TSTP Solution File: SYN706-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN706-1 : 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 : n005.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 0.20s 0.64s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN706-1 : TPTP v8.1.2. Released v2.5.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 21:02:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.64 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.20/0.64
% 0.20/0.64 % SZS status Unsatisfiable
% 0.20/0.64
% 0.20/0.64 % SZS output start Proof
% 0.20/0.64 Take the following subset of the input axioms:
% 0.20/0.64 fof(not_p48_29, negated_conjecture, ~p48(f38(f40(c59, c50), c58), c60)).
% 0.20/0.64 fof(p36_11, negated_conjecture, ![X88]: p36(X88, X88)).
% 0.20/0.64 fof(p37_67, negated_conjecture, ![X98, X99, X100, X101]: (p37(f38(X98, X99), f38(X100, X101)) | (~p36(X98, X100) | ~p7(X99, X101)))).
% 0.20/0.64 fof(p45_27, negated_conjecture, p45(f20(c52, c50), c58)).
% 0.20/0.64 fof(p46_78, negated_conjecture, ![X137, X142, X136]: (p46(f23(c53, f35(X137, X142)), f5(c49, X136)) | ~p45(f20(c52, X136), X137))).
% 0.20/0.64 fof(p47_5, negated_conjecture, ![X143]: p47(X143, X143)).
% 0.20/0.64 fof(p48_57, negated_conjecture, ![X146, X147, X149, X148]: (p48(X146, X147) | (~p47(X149, X147) | (~p48(X148, X149) | ~p37(X148, X146))))).
% 0.20/0.64 fof(p48_81, negated_conjecture, ![X150, X151]: (p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60) | (~p45(f20(c52, c50), X151) | ~p46(f23(c53, X150), f5(c49, c50))))).
% 0.20/0.64 fof(p7_59, negated_conjecture, ![X166, X167]: p7(f8(f11(c54, f14(f17(c55, X166), f35(X167, X166))), X167), X167)).
% 0.20/0.64
% 0.20/0.64 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.64 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.64 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.64 fresh(y, y, x1...xn) = u
% 0.20/0.64 C => fresh(s, t, x1...xn) = v
% 0.20/0.64 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.64 variables of u and v.
% 0.20/0.64 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.64 input problem has no model of domain size 1).
% 0.20/0.64
% 0.20/0.64 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.64
% 0.20/0.64 Axiom 1 (p36_11): p36(X, X) = true.
% 0.20/0.64 Axiom 2 (p47_5): p47(X, X) = true.
% 0.20/0.64 Axiom 3 (p45_27): p45(f20(c52, c50), c58) = true.
% 0.20/0.64 Axiom 4 (p48_57): fresh99(X, X, Y, Z) = true.
% 0.20/0.64 Axiom 5 (p48_81): fresh93(X, X, Y, Z) = true.
% 0.20/0.64 Axiom 6 (p46_78): fresh20(X, X, Y, Z, W) = true.
% 0.20/0.64 Axiom 7 (p48_57): fresh17(X, X, Y, Z, W) = p48(Y, Z).
% 0.20/0.64 Axiom 8 (p48_57): fresh98(X, X, Y, Z, W, V) = fresh99(p47(W, Z), true, Y, Z).
% 0.20/0.64 Axiom 9 (p37_67): fresh35(X, X, Y, Z, W, V) = p37(f38(Y, Z), f38(W, V)).
% 0.20/0.64 Axiom 10 (p37_67): fresh34(X, X, Y, Z, W, V) = true.
% 0.20/0.64 Axiom 11 (p48_57): fresh98(p48(X, Y), true, Z, W, Y, X) = fresh17(p37(X, Z), true, Z, W, Y).
% 0.20/0.64 Axiom 12 (p48_81): fresh92(X, X, Y, Z) = fresh93(p45(f20(c52, c50), Z), true, Y, Z).
% 0.20/0.64 Axiom 13 (p37_67): fresh35(p36(X, Y), true, X, Z, Y, W) = fresh34(p7(Z, W), true, X, Z, Y, W).
% 0.20/0.64 Axiom 14 (p46_78): fresh20(p45(f20(c52, X), Y), true, Y, Z, X) = p46(f23(c53, f35(Y, Z)), f5(c49, X)).
% 0.20/0.64 Axiom 15 (p7_59): p7(f8(f11(c54, f14(f17(c55, X), f35(Y, X))), Y), Y) = true.
