TSTP Solution File: LCL076-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL076-2 : 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 : n013.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 08:17:17 EDT 2023
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% 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 : LCL076-2 : 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
% 0.13/0.34 % Computer : n013.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 : Fri Aug 25 04:43:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.38 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.19/0.38
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 Take the following subset of the input axioms:
% 0.19/0.38 fof(cn_49, axiom, ![X, Y]: is_a_theorem(implies(implies(not(X), not(Y)), implies(Y, X)))).
% 0.19/0.38 fof(condensed_detachment, axiom, ![X2, Y2]: (~is_a_theorem(implies(X2, Y2)) | (~is_a_theorem(X2) | is_a_theorem(Y2)))).
% 0.19/0.38 fof(extra_lemma, axiom, ![X1]: is_a_theorem(implies(not(not(X1)), X1))).
% 0.19/0.38 fof(prove_cn_40, negated_conjecture, ~is_a_theorem(implies(a, not(not(a))))).
% 0.19/0.38
% 0.19/0.38 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.38 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.38 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.38 fresh(y, y, x1...xn) = u
% 0.19/0.38 C => fresh(s, t, x1...xn) = v
% 0.19/0.38 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.38 variables of u and v.
% 0.19/0.38 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.38 input problem has no model of domain size 1).
% 0.19/0.38
% 0.19/0.38 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.38
% 0.19/0.38 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 0.19/0.38 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 0.19/0.38 Axiom 3 (extra_lemma): is_a_theorem(implies(not(not(X)), X)) = true.
% 0.19/0.38 Axiom 4 (condensed_detachment): fresh(is_a_theorem(implies(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 0.19/0.38 Axiom 5 (cn_49): is_a_theorem(implies(implies(not(X), not(Y)), implies(Y, X))) = true.
% 0.19/0.38
% 0.19/0.38 Goal 1 (prove_cn_40): is_a_theorem(implies(a, not(not(a)))) = true.
% 0.19/0.38 Proof:
% 0.19/0.38 is_a_theorem(implies(a, not(not(a))))
% 0.19/0.38 = { by axiom 2 (condensed_detachment) R->L }
% 0.19/0.38 fresh(true, true, implies(not(not(not(a))), not(a)), implies(a, not(not(a))))
% 0.19/0.38 = { by axiom 5 (cn_49) R->L }
% 0.19/0.38 fresh(is_a_theorem(implies(implies(not(not(not(a))), not(a)), implies(a, not(not(a))))), true, implies(not(not(not(a))), not(a)), implies(a, not(not(a))))
% 0.19/0.38 = { by axiom 4 (condensed_detachment) }
% 0.19/0.38 fresh2(is_a_theorem(implies(not(not(not(a))), not(a))), true, implies(a, not(not(a))))
% 0.19/0.38 = { by axiom 3 (extra_lemma) }
% 0.19/0.38 fresh2(true, true, implies(a, not(not(a))))
% 0.19/0.38 = { by axiom 1 (condensed_detachment) }
% 0.19/0.38 true
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38
% 0.19/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
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