TSTP Solution File: SYN565-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN565-1 : 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 115.52s 15.08s
% Output : Proof 115.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN565-1 : TPTP v8.1.2. Released v2.5.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n031.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 19:07:53 EDT 2023
% 0.14/0.34 % CPUTime :
% 115.52/15.08 Command-line arguments: --no-flatten-goal
% 115.52/15.08
% 115.52/15.08 % SZS status Unsatisfiable
% 115.52/15.08
% 115.52/15.09 % SZS output start Proof
% 115.52/15.09 Take the following subset of the input axioms:
% 115.52/15.09 fof(not_p10_11, negated_conjecture, ~p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11)))).
% 115.52/15.09 fof(p10_10, negated_conjecture, ![X7, X8]: p10(f5(X7), f3(f5(f6(X7, X8)), f5(X8)))).
% 115.52/15.09 fof(p10_13, negated_conjecture, ![X4, X5, X6]: (p10(f9(X4, X6), X5) | ~p10(X4, f3(X5, X6)))).
% 115.52/15.09 fof(p10_14, negated_conjecture, ![X0, X1, X2, X3]: (p10(X0, X1) | (~p2(X2, X0) | (~p2(X3, X1) | ~p10(X2, X3))))).
% 115.52/15.09 fof(p2_1, negated_conjecture, ![X9]: p2(X9, X9)).
% 115.52/15.09 fof(p2_17, negated_conjecture, ![X19, X20, X21, X22]: (p2(f9(X19, X20), f9(X21, X22)) | (~p2(X19, X21) | ~p2(X20, X22)))).
% 115.52/15.09 fof(p2_3, negated_conjecture, ![X18]: p2(f5(f7(X18)), f5(X18))).
% 115.52/15.09 fof(p2_6, negated_conjecture, ![X16, X17]: (p2(f5(X16), f5(X17)) | ~p4(X16, X17))).
% 115.52/15.09 fof(p2_8, negated_conjecture, ![X10, X11, X9_2]: (p2(X10, X11) | (~p2(X9_2, X10) | ~p2(X9_2, X11)))).
% 115.52/15.09 fof(p4_4, negated_conjecture, ![X38, X39]: p4(f8(X38, X39), f6(X38, f7(X39)))).
% 115.52/15.09 fof(p4_5, negated_conjecture, ![X32, X33]: p4(f7(f8(X32, X33)), f8(X33, X32))).
% 115.52/15.09 fof(p4_7, negated_conjecture, ![X30, X31]: (p4(f7(X30), f7(X31)) | ~p4(X30, X31))).
% 115.52/15.09 fof(p4_9, negated_conjecture, ![X23, X24, X25]: (p4(X24, X25) | (~p4(X23, X24) | ~p4(X23, X25)))).
% 115.52/15.09
% 115.52/15.09 Now clausify the problem and encode Horn clauses using encoding 3 of
% 115.52/15.09 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 115.52/15.09 We repeatedly replace C & s=t => u=v by the two clauses:
% 115.52/15.09 fresh(y, y, x1...xn) = u
% 115.52/15.09 C => fresh(s, t, x1...xn) = v
% 115.52/15.09 where fresh is a fresh function symbol and x1..xn are the free
% 115.52/15.09 variables of u and v.
% 115.52/15.09 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 115.52/15.09 input problem has no model of domain size 1).
% 115.52/15.09
% 115.52/15.09 The encoding turns the above axioms into the following unit equations and goals:
% 115.52/15.09
% 115.52/15.09 Axiom 1 (p2_1): p2(X, X) = true.
% 115.52/15.09 Axiom 2 (p4_9): fresh(X, X, Y, Z) = true.
% 115.52/15.09 Axiom 3 (p10_14): fresh19(X, X, Y, Z) = true.
% 115.52/15.09 Axiom 4 (p2_6): fresh10(X, X, Y, Z) = true.
% 115.52/15.09 Axiom 5 (p2_8): fresh8(X, X, Y, Z) = true.
% 115.52/15.09 Axiom 6 (p4_7): fresh3(X, X, Y, Z) = true.
