TSTP Solution File: SYN703-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN703-1 : 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 : n024.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 03:35:46 EDT 2023
% Result : Unsatisfiable 0.21s 0.67s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SYN703-1 : TPTP v8.1.2. Released v2.5.0.
% 0.13/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 16:49:23 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.21/0.67 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.67
% 0.21/0.67 % SZS status Unsatisfiable
% 0.21/0.67
% 0.21/0.68 % SZS output start Proof
% 0.21/0.68 Take the following subset of the input axioms:
% 0.21/0.68 fof(not_p47_51, negated_conjecture, ~p47(f5(c48, f8(f11(f13(c49, c50), c51), c52)), c53)).
% 0.21/0.68 fof(p15_5, negated_conjecture, ![X17]: p15(X17, X17)).
% 0.21/0.68 fof(p2_8, negated_conjecture, ![X30]: p2(X30, X30)).
% 0.21/0.68 fof(p3_80, negated_conjecture, ![X57, X58, X59, X60]: p3(f16(f18(c54, f8(f11(f13(c49, X57), X58), X59)), X60), f8(f11(f13(c49, f20(f22(f24(f26(c56, X57), X58), X59), X60)), f30(f32(f34(f36(c57, X57), X58), X59), X60)), f40(f42(f44(f46(c58, X57), X58), X59), X60)))).
% 0.21/0.68 fof(p47_53, negated_conjecture, ![X143, X144, X146, X145]: (p47(X143, X144) | (~p4(X146, X143) | (~p47(X146, X145) | ~p15(X145, X144))))).
% 0.21/0.68 fof(p47_74, negated_conjecture, ![X139, X140, X141, X142]: (p47(X139, X140) | ~p47(f5(c48, f8(f11(f13(c49, X139), X141), X142)), X140))).
% 0.21/0.68 fof(p47_75, negated_conjecture, ![X61, X57_2, X58_2, X59_2, X60_2]: (p47(X57_2, X61) | ~p47(f20(f22(f24(f26(c56, X57_2), X58_2), X59_2), X60_2), X61))).
% 0.21/0.68 fof(p47_76, negated_conjecture, ![X139_2, X140_2, X141_2, X142_2]: (p47(f5(c48, f8(f11(f13(c49, X139_2), X141_2), X142_2)), X140_2) | ~p47(X139_2, X140_2))).
% 0.21/0.68 fof(p47_77, negated_conjecture, p47(f5(c48, f16(f18(c54, f8(f11(f13(c49, c50), c51), c52)), c55)), c53)).
% 0.21/0.68 fof(p4_60, negated_conjecture, ![X118, X119, X120, X121]: (p4(f5(X118, X119), f5(X120, X121)) | (~p2(X118, X120) | ~p3(X119, X121)))).
% 0.21/0.68
% 0.21/0.68 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.68 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.68 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.68 fresh(y, y, x1...xn) = u
% 0.21/0.68 C => fresh(s, t, x1...xn) = v
% 0.21/0.68 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.68 variables of u and v.
% 0.21/0.68 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.68 input problem has no model of domain size 1).
% 0.21/0.68
% 0.21/0.68 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.68
% 0.21/0.68 Axiom 1 (p15_5): p15(X, X) = true2.
% 0.21/0.68 Axiom 2 (p2_8): p2(X, X) = true2.
% 0.21/0.68 Axiom 3 (p47_53): fresh98(X, X, Y, Z) = true2.
% 0.21/0.68 Axiom 4 (p47_74): fresh21(X, X, Y, Z) = true2.
% 0.21/0.68 Axiom 5 (p47_75): fresh20(X, X, Y, Z) = true2.
% 0.21/0.68 Axiom 6 (p47_53): fresh22(X, X, Y, Z, W) = p47(Y, Z).
% 0.21/0.68 Axiom 7 (p47_53): fresh97(X, X, Y, Z, W, V) = fresh98(p15(V, Z), true2, Y, Z).
% 0.21/0.68 Axiom 8 (p47_76): fresh19(X, X, Y, Z, W, V) = true2.
