TSTP Solution File: SYN643-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN643-1 : 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 : n014.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 03:35:33 EDT 2023
% Result : Unsatisfiable 0.22s 0.56s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SYN643-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 20:08:02 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.56 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.22/0.56
% 0.22/0.56 % SZS status Unsatisfiable
% 0.22/0.56
% 0.22/0.57 % SZS output start Proof
% 0.22/0.57 Take the following subset of the input axioms:
% 0.22/0.57 fof(f3_is_p15_1, negated_conjecture, p15(f3(c19))).
% 0.22/0.57 fof(f3_is_p15_2, negated_conjecture, p15(f3(c18))).
% 0.22/0.57 fof(not_p4_28, negated_conjecture, ~p4(f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)))).
% 0.22/0.57 fof(p4_10, negated_conjecture, p4(f5(f3(c18)), f5(c18))).
% 0.22/0.57 fof(p4_11, negated_conjecture, p4(f5(f3(c19)), f5(c19))).
% 0.22/0.57 fof(p4_24, negated_conjecture, ![X36, X37, X38]: (p4(X37, X38) | (~p4(X36, X37) | ~p4(X36, X38)))).
% 0.22/0.57 fof(p4_35, negated_conjecture, ![X41, X42, X43, X44]: (p4(f9(X41, X42), f9(X43, X44)) | (~p4(X42, X44) | ~p4(X41, X43)))).
% 0.22/0.57 fof(p4_37, negated_conjecture, ![X14, X15]: (p4(f5(f10(X14, X15)), f9(f5(X14), f5(X15))) | (~p15(X14) | ~p15(X15)))).
% 0.22/0.57 fof(p4_5, negated_conjecture, ![X36_2]: p4(X36_2, X36_2)).
% 0.22/0.57
% 0.22/0.57 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.57 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.57 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.57 fresh(y, y, x1...xn) = u
% 0.22/0.57 C => fresh(s, t, x1...xn) = v
% 0.22/0.57 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.57 variables of u and v.
% 0.22/0.57 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.57 input problem has no model of domain size 1).
% 0.22/0.57
% 0.22/0.57 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.57
% 0.22/0.57 Axiom 1 (p4_5): p4(X, X) = true.
% 0.22/0.57 Axiom 2 (f3_is_p15_1): p15(f3(c19)) = true.
% 0.22/0.57 Axiom 3 (f3_is_p15_2): p15(f3(c18)) = true.
% 0.22/0.57 Axiom 4 (p4_37): fresh35(X, X, Y, Z) = true.
% 0.22/0.57 Axiom 5 (p4_24): fresh9(X, X, Y, Z) = true.
% 0.22/0.57 Axiom 6 (p4_11): p4(f5(f3(c19)), f5(c19)) = true.
% 0.22/0.57 Axiom 7 (p4_10): p4(f5(f3(c18)), f5(c18)) = true.
% 0.22/0.57 Axiom 8 (p4_37): fresh34(X, X, Y, Z) = fresh35(p15(Y), true, Y, Z).
% 0.22/0.57 Axiom 9 (p4_24): fresh10(X, X, Y, Z, W) = p4(Y, Z).
% 0.22/0.57 Axiom 10 (p4_24): fresh10(p4(X, Y), true, Z, Y, X) = fresh9(p4(X, Z), true, Z, Y).
% 0.22/0.57 Axiom 11 (p4_35): fresh8(X, X, Y, Z, W, V) = p4(f9(Y, Z), f9(W, V)).
% 0.22/0.57 Axiom 12 (p4_35): fresh7(X, X, Y, Z, W, V) = true.
% 0.22/0.57 Axiom 13 (p4_37): fresh34(p15(X), true, Y, X) = p4(f5(f10(Y, X)), f9(f5(Y), f5(X))).
% 0.22/0.57 Axiom 14 (p4_35): fresh8(p4(X, Y), true, Z, X, W, Y) = fresh7(p4(Z, W), true, Z, X, W, Y).
% 0.22/0.57
% 0.22/0.57 Goal 1 (not_p4_28): p4(f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18))) = true.
