TSTP Solution File: SYN641-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN641-1 : 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 : n009.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 03:35:32 EDT 2023
% Result : Unsatisfiable 1.72s 0.58s
% Output : Proof 1.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN641-1 : TPTP v8.1.2. Released v2.5.0.
% 0.11/0.13 % 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 : n009.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 18:13:05 EDT 2023
% 0.13/0.34 % CPUTime :
% 1.72/0.58 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 1.72/0.58
% 1.72/0.58 % SZS status Unsatisfiable
% 1.72/0.58
% 1.72/0.59 % SZS output start Proof
% 1.72/0.59 Take the following subset of the input axioms:
% 1.72/0.59 fof(f3_is_p15_1, negated_conjecture, p15(f3(c19))).
% 1.72/0.59 fof(f3_is_p15_2, negated_conjecture, p15(f3(c18))).
% 1.72/0.59 fof(not_p6_28, negated_conjecture, ~p6(f7(f10(f3(c19), f3(c18))), f9(f7(c19), f7(c18)))).
% 1.72/0.59 fof(p6_12, negated_conjecture, p6(f7(f3(c18)), f7(c18))).
% 1.72/0.59 fof(p6_13, negated_conjecture, p6(f7(f3(c19)), f7(c19))).
% 1.72/0.59 fof(p6_23, negated_conjecture, ![X45, X46, X47]: (p6(X46, X47) | (~p6(X45, X46) | ~p6(X45, X47)))).
% 1.72/0.59 fof(p6_33, negated_conjecture, ![X52, X53, X54, X55]: (p6(f9(X52, X53), f9(X54, X55)) | (~p6(X53, X55) | ~p6(X52, X54)))).
% 1.72/0.59 fof(p6_38, negated_conjecture, ![X14, X15]: (p6(f7(f10(X14, X15)), f9(f7(X14), f7(X15))) | (~p15(X14) | ~p15(X15)))).
% 1.72/0.59 fof(p6_4, negated_conjecture, ![X45_2]: p6(X45_2, X45_2)).
% 1.72/0.59
% 1.72/0.59 Now clausify the problem and encode Horn clauses using encoding 3 of
% 1.72/0.59 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 1.72/0.59 We repeatedly replace C & s=t => u=v by the two clauses:
% 1.72/0.59 fresh(y, y, x1...xn) = u
% 1.72/0.59 C => fresh(s, t, x1...xn) = v
% 1.72/0.59 where fresh is a fresh function symbol and x1..xn are the free
% 1.72/0.59 variables of u and v.
% 1.72/0.59 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 1.72/0.59 input problem has no model of domain size 1).
% 1.72/0.59
% 1.72/0.59 The encoding turns the above axioms into the following unit equations and goals:
% 1.72/0.59
% 1.72/0.59 Axiom 1 (p6_4): p6(X, X) = true.
% 1.72/0.59 Axiom 2 (f3_is_p15_1): p15(f3(c19)) = true.
% 1.72/0.59 Axiom 3 (f3_is_p15_2): p15(f3(c18)) = true.
% 1.72/0.59 Axiom 4 (p6_38): fresh33(X, X, Y, Z) = true.
% 1.72/0.59 Axiom 5 (p6_23): fresh3(X, X, Y, Z) = true.
% 1.72/0.59 Axiom 6 (p6_13): p6(f7(f3(c19)), f7(c19)) = true.
% 1.72/0.59 Axiom 7 (p6_12): p6(f7(f3(c18)), f7(c18)) = true.
% 1.72/0.59 Axiom 8 (p6_38): fresh32(X, X, Y, Z) = fresh33(p15(Y), true, Y, Z).
% 1.72/0.59 Axiom 9 (p6_23): fresh4(X, X, Y, Z, W) = p6(Y, Z).
% 1.72/0.59 Axiom 10 (p6_33): fresh(X, X, Y, Z, W, V) = true.
% 1.72/0.59 Axiom 11 (p6_23): fresh4(p6(X, Y), true, Z, Y, X) = fresh3(p6(X, Z), true, Z, Y).
% 1.72/0.59 Axiom 12 (p6_33): fresh2(X, X, Y, Z, W, V) = p6(f9(Y, Z), f9(W, V)).
% 1.72/0.59 Axiom 13 (p6_38): fresh32(p15(X), true, Y, X) = p6(f7(f10(Y, X)), f9(f7(Y), f7(X))).
% 1.72/0.59 Axiom 14 (p6_33): fresh2(p6(X, Y), true, Z, X, W, Y) = fresh(p6(Z, W), true, Z, X, W, Y).
% 1.72/0.59
% 1.72/0.59 Goal 1 (not_p6_28): p6(f7(f10(f3(c19), f3(c18))), f9(f7(c19), f7(c18))) = true.