% 0.21/0.68 Axiom 9 (p4_60): fresh16(X, X, Y, Z, W, V) = p4(f5(Y, Z), f5(W, V)).
% 0.21/0.68 Axiom 10 (p4_60): fresh15(X, X, Y, Z, W, V) = true2.
% 0.21/0.68 Axiom 11 (p47_53): fresh97(p47(X, Y), true2, Z, W, X, Y) = fresh22(p4(X, Z), true2, Z, W, Y).
% 0.21/0.68 Axiom 12 (p4_60): fresh16(p3(X, Y), true2, Z, X, W, Y) = fresh15(p2(Z, W), true2, Z, X, W, Y).
% 0.21/0.68 Axiom 13 (p47_76): fresh19(p47(X, Y), true2, X, Z, W, Y) = p47(f5(c48, f8(f11(f13(c49, X), Z), W)), Y).
% 0.21/0.68 Axiom 14 (p47_77): p47(f5(c48, f16(f18(c54, f8(f11(f13(c49, c50), c51), c52)), c55)), c53) = true2.
% 0.21/0.68 Axiom 15 (p47_74): fresh21(p47(f5(c48, f8(f11(f13(c49, X), Y), Z)), W), true2, X, W) = p47(X, W).
% 0.21/0.68 Axiom 16 (p47_75): fresh20(p47(f20(f22(f24(f26(c56, X), Y), Z), W), V), true2, X, V) = p47(X, V).
% 0.21/0.68 Axiom 17 (p3_80): p3(f16(f18(c54, f8(f11(f13(c49, X), Y), Z)), W), f8(f11(f13(c49, 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.
% 0.21/0.68
% 0.21/0.68 Goal 1 (not_p47_51): p47(f5(c48, f8(f11(f13(c49, c50), c51), c52)), c53) = true2.
% 0.21/0.68 Proof:
% 0.21/0.68 p47(f5(c48, f8(f11(f13(c49, c50), c51), c52)), c53)
% 0.21/0.68 = { by axiom 13 (p47_76) R->L }
% 0.21/0.68 fresh19(p47(c50, c53), true2, c50, c51, c52, c53)
% 0.21/0.68 = { by axiom 16 (p47_75) R->L }
% 0.21/0.68 fresh19(fresh20(p47(f20(f22(f24(f26(c56, c50), c51), c52), c55), c53), true2, c50, c53), true2, c50, c51, c52, c53)
% 0.21/0.68 = { by axiom 15 (p47_74) R->L }
% 0.21/0.68 fresh19(fresh20(fresh21(p47(f5(c48, f8(f11(f13(c49, f20(f22(f24(f26(c56, c50), c51), c52), c55)), f30(f32(f34(f36(c57, c50), c51), c52), c55)), f40(f42(f44(f46(c58, c50), c51), c52), c55))), c53), true2, f20(f22(f24(f26(c56, c50), c51), c52), c55), c53), true2, c50, c53), true2, c50, c51, c52, c53)
% 0.21/0.68 = { by axiom 6 (p47_53) R->L }
% 0.21/0.68 fresh19(fresh20(fresh21(fresh22(true2, true2, f5(c48, f8(f11(f13(c49, f20(f22(f24(f26(c56, c50), c51), c52), c55)), f30(f32(f34(f36(c57, c50), c51), c52), c55)), f40(f42(f44(f46(c58, c50), c51), c52), c55))), c53, c53), true2, f20(f22(f24(f26(c56, c50), c51), c52), c55), c53), true2, c50, c53), true2, c50, c51, c52, c53)
% 0.21/0.68 = { by axiom 10 (p4_60) R->L }
% 0.21/0.68 fresh19(fresh20(fresh21(fresh22(fresh15(true2, true2, c48, f16(f18(c54, f8(f11(f13(c49, c50), c51), c52)), c55), c48, f8(f11(f13(c49, f20(f22(f24(f26(c56, c50), c51), c52), c55)), f30(f32(f34(f36(c57, c50), c51), c52), c55)), f40(f42(f44(f46(c58, c50), c51), c52), c55))), true2, f5(c48, f8(f11(f13(c49, f20(f22(f24(f26(c56, c50), c51), c52), c55)), f30(f32(f34(f36(c57, c50), c51), c52), c55)), f40(f42(f44(f46(c58, c50), c51), c52), c55))), c53, c53), true2, f20(f22(f24(f26(c56, c50), c51), c52), c55), c53), true2, c50, c53), true2, c50, c51, c52, c53)
