TSTP Solution File: SYO633-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYO633-1 : TPTP v8.1.2. Released v7.1.0.
% 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 : n023.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 04:58:44 EDT 2023
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYO633-1 : TPTP v8.1.2. Released v7.1.0.
% 0.10/0.13 % 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 : n023.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 23:11:56 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.42 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.42
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 Take the following subset of the input axioms:
% 0.20/0.46 fof(clause_12_09, axiom, ![A_0, B_0, A_1, K, A_2]: (~'E'(f(A_0), s(s(s(s('0'))))) | (~'E'(f(B_0), s(s(s(s(s('0')))))) | (~'E'(f(A_1), s(s(s('0')))) | (~'E'(f(A_2), s(s('0'))) | 'E'(f('AP'(s(s(s(s(s(s('0')))))), K)), s('0'))))))).
% 0.20/0.46 fof(clause_1_10, axiom, ![B_0_2, A_0_2]: (~'E'(f(A_0_2), s(s(s(s('0'))))) | (~'E'(f(B_0_2), s(s(s(s(s('0')))))) | 'E'(f(B_0_2), s(s(s('0'))))))).
% 0.20/0.46 fof(clause_2_07, axiom, ![A_3, B_0_2, A_0_2, A_1_2, A_2_2, K2]: (~'E'(f(A_2_2), s(s('0'))) | (~'E'(f(A_0_2), s(s(s(s('0'))))) | (~'E'(f(A_1_2), s(s(s('0')))) | (~'E'(f(A_3), s('0')) | (~'E'(f(B_0_2), s(s(s(s(s('0')))))) | 'E'(f('AP'(s(s(s(s(s(s('0')))))), K2)), '0'))))))).
% 0.20/0.46 fof(clause_4_12, axiom, ![B_0_2, A_0_2, A_1_2, K2]: (~'E'(f(A_0_2), s(s(s(s('0'))))) | (~'E'(f(B_0_2), s(s(s(s(s('0')))))) | (~'E'(f(A_1_2), s(s(s('0')))) | 'E'(f('AP'(s(s(s(s(s(s('0')))))), K2)), s(s('0'))))))).
% 0.20/0.46 fof(clause_5_03, axiom, ![A_4, B_0_2, A_0_2, A_1_2, A_2_2, A_3_2]: (~'E'(f(A_2_2), s(s('0'))) | (~'E'(f(A_0_2), s(s(s(s('0'))))) | (~'E'(f(A_1_2), s(s(s('0')))) | (~'E'(f(A_3_2), s('0')) | (~'E'(f(A_4), '0') | ~'E'(f(B_0_2), s(s(s(s(s('0')))))))))))).
% 0.20/0.46 fof(clause_6_04, axiom, ![B_0_2]: 'E'(f(B_0_2), s(s(s(s('0')))))).
% 0.20/0.46 fof(clause_8_05, axiom, ![B]: 'E'(f(B), s(s(s(s(s('0'))))))).
% 0.20/0.46
% 0.20/0.46 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.46 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.46 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.46 fresh(y, y, x1...xn) = u
% 0.20/0.46 C => fresh(s, t, x1...xn) = v
% 0.20/0.46 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.46 variables of u and v.
% 0.20/0.46 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.46 input problem has no model of domain size 1).
% 0.20/0.46
% 0.20/0.46 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.46
% 0.20/0.46 Axiom 1 (clause_2_07): fresh21(X, X, Y) = true2.
% 0.20/0.46 Axiom 2 (clause_12_09): fresh17(X, X, Y) = true2.
% 0.20/0.46 Axiom 3 (clause_4_12): fresh13(X, X, Y) = true2.
% 0.20/0.46 Axiom 4 (clause_1_10): fresh4(X, X, Y) = true2.
% 0.20/0.46 Axiom 5 (clause_1_10): fresh5(X, X, Y, Z) = E(f(Z), s(s(s(0)))).
% 0.20/0.46 Axiom 6 (clause_6_04): E(f(X), s(s(s(s(0))))) = true2.
% 0.20/0.46 Axiom 7 (clause_8_05): E(f(X), s(s(s(s(s(0)))))) = true2.
% 0.20/0.47 Axiom 8 (clause_2_07): fresh20(X, X, Y, Z) = fresh21(E(f(Y), s(s(0))), true2, Z).
% 0.20/0.47 Axiom 9 (clause_2_07): fresh18(X, X, Y, Z, W, V, U) = fresh19(E(f(V), s(0)), true2, Y, Z, W, U).