% 115.52/15.09 Axiom 7 (p10_13): fresh17(X, X, Y, Z, W) = true.
% 115.52/15.09 Axiom 8 (p10_14): fresh15(X, X, Y, Z, W) = p10(Y, Z).
% 115.52/15.09 Axiom 9 (p2_8): fresh9(X, X, Y, Z, W) = p2(Y, Z).
% 115.52/15.09 Axiom 10 (p4_9): fresh2(X, X, Y, Z, W) = p4(Y, Z).
% 115.52/15.09 Axiom 11 (p2_3): p2(f5(f7(X)), f5(X)) = true.
% 115.52/15.09 Axiom 12 (p10_14): fresh18(X, X, Y, Z, W, V) = fresh19(p2(W, Y), true, Y, Z).
% 115.52/15.09 Axiom 13 (p2_17): fresh11(X, X, Y, Z, W, V) = true.
% 115.52/15.09 Axiom 14 (p2_6): fresh10(p4(X, Y), true, X, Y) = p2(f5(X), f5(Y)).
% 115.52/15.09 Axiom 15 (p4_7): fresh3(p4(X, Y), true, X, Y) = p4(f7(X), f7(Y)).
% 115.52/15.09 Axiom 16 (p2_17): fresh12(X, X, Y, Z, W, V) = p2(f9(Y, Z), f9(W, V)).
% 115.52/15.09 Axiom 17 (p2_8): fresh9(p2(X, Y), true, Z, Y, X) = fresh8(p2(X, Z), true, Z, Y).
% 115.52/15.09 Axiom 18 (p4_9): fresh2(p4(X, Y), true, Z, Y, X) = fresh(p4(X, Z), true, Z, Y).
% 115.52/15.09 Axiom 19 (p4_4): p4(f8(X, Y), f6(X, f7(Y))) = true.
% 115.52/15.09 Axiom 20 (p4_5): p4(f7(f8(X, Y)), f8(Y, X)) = true.
% 115.52/15.09 Axiom 21 (p10_14): fresh18(p10(X, Y), true, Z, W, X, Y) = fresh15(p2(Y, W), true, Z, W, X).
% 115.52/15.09 Axiom 22 (p2_17): fresh12(p2(X, Y), true, Z, X, W, Y) = fresh11(p2(Z, W), true, Z, X, W, Y).
% 115.52/15.09 Axiom 23 (p10_13): fresh17(p10(X, f3(Y, Z)), true, X, Z, Y) = p10(f9(X, Z), Y).
% 115.52/15.09 Axiom 24 (p10_10): p10(f5(X), f3(f5(f6(X, Y)), f5(Y))) = true.
% 115.52/15.09
% 115.52/15.09 Goal 1 (not_p10_11): p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11))) = true.
% 115.52/15.09 Proof:
% 115.52/15.09 p10(f9(f5(c11), f5(c12)), f5(f8(c12, c11)))
% 115.52/15.09 = { by axiom 8 (p10_14) R->L }
% 115.52/15.10 fresh15(true, true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)), f9(f5(c11), f5(f7(c12))))
% 115.52/15.10 = { by axiom 5 (p2_8) R->L }
% 115.52/15.10 fresh15(fresh8(true, true, f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)), f9(f5(c11), f5(f7(c12))))
% 115.52/15.10 = { by axiom 5 (p2_8) R->L }
% 115.52/15.10 fresh15(fresh8(fresh8(true, true, f5(f8(c12, c11)), f5(f6(c11, f7(c12)))), true, f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)), f9(f5(c11), f5(f7(c12))))
% 115.52/15.10 = { by axiom 4 (p2_6) R->L }
% 115.52/15.10 fresh15(fresh8(fresh8(fresh10(true, true, f7(f6(c11, f7(c12))), f8(c12, c11)), true, f5(f8(c12, c11)), f5(f6(c11, f7(c12)))), true, f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)), f9(f5(c11), f5(f7(c12))))
% 115.52/15.10 = { by axiom 2 (p4_9) R->L }
% 115.52/15.10 fresh15(fresh8(fresh8(fresh10(fresh(true, true, f7(f6(c11, f7(c12))), f8(c12, c11)), true, f7(f6(c11, f7(c12))), f8(c12, c11)), true, f5(f8(c12, c11)), f5(f6(c11, f7(c12)))), true, f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)), f9(f5(c11), f5(f7(c12))))
% 115.52/15.10 = { by axiom 6 (p4_7) R->L }
