TSTP Solution File: LCL035-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL035-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n021.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 : Thu Aug 31 08:17:07 EDT 2023
% Result : Unsatisfiable 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL035-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.33 % Computer : n021.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Thu Aug 24 16:58:55 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.18/0.38 Command-line arguments: --no-flatten-goal
% 0.18/0.38
% 0.18/0.38 % SZS status Unsatisfiable
% 0.18/0.38
% 0.18/0.39 % SZS output start Proof
% 0.18/0.39 Take the following subset of the input axioms:
% 0.18/0.39 fof(c0_CAMerideth, axiom, ![X, Y, Z, U, V]: is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), U), V), implies(implies(V, X), implies(Z, X))))).
% 0.18/0.39 fof(condensed_detachment, axiom, ![X2, Y2]: (~is_a_theorem(implies(X2, Y2)) | (~is_a_theorem(X2) | is_a_theorem(Y2)))).
% 0.18/0.39 fof(prove_c0_4, negated_conjecture, ~is_a_theorem(implies(falsehood, a))).
% 0.18/0.39
% 0.18/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.18/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.18/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.18/0.39 fresh(y, y, x1...xn) = u
% 0.18/0.39 C => fresh(s, t, x1...xn) = v
% 0.18/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.18/0.39 variables of u and v.
% 0.18/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.18/0.39 input problem has no model of domain size 1).
% 0.18/0.39
% 0.18/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.18/0.39
% 0.18/0.39 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 0.18/0.39 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 0.18/0.39 Axiom 3 (condensed_detachment): fresh(is_a_theorem(implies(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 0.18/0.39 Axiom 4 (c0_CAMerideth): is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X)))) = true.
% 0.18/0.39
% 0.18/0.39 Lemma 5: fresh2(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V)), true, implies(implies(V, X), implies(Z, X))) = is_a_theorem(implies(implies(V, X), implies(Z, X))).
% 0.18/0.39 Proof:
% 0.18/0.39 fresh2(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V)), true, implies(implies(V, X), implies(Z, X)))
% 0.18/0.39 = { by axiom 3 (condensed_detachment) R->L }
% 0.18/0.39 fresh(is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X)))), true, implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X)))
% 0.18/0.39 = { by axiom 4 (c0_CAMerideth) }
% 0.18/0.39 fresh(true, true, implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X)))
% 0.18/0.39 = { by axiom 2 (condensed_detachment) }
% 0.18/0.39 is_a_theorem(implies(implies(V, X), implies(Z, X)))
% 0.18/0.39
% 0.18/0.39 Lemma 6: is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W)))) = true.
% 0.18/0.39 Proof:
% 0.18/0.39 is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))
% 0.18/0.39 = { by lemma 5 R->L }
% 0.18/0.39 fresh2(is_a_theorem(implies(implies(implies(implies(implies(Y, W), implies(Z, falsehood)), implies(V, falsehood)), X), implies(implies(X, Y), implies(Z, Y)))), true, implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))
% 0.18/0.39 = { by axiom 4 (c0_CAMerideth) }
% 0.18/0.39 fresh2(true, true, implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))
% 0.18/0.39 = { by axiom 1 (condensed_detachment) }
% 0.18/0.39 true
% 0.18/0.39
% 0.18/0.39 Goal 1 (prove_c0_4): is_a_theorem(implies(falsehood, a)) = true.
% 0.18/0.39 Proof:
% 0.18/0.39 is_a_theorem(implies(falsehood, a))
% 0.18/0.39 = { by axiom 2 (condensed_detachment) R->L }
% 0.18/0.39 fresh(true, true, implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))
% 0.18/0.39 = { by axiom 1 (condensed_detachment) R->L }
% 0.18/0.39 fresh(fresh2(true, true, implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))), true, implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))
% 0.18/0.39 = { by axiom 4 (c0_CAMerideth) R->L }
% 0.18/0.39 fresh(fresh2(is_a_theorem(implies(implies(implies(implies(implies(U, T), implies(S, falsehood)), X2), Y2), implies(implies(Y2, U), implies(S, U)))), true, implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))), true, implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))
% 0.18/0.39 = { by axiom 3 (condensed_detachment) R->L }
% 0.18/0.39 fresh(fresh(is_a_theorem(implies(implies(implies(implies(implies(implies(U, T), implies(S, falsehood)), X2), Y2), implies(implies(Y2, U), implies(S, U))), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a)))), true, implies(implies(implies(implies(implies(U, T), implies(S, falsehood)), X2), Y2), implies(implies(Y2, U), implies(S, U))), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))), true, implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))
% 0.18/0.39 = { by axiom 2 (condensed_detachment) R->L }
% 0.18/0.39 fresh(fresh(fresh(true, true, implies(implies(implies(implies(Z2, falsehood), implies(W2, falsehood)), implies(falsehood, a)), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))), implies(implies(implies(implies(implies(implies(U, T), implies(S, falsehood)), X2), Y2), implies(implies(Y2, U), implies(S, U))), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a)))), true, implies(implies(implies(implies(implies(U, T), implies(S, falsehood)), X2), Y2), implies(implies(Y2, U), implies(S, U))), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))), true, implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))
% 0.18/0.39 = { by axiom 1 (condensed_detachment) R->L }
