TSTP Solution File: SYN553-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN553-1 : 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 03:35:13 EDT 2023
% Result : Unsatisfiable 3.45s 0.80s
% Output : Proof 3.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYN553-1 : TPTP v8.1.2. Released v2.5.0.
% 0.07/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 17:19:35 EDT 2023
% 0.12/0.33 % CPUTime :
% 3.45/0.80 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 3.45/0.80
% 3.45/0.80 % SZS status Unsatisfiable
% 3.45/0.80
% 3.45/0.80 % SZS output start Proof
% 3.45/0.80 Take the following subset of the input axioms:
% 3.45/0.80 fof(not_p2_9, negated_conjecture, ~p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4)))).
% 3.45/0.80 fof(p2_1, negated_conjecture, ![X0]: p2(X0, X0)).
% 3.45/0.80 fof(p2_5, negated_conjecture, ![X11, X12]: p2(f8(X11, X12), f8(X12, X11))).
% 3.45/0.80 fof(p2_6, negated_conjecture, ![X1, X2, X3]: (p2(X1, X2) | (~p2(X1, X3) | ~p2(X3, X2)))).
% 3.45/0.80 fof(p2_7, negated_conjecture, ![X8, X9, X10]: p2(f8(X8, f8(X9, X10)), f8(f8(X8, X9), X10))).
% 3.45/0.80 fof(p2_8, negated_conjecture, ![X4, X5, X6, X7]: (p2(f8(X4, X5), f8(X6, X7)) | (~p2(X4, X6) | ~p2(X5, X7)))).
% 3.45/0.80
% 3.45/0.80 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.45/0.80 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.45/0.80 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.45/0.80 fresh(y, y, x1...xn) = u
% 3.45/0.80 C => fresh(s, t, x1...xn) = v
% 3.45/0.80 where fresh is a fresh function symbol and x1..xn are the free
% 3.45/0.80 variables of u and v.
% 3.45/0.80 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.45/0.80 input problem has no model of domain size 1).
% 3.45/0.80
% 3.45/0.80 The encoding turns the above axioms into the following unit equations and goals:
% 3.45/0.80
% 3.45/0.80 Axiom 1 (p2_1): p2(X, X) = true.
% 3.45/0.80 Axiom 2 (p2_6): fresh4(X, X, Y, Z) = true.
% 3.45/0.80 Axiom 3 (p2_6): fresh3(X, X, Y, Z, W) = p2(Y, Z).
% 3.45/0.80 Axiom 4 (p2_5): p2(f8(X, Y), f8(Y, X)) = true.
% 3.45/0.80 Axiom 5 (p2_8): fresh(X, X, Y, Z, W, V) = true.
% 3.45/0.80 Axiom 6 (p2_8): fresh2(X, X, Y, Z, W, V) = p2(f8(Y, Z), f8(W, V)).
% 3.45/0.80 Axiom 7 (p2_6): fresh3(p2(X, Y), true, Z, Y, X) = fresh4(p2(Z, X), true, Z, Y).
% 3.45/0.80 Axiom 8 (p2_8): fresh2(p2(X, Y), true, Z, X, W, Y) = fresh(p2(Z, W), true, Z, X, W, Y).
% 3.45/0.80 Axiom 9 (p2_7): p2(f8(X, f8(Y, Z)), f8(f8(X, Y), Z)) = true.
% 3.45/0.80
% 3.45/0.80 Lemma 10: fresh4(p2(X, f8(Y, Z)), true, X, f8(Z, Y)) = p2(X, f8(Z, Y)).
% 3.45/0.80 Proof:
% 3.45/0.80 fresh4(p2(X, f8(Y, Z)), true, X, f8(Z, Y))
% 3.45/0.80 = { by axiom 7 (p2_6) R->L }
% 3.45/0.80 fresh3(p2(f8(Y, Z), f8(Z, Y)), true, X, f8(Z, Y), f8(Y, Z))
% 3.45/0.80 = { by axiom 4 (p2_5) }
% 3.45/0.80 fresh3(true, true, X, f8(Z, Y), f8(Y, Z))
% 3.45/0.80 = { by axiom 3 (p2_6) }
% 3.45/0.80 p2(X, f8(Z, Y))
% 3.45/0.80
% 3.45/0.80 Goal 1 (not_p2_9): p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4))) = true.
