fresh88(ssItem(sk10), true2, sk5, sk5, sk7, sk8, sk9, sk10))
% 149.78/19.61 = { by axiom 43 (co1_9) R->L }
% 149.78/19.61 tuple2(true2, leq(sk5, sk10), fresh87(true2, true2, sk5, sk5, sk7, sk8, sk9, sk10))
% 149.78/19.61 = { by lemma 51 R->L }
% 149.78/19.61 tuple2(true2, leq(sk5, sk10), fresh87(leq(sk5, sk5), true2, sk5, sk5, sk7, sk8, sk9, sk10))
% 149.78/19.61 = { by axiom 44 (co1_9) R->L }
% 149.78/19.61 tuple2(true2, leq(sk5, sk10), fresh86(true2, true2, sk5, sk5, sk7, sk8, sk9, sk10))
% 149.78/19.61 = { by lemma 52 R->L }
% 149.78/19.61 tuple2(true2, leq(sk5, sk10), fresh86(memberP(sk8, sk10), true2, sk5, sk5, sk7, sk8, sk9, sk10))
% 149.78/19.61 = { by axiom 47 (co1_9) }
% 149.78/19.61 tuple2(true2, leq(sk5, sk10), fresh14(app(app(app(app(sk7, cons(sk5, nil)), sk8), cons(sk5, nil)), sk9), sk3, sk5, sk10))
% 149.78/19.61 = { by lemma 53 }
% 149.78/19.61 tuple2(true2, leq(sk5, sk10), fresh14(sk3, sk3, sk5, sk10))
% 149.78/19.61 = { by axiom 18 (co1_9) }
% 149.78/19.61 tuple2(true2, leq(sk5, sk10), true2)
% 149.78/19.61 = { by axiom 29 (co1_8) R->L }
% 149.78/19.61 tuple2(true2, fresh101(true2, true2, sk5, sk5, sk7, sk8, sk9, sk10), true2)
% 149.78/19.61 = { by axiom 3 (co1_12) R->L }
% 149.78/19.61 tuple2(true2, fresh101(ssList(sk7), true2, sk5, sk5, sk7, sk8, sk9, sk10), true2)
% 149.78/19.61 = { by axiom 31 (co1_8) R->L }
% 149.78/19.61 tuple2(true2, fresh100(true2, true2, sk5, sk5, sk7, sk8, sk9, sk10), true2)
% 149.78/19.61 = { by axiom 2 (co1_13) R->L }
% 149.78/19.61 tuple2(true2, fresh100(ssList(sk8), true2, sk5, sk5, sk7, sk8, sk9, sk10), true2)
% 149.78/19.61 = { by axiom 32 (co1_8) R->L }
% 149.78/19.61 tuple2(true2, fresh99(true2, true2, sk5, sk5, sk7, sk8, sk9, sk10), true2)
% 149.78/19.61 = { by axiom 4 (co1_14) R->L }
% 149.78/19.61 tuple2(true2, fresh99(ssList(sk9), true2, sk5, sk5, sk7, sk8, sk9, sk10), true2)
% 149.78/19.61 = { by axiom 33 (co1_8) R->L }
% 149.78/19.61 tuple2(true2, fresh98(true2, true2, sk5, sk5, sk7, sk8, sk9, sk10), true2)
% 149.78/19.61 = { by axiom 5 (co1_10) R->L }
% 149.78/19.61 tuple2(true2, fresh98(ssItem(sk5), true2, sk5, sk5, sk7, sk8, sk9, sk10), true2)
% 149.78/19.61 = { by axiom 34 (co1_8) R->L }
% 149.78/19.61 tuple2(true2, fresh97(true2, true2, sk5, sk5, sk7, sk8, sk9, sk10), true2)
% 149.78/19.61 = { by axiom 5 (co1_10) R->L }
% 149.78/19.61 tuple2(true2, fresh97(ssItem(sk5), true2, sk5, sk5, sk7, sk8, sk9, sk10), true2)
% 149.78/19.61 = { by axiom 35 (co1_8) R->L }
% 149.78/19.61 tuple2(true2, fresh96(true2, true2, sk5, sk5, sk7, sk8, sk9, sk10), true2)
% 149.78/19.61 = { by lemma 50 R->L }
% 149.78/19.61 tuple2(true2, fresh96(ssItem(sk10), true2, sk5, sk5, sk7, sk8, sk9, sk10), true2)
% 149.78/19.61 = { by axiom 36 (co1_8) R->L }
% 149.78/19.61 tuple2(true2, fresh95(true2, true2, sk5, sk5, sk7, sk8, sk9, sk10), true2)
% 149.78/19.61 = { by lemma 51 R->L }
% 149.78/19.61 tuple2(true2, fresh95(leq(sk5, sk5), true2, sk5, sk5, sk7, sk8, sk9, sk10), true2)
% 149.78/19.61 = { by axiom 37 (co1_8) R->L }
% 149.78/19.61 tuple2(true2, fresh94(true2, true2, sk5, sk5, sk7, sk8, sk9, sk10), true2)
% 149.78/19.61 = { by lemma 52 R->L }
% 149.78/19.61 tuple2(true2, fresh94(memberP(sk8, sk10), true2, sk5, sk5, sk7, sk8, sk9, sk10), true2)
% 149.78/19.61 = { by axiom 46 (co1_8) }
% 149.78/19.61 tuple2(true2, fresh15(app(app(app(app(sk7, cons(sk5, nil)), sk8), cons(sk5, nil)), sk9), sk3, sk5, sk10), true2)
% 149.78/19.61 = { by lemma 53 }
% 149.78/19.61 tuple2(true2, fresh15(sk3, sk3, sk5, sk10), true2)
% 149.78/19.61 = { by axiom 17 (co1_8) }
% 149.78/19.61 tuple2(true2, true2, true2)
% 149.78/19.61 % SZS output end Proof
% 149.78/19.61
% 149.78/19.61 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------