TSTP Solution File: SWC333+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC333+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 20:55:01 EDT 2023
% Result : Theorem 3.89s 0.84s
% Output : Proof 3.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC333+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 14:57:35 EDT 2023
% 0.12/0.33 % CPUTime :
% 3.89/0.84 Command-line arguments: --no-flatten-goal
% 3.89/0.84
% 3.89/0.84 % SZS status Theorem
% 3.89/0.84
% 3.89/0.85 % SZS output start Proof
% 3.89/0.85 Take the following subset of the input axioms:
% 3.89/0.86 fof(ax1, axiom, ![U]: (ssItem(U) => ![V]: (ssItem(V) => (neq(U, V) <=> U!=V)))).
% 3.89/0.86 fof(ax13, axiom, ![U2]: (ssList(U2) => (duplicatefreeP(U2) <=> ![V2]: (ssItem(V2) => ![W]: (ssItem(W) => ![X]: (ssList(X) => ![Y]: (ssList(Y) => ![Z]: (ssList(Z) => (app(app(X, cons(V2, Y)), cons(W, Z))=U2 => V2!=W))))))))).
% 3.89/0.86 fof(ax15, axiom, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => (neq(U2, V2) <=> U2!=V2)))).
% 3.89/0.86 fof(ax18, axiom, ![U2]: (ssList(U2) => ![V2]: (ssItem(V2) => cons(V2, U2)!=U2))).
% 3.89/0.86 fof(ax21, axiom, ![U2]: (ssList(U2) => ![V2]: (ssItem(V2) => nil!=cons(V2, U2)))).
% 3.89/0.86 fof(ax33, axiom, ![U2]: (ssItem(U2) => ![V2]: (ssItem(V2) => (lt(U2, V2) => ~lt(V2, U2))))).
% 3.89/0.86 fof(ax38, axiom, ![U2]: (ssItem(U2) => ~memberP(nil, U2))).
% 3.89/0.86 fof(ax8, axiom, ![U2]: (ssList(U2) => (cyclefreeP(U2) <=> ![V2]: (ssItem(V2) => ![W2]: (ssItem(W2) => ![X2]: (ssList(X2) => ![Y2]: (ssList(Y2) => ![Z2]: (ssList(Z2) => (app(app(X2, cons(V2, Y2)), cons(W2, Z2))=U2 => ~(leq(V2, W2) & leq(W2, V2))))))))))).
% 3.89/0.86 fof(ax90, axiom, ![U2]: (ssItem(U2) => ~lt(U2, U2))).
% 3.89/0.86 fof(ax93, axiom, ![U2]: (ssItem(U2) => ![V2]: (ssItem(V2) => (lt(U2, V2) <=> (U2!=V2 & leq(U2, V2)))))).
% 3.89/0.86 fof(ax94, axiom, ![U2]: (ssItem(U2) => ![V2]: (ssItem(V2) => (gt(U2, V2) => ~gt(V2, U2))))).
% 3.89/0.86 fof(co1, conjecture, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => ![W2]: (ssList(W2) => ![X2]: (ssList(X2) => (V2!=X2 | (U2!=W2 | (~segmentP(X2, W2) | (~totalorderedP(W2) | (?[Y2]: (ssList(Y2) & (neq(W2, Y2) & (segmentP(X2, Y2) & (segmentP(Y2, W2) & totalorderedP(Y2))))) | (![Z2]: (ssList(Z2) => (~neq(U2, Z2) | (~segmentP(V2, Z2) | (~segmentP(Z2, U2) | ~totalorderedP(Z2))))) & (segmentP(V2, U2) & totalorderedP(U2))))))))))))).
% 3.89/0.86
% 3.89/0.86 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.89/0.86 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.89/0.86 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.89/0.86 fresh(y, y, x1...xn) = u
% 3.89/0.86 C => fresh(s, t, x1...xn) = v
% 3.89/0.86 where fresh is a fresh function symbol and x1..xn are the free
% 3.89/0.86 variables of u and v.
% 3.89/0.86 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.89/0.86 input problem has no model of domain size 1).
% 3.89/0.86
% 3.89/0.86 The encoding turns the above axioms into the following unit equations and goals:
% 3.89/0.86
% 3.89/0.87 Axiom 1 (co1_1): v = x.
% 3.89/0.87 Axiom 2 (co1): u = w.
% 3.89/0.87 Axiom 3 (co1_7): totalorderedP(w) = true2.
