TSTP Solution File: LCL414-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LCL414-1 : 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 : 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 : Thu Aug 31 08:18:51 EDT 2023
% Result : Unsatisfiable 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL414-1 : 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
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 18:43:42 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.39 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.14/0.39
% 0.14/0.39 % SZS status Unsatisfiable
% 0.14/0.39
% 0.14/0.39 % SZS output start Proof
% 0.14/0.39 Take the following subset of the input axioms:
% 0.14/0.39 fof(thm147_1, negated_conjecture, ![B, A2]: (a_truth(B) | (~a_truth(A2) | ~a_truth(implies(A2, B))))).
% 0.14/0.39 fof(thm147_2, negated_conjecture, ![A, B2]: a_truth(implies(A, implies(B2, A)))).
% 0.14/0.39 fof(thm147_3, negated_conjecture, ![C, B2, A3]: a_truth(implies(implies(A3, implies(B2, C)), implies(implies(A3, B2), implies(A3, C))))).
% 0.14/0.39 fof(thm147_5, negated_conjecture, ~a_truth(implies(sk1, sk1))).
% 0.14/0.39
% 0.14/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.14/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.14/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.14/0.39 fresh(y, y, x1...xn) = u
% 0.14/0.39 C => fresh(s, t, x1...xn) = v
% 0.14/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.14/0.39 variables of u and v.
% 0.14/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.14/0.39 input problem has no model of domain size 1).
% 0.14/0.39
% 0.14/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.14/0.39
% 0.14/0.39 Axiom 1 (thm147_1): fresh2(X, X, Y) = true.
% 0.14/0.39 Axiom 2 (thm147_1): fresh(X, X, Y, Z) = a_truth(Y).
% 0.14/0.39 Axiom 3 (thm147_2): a_truth(implies(X, implies(Y, X))) = true.
% 0.14/0.39 Axiom 4 (thm147_1): fresh(a_truth(implies(X, Y)), true, Y, X) = fresh2(a_truth(X), true, Y).
% 0.14/0.39 Axiom 5 (thm147_3): a_truth(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))) = true.
% 0.14/0.39
% 0.14/0.39 Goal 1 (thm147_5): a_truth(implies(sk1, sk1)) = true.
% 0.14/0.39 Proof:
% 0.14/0.39 a_truth(implies(sk1, sk1))
% 0.14/0.39 = { by axiom 2 (thm147_1) R->L }
% 0.14/0.39 fresh(true, true, implies(sk1, sk1), implies(sk1, implies(X, sk1)))
% 0.14/0.39 = { by axiom 1 (thm147_1) R->L }
% 0.14/0.39 fresh(fresh2(true, true, implies(implies(sk1, implies(X, sk1)), implies(sk1, sk1))), true, implies(sk1, sk1), implies(sk1, implies(X, sk1)))
% 0.14/0.39 = { by axiom 3 (thm147_2) R->L }
% 0.14/0.39 fresh(fresh2(a_truth(implies(sk1, implies(implies(X, sk1), sk1))), true, implies(implies(sk1, implies(X, sk1)), implies(sk1, sk1))), true, implies(sk1, sk1), implies(sk1, implies(X, sk1)))
% 0.14/0.39 = { by axiom 4 (thm147_1) R->L }
% 0.14/0.39 fresh(fresh(a_truth(implies(implies(sk1, implies(implies(X, sk1), sk1)), implies(implies(sk1, implies(X, sk1)), implies(sk1, sk1)))), true, implies(implies(sk1, implies(X, sk1)), implies(sk1, sk1)), implies(sk1, implies(implies(X, sk1), sk1))), true, implies(sk1, sk1), implies(sk1, implies(X, sk1)))
% 0.14/0.39 = { by axiom 5 (thm147_3) }
% 0.14/0.39 fresh(fresh(true, true, implies(implies(sk1, implies(X, sk1)), implies(sk1, sk1)), implies(sk1, implies(implies(X, sk1), sk1))), true, implies(sk1, sk1), implies(sk1, implies(X, sk1)))
% 0.14/0.39 = { by axiom 2 (thm147_1) }
% 0.14/0.39 fresh(a_truth(implies(implies(sk1, implies(X, sk1)), implies(sk1, sk1))), true, implies(sk1, sk1), implies(sk1, implies(X, sk1)))
% 0.14/0.39 = { by axiom 4 (thm147_1) }
% 0.14/0.39 fresh2(a_truth(implies(sk1, implies(X, sk1))), true, implies(sk1, sk1))
% 0.14/0.39 = { by axiom 3 (thm147_2) }
% 0.14/0.39 fresh2(true, true, implies(sk1, sk1))
% 0.14/0.39 = { by axiom 1 (thm147_1) }
% 0.14/0.39 true
% 0.14/0.39 % SZS output end Proof
% 0.14/0.39
% 0.14/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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