% 0.18/0.39 fresh(fresh(fresh(fresh2(true, true, implies(implies(implies(implies(implies(Z2, falsehood), implies(W2, falsehood)), implies(falsehood, a)), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))), implies(implies(implies(implies(implies(implies(U, T), implies(S, falsehood)), X2), Y2), implies(implies(Y2, U), implies(S, U))), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))))), true, implies(implies(implies(implies(Z2, falsehood), implies(W2, falsehood)), implies(falsehood, a)), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))), implies(implies(implies(implies(implies(implies(U, T), implies(S, falsehood)), X2), Y2), implies(implies(Y2, U), implies(S, U))), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a)))), true, implies(implies(implies(implies(implies(U, T), implies(S, falsehood)), X2), Y2), implies(implies(Y2, U), implies(S, U))), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))), true, implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))
% 0.18/0.39 = { by lemma 6 R->L }
% 0.18/0.40 fresh(fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a)), falsehood), implies(implies(implies(implies(implies(implies(U, T), implies(S, falsehood)), X2), Y2), implies(implies(Y2, U), implies(S, U))), falsehood)), implies(falsehood, a)), implies(implies(implies(Z2, falsehood), implies(W2, falsehood)), implies(falsehood, a)))), true, implies(implies(implies(implies(implies(Z2, falsehood), implies(W2, falsehood)), implies(falsehood, a)), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))), implies(implies(implies(implies(implies(implies(U, T), implies(S, falsehood)), X2), Y2), implies(implies(Y2, U), implies(S, U))), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))))), true, implies(implies(implies(implies(Z2, falsehood), implies(W2, falsehood)), implies(falsehood, a)), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))), implies(implies(implies(implies(implies(implies(U, T), implies(S, falsehood)), X2), Y2), implies(implies(Y2, U), implies(S, U))), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a)))), true, implies(implies(implies(implies(implies(U, T), implies(S, falsehood)), X2), Y2), implies(implies(Y2, U), implies(S, U))), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))), true, implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))
% 0.18/0.40 = { by lemma 5 }
% 0.18/0.40 fresh(fresh(fresh(is_a_theorem(implies(implies(implies(implies(implies(Z2, falsehood), implies(W2, falsehood)), implies(falsehood, a)), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))), implies(implies(implies(implies(implies(implies(U, T), implies(S, falsehood)), X2), Y2), implies(implies(Y2, U), implies(S, U))), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))))), true, implies(implies(implies(implies(Z2, falsehood), implies(W2, falsehood)), implies(falsehood, a)), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))), implies(implies(implies(implies(implies(implies(U, T), implies(S, falsehood)), X2), Y2), implies(implies(Y2, U), implies(S, U))), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a)))), true, implies(implies(implies(implies(implies(U, T), implies(S, falsehood)), X2), Y2), implies(implies(Y2, U), implies(S, U))), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))), true, implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))
% 0.18/0.40 = { by axiom 3 (condensed_detachment) }
% 0.18/0.40 fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(Z2, falsehood), implies(W2, falsehood)), implies(falsehood, a)), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a)))), true, implies(implies(implies(implies(implies(implies(U, T), implies(S, falsehood)), X2), Y2), implies(implies(Y2, U), implies(S, U))), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a)))), true, implies(implies(implies(implies(implies(U, T), implies(S, falsehood)), X2), Y2), implies(implies(Y2, U), implies(S, U))), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))), true, implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))
% 0.18/0.40 = { by lemma 6 }
% 0.18/0.40 fresh(fresh(fresh2(true, true, implies(implies(implies(implies(implies(implies(U, T), implies(S, falsehood)), X2), Y2), implies(implies(Y2, U), implies(S, U))), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a)))), true, implies(implies(implies(implies(implies(U, T), implies(S, falsehood)), X2), Y2), implies(implies(Y2, U), implies(S, U))), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))), true, implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))
% 0.18/0.40 = { by axiom 1 (condensed_detachment) }
% 0.18/0.40 fresh(fresh(true, true, implies(implies(implies(implies(implies(U, T), implies(S, falsehood)), X2), Y2), implies(implies(Y2, U), implies(S, U))), implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))), true, implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))
% 0.18/0.40 = { by axiom 2 (condensed_detachment) }
% 0.18/0.40 fresh(is_a_theorem(implies(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))), true, implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X))), implies(falsehood, a))
% 0.18/0.40 = { by axiom 3 (condensed_detachment) }
% 0.18/0.40 fresh2(is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), W), V), implies(implies(V, X), implies(Z, X)))), true, implies(falsehood, a))
% 0.18/0.40 = { by axiom 4 (c0_CAMerideth) }
% 0.18/0.40 fresh2(true, true, implies(falsehood, a))
% 0.18/0.40 = { by axiom 1 (condensed_detachment) }
% 0.18/0.40 true
% 0.18/0.40 % SZS output end Proof
% 0.18/0.40
% 0.18/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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