% 0.20/0.47 Axiom 10 (clause_12_09): fresh16(X, X, Y, Z) = fresh17(E(f(Y), s(s(s(s(0))))), true2, Z).
% 0.20/0.47 Axiom 11 (clause_4_12): fresh12(X, X, Y, Z) = fresh13(E(f(Y), s(s(s(s(0))))), true2, Z).
% 0.20/0.47 Axiom 12 (clause_2_07): fresh3(X, X, Y, Z, W) = E(f(AP(s(s(s(s(s(s(0)))))), W)), 0).
% 0.20/0.47 Axiom 13 (clause_2_07): fresh19(X, X, Y, Z, W, V) = fresh20(E(f(Z), s(s(s(s(0))))), true2, Y, V).
% 0.20/0.47 Axiom 14 (clause_12_09): fresh14(X, X, Y, Z, W, V) = fresh15(E(f(W), s(s(s(0)))), true2, Y, Z, V).
% 0.20/0.47 Axiom 15 (clause_12_09): fresh15(X, X, Y, Z, W) = E(f(AP(s(s(s(s(s(s(0)))))), W)), s(0)).
% 0.20/0.47 Axiom 16 (clause_12_09): fresh14(E(f(X), s(s(0))), true2, Y, Z, W, V) = fresh16(E(f(Z), s(s(s(s(s(0)))))), true2, Y, V).
% 0.20/0.47 Axiom 17 (clause_4_12): fresh11(X, X, Y, Z, W) = fresh12(E(f(Z), s(s(s(s(s(0)))))), true2, Y, W).
% 0.20/0.47 Axiom 18 (clause_1_10): fresh5(E(f(X), s(s(s(s(s(0)))))), true2, Y, X) = fresh4(E(f(Y), s(s(s(s(0))))), true2, X).
% 0.20/0.47 Axiom 19 (clause_4_12): fresh11(E(f(X), s(s(s(0)))), true2, Y, Z, W) = E(f(AP(s(s(s(s(s(s(0)))))), W)), s(s(0))).
% 0.20/0.47 Axiom 20 (clause_2_07): fresh18(E(f(X), s(s(s(s(s(0)))))), true2, Y, Z, W, V, U) = fresh3(E(f(W), s(s(s(0)))), true2, Y, Z, U).
% 0.20/0.47
% 0.20/0.47 Lemma 21: E(f(X), s(s(s(0)))) = true2.
% 0.20/0.47 Proof:
% 0.20/0.47 E(f(X), s(s(s(0))))
% 0.20/0.47 = { by axiom 5 (clause_1_10) R->L }
% 0.20/0.47 fresh5(true2, true2, Y, X)
% 0.20/0.47 = { by axiom 7 (clause_8_05) R->L }
% 0.20/0.47 fresh5(E(f(X), s(s(s(s(s(0)))))), true2, Y, X)
% 0.20/0.47 = { by axiom 18 (clause_1_10) }
% 0.20/0.47 fresh4(E(f(Y), s(s(s(s(0))))), true2, X)
% 0.20/0.47 = { by axiom 6 (clause_6_04) }
% 0.20/0.47 fresh4(true2, true2, X)
% 0.20/0.47 = { by axiom 4 (clause_1_10) }
% 0.20/0.47 true2
% 0.20/0.47
% 0.20/0.47 Lemma 22: E(f(AP(s(s(s(s(s(s(0)))))), X)), s(s(0))) = true2.
% 0.20/0.47 Proof:
% 0.20/0.47 E(f(AP(s(s(s(s(s(s(0)))))), X)), s(s(0)))
% 0.20/0.47 = { by axiom 19 (clause_4_12) R->L }
% 0.20/0.47 fresh11(E(f(Y), s(s(s(0)))), true2, Z, W, X)
% 0.20/0.47 = { by lemma 21 }
% 0.20/0.47 fresh11(true2, true2, Z, W, X)
% 0.20/0.47 = { by axiom 17 (clause_4_12) }
% 0.20/0.47 fresh12(E(f(W), s(s(s(s(s(0)))))), true2, Z, X)
% 0.20/0.47 = { by axiom 7 (clause_8_05) }
% 0.20/0.47 fresh12(true2, true2, Z, X)
% 0.20/0.47 = { by axiom 11 (clause_4_12) }
% 0.20/0.47 fresh13(E(f(Z), s(s(s(s(0))))), true2, X)
% 0.20/0.47 = { by axiom 6 (clause_6_04) }
% 0.20/0.47 fresh13(true2, true2, X)
% 0.20/0.47 = { by axiom 3 (clause_4_12) }
% 0.20/0.47 true2
% 0.20/0.47
% 0.20/0.47 Lemma 23: fresh15(X, X, Y, Z, W) = true2.