% 3.89/0.87 Axiom 4 (co1_10): fresh23(X, X) = ssList(z).
% 3.89/0.87 Axiom 5 (co1_10): fresh22(X, X) = true2.
% 3.89/0.87 Axiom 6 (co1_11): fresh20(X, X) = true2.
% 3.89/0.87 Axiom 7 (co1_12): fresh18(X, X) = true2.
% 3.89/0.87 Axiom 8 (co1_13): fresh17(X, X) = totalorderedP(z).
% 3.89/0.87 Axiom 9 (co1_13): fresh16(X, X) = true2.
% 3.89/0.87 Axiom 10 (co1_9): fresh14(X, X) = true2.
% 3.89/0.87 Axiom 11 (co1_9): fresh15(X, X) = neq(u, z).
% 3.89/0.87 Axiom 12 (co1_6): segmentP(x, w) = true2.
% 3.89/0.87 Axiom 13 (co1_12): fresh19(X, X) = segmentP(z, u).
% 3.89/0.87 Axiom 14 (co1_11): fresh21(X, X) = segmentP(v, z).
% 3.89/0.87 Axiom 15 (co1_10): fresh23(totalorderedP(u), true2) = fresh22(segmentP(v, u), true2).
% 3.89/0.87 Axiom 16 (co1_11): fresh21(totalorderedP(u), true2) = fresh20(segmentP(v, u), true2).
% 3.89/0.87 Axiom 17 (co1_12): fresh19(totalorderedP(u), true2) = fresh18(segmentP(v, u), true2).
% 3.89/0.87 Axiom 18 (co1_13): fresh17(totalorderedP(u), true2) = fresh16(segmentP(v, u), true2).
% 3.89/0.87 Axiom 19 (co1_9): fresh15(totalorderedP(u), true2) = fresh14(segmentP(v, u), true2).
% 3.89/0.87
% 3.89/0.87 Goal 1 (co1_8): tuple(neq(w, X), ssList(X), segmentP(X, w), segmentP(x, X), totalorderedP(X)) = tuple(true2, true2, true2, true2, true2).
% 3.89/0.87 The goal is true when:
% 3.89/0.87 X = z
% 3.89/0.87
% 3.89/0.87 Proof:
% 3.89/0.87 tuple(neq(w, z), ssList(z), segmentP(z, w), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 2 (co1) R->L }
% 3.89/0.87 tuple(neq(u, z), ssList(z), segmentP(z, w), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 11 (co1_9) R->L }
% 3.89/0.87 tuple(fresh15(true2, true2), ssList(z), segmentP(z, w), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 3 (co1_7) R->L }
% 3.89/0.87 tuple(fresh15(totalorderedP(w), true2), ssList(z), segmentP(z, w), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 2 (co1) R->L }
% 3.89/0.87 tuple(fresh15(totalorderedP(u), true2), ssList(z), segmentP(z, w), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 19 (co1_9) }
% 3.89/0.87 tuple(fresh14(segmentP(v, u), true2), ssList(z), segmentP(z, w), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 1 (co1_1) }
% 3.89/0.87 tuple(fresh14(segmentP(x, u), true2), ssList(z), segmentP(z, w), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 2 (co1) }
% 3.89/0.87 tuple(fresh14(segmentP(x, w), true2), ssList(z), segmentP(z, w), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 12 (co1_6) }
% 3.89/0.87 tuple(fresh14(true2, true2), ssList(z), segmentP(z, w), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 10 (co1_9) }
% 3.89/0.87 tuple(true2, ssList(z), segmentP(z, w), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 4 (co1_10) R->L }
% 3.89/0.87 tuple(true2, fresh23(true2, true2), segmentP(z, w), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 3 (co1_7) R->L }
% 3.89/0.87 tuple(true2, fresh23(totalorderedP(w), true2), segmentP(z, w), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 2 (co1) R->L }
% 3.89/0.87 tuple(true2, fresh23(totalorderedP(u), true2), segmentP(z, w), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 15 (co1_10) }
% 3.89/0.87 tuple(true2, fresh22(segmentP(v, u), true2), segmentP(z, w), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 1 (co1_1) }
% 3.89/0.87 tuple(true2, fresh22(segmentP(x, u), true2), segmentP(z, w), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 2 (co1) }
% 3.89/0.87 tuple(true2, fresh22(segmentP(x, w), true2), segmentP(z, w), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 12 (co1_6) }
