TSTP Solution File: SYN564-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN564-1 : 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 : n031.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 03:35:16 EDT 2023
% Result : Unsatisfiable 27.90s 3.96s
% Output : Proof 27.90s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN564-1 : 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 : n031.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 19:21:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 27.90/3.96 Command-line arguments: --no-flatten-goal
% 27.90/3.96
% 27.90/3.96 % SZS status Unsatisfiable
% 27.90/3.96
% 27.90/3.96 % SZS output start Proof
% 27.90/3.96 Take the following subset of the input axioms:
% 27.90/3.97 fof(not_p10_11, negated_conjecture, ~p10(f9(f5(c11), f5(c12)), f5(f8(c11, c12)))).
% 27.90/3.97 fof(p10_10, negated_conjecture, ![X7, X8]: p10(f5(X7), f3(f5(f6(X7, X8)), f5(X8)))).
% 27.90/3.97 fof(p10_13, negated_conjecture, ![X4, X5, X6]: (p10(f9(X4, X6), X5) | ~p10(X4, f3(X5, X6)))).
% 27.90/3.97 fof(p10_14, negated_conjecture, ![X0, X1, X2, X3]: (p10(X0, X1) | (~p2(X2, X0) | (~p2(X3, X1) | ~p10(X2, X3))))).
% 27.90/3.97 fof(p2_1, negated_conjecture, ![X9]: p2(X9, X9)).
% 27.90/3.97 fof(p2_17, negated_conjecture, ![X19, X20, X21, X22]: (p2(f9(X19, X20), f9(X21, X22)) | (~p2(X19, X21) | ~p2(X20, X22)))).
% 27.90/3.97 fof(p2_3, negated_conjecture, ![X18]: p2(f5(f7(X18)), f5(X18))).
% 27.90/3.97 fof(p2_6, negated_conjecture, ![X16, X17]: (p2(f5(X16), f5(X17)) | ~p4(X16, X17))).
% 27.90/3.97 fof(p2_8, negated_conjecture, ![X10, X11, X9_2]: (p2(X10, X11) | (~p2(X9_2, X10) | ~p2(X9_2, X11)))).
% 27.90/3.97 fof(p4_4, negated_conjecture, ![X38, X39]: p4(f8(X38, X39), f6(X38, f7(X39)))).
% 27.90/3.97
% 27.90/3.97 Now clausify the problem and encode Horn clauses using encoding 3 of
% 27.90/3.97 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 27.90/3.97 We repeatedly replace C & s=t => u=v by the two clauses:
% 27.90/3.97 fresh(y, y, x1...xn) = u
% 27.90/3.97 C => fresh(s, t, x1...xn) = v
% 27.90/3.97 where fresh is a fresh function symbol and x1..xn are the free
% 27.90/3.97 variables of u and v.
% 27.90/3.97 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 27.90/3.97 input problem has no model of domain size 1).
% 27.90/3.97
% 27.90/3.97 The encoding turns the above axioms into the following unit equations and goals:
% 27.90/3.97
% 27.90/3.97 Axiom 1 (p2_1): p2(X, X) = true.
% 27.90/3.97 Axiom 2 (p10_14): fresh19(X, X, Y, Z) = true.
% 27.90/3.97 Axiom 3 (p2_6): fresh10(X, X, Y, Z) = true.
% 27.90/3.97 Axiom 4 (p2_8): fresh8(X, X, Y, Z) = true.
% 27.90/3.97 Axiom 5 (p10_13): fresh17(X, X, Y, Z, W) = true.
% 27.90/3.97 Axiom 6 (p10_14): fresh15(X, X, Y, Z, W) = p10(Y, Z).
% 27.90/3.97 Axiom 7 (p2_8): fresh9(X, X, Y, Z, W) = p2(Y, Z).
% 27.90/3.97 Axiom 8 (p2_3): p2(f5(f7(X)), f5(X)) = true.
% 27.90/3.97 Axiom 9 (p10_14): fresh18(X, X, Y, Z, W, V) = fresh19(p2(W, Y), true, Y, Z).