% 3.45/0.80 Proof:
% 3.45/0.80 p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4)))
% 3.45/0.81 = { by axiom 3 (p2_6) R->L }
% 3.45/0.81 fresh3(true, true, f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4)), f8(f9(c3), f8(c4, f9(c4))))
% 3.45/0.81 = { by axiom 2 (p2_6) R->L }
% 3.45/0.81 fresh3(fresh4(true, true, f8(f9(c3), f8(c4, f9(c4))), f8(f9(c4), f8(f9(c3), c4))), true, f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4)), f8(f9(c3), f8(c4, f9(c4))))
% 3.45/0.81 = { by axiom 9 (p2_7) R->L }
% 3.45/0.81 fresh3(fresh4(p2(f8(f9(c3), f8(c4, f9(c4))), f8(f8(f9(c3), c4), f9(c4))), true, f8(f9(c3), f8(c4, f9(c4))), f8(f9(c4), f8(f9(c3), c4))), true, f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4)), f8(f9(c3), f8(c4, f9(c4))))
% 3.45/0.81 = { by lemma 10 }
% 3.45/0.81 fresh3(p2(f8(f9(c3), f8(c4, f9(c4))), f8(f9(c4), f8(f9(c3), c4))), true, f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4)), f8(f9(c3), f8(c4, f9(c4))))
% 3.45/0.81 = { by axiom 7 (p2_6) }
% 3.45/0.81 fresh4(p2(f8(f8(f9(c4), c4), f9(c3)), f8(f9(c3), f8(c4, f9(c4)))), true, f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4)))
% 3.45/0.81 = { by lemma 10 R->L }
% 3.45/0.81 fresh4(fresh4(p2(f8(f8(f9(c4), c4), f9(c3)), f8(f8(c4, f9(c4)), f9(c3))), true, f8(f8(f9(c4), c4), f9(c3)), f8(f9(c3), f8(c4, f9(c4)))), true, f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4)))
% 3.45/0.81 = { by axiom 6 (p2_8) R->L }
% 3.45/0.81 fresh4(fresh4(fresh2(true, true, f8(f9(c4), c4), f9(c3), f8(c4, f9(c4)), f9(c3)), true, f8(f8(f9(c4), c4), f9(c3)), f8(f9(c3), f8(c4, f9(c4)))), true, f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4)))
% 3.45/0.81 = { by axiom 1 (p2_1) R->L }
% 3.45/0.81 fresh4(fresh4(fresh2(p2(f9(c3), f9(c3)), true, f8(f9(c4), c4), f9(c3), f8(c4, f9(c4)), f9(c3)), true, f8(f8(f9(c4), c4), f9(c3)), f8(f9(c3), f8(c4, f9(c4)))), true, f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4)))
% 3.45/0.81 = { by axiom 8 (p2_8) }
% 3.45/0.81 fresh4(fresh4(fresh(p2(f8(f9(c4), c4), f8(c4, f9(c4))), true, f8(f9(c4), c4), f9(c3), f8(c4, f9(c4)), f9(c3)), true, f8(f8(f9(c4), c4), f9(c3)), f8(f9(c3), f8(c4, f9(c4)))), true, f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4)))
% 3.45/0.81 = { by axiom 4 (p2_5) }
% 3.45/0.81 fresh4(fresh4(fresh(true, true, f8(f9(c4), c4), f9(c3), f8(c4, f9(c4)), f9(c3)), true, f8(f8(f9(c4), c4), f9(c3)), f8(f9(c3), f8(c4, f9(c4)))), true, f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4)))
% 3.45/0.81 = { by axiom 5 (p2_8) }
% 3.45/0.81 fresh4(fresh4(true, true, f8(f8(f9(c4), c4), f9(c3)), f8(f9(c3), f8(c4, f9(c4)))), true, f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4)))
% 3.45/0.81 = { by axiom 2 (p2_6) }
% 3.45/0.81 fresh4(true, true, f8(f8(f9(c4), c4), f9(c3)), f8(f9(c4), f8(f9(c3), c4)))
% 3.45/0.81 = { by axiom 2 (p2_6) }
% 3.45/0.81 true
% 3.45/0.81 % SZS output end Proof
% 3.45/0.81
% 3.45/0.81 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------