TSTP Solution File: SYN624-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN624-1 : 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 : n008.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 03:35:29 EDT 2023
% Result : Unsatisfiable 0.21s 0.58s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN624-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 21:35:32 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.58
% 0.21/0.58 % SZS status Unsatisfiable
% 0.21/0.58
% 0.21/0.58 % SZS output start Proof
% 0.21/0.58 Take the following subset of the input axioms:
% 0.21/0.58 fof(not_p10_28, negated_conjecture, ~p10(f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25)))))).
% 0.21/0.58 fof(p10_1, negated_conjecture, ![X0]: p10(X0, X0)).
% 0.21/0.58 fof(p10_11, negated_conjecture, ![X16]: p10(f16(X16, f14(f15(f7(c25)))), X16)).
% 0.21/0.58 fof(p10_21, negated_conjecture, ![X1, X2, X0_2]: (p10(X1, X2) | (~p10(X0_2, X1) | ~p10(X0_2, X2)))).
% 0.21/0.58 fof(p10_26, negated_conjecture, ![X9]: p10(f13(f6(c22), X9), f13(f6(c24), f16(c26, X9)))).
% 0.21/0.58 fof(p10_32, negated_conjecture, ![X3, X4, X5, X6]: (p10(f13(X3, X4), f13(X5, X6)) | (~p10(X4, X6) | ~p5(X3, X5)))).
% 0.21/0.58 fof(p5_2, negated_conjecture, ![X57]: p5(X57, X57)).
% 0.21/0.58
% 0.21/0.58 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.58 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.58 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.58 fresh(y, y, x1...xn) = u
% 0.21/0.58 C => fresh(s, t, x1...xn) = v
% 0.21/0.58 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.58 variables of u and v.
% 0.21/0.58 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.58 input problem has no model of domain size 1).
% 0.21/0.58
% 0.21/0.58 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.58
% 0.21/0.58 Axiom 1 (p10_1): p10(X, X) = true.
% 0.21/0.58 Axiom 2 (p5_2): p5(X, X) = true.
% 0.21/0.58 Axiom 3 (p10_21): fresh27(X, X, Y, Z) = true.
% 0.21/0.58 Axiom 4 (p10_21): fresh29(X, X, Y, Z, W) = p10(Y, Z).
% 0.21/0.58 Axiom 5 (p10_32): fresh26(X, X, Y, Z, W, V) = p10(f13(Y, Z), f13(W, V)).
% 0.21/0.58 Axiom 6 (p10_32): fresh25(X, X, Y, Z, W, V) = true.
% 0.21/0.58 Axiom 7 (p10_11): p10(f16(X, f14(f15(f7(c25)))), X) = true.
% 0.21/0.58 Axiom 8 (p10_21): fresh29(p10(X, Y), true, Z, Y, X) = fresh27(p10(X, Z), true, Z, Y).
% 0.21/0.58 Axiom 9 (p10_32): fresh26(p5(X, Y), true, X, Z, Y, W) = fresh25(p10(Z, W), true, X, Z, Y, W).
% 0.21/0.58 Axiom 10 (p10_26): p10(f13(f6(c22), X), f13(f6(c24), f16(c26, X))) = true.
% 0.21/0.58
% 0.21/0.58 Goal 1 (not_p10_28): p10(f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25))))) = true.
% 0.21/0.58 Proof:
% 0.21/0.58 p10(f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25)))))
% 0.21/0.58 = { by axiom 4 (p10_21) R->L }
% 0.21/0.58 fresh29(true, true, f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25))))))
% 0.21/0.58 = { by axiom 3 (p10_21) R->L }
% 0.21/0.58 fresh29(fresh27(true, true, f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25))))), true, f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25))))))
% 0.21/0.58 = { by axiom 10 (p10_26) R->L }
% 0.21/0.58 fresh29(fresh27(p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), true, f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25))))), true, f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25))))))
% 0.21/0.58 = { by axiom 8 (p10_21) R->L }
% 0.21/0.59 fresh29(fresh29(p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25))))), true, f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25))))), true, f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25))))))
% 0.21/0.59 = { by axiom 1 (p10_1) }
% 0.21/0.59 fresh29(fresh29(true, true, f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25))))), true, f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25))))))
% 0.21/0.59 = { by axiom 4 (p10_21) }
% 0.21/0.59 fresh29(p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25))))), true, f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25))))))
% 0.21/0.59 = { by axiom 8 (p10_21) }
% 0.21/0.59 fresh27(p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c24), c26)), true, f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25)))))
% 0.21/0.59 = { by axiom 5 (p10_32) R->L }
% 0.21/0.59 fresh27(fresh26(true, true, f6(c24), f16(c26, f14(f15(f7(c25)))), f6(c24), c26), true, f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25)))))
% 0.21/0.59 = { by axiom 2 (p5_2) R->L }
% 0.21/0.59 fresh27(fresh26(p5(f6(c24), f6(c24)), true, f6(c24), f16(c26, f14(f15(f7(c25)))), f6(c24), c26), true, f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25)))))
% 0.21/0.59 = { by axiom 9 (p10_32) }
% 0.21/0.59 fresh27(fresh25(p10(f16(c26, f14(f15(f7(c25)))), c26), true, f6(c24), f16(c26, f14(f15(f7(c25)))), f6(c24), c26), true, f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25)))))
% 0.21/0.59 = { by axiom 7 (p10_11) }
% 0.21/0.59 fresh27(fresh25(true, true, f6(c24), f16(c26, f14(f15(f7(c25)))), f6(c24), c26), true, f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25)))))
% 0.21/0.59 = { by axiom 6 (p10_32) }
% 0.21/0.59 fresh27(true, true, f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25)))))
% 0.21/0.59 = { by axiom 3 (p10_21) }
% 0.21/0.59 true
% 0.21/0.59 % SZS output end Proof
% 0.21/0.59
% 0.21/0.59 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------