% 27.90/3.97 Axiom 10 (p2_17): fresh11(X, X, Y, Z, W, V) = true.
% 27.90/3.97 Axiom 11 (p2_6): fresh10(p4(X, Y), true, X, Y) = p2(f5(X), f5(Y)).
% 27.90/3.97 Axiom 12 (p2_17): fresh12(X, X, Y, Z, W, V) = p2(f9(Y, Z), f9(W, V)).
% 27.90/3.97 Axiom 13 (p2_8): fresh9(p2(X, Y), true, Z, Y, X) = fresh8(p2(X, Z), true, Z, Y).
% 27.90/3.97 Axiom 14 (p4_4): p4(f8(X, Y), f6(X, f7(Y))) = true.
% 27.90/3.97 Axiom 15 (p10_14): fresh18(p10(X, Y), true, Z, W, X, Y) = fresh15(p2(Y, W), true, Z, W, X).
% 27.90/3.97 Axiom 16 (p2_17): fresh12(p2(X, Y), true, Z, X, W, Y) = fresh11(p2(Z, W), true, Z, X, W, Y).
% 27.90/3.97 Axiom 17 (p10_13): fresh17(p10(X, f3(Y, Z)), true, X, Z, Y) = p10(f9(X, Z), Y).
% 27.90/3.97 Axiom 18 (p10_10): p10(f5(X), f3(f5(f6(X, Y)), f5(Y))) = true.
% 27.90/3.97
% 27.90/3.97 Goal 1 (not_p10_11): p10(f9(f5(c11), f5(c12)), f5(f8(c11, c12))) = true.
% 27.90/3.97 Proof:
% 27.90/3.97 p10(f9(f5(c11), f5(c12)), f5(f8(c11, c12)))
% 27.90/3.97 = { by axiom 6 (p10_14) R->L }
% 27.90/3.97 fresh15(true, true, f9(f5(c11), f5(c12)), f5(f8(c11, c12)), f9(f5(c11), f5(f7(c12))))
% 27.90/3.97 = { by axiom 4 (p2_8) R->L }
% 27.90/3.97 fresh15(fresh8(true, true, f5(f6(c11, f7(c12))), f5(f8(c11, c12))), true, f9(f5(c11), f5(c12)), f5(f8(c11, c12)), f9(f5(c11), f5(f7(c12))))
% 27.90/3.97 = { by axiom 3 (p2_6) R->L }
% 27.90/3.97 fresh15(fresh8(fresh10(true, true, f8(c11, c12), f6(c11, f7(c12))), true, f5(f6(c11, f7(c12))), f5(f8(c11, c12))), true, f9(f5(c11), f5(c12)), f5(f8(c11, c12)), f9(f5(c11), f5(f7(c12))))
% 27.90/3.97 = { by axiom 14 (p4_4) R->L }
% 27.90/3.97 fresh15(fresh8(fresh10(p4(f8(c11, c12), f6(c11, f7(c12))), true, f8(c11, c12), f6(c11, f7(c12))), true, f5(f6(c11, f7(c12))), f5(f8(c11, c12))), true, f9(f5(c11), f5(c12)), f5(f8(c11, c12)), f9(f5(c11), f5(f7(c12))))
% 27.90/3.97 = { by axiom 11 (p2_6) }
% 27.90/3.97 fresh15(fresh8(p2(f5(f8(c11, c12)), f5(f6(c11, f7(c12)))), true, f5(f6(c11, f7(c12))), f5(f8(c11, c12))), true, f9(f5(c11), f5(c12)), f5(f8(c11, c12)), f9(f5(c11), f5(f7(c12))))
% 27.90/3.97 = { by axiom 13 (p2_8) R->L }
% 27.90/3.97 fresh15(fresh9(p2(f5(f8(c11, c12)), f5(f8(c11, c12))), true, f5(f6(c11, f7(c12))), f5(f8(c11, c12)), f5(f8(c11, c12))), true, f9(f5(c11), f5(c12)), f5(f8(c11, c12)), f9(f5(c11), f5(f7(c12))))
% 27.90/3.97 = { by axiom 1 (p2_1) }
