TSTP Solution File: LCL118-1 by Twee---2.4.2
View Problem
- Process Solution
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% File : Twee---2.4.2
% Problem : LCL118-1 : 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 : n024.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 08:17:32 EDT 2023
% Result : Unsatisfiable 0.19s 0.56s
% 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
% 0.06/0.12 % Problem : LCL118-1 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.13 % 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 : n024.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Aug 24 19:53:39 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 Command-line arguments: --no-flatten-goal
% 0.19/0.56
% 0.19/0.56 % SZS status Unsatisfiable
% 0.19/0.56
% 0.19/0.57 % SZS output start Proof
% 0.19/0.57 Take the following subset of the input axioms:
% 0.19/0.57 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 0.19/0.57 fof(prove_yqm, negated_conjecture, ~is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))).
% 0.19/0.57 fof(wo, axiom, ![Z, X2, Y2]: is_a_theorem(equivalent(equivalent(X2, equivalent(Y2, Z)), equivalent(Z, equivalent(Y2, X2))))).
% 0.19/0.57
% 0.19/0.57 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.57 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.57 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.57 fresh(y, y, x1...xn) = u
% 0.19/0.