% 0.20/0.47 Proof:
% 0.20/0.47 fresh15(X, X, Y, Z, W)
% 0.20/0.47 = { by axiom 15 (clause_12_09) }
% 0.20/0.47 E(f(AP(s(s(s(s(s(s(0)))))), W)), s(0))
% 0.20/0.47 = { by axiom 15 (clause_12_09) R->L }
% 0.20/0.47 fresh15(true2, true2, V, U, W)
% 0.20/0.47 = { by lemma 21 R->L }
% 0.20/0.47 fresh15(E(f(T), s(s(s(0)))), true2, V, U, W)
% 0.20/0.47 = { by axiom 14 (clause_12_09) R->L }
% 0.20/0.47 fresh14(true2, true2, V, U, T, W)
% 0.20/0.47 = { by lemma 22 R->L }
% 0.20/0.47 fresh14(E(f(AP(s(s(s(s(s(s(0)))))), S)), s(s(0))), true2, V, U, T, W)
% 0.20/0.47 = { by axiom 16 (clause_12_09) }
% 0.20/0.47 fresh16(E(f(U), s(s(s(s(s(0)))))), true2, V, W)
% 0.20/0.47 = { by axiom 7 (clause_8_05) }
% 0.20/0.47 fresh16(true2, true2, V, W)
% 0.20/0.47 = { by axiom 10 (clause_12_09) }
% 0.20/0.47 fresh17(E(f(V), s(s(s(s(0))))), true2, W)
% 0.20/0.47 = { by axiom 6 (clause_6_04) }
% 0.20/0.47 fresh17(true2, true2, W)
% 0.20/0.47 = { by axiom 2 (clause_12_09) }
% 0.20/0.47 true2
% 0.20/0.47
% 0.20/0.47 Goal 1 (clause_5_03): tuple(E(f(X), s(s(0))), E(f(Y), s(s(s(s(0))))), E(f(Z), s(s(s(0)))), E(f(W), s(0)), E(f(V), 0), E(f(U), s(s(s(s(s(0))))))) = tuple(true2, true2, true2, true2, true2, true2).
% 0.20/0.47 The goal is true when:
% 0.20/0.47 X = AP(s(s(s(s(s(s(0)))))), U2)
% 0.20/0.47 Y = X3
% 0.20/0.47 Z = S2
% 0.20/0.47 W = AP(s(s(s(s(s(s(0)))))), W)
% 0.20/0.47 V = AP(s(s(s(s(s(s(0)))))), V)
% 0.20/0.47 U = T2
% 0.20/0.47
% 0.20/0.47 Proof:
% 0.20/0.47 tuple(E(f(AP(s(s(s(s(s(s(0)))))), U2)), s(s(0))), E(f(X3), s(s(s(s(0))))), E(f(S2), s(s(s(0)))), E(f(AP(s(s(s(s(s(s(0)))))), W)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), V)), 0), E(f(T2), s(s(s(s(s(0)))))))
% 0.20/0.47 = { by axiom 6 (clause_6_04) }
% 0.20/0.47 tuple(E(f(AP(s(s(s(s(s(s(0)))))), U2)), s(s(0))), true2, E(f(S2), s(s(s(0)))), E(f(AP(s(s(s(s(s(s(0)))))), W)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), V)), 0), E(f(T2), s(s(s(s(s(0)))))))
% 0.20/0.47 = { by lemma 21 }
% 0.20/0.47 tuple(E(f(AP(s(s(s(s(s(s(0)))))), U2)), s(s(0))), true2, true2, E(f(AP(s(s(s(s(s(s(0)))))), W)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), V)), 0), E(f(T2), s(s(s(s(s(0)))))))
% 0.20/0.47 = { by axiom 7 (clause_8_05) }
% 0.20/0.47 tuple(E(f(AP(s(s(s(s(s(s(0)))))), U2)), s(s(0))), true2, true2, E(f(AP(s(s(s(s(s(s(0)))))), W)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), V)), 0), true2)
% 0.20/0.47 = { by lemma 22 }
% 0.20/0.47 tuple(true2, true2, true2, E(f(AP(s(s(s(s(s(s(0)))))), W)), s(0)), E(f(AP(s(s(s(s(s(s(0)))))), V)), 0), true2)
% 0.20/0.47 = { by axiom 12 (clause_2_07) R->L }