% 0.20/0.64 Axiom 16 (p48_81): fresh92(p46(f23(c53, X), f5(c49, c50)), true, X, Y) = p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X)), Y)), c60).
% 0.20/0.64
% 0.20/0.64 Goal 1 (not_p48_29): p48(f38(f40(c59, c50), c58), c60) = true.
% 0.20/0.64 Proof:
% 0.20/0.64 p48(f38(f40(c59, c50), c58), c60)
% 0.20/0.64 = { by axiom 7 (p48_57) R->L }
% 0.20/0.64 fresh17(true, true, f38(f40(c59, c50), c58), c60, c60)
% 0.20/0.64 = { by axiom 10 (p37_67) R->L }
% 0.20/0.64 fresh17(fresh34(true, true, f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58), f40(c59, c50), c58), true, f38(f40(c59, c50), c58), c60, c60)
% 0.20/0.64 = { by axiom 15 (p7_59) R->L }
% 0.20/0.64 fresh17(fresh34(p7(f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58), c58), true, f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58), f40(c59, c50), c58), true, f38(f40(c59, c50), c58), c60, c60)
% 0.20/0.64 = { by axiom 13 (p37_67) R->L }
% 0.20/0.64 fresh17(fresh35(p36(f40(c59, c50), f40(c59, c50)), true, f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58), f40(c59, c50), c58), true, f38(f40(c59, c50), c58), c60, c60)
% 0.20/0.64 = { by axiom 1 (p36_11) }
% 0.20/0.64 fresh17(fresh35(true, true, f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58), f40(c59, c50), c58), true, f38(f40(c59, c50), c58), c60, c60)
% 0.20/0.64 = { by axiom 9 (p37_67) }
% 0.20/0.64 fresh17(p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58)), true, f38(f40(c59, c50), c58), c60, c60)
% 0.20/0.64 = { by axiom 11 (p48_57) R->L }
% 0.20/0.64 fresh98(p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60), true, f38(f40(c59, c50), c58), c60, c60, f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)))
% 0.20/0.64 = { by axiom 16 (p48_81) R->L }
% 0.20/0.65 fresh98(fresh92(p46(f23(c53, f35(c58, c61)), f5(c49, c50)), true, f35(c58, c61), c58), true, f38(f40(c59, c50), c58), c60, c60, f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)))
% 0.20/0.65 = { by axiom 14 (p46_78) R->L }
% 0.20/0.65 fresh98(fresh92(fresh20(p45(f20(c52, c50), c58), true, c58, c61, c50), true, f35(c58, c61), c58), true, f38(f40(c59, c50), c58), c60, c60, f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)))
% 0.20/0.65 = { by axiom 3 (p45_27) }
% 0.20/0.65 fresh98(fresh92(fresh20(true, true, c58, c61, c50), true, f35(c58, c61), c58), true, f38(f40(c59, c50), c58), c60, c60, f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)))
% 0.20/0.65 = { by axiom 6 (p46_78) }
% 0.20/0.65 fresh98(fresh92(true, true, f35(c58, c61), c58), true, f38(f40(c59, c50), c58), c60, c60, f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)))
% 0.20/0.65 = { by axiom 12 (p48_81) }
% 0.20/0.65 fresh98(fresh93(p45(f20(c52, c50), c58), true, f35(c58, c61), c58), true, f38(f40(c59, c50), c58), c60, c60, f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)))
% 0.20/0.65 = { by axiom 3 (p45_27) }
% 0.20/0.65 fresh98(fresh93(true, true, f35(c58, c61), c58), true, f38(f40(c59, c50), c58), c60, c60, f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)))
% 0.20/0.65 = { by axiom 5 (p48_81) }
% 0.20/0.65 fresh98(true, true, f38(f40(c59, c50), c58), c60, c60, f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)))
% 0.20/0.65 = { by axiom 8 (p48_57) }
% 0.20/0.65 fresh99(p47(c60, c60), true, f38(f40(c59, c50), c58), c60)
% 0.20/0.65 = { by axiom 2 (p47_5) }
% 0.20/0.65 fresh99(true, true, f38(f40(c59, c50), c58), c60)
% 0.20/0.65 = { by axiom 4 (p48_57) }
% 0.20/0.65 true
% 0.20/0.65 % SZS output end Proof
% 0.20/0.65
% 0.20/0.65 RESULT: Unsatisfiable (the axioms are contradictory).
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