% 1.72/0.59 Proof:
% 1.72/0.59 p6(f7(f10(f3(c19), f3(c18))), f9(f7(c19), f7(c18)))
% 1.72/0.59 = { by axiom 9 (p6_23) R->L }
% 1.72/0.59 fresh4(true, true, f7(f10(f3(c19), f3(c18))), f9(f7(c19), f7(c18)), f9(f7(f3(c19)), f7(f3(c18))))
% 1.72/0.59 = { by axiom 10 (p6_33) R->L }
% 1.72/0.59 fresh4(fresh(true, true, f7(f3(c19)), f7(f3(c18)), f7(c19), f7(c18)), true, f7(f10(f3(c19), f3(c18))), f9(f7(c19), f7(c18)), f9(f7(f3(c19)), f7(f3(c18))))
% 1.72/0.59 = { by axiom 6 (p6_13) R->L }
% 1.72/0.59 fresh4(fresh(p6(f7(f3(c19)), f7(c19)), true, f7(f3(c19)), f7(f3(c18)), f7(c19), f7(c18)), true, f7(f10(f3(c19), f3(c18))), f9(f7(c19), f7(c18)), f9(f7(f3(c19)), f7(f3(c18))))
% 1.72/0.59 = { by axiom 14 (p6_33) R->L }
% 1.72/0.59 fresh4(fresh2(p6(f7(f3(c18)), f7(c18)), true, f7(f3(c19)), f7(f3(c18)), f7(c19), f7(c18)), true, f7(f10(f3(c19), f3(c18))), f9(f7(c19), f7(c18)), f9(f7(f3(c19)), f7(f3(c18))))
% 1.72/0.59 = { by axiom 7 (p6_12) }
% 1.72/0.59 fresh4(fresh2(true, true, f7(f3(c19)), f7(f3(c18)), f7(c19), f7(c18)), true, f7(f10(f3(c19), f3(c18))), f9(f7(c19), f7(c18)), f9(f7(f3(c19)), f7(f3(c18))))
% 1.72/0.59 = { by axiom 12 (p6_33) }
% 1.72/0.59 fresh4(p6(f9(f7(f3(c19)), f7(f3(c18))), f9(f7(c19), f7(c18))), true, f7(f10(f3(c19), f3(c18))), f9(f7(c19), f7(c18)), f9(f7(f3(c19)), f7(f3(c18))))
% 1.72/0.59 = { by axiom 11 (p6_23) }
% 1.72/0.59 fresh3(p6(f9(f7(f3(c19)), f7(f3(c18))), f7(f10(f3(c19), f3(c18)))), true, f7(f10(f3(c19), f3(c18))), f9(f7(c19), f7(c18)))
% 1.72/0.59 = { by axiom 9 (p6_23) R->L }
% 1.72/0.59 fresh3(fresh4(true, true, f9(f7(f3(c19)), f7(f3(c18))), f7(f10(f3(c19), f3(c18))), f7(f10(f3(c19), f3(c18)))), true, f7(f10(f3(c19), f3(c18))), f9(f7(c19), f7(c18)))
% 1.72/0.59 = { by axiom 1 (p6_4) R->L }
% 1.72/0.59 fresh3(fresh4(p6(f7(f10(f3(c19), f3(c18))), f7(f10(f3(c19), f3(c18)))), true, f9(f7(f3(c19)), f7(f3(c18))), f7(f10(f3(c19), f3(c18))), f7(f10(f3(c19), f3(c18)))), true, f7(f10(f3(c19), f3(c18))), f9(f7(c19), f7(c18)))
% 1.72/0.59 = { by axiom 11 (p6_23) }
% 1.72/0.59 fresh3(fresh3(p6(f7(f10(f3(c19), f3(c18))), f9(f7(f3(c19)), f7(f3(c18)))), true, f9(f7(f3(c19)), f7(f3(c18))), f7(f10(f3(c19), f3(c18)))), true, f7(f10(f3(c19), f3(c18))), f9(f7(c19), f7(c18)))
% 1.72/0.59 = { by axiom 13 (p6_38) R->L }
% 1.72/0.59 fresh3(fresh3(fresh32(p15(f3(c18)), true, f3(c19), f3(c18)), true, f9(f7(f3(c19)), f7(f3(c18))), f7(f10(f3(c19), f3(c18)))), true, f7(f10(f3(c19), f3(c18))), f9(f7(c19), f7(c18)))
% 1.72/0.59 = { by axiom 3 (f3_is_p15_2) }
% 1.72/0.59 fresh3(fresh3(fresh32(true, true, f3(c19), f3(c18)), true, f9(f7(f3(c19)), f7(f3(c18))), f7(f10(f3(c19), f3(c18)))), true, f7(f10(f3(c19), f3(c18))), f9(f7(c19), f7(c18)))
% 1.72/0.59 = { by axiom 8 (p6_38) }
% 1.72/0.59 fresh3(fresh3(fresh33(p15(f3(c19)), true, f3(c19), f3(c18)), true, f9(f7(f3(c19)), f7(f3(c18))), f7(f10(f3(c19), f3(c18)))), true, f7(f10(f3(c19), f3(c18))), f9(f7(c19), f7(c18)))
% 1.72/0.59 = { by axiom 2 (f3_is_p15_1) }
% 1.72/0.59 fresh3(fresh3(fresh33(true, true, f3(c19), f3(c18)), true, f9(f7(f3(c19)), f7(f3(c18))), f7(f10(f3(c19), f3(c18)))), true, f7(f10(f3(c19), f3(c18))), f9(f7(c19), f7(c18)))
% 1.72/0.59 = { by axiom 4 (p6_38) }
% 1.72/0.59 fresh3(fresh3(true, true, f9(f7(f3(c19)), f7(f3(c18))), f7(f10(f3(c19), f3(c18)))), true, f7(f10(f3(c19), f3(c18))), f9(f7(c19), f7(c18)))
% 1.72/0.59 = { by axiom 5 (p6_23) }
% 1.72/0.59 fresh3(true, true, f7(f10(f3(c19), f3(c18))), f9(f7(c19), f7(c18)))
% 1.72/0.59 = { by axiom 5 (p6_23) }
% 1.72/0.59 true
% 1.72/0.59 % SZS output end Proof
% 1.72/0.59
% 1.72/0.59 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------