% 0.22/0.57 Proof:
% 0.22/0.57 p4(f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)))
% 0.22/0.57 = { by axiom 9 (p4_24) R->L }
% 0.22/0.57 fresh10(true, true, f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)), f9(f5(f3(c19)), f5(f3(c18))))
% 0.22/0.57 = { by axiom 12 (p4_35) R->L }
% 0.22/0.57 fresh10(fresh7(true, true, f5(f3(c19)), f5(f3(c18)), f5(c19), f5(c18)), true, f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)), f9(f5(f3(c19)), f5(f3(c18))))
% 0.22/0.57 = { by axiom 6 (p4_11) R->L }
% 0.22/0.57 fresh10(fresh7(p4(f5(f3(c19)), f5(c19)), true, f5(f3(c19)), f5(f3(c18)), f5(c19), f5(c18)), true, f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)), f9(f5(f3(c19)), f5(f3(c18))))
% 0.22/0.57 = { by axiom 14 (p4_35) R->L }
% 0.22/0.57 fresh10(fresh8(p4(f5(f3(c18)), f5(c18)), true, f5(f3(c19)), f5(f3(c18)), f5(c19), f5(c18)), true, f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)), f9(f5(f3(c19)), f5(f3(c18))))
% 0.22/0.57 = { by axiom 7 (p4_10) }
% 0.22/0.57 fresh10(fresh8(true, true, f5(f3(c19)), f5(f3(c18)), f5(c19), f5(c18)), true, f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)), f9(f5(f3(c19)), f5(f3(c18))))
% 0.22/0.57 = { by axiom 11 (p4_35) }
% 0.22/0.57 fresh10(p4(f9(f5(f3(c19)), f5(f3(c18))), f9(f5(c19), f5(c18))), true, f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)), f9(f5(f3(c19)), f5(f3(c18))))
% 0.22/0.57 = { by axiom 10 (p4_24) }
% 0.22/0.57 fresh9(p4(f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18)))), true, f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)))
% 0.22/0.57 = { by axiom 9 (p4_24) R->L }
% 0.22/0.57 fresh9(fresh10(true, true, f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18))), f5(f10(f3(c19), f3(c18)))), true, f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)))
% 0.22/0.57 = { by axiom 1 (p4_5) R->L }
% 0.22/0.57 fresh9(fresh10(p4(f5(f10(f3(c19), f3(c18))), f5(f10(f3(c19), f3(c18)))), true, f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18))), f5(f10(f3(c19), f3(c18)))), true, f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)))
% 0.22/0.57 = { by axiom 10 (p4_24) }
% 0.22/0.57 fresh9(fresh9(p4(f5(f10(f3(c19), f3(c18))), f9(f5(f3(c19)), f5(f3(c18)))), true, f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18)))), true, f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)))
% 0.22/0.57 = { by axiom 13 (p4_37) R->L }
% 0.22/0.57 fresh9(fresh9(fresh34(p15(f3(c18)), true, f3(c19), f3(c18)), true, f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18)))), true, f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)))
% 0.22/0.57 = { by axiom 3 (f3_is_p15_2) }
% 0.22/0.57 fresh9(fresh9(fresh34(true, true, f3(c19), f3(c18)), true, f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18)))), true, f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)))
% 0.22/0.57 = { by axiom 8 (p4_37) }
% 0.22/0.57 fresh9(fresh9(fresh35(p15(f3(c19)), true, f3(c19), f3(c18)), true, f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18)))), true, f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)))
% 0.22/0.57 = { by axiom 2 (f3_is_p15_1) }
% 0.22/0.57 fresh9(fresh9(fresh35(true, true, f3(c19), f3(c18)), true, f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18)))), true, f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)))
% 0.22/0.57 = { by axiom 4 (p4_37) }
% 0.22/0.57 fresh9(fresh9(true, true, f9(f5(f3(c19)), f5(f3(c18))), f5(f10(f3(c19), f3(c18)))), true, f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)))
% 0.22/0.57 = { by axiom 5 (p4_24) }
% 0.22/0.57 fresh9(true, true, f5(f10(f3(c19), f3(c18))), f9(f5(c19), f5(c18)))
% 0.22/0.57 = { by axiom 5 (p4_24) }
% 0.22/0.57 true
% 0.22/0.57 % SZS output end Proof
% 0.22/0.57
% 0.22/0.57 RESULT: Unsatisfiable (the axioms are contradictory).
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