% 0.21/0.68 = { by axiom 2 (p2_8) R->L }
% 0.21/0.68 fresh19(fresh20(fresh21(fresh22(fresh15(p2(c48, c48), true2, c48, f16(f18(c54, f8(f11(f13(c49, c50), c51), c52)), c55), c48, f8(f11(f13(c49, f20(f22(f24(f26(c56, c50), c51), c52), c55)), f30(f32(f34(f36(c57, c50), c51), c52), c55)), f40(f42(f44(f46(c58, c50), c51), c52), c55))), true2, f5(c48, f8(f11(f13(c49, f20(f22(f24(f26(c56, c50), c51), c52), c55)), f30(f32(f34(f36(c57, c50), c51), c52), c55)), f40(f42(f44(f46(c58, c50), c51), c52), c55))), c53, c53), true2, f20(f22(f24(f26(c56, c50), c51), c52), c55), c53), true2, c50, c53), true2, c50, c51, c52, c53)
% 0.21/0.68 = { by axiom 12 (p4_60) R->L }
% 0.21/0.68 fresh19(fresh20(fresh21(fresh22(fresh16(p3(f16(f18(c54, f8(f11(f13(c49, c50), c51), c52)), c55), f8(f11(f13(c49, f20(f22(f24(f26(c56, c50), c51), c52), c55)), f30(f32(f34(f36(c57, c50), c51), c52), c55)), f40(f42(f44(f46(c58, c50), c51), c52), c55))), true2, c48, f16(f18(c54, f8(f11(f13(c49, c50), c51), c52)), c55), c48, f8(f11(f13(c49, f20(f22(f24(f26(c56, c50), c51), c52), c55)), f30(f32(f34(f36(c57, c50), c51), c52), c55)), f40(f42(f44(f46(c58, c50), c51), c52), c55))), true2, f5(c48, f8(f11(f13(c49, f20(f22(f24(f26(c56, c50), c51), c52), c55)), f30(f32(f34(f36(c57, c50), c51), c52), c55)), f40(f42(f44(f46(c58, c50), c51), c52), c55))), c53, c53), true2, f20(f22(f24(f26(c56, c50), c51), c52), c55), c53), true2, c50, c53), true2, c50, c51, c52, c53)
% 0.21/0.68 = { by axiom 17 (p3_80) }
% 0.21/0.68 fresh19(fresh20(fresh21(fresh22(fresh16(true2, true2, c48, f16(f18(c54, f8(f11(f13(c49, c50), c51), c52)), c55), c48, f8(f11(f13(c49, f20(f22(f24(f26(c56, c50), c51), c52), c55)), f30(f32(f34(f36(c57, c50), c51), c52), c55)), f40(f42(f44(f46(c58, c50), c51), c52), c55))), true2, f5(c48, f8(f11(f13(c49, f20(f22(f24(f26(c56, c50), c51), c52), c55)), f30(f32(f34(f36(c57, c50), c51), c52), c55)), f40(f42(f44(f46(c58, c50), c51), c52), c55))), c53, c53), true2, f20(f22(f24(f26(c56, c50), c51), c52), c55), c53), true2, c50, c53), true2, c50, c51, c52, c53)
% 0.21/0.68 = { by axiom 9 (p4_60) }