% 0.20/0.47 tuple(true2, true2, true2, E(f(AP(s(s(s(s(s(s(0)))))), W)), s(0)), fresh3(true2, true2, AP(s(s(s(s(s(s(0)))))), U), T, V), true2)
% 0.20/0.47 = { by lemma 21 R->L }
% 0.20/0.47 tuple(true2, true2, true2, E(f(AP(s(s(s(s(s(s(0)))))), W)), s(0)), fresh3(E(f(S), s(s(s(0)))), true2, AP(s(s(s(s(s(s(0)))))), U), T, V), true2)
% 0.20/0.47 = { by axiom 20 (clause_2_07) R->L }
% 0.20/0.47 tuple(true2, true2, true2, E(f(AP(s(s(s(s(s(s(0)))))), W)), s(0)), fresh18(E(f(V2), s(s(s(s(s(0)))))), true2, AP(s(s(s(s(s(s(0)))))), U), T, S, AP(s(s(s(s(s(s(0)))))), W2), V), true2)
% 0.20/0.47 = { by axiom 7 (clause_8_05) }
% 0.20/0.47 tuple(true2, true2, true2, E(f(AP(s(s(s(s(s(s(0)))))), W)), s(0)), fresh18(true2, true2, AP(s(s(s(s(s(s(0)))))), U), T, S, AP(s(s(s(s(s(s(0)))))), W2), V), true2)
% 0.20/0.47 = { by axiom 9 (clause_2_07) }
% 0.20/0.47 tuple(true2, true2, true2, E(f(AP(s(s(s(s(s(s(0)))))), W)), s(0)), fresh19(E(f(AP(s(s(s(s(s(s(0)))))), W2)), s(0)), true2, AP(s(s(s(s(s(s(0)))))), U), T, S, V), true2)
% 0.20/0.47 = { by axiom 15 (clause_12_09) R->L }
% 0.20/0.47 tuple(true2, true2, true2, E(f(AP(s(s(s(s(s(s(0)))))), W)), s(0)), fresh19(fresh15(X2, X2, Y2, Z2, W2), true2, AP(s(s(s(s(s(s(0)))))), U), T, S, V), true2)
% 0.20/0.47 = { by lemma 23 }
% 0.20/0.47 tuple(true2, true2, true2, E(f(AP(s(s(s(s(s(s(0)))))), W)), s(0)), fresh19(true2, true2, AP(s(s(s(s(s(s(0)))))), U), T, S, V), true2)
% 0.20/0.47 = { by axiom 13 (clause_2_07) }
% 0.20/0.47 tuple(true2, true2, true2, E(f(AP(s(s(s(s(s(s(0)))))), W)), s(0)), fresh20(E(f(T), s(s(s(s(0))))), true2, AP(s(s(s(s(s(s(0)))))), U), V), true2)
% 0.20/0.47 = { by axiom 6 (clause_6_04) }
% 0.20/0.47 tuple(true2, true2, true2, E(f(AP(s(s(s(s(s(s(0)))))), W)), s(0)), fresh20(true2, true2, AP(s(s(s(s(s(s(0)))))), U), V), true2)
% 0.20/0.47 = { by axiom 8 (clause_2_07) }
% 0.20/0.47 tuple(true2, true2, true2, E(f(AP(s(s(s(s(s(s(0)))))), W)), s(0)), fresh21(E(f(AP(s(s(s(s(s(s(0)))))), U)), s(s(0))), true2, V), true2)
% 0.20/0.47 = { by lemma 22 }
% 0.20/0.47 tuple(true2, true2, true2, E(f(AP(s(s(s(s(s(s(0)))))), W)), s(0)), fresh21(true2, true2, V), true2)
% 0.20/0.47 = { by axiom 1 (clause_2_07) }
% 0.20/0.47 tuple(true2, true2, true2, E(f(AP(s(s(s(s(s(s(0)))))), W)), s(0)), true2, true2)
% 0.20/0.47 = { by axiom 15 (clause_12_09) R->L }
% 0.20/0.47 tuple(true2, true2, true2, fresh15(X, X, Y, Z, W), true2, true2)
% 0.20/0.47 = { by lemma 23 }
% 0.20/0.47 tuple(true2, true2, true2, true2, true2, true2)
% 0.20/0.47 % SZS output end Proof
% 0.20/0.47
% 0.20/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------