TSTP Solution File: LCL097-1 by Twee---2.4.2
View Problem
- Process Solution
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% File : Twee---2.4.2
% Problem : LCL097-1 : 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 : n019.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 08:17:24 EDT 2023
% Result : Unsatisfiable 29.23s 4.13s
% Output : Proof 29.23s
% 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 : LCL097-1 : 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
% 0.15/0.34 % Computer : n019.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Fri Aug 25 04:47:43 EDT 2023
% 0.15/0.34 % CPUTime :
% 29.23/4.13 Command-line arguments: --flatten
% 29.23/4.13
% 29.23/4.13 % SZS status Unsatisfiable
% 29.23/4.13
% 29.23/4.14 % SZS output start Proof
% 29.23/4.14 Take the following subset of the input axioms:
% 29.23/4.14 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 29.23/4.14 fof(lg_2, axiom, ![Z, U, X2, Y2]: is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X2, Y2), equivalent(X2, Z)), equivalent(Y2, Z)), U), U))).
% 29.23/4.14 fof(lg_3, axiom, ![V, X2, Y2, Z2, U2]: is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X2, Y2), equivalent(X2, Z2)), U2), equivalent(equivalent(Y2, Z2), U2)), V), V))).
% 29.23/4.14 fof(prove_lg_4, negated_conjecture, ~is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))).
% 29.23/4.14
% 29.23/4.14 Now clausify the problem and encode Horn clauses using encoding 3 of
% 29.23/4.14 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 29.23/4.14 We repeatedly replace C & s=t => u=v by the two clauses:
% 29.23/4.14 fresh(y, y, x1...xn) = u
% 29.23/4.14 C => fresh(s, t, x1...xn) = v
% 29.23/4.14 where fresh is a fresh function symbol and x1..xn are the free
% 29.23/4.14 variables of u and v.
% 29.23/4.14 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 29.23/4.14 input problem has no model of domain size 1).
% 29.23/4.14
% 29.23/4.14 The encoding turns the above axioms into the following unit equations and goals:
% 29.23/4.14
% 29.23/4.14 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 29.23/4.14 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 29.23/4.14 Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 29.23/4.14 Axiom 4 (lg_2): is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W), W)) = true.
% 29.23/4.14 Axiom 5 (lg_3): is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)), V), V)) = true.
% 29.23/4.14
% 29.23/4.14 Lemma 6: fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)), V)), true, V) = is_a_theorem(V).
% 29.23/4.14 Proof:
% 29.23/4.14 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)), V)), true, V)
% 29.23/4.14 = { by axiom 3 (condensed_detachment) R->L }
% 29.23/4.14 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)), V), V)), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)), V), V)
% 29.23/4.14 = { by axiom 5 (lg_3) }
% 29.23/4.14 fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)), V), V)
% 29.23/4.14 = { by axiom 2 (condensed_detachment) }
% 29.23/4.14 is_a_theorem(V)
% 29.23/4.14
% 29.23/4.14 Goal 1 (prove_lg_4): is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))) = true.
% 29.23/4.14 Proof:
% 29.23/4.14 is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))
% 29.23/4.14 = { by axiom 2 (condensed_detachment) R->L }
% 29.23/4.14 fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))
% 29.23/4.15 = { by axiom 1 (condensed_detachment) R->L }
% 29.23/4.15 fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))
% 29.23/4.15 = { by axiom 1 (condensed_detachment) R->L }
% 29.23/4.15 fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))
% 29.23/4.15 = { by axiom 4 (lg_2) R->L }
% 29.23/4.15 fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(X, equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))
% 29.23/4.15 = { by lemma 6 }
% 29.23/4.15 fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))
% 29.23/4.15 = { by lemma 6 }
% 29.23/4.15 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))
% 29.23/4.15 = { by axiom 3 (condensed_detachment) }
% 29.23/4.15 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))
% 29.23/4.15 = { by lemma 6 R->L }
% 29.23/4.15 fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))
% 29.23/4.15 = { by lemma 6 R->L }
% 29.23/4.15 fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))
% 29.23/4.15 = { by lemma 6 R->L }
% 29.23/4.15 fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))
% 29.23/4.15 = { by axiom 5 (lg_3) }
% 29.23/4.15 fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))
% 29.23/4.15 = { by axiom 1 (condensed_detachment) }
% 29.23/4.15 fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e), equivalent(equivalent(b, falsehood), e)), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))
% 29.23/4.15 = { by axiom 1 (condensed_detachment) }
% 29.23/4.16 fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, falsehood)), e)), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e)))), true, equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))
% 29.23/4.16 = { by axiom 1 (condensed_detachment) }
% 29.23/4.16 fresh2(true, true, equivalent(equivalent(equivalent(equivalent(a, b), c), e), equivalent(equivalent(equivalent(a, falsehood), c), equivalent(equivalent(b, falsehood), e))))
% 29.23/4.16 = { by axiom 1 (condensed_detachment) }
% 29.23/4.16 true
% 29.23/4.16 % SZS output end Proof
% 29.23/4.16
% 29.23/4.16 RESULT: Unsatisfiable (the axioms are contradictory).
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