% 3.89/0.87 tuple(true2, fresh22(true2, true2), segmentP(z, w), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 5 (co1_10) }
% 3.89/0.87 tuple(true2, true2, segmentP(z, w), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 2 (co1) R->L }
% 3.89/0.87 tuple(true2, true2, segmentP(z, u), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 13 (co1_12) R->L }
% 3.89/0.87 tuple(true2, true2, fresh19(true2, true2), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 3 (co1_7) R->L }
% 3.89/0.87 tuple(true2, true2, fresh19(totalorderedP(w), true2), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 2 (co1) R->L }
% 3.89/0.87 tuple(true2, true2, fresh19(totalorderedP(u), true2), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 17 (co1_12) }
% 3.89/0.87 tuple(true2, true2, fresh18(segmentP(v, u), true2), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 1 (co1_1) }
% 3.89/0.87 tuple(true2, true2, fresh18(segmentP(x, u), true2), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 2 (co1) }
% 3.89/0.87 tuple(true2, true2, fresh18(segmentP(x, w), true2), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 12 (co1_6) }
% 3.89/0.87 tuple(true2, true2, fresh18(true2, true2), segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 7 (co1_12) }
% 3.89/0.87 tuple(true2, true2, true2, segmentP(x, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 1 (co1_1) R->L }
% 3.89/0.87 tuple(true2, true2, true2, segmentP(v, z), totalorderedP(z))
% 3.89/0.87 = { by axiom 14 (co1_11) R->L }
% 3.89/0.87 tuple(true2, true2, true2, fresh21(true2, true2), totalorderedP(z))
% 3.89/0.87 = { by axiom 3 (co1_7) R->L }
% 3.89/0.87 tuple(true2, true2, true2, fresh21(totalorderedP(w), true2), totalorderedP(z))
% 3.89/0.87 = { by axiom 2 (co1) R->L }
% 3.89/0.87 tuple(true2, true2, true2, fresh21(totalorderedP(u), true2), totalorderedP(z))
% 3.89/0.87 = { by axiom 16 (co1_11) }
% 3.89/0.87 tuple(true2, true2, true2, fresh20(segmentP(v, u), true2), totalorderedP(z))
% 3.89/0.87 = { by axiom 1 (co1_1) }
% 3.89/0.87 tuple(true2, true2, true2, fresh20(segmentP(x, u), true2), totalorderedP(z))
% 3.89/0.87 = { by axiom 2 (co1) }
% 3.89/0.87 tuple(true2, true2, true2, fresh20(segmentP(x, w), true2), totalorderedP(z))
% 3.89/0.87 = { by axiom 12 (co1_6) }
% 3.89/0.87 tuple(true2, true2, true2, fresh20(true2, true2), totalorderedP(z))
% 3.89/0.87 = { by axiom 6 (co1_11) }
% 3.89/0.87 tuple(true2, true2, true2, true2, totalorderedP(z))
% 3.89/0.87 = { by axiom 8 (co1_13) R->L }
% 3.89/0.87 tuple(true2, true2, true2, true2, fresh17(true2, true2))
% 3.89/0.87 = { by axiom 3 (co1_7) R->L }
% 3.89/0.87 tuple(true2, true2, true2, true2, fresh17(totalorderedP(w), true2))
% 3.89/0.87 = { by axiom 2 (co1) R->L }
% 3.89/0.87 tuple(true2, true2, true2, true2, fresh17(totalorderedP(u), true2))
% 3.89/0.87 = { by axiom 18 (co1_13) }
% 3.89/0.87 tuple(true2, true2, true2, true2, fresh16(segmentP(v, u), true2))
% 3.89/0.87 = { by axiom 1 (co1_1) }
% 3.89/0.87 tuple(true2, true2, true2, true2, fresh16(segmentP(x, u), true2))
% 3.89/0.87 = { by axiom 2 (co1) }
% 3.89/0.87 tuple(true2, true2, true2, true2, fresh16(segmentP(x, w), true2))
% 3.89/0.87 = { by axiom 12 (co1_6) }
% 3.89/0.87 tuple(true2, true2, true2, true2, fresh16(true2, true2))
% 3.89/0.87 = { by axiom 9 (co1_13) }
% 3.89/0.87 tuple(true2, true2, true2, true2, true2)
% 3.89/0.87 % SZS output end Proof
% 3.89/0.87
% 3.89/0.87 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------