% 0.21/0.68 fresh19(fresh20(fresh21(fresh22(p4(f5(c48, f16(f18(c54, f8(f11(f13(c49, c50), c51), c52)), c55)), f5(c48, f8(f11(f13(c49, f20(f22(f24(f26(c56, c50), c51), c52), c55)), f30(f32(f34(f36(c57, c50), c51), c52), c55)), f40(f42(f44(f46(c58, c50), c51), c52), c55)))), true2, f5(c48, f8(f11(f13(c49, f20(f22(f24(f26(c56, c50), c51), c52), c55)), f30(f32(f34(f36(c57, c50), c51), c52), c55)), f40(f42(f44(f46(c58, c50), c51), c52), c55))), c53, c53), true2, f20(f22(f24(f26(c56, c50), c51), c52), c55), c53), true2, c50, c53), true2, c50, c51, c52, c53)
% 0.21/0.68 = { by axiom 11 (p47_53) R->L }
% 0.21/0.68 fresh19(fresh20(fresh21(fresh97(p47(f5(c48, f16(f18(c54, f8(f11(f13(c49, c50), c51), c52)), c55)), c53), true2, f5(c48, f8(f11(f13(c49, f20(f22(f24(f26(c56, c50), c51), c52), c55)), f30(f32(f34(f36(c57, c50), c51), c52), c55)), f40(f42(f44(f46(c58, c50), c51), c52), c55))), c53, f5(c48, f16(f18(c54, f8(f11(f13(c49, c50), c51), c52)), c55)), c53), true2, f20(f22(f24(f26(c56, c50), c51), c52), c55), c53), true2, c50, c53), true2, c50, c51, c52, c53)
% 0.21/0.68 = { by axiom 14 (p47_77) }
% 0.21/0.68 fresh19(fresh20(fresh21(fresh97(true2, true2, f5(c48, f8(f11(f13(c49, f20(f22(f24(f26(c56, c50), c51), c52), c55)), f30(f32(f34(f36(c57, c50), c51), c52), c55)), f40(f42(f44(f46(c58, c50), c51), c52), c55))), c53, f5(c48, f16(f18(c54, f8(f11(f13(c49, c50), c51), c52)), c55)), c53), true2, f20(f22(f24(f26(c56, c50), c51), c52), c55), c53), true2, c50, c53), true2, c50, c51, c52, c53)
% 0.21/0.68 = { by axiom 7 (p47_53) }
% 0.21/0.68 fresh19(fresh20(fresh21(fresh98(p15(c53, c53), true2, f5(c48, f8(f11(f13(c49, f20(f22(f24(f26(c56, c50), c51), c52), c55)), f30(f32(f34(f36(c57, c50), c51), c52), c55)), f40(f42(f44(f46(c58, c50), c51), c52), c55))), c53), true2, f20(f22(f24(f26(c56, c50), c51), c52), c55), c53), true2, c50, c53), true2, c50, c51, c52, c53)
% 0.21/0.68 = { by axiom 1 (p15_5) }
% 0.21/0.68 fresh19(fresh20(fresh21(fresh98(true2, true2, f5(c48, f8(f11(f13(c49, f20(f22(f24(f26(c56, c50), c51), c52), c55)), f30(f32(f34(f36(c57, c50), c51), c52), c55)), f40(f42(f44(f46(c58, c50), c51), c52), c55))), c53), true2, f20(f22(f24(f26(c56, c50), c51), c52), c55), c53), true2, c50, c53), true2, c50, c51, c52, c53)
% 0.21/0.68 = { by axiom 3 (p47_53) }
% 0.21/0.68 fresh19(fresh20(fresh21(true2, true2, f20(f22(f24(f26(c56, c50), c51), c52), c55), c53), true2, c50, c53), true2, c50, c51, c52, c53)
% 0.21/0.68 = { by axiom 4 (p47_74) }
% 0.21/0.68 fresh19(fresh20(true2, true2, c50, c53), true2, c50, c51, c52, c53)
% 0.21/0.68 = { by axiom 5 (p47_75) }
% 0.21/0.68 fresh19(true2, true2, c50, c51, c52, c53)
% 0.21/0.68 = { by axiom 8 (p47_76) }
% 0.21/0.68 true2
% 0.21/0.68 % SZS output end Proof
% 0.21/0.68
% 0.21/0.68 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------