TSTP Solution File: SYN584-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN584-1 : 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 : n029.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 03:35:20 EDT 2023
% Result : Unsatisfiable 0.21s 0.46s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN584-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.14 % 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 : n029.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 18:12:55 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.46 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.46
% 0.21/0.46 % SZS status Unsatisfiable
% 0.21/0.46
% 0.21/0.47 % SZS output start Proof
% 0.21/0.47 Take the following subset of the input axioms:
% 0.21/0.47 fof(not_p15_25, negated_conjecture, ~p15(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))).
% 0.21/0.47 fof(p12_1, negated_conjecture, ![X0]: p12(X0, X0)).
% 0.21/0.47 fof(p12_23, negated_conjecture, p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), c22)).
% 0.21/0.47 fof(p12_9, negated_conjecture, ![X1, X2, X0_2]: (p12(X1, X2) | (~p12(X0_2, X1) | ~p12(X0_2, X2)))).
% 0.21/0.47 fof(p15_15, negated_conjecture, ![X11, X12, X13, X14]: (p15(X11, X12) | (~p15(X13, X14) | (~p3(X14, X12) | ~p12(X13, X11))))).
% 0.21/0.47 fof(p15_21, negated_conjecture, p15(c22, f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))).
% 0.21/0.47 fof(p3_4, negated_conjecture, ![X26]: p3(X26, X26)).
% 0.21/0.47
% 0.21/0.47 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.47 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.47 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.47 fresh(y, y, x1...xn) = u
% 0.21/0.47 C => fresh(s, t, x1...xn) = v
% 0.21/0.47 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.47 variables of u and v.
% 0.21/0.47 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.47 input problem has no model of domain size 1).
% 0.21/0.47
% 0.21/0.47 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.47
% 0.21/0.47 Axiom 1 (p12_1): p12(X, X) = true2.
% 0.21/0.47 Axiom 2 (p3_4): p3(X, X) = true2.
% 0.21/0.47 Axiom 3 (p15_15): fresh27(X, X, Y, Z) = true2.
% 0.21/0.47 Axiom 4 (p12_9): fresh20(X, X, Y, Z) = true2.
% 0.21/0.47 Axiom 5 (p12_9): fresh21(X, X, Y, Z, W) = p12(Y, Z).
% 0.21/0.47 Axiom 6 (p15_15): fresh19(X, X, Y, Z, W) = p15(Y, Z).
% 0.21/0.47 Axiom 7 (p15_15): fresh26(X, X, Y, Z, W, V) = fresh27(p12(W, Y), true2, Y, Z).
% 0.21/0.47 Axiom 8 (p12_9): fresh21(p12(X, Y), true2, Z, Y, X) = fresh20(p12(X, Z), true2, Z, Y).
% 0.21/0.47 Axiom 9 (p15_15): fresh26(p15(X, Y), true2, Z, W, X, Y) = fresh19(p3(Y, W), true2, Z, W, X).
% 0.21/0.47 Axiom 10 (p15_21): p15(c22, f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))) = true2.
% 0.21/0.47 Axiom 11 (p12_23): p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), c22) = true2.
% 0.21/0.47
% 0.21/0.47 Goal 1 (not_p15_25): p15(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))) = true2.
% 0.21/0.47 Proof:
% 0.21/0.47 p15(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))
% 0.21/0.47 = { by axiom 6 (p15_15) R->L }
% 0.21/0.47 fresh19(true2, true2, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))), c22)
% 0.21/0.47 = { by axiom 2 (p3_4) R->L }
% 0.21/0.47 fresh19(p3(f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))), true2, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))), c22)
% 0.21/0.47 = { by axiom 9 (p15_15) R->L }
% 0.21/0.47 fresh26(p15(c22, f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))))), true2, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))), c22, f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))
% 0.21/0.47 = { by axiom 10 (p15_21) }
% 0.21/0.47 fresh26(true2, true2, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))), c22, f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))
% 0.21/0.47 = { by axiom 7 (p15_15) }
% 0.21/0.47 fresh27(p12(c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))), true2, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))
% 0.21/0.47 = { by axiom 5 (p12_9) R->L }
% 0.21/0.47 fresh27(fresh21(true2, true2, c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))), true2, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))
% 0.21/0.47 = { by axiom 1 (p12_1) R->L }
% 0.21/0.47 fresh27(fresh21(p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))), true2, c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))), true2, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))
% 0.21/0.47 = { by axiom 8 (p12_9) }
% 0.21/0.47 fresh27(fresh20(p12(f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), c22), true2, c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))), true2, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))
% 0.21/0.47 = { by axiom 11 (p12_23) }
% 0.21/0.47 fresh27(fresh20(true2, true2, c22, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17))), true2, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))
% 0.21/0.47 = { by axiom 4 (p12_9) }
% 0.21/0.47 fresh27(true2, true2, f13(c17, f14(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20))))), c17)), f4(f7(c18, f8(f9(c19, f10(f11(c20))), f9(c21, f10(f11(c20)))))))
% 0.21/0.47 = { by axiom 3 (p15_15) }
% 0.21/0.47 true2
% 0.21/0.47 % SZS output end Proof
% 0.21/0.47
% 0.21/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
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