% 115.52/15.10 fresh15(fresh8(fresh8(fresh10(fresh(fresh3(true, true, f8(c11, c12), f6(c11, f7(c12))), true, f7(f6(c11, f7(c12))), f8(c12, c11)), true, f7(f6(c11, f7(c12))), f8(c12, c11)), true, f5(f8(c12, c11)), f5(f6(c11, f7(c12)))), true, f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)), f9(f5(c11), f5(f7(c12))))
% 115.52/15.10 = { by axiom 19 (p4_4) R->L }
% 115.52/15.10 fresh15(fresh8(fresh8(fresh10(fresh(fresh3(p4(f8(c11, c12), f6(c11, f7(c12))), true, f8(c11, c12), f6(c11, f7(c12))), true, f7(f6(c11, f7(c12))), f8(c12, c11)), true, f7(f6(c11, f7(c12))), f8(c12, c11)), true, f5(f8(c12, c11)), f5(f6(c11, f7(c12)))), true, f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)), f9(f5(c11), f5(f7(c12))))
% 115.52/15.10 = { by axiom 15 (p4_7) }
% 115.52/15.10 fresh15(fresh8(fresh8(fresh10(fresh(p4(f7(f8(c11, c12)), f7(f6(c11, f7(c12)))), true, f7(f6(c11, f7(c12))), f8(c12, c11)), true, f7(f6(c11, f7(c12))), f8(c12, c11)), true, f5(f8(c12, c11)), f5(f6(c11, f7(c12)))), true, f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)), f9(f5(c11), f5(f7(c12))))
% 115.52/15.10 = { by axiom 18 (p4_9) R->L }
% 115.52/15.10 fresh15(fresh8(fresh8(fresh10(fresh2(p4(f7(f8(c11, c12)), f8(c12, c11)), true, f7(f6(c11, f7(c12))), f8(c12, c11), f7(f8(c11, c12))), true, f7(f6(c11, f7(c12))), f8(c12, c11)), true, f5(f8(c12, c11)), f5(f6(c11, f7(c12)))), true, f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)), f9(f5(c11), f5(f7(c12))))
% 115.52/15.10 = { by axiom 20 (p4_5) }
% 115.52/15.10 fresh15(fresh8(fresh8(fresh10(fresh2(true, true, f7(f6(c11, f7(c12))), f8(c12, c11), f7(f8(c11, c12))), true, f7(f6(c11, f7(c12))), f8(c12, c11)), true, f5(f8(c12, c11)), f5(f6(c11, f7(c12)))), true, f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)), f9(f5(c11), f5(f7(c12))))
% 115.52/15.10 = { by axiom 10 (p4_9) }
% 115.52/15.10 fresh15(fresh8(fresh8(fresh10(p4(f7(f6(c11, f7(c12))), f8(c12, c11)), true, f7(f6(c11, f7(c12))), f8(c12, c11)), true, f5(f8(c12, c11)), f5(f6(c11, f7(c12)))), true, f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)), f9(f5(c11), f5(f7(c12))))
% 115.52/15.10 = { by axiom 14 (p2_6) }
% 115.52/15.10 fresh15(fresh8(fresh8(p2(f5(f7(f6(c11, f7(c12)))), f5(f8(c12, c11))), true, f5(f8(c12, c11)), f5(f6(c11, f7(c12)))), true, f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)), f9(f5(c11), f5(f7(c12))))
% 115.52/15.10 = { by axiom 17 (p2_8) R->L }
% 115.52/15.10 fresh15(fresh8(fresh9(p2(f5(f7(f6(c11, f7(c12)))), f5(f6(c11, f7(c12)))), true, f5(f8(c12, c11)), f5(f6(c11, f7(c12))), f5(f7(f6(c11, f7(c12))))), true, f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)), f9(f5(c11), f5(f7(c12))))
% 115.52/15.10 = { by axiom 11 (p2_3) }
% 115.52/15.10 fresh15(fresh8(fresh9(true, true, f5(f8(c12, c11)), f5(f6(c11, f7(c12))), f5(f7(f6(c11, f7(c12))))), true, f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)), f9(f5(c11), f5(f7(c12))))
