TSTP Solution File: SYN705-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN705-1 : TPTP v8.1.2. Released v2.5.0.
% 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 : n011.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 : Fri Sep 1 03:35:47 EDT 2023
% Result : Unsatisfiable 0.21s 0.65s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN705-1 : TPTP v8.1.2. Released v2.5.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 20:01:24 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.65 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.65
% 0.21/0.65 % SZS status Unsatisfiable
% 0.21/0.65
% 0.21/0.66 % SZS output start Proof
% 0.21/0.66 Take the following subset of the input axioms:
% 0.21/0.66 fof(not_p47_51, negated_conjecture, ~p47(f5(c48, f13(f16(f18(c50, c51), c52), c53)), c55)).
% 0.21/0.66 fof(p2_20, negated_conjecture, ![X38]: p2(X38, X38)).
% 0.21/0.66 fof(p3_80, negated_conjecture, ![X65, X66, X67, X68]: p3(f8(f10(c49, f13(f16(f18(c50, X65), X66), X67)), X68), f13(f16(f18(c50, f20(f22(f24(f26(c56, X65), X66), X67), X68)), f30(f32(f34(f36(c57, X65), X66), X67), X68)), f40(f42(f44(f46(c58, X65), X66), X67), X68)))).
% 0.21/0.66 fof(p47_53, negated_conjecture, ![X151, X152, X153, X154]: (p47(X151, X152) | (~p47(X153, X154) | (~p7(X154, X152) | ~p4(X153, X151))))).
% 0.21/0.66 fof(p47_74, negated_conjecture, ![X147, X148, X149, X150]: (p47(X147, X148) | ~p47(f5(c48, f13(f16(f18(c50, X147), X149), X150)), X148))).
% 0.21/0.66 fof(p47_75, negated_conjecture, ![X69, X65_2, X66_2, X67_2, X68_2]: (p47(X65_2, X69) | ~p47(f20(f22(f24(f26(c56, X65_2), X66_2), X67_2), X68_2), X69))).
% 0.21/0.66 fof(p47_76, negated_conjecture, ![X147_2, X148_2, X149_2, X150_2]: (p47(f5(c48, f13(f16(f18(c50, X147_2), X149_2), X150_2)), X148_2) | ~p47(X147_2, X148_2))).
% 0.21/0.66 fof(p47_77, negated_conjecture, p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c55)).
% 0.21/0.66 fof(p4_58, negated_conjecture, ![X126, X127, X128, X129]: (p4(f5(X126, X127), f5(X128, X129)) | (~p2(X126, X128) | ~p3(X127, X129)))).
% 0.21/0.66 fof(p7_3, negated_conjecture, ![X162]: p7(X162, X162)).
% 0.21/0.66
% 0.21/0.66 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.66 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.66 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.66 fresh(y, y, x1...xn) = u
% 0.21/0.66 C => fresh(s, t, x1...xn) = v
% 0.21/0.66 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.66 variables of u and v.
% 0.21/0.66 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.66 input problem has no model of domain size 1).
% 0.21/0.66
% 0.21/0.66 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.66
% 0.21/0.66 Axiom 1 (p7_3): p7(X, X) = true2.
% 0.21/0.66 Axiom 2 (p2_20): p2(X, X) = true2.
% 0.21/0.66 Axiom 3 (p47_53): fresh98(X, X, Y, Z) = true2.
% 0.21/0.66 Axiom 4 (p47_74): fresh17(X, X, Y, Z) = true2.
% 0.21/0.66 Axiom 5 (p47_75): fresh16(X, X, Y, Z) = true2.
% 0.21/0.66 Axiom 6 (p47_53): fresh18(X, X, Y, Z, W) = p47(Y, Z).
% 0.21/0.66 Axiom 7 (p47_53): fresh97(X, X, Y, Z, W, V) = fresh98(p7(V, Z), true2, Y, Z).
% 0.21/0.66 Axiom 8 (p47_76): fresh15(X, X, Y, Z, W, V) = true2.
% 0.21/0.66 Axiom 9 (p4_58): fresh12(X, X, Y, Z, W, V) = p4(f5(Y, Z), f5(W, V)).
% 0.21/0.66 Axiom 10 (p4_58): fresh11(X, X, Y, Z, W, V) = true2.
% 0.21/0.66 Axiom 11 (p47_53): fresh97(p47(X, Y), true2, Z, W, X, Y) = fresh18(p4(X, Z), true2, Z, W, Y).
% 0.21/0.66 Axiom 12 (p4_58): fresh12(p2(X, Y), true2, X, Z, Y, W) = fresh11(p3(Z, W), true2, X, Z, Y, W).
% 0.21/0.66 Axiom 13 (p47_76): fresh15(p47(X, Y), true2, X, Z, W, Y) = p47(f5(c48, f13(f16(f18(c50, X), Z), W)), Y).
% 0.21/0.66 Axiom 14 (p47_77): p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c55) = true2.
% 0.21/0.66 Axiom 15 (p47_74): fresh17(p47(f5(c48, f13(f16(f18(c50, X), Y), Z)), W), true2, X, W) = p47(X, W).
% 0.21/0.66 Axiom 16 (p47_75): fresh16(p47(f20(f22(f24(f26(c56, X), Y), Z), W), V), true2, X, V) = p47(X, V).
% 0.21/0.67 Axiom 17 (p3_80): p3(f8(f10(c49, f13(f16(f18(c50, X), Y), Z)), W), f13(f16(f18(c50, f20(f22(f24(f26(c56, X), Y), Z), W)), f30(f32(f34(f36(c57, X), Y), Z), W)), f40(f42(f44(f46(c58, X), Y), Z), W))) = true2.