% 27.90/3.97 fresh15(fresh9(true, true, f5(f6(c11, f7(c12))), f5(f8(c11, c12)), f5(f8(c11, c12))), true, f9(f5(c11), f5(c12)), f5(f8(c11, c12)), f9(f5(c11), f5(f7(c12))))
% 27.90/3.97 = { by axiom 7 (p2_8) }
% 27.90/3.97 fresh15(p2(f5(f6(c11, f7(c12))), f5(f8(c11, c12))), true, f9(f5(c11), f5(c12)), f5(f8(c11, c12)), f9(f5(c11), f5(f7(c12))))
% 27.90/3.97 = { by axiom 15 (p10_14) R->L }
% 27.90/3.97 fresh18(p10(f9(f5(c11), f5(f7(c12))), f5(f6(c11, f7(c12)))), true, f9(f5(c11), f5(c12)), f5(f8(c11, c12)), f9(f5(c11), f5(f7(c12))), f5(f6(c11, f7(c12))))
% 27.90/3.97 = { by axiom 17 (p10_13) R->L }
% 27.90/3.97 fresh18(fresh17(p10(f5(c11), f3(f5(f6(c11, f7(c12))), f5(f7(c12)))), true, f5(c11), f5(f7(c12)), f5(f6(c11, f7(c12)))), true, f9(f5(c11), f5(c12)), f5(f8(c11, c12)), f9(f5(c11), f5(f7(c12))), f5(f6(c11, f7(c12))))
% 27.90/3.97 = { by axiom 18 (p10_10) }
% 27.90/3.97 fresh18(fresh17(true, true, f5(c11), f5(f7(c12)), f5(f6(c11, f7(c12)))), true, f9(f5(c11), f5(c12)), f5(f8(c11, c12)), f9(f5(c11), f5(f7(c12))), f5(f6(c11, f7(c12))))
% 27.90/3.97 = { by axiom 5 (p10_13) }
% 27.90/3.97 fresh18(true, true, f9(f5(c11), f5(c12)), f5(f8(c11, c12)), f9(f5(c11), f5(f7(c12))), f5(f6(c11, f7(c12))))
% 27.90/3.97 = { by axiom 9 (p10_14) }
% 27.90/3.97 fresh19(p2(f9(f5(c11), f5(f7(c12))), f9(f5(c11), f5(c12))), true, f9(f5(c11), f5(c12)), f5(f8(c11, c12)))
% 27.90/3.97 = { by axiom 12 (p2_17) R->L }
% 27.90/3.97 fresh19(fresh12(true, true, f5(c11), f5(f7(c12)), f5(c11), f5(c12)), true, f9(f5(c11), f5(c12)), f5(f8(c11, c12)))
% 27.90/3.97 = { by axiom 8 (p2_3) R->L }
% 27.90/3.97 fresh19(fresh12(p2(f5(f7(c12)), f5(c12)), true, f5(c11), f5(f7(c12)), f5(c11), f5(c12)), true, f9(f5(c11), f5(c12)), f5(f8(c11, c12)))
% 27.90/3.97 = { by axiom 16 (p2_17) }
% 27.90/3.97 fresh19(fresh11(p2(f5(c11), f5(c11)), true, f5(c11), f5(f7(c12)), f5(c11), f5(c12)), true, f9(f5(c11), f5(c12)), f5(f8(c11, c12)))
% 27.90/3.97 = { by axiom 1 (p2_1) }
% 27.90/3.97 fresh19(fresh11(true, true, f5(c11), f5(f7(c12)), f5(c11), f5(c12)), true, f9(f5(c11), f5(c12)), f5(f8(c11, c12)))
% 27.90/3.97 = { by axiom 10 (p2_17) }
% 27.90/3.97 fresh19(true, true, f9(f5(c11), f5(c12)), f5(f8(c11, c12)))
% 27.90/3.97 = { by axiom 2 (p10_14) }
% 27.90/3.97 true
% 27.90/3.97 % SZS output end Proof
% 27.90/3.97
% 27.90/3.97 RESULT: Unsatisfiable (the axioms are contradictory).
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