% 115.52/15.10 = { by axiom 9 (p2_8) }
% 115.52/15.10 fresh15(fresh8(p2(f5(f8(c12, c11)), f5(f6(c11, f7(c12)))), true, f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)), f9(f5(c11), f5(f7(c12))))
% 115.52/15.10 = { by axiom 17 (p2_8) R->L }
% 115.52/15.10 fresh15(fresh9(p2(f5(f8(c12, c11)), f5(f8(c12, c11))), true, f5(f6(c11, f7(c12))), f5(f8(c12, c11)), f5(f8(c12, c11))), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)), f9(f5(c11), f5(f7(c12))))
% 115.52/15.10 = { by axiom 1 (p2_1) }
% 115.52/15.10 fresh15(fresh9(true, true, f5(f6(c11, f7(c12))), f5(f8(c12, c11)), f5(f8(c12, c11))), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)), f9(f5(c11), f5(f7(c12))))
% 115.52/15.10 = { by axiom 9 (p2_8) }
% 115.52/15.10 fresh15(p2(f5(f6(c11, f7(c12))), f5(f8(c12, c11))), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)), f9(f5(c11), f5(f7(c12))))
% 115.52/15.10 = { by axiom 21 (p10_14) R->L }
% 115.52/15.10 fresh18(p10(f9(f5(c11), f5(f7(c12))), f5(f6(c11, f7(c12)))), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)), f9(f5(c11), f5(f7(c12))), f5(f6(c11, f7(c12))))
% 115.52/15.10 = { by axiom 23 (p10_13) R->L }
% 115.52/15.10 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(c12, c11)), f9(f5(c11), f5(f7(c12))), f5(f6(c11, f7(c12))))
% 115.52/15.10 = { by axiom 24 (p10_10) }
% 115.52/15.10 fresh18(fresh17(true, true, f5(c11), f5(f7(c12)), f5(f6(c11, f7(c12)))), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)), f9(f5(c11), f5(f7(c12))), f5(f6(c11, f7(c12))))
% 115.52/15.10 = { by axiom 7 (p10_13) }
% 115.52/15.10 fresh18(true, true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)), f9(f5(c11), f5(f7(c12))), f5(f6(c11, f7(c12))))
% 115.52/15.10 = { by axiom 12 (p10_14) }
% 115.52/15.10 fresh19(p2(f9(f5(c11), f5(f7(c12))), f9(f5(c11), f5(c12))), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)))
% 115.52/15.10 = { by axiom 16 (p2_17) R->L }
% 115.52/15.10 fresh19(fresh12(true, true, f5(c11), f5(f7(c12)), f5(c11), f5(c12)), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)))
% 115.52/15.10 = { by axiom 11 (p2_3) R->L }
% 115.52/15.10 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(c12, c11)))
% 115.52/15.10 = { by axiom 22 (p2_17) }
% 115.52/15.10 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(c12, c11)))
% 115.52/15.10 = { by axiom 1 (p2_1) }
% 115.52/15.10 fresh19(fresh11(true, true, f5(c11), f5(f7(c12)), f5(c11), f5(c12)), true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)))
% 115.52/15.10 = { by axiom 13 (p2_17) }
% 115.52/15.10 fresh19(true, true, f9(f5(c11), f5(c12)), f5(f8(c12, c11)))
% 115.52/15.10 = { by axiom 3 (p10_14) }
% 115.52/15.10 true
% 115.52/15.10 % SZS output end Proof
% 115.52/15.10
% 115.52/15.10 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------