% 0.21/0.67
% 0.21/0.67 Goal 1 (not_p47_51): p47(f5(c48, f13(f16(f18(c50, c51), c52), c53)), c55) = true2.
% 0.21/0.67 Proof:
% 0.21/0.67 p47(f5(c48, f13(f16(f18(c50, c51), c52), c53)), c55)
% 0.21/0.67 = { by axiom 13 (p47_76) R->L }
% 0.21/0.67 fresh15(p47(c51, c55), true2, c51, c52, c53, c55)
% 0.21/0.67 = { by axiom 16 (p47_75) R->L }
% 0.21/0.67 fresh15(fresh16(p47(f20(f22(f24(f26(c56, c51), c52), c53), c54), c55), true2, c51, c55), true2, c51, c52, c53, c55)
% 0.21/0.67 = { by axiom 15 (p47_74) R->L }
% 0.21/0.67 fresh15(fresh16(fresh17(p47(f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55), true2, f20(f22(f24(f26(c56, c51), c52), c53), c54), c55), true2, c51, c55), true2, c51, c52, c53, c55)
% 0.21/0.67 = { by axiom 6 (p47_53) R->L }
% 0.21/0.67 fresh15(fresh16(fresh17(fresh18(true2, true2, f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55, c55), true2, f20(f22(f24(f26(c56, c51), c52), c53), c54), c55), true2, c51, c55), true2, c51, c52, c53, c55)
% 0.21/0.67 = { by axiom 10 (p4_58) R->L }
% 0.21/0.67 fresh15(fresh16(fresh17(fresh18(fresh11(true2, true2, c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), true2, f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55, c55), true2, f20(f22(f24(f26(c56, c51), c52), c53), c54), c55), true2, c51, c55), true2, c51, c52, c53, c55)
% 0.21/0.67 = { by axiom 17 (p3_80) R->L }
% 0.21/0.67 fresh15(fresh16(fresh17(fresh18(fresh11(p3(f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), true2, c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), true2, f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55, c55), true2, f20(f22(f24(f26(c56, c51), c52), c53), c54), c55), true2, c51, c55), true2, c51, c52, c53, c55)
% 0.21/0.67 = { by axiom 12 (p4_58) R->L }
% 0.21/0.67 fresh15(fresh16(fresh17(fresh18(fresh12(p2(c48, c48), true2, c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), true2, f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55, c55), true2, f20(f22(f24(f26(c56, c51), c52), c53), c54), c55), true2, c51, c55), true2, c51, c52, c53, c55)
% 0.21/0.67 = { by axiom 2 (p2_20) }
% 0.21/0.67 fresh15(fresh16(fresh17(fresh18(fresh12(true2, true2, c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54), c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), true2, f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55, c55), true2, f20(f22(f24(f26(c56, c51), c52), c53), c54), c55), true2, c51, c55), true2, c51, c52, c53, c55)
% 0.21/0.67 = { by axiom 9 (p4_58) }
% 0.21/0.67 fresh15(fresh16(fresh17(fresh18(p4(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54)))), true2, f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55, c55), true2, f20(f22(f24(f26(c56, c51), c52), c53), c54), c55), true2, c51, c55), true2, c51, c52, c53, c55)
% 0.21/0.67 = { by axiom 11 (p47_53) R->L }
% 0.21/0.67 fresh15(fresh16(fresh17(fresh97(p47(f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c55), true2, f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55, f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c55), true2, f20(f22(f24(f26(c56, c51), c52), c53), c54), c55), true2, c51, c55), true2, c51, c52, c53, c55)
% 0.21/0.67 = { by axiom 14 (p47_77) }
% 0.21/0.67 fresh15(fresh16(fresh17(fresh97(true2, true2, f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55, f5(c48, f8(f10(c49, f13(f16(f18(c50, c51), c52), c53)), c54)), c55), true2, f20(f22(f24(f26(c56, c51), c52), c53), c54), c55), true2, c51, c55), true2, c51, c52, c53, c55)
% 0.21/0.67 = { by axiom 7 (p47_53) }
% 0.21/0.67 fresh15(fresh16(fresh17(fresh98(p7(c55, c55), true2, f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55), true2, f20(f22(f24(f26(c56, c51), c52), c53), c54), c55), true2, c51, c55), true2, c51, c52, c53, c55)
% 0.21/0.67 = { by axiom 1 (p7_3) }
% 0.21/0.67 fresh15(fresh16(fresh17(fresh98(true2, true2, f5(c48, f13(f16(f18(c50, f20(f22(f24(f26(c56, c51), c52), c53), c54)), f30(f32(f34(f36(c57, c51), c52), c53), c54)), f40(f42(f44(f46(c58, c51), c52), c53), c54))), c55), true2, f20(f22(f24(f26(c56, c51), c52), c53), c54), c55), true2, c51, c55), true2, c51, c52, c53, c55)
% 0.21/0.67 = { by axiom 3 (p47_53) }
% 0.21/0.67 fresh15(fresh16(fresh17(true2, true2, f20(f22(f24(f26(c56, c51), c52), c53), c54), c55), true2, c51, c55), true2, c51, c52, c53, c55)
% 0.21/0.67 = { by axiom 4 (p47_74) }
% 0.21/0.67 fresh15(fresh16(true2, true2, c51, c55), true2, c51, c52, c53, c55)
% 0.21/0.67 = { by axiom 5 (p47_75) }
% 0.21/0.67 fresh15(true2, true2, c51, c52, c53, c55)
% 0.21/0.67 = { by axiom 8 (p47_76) }
% 0.21/0.67 true2
% 0.21/0.67 % SZS output end Proof
% 0.21/0.67
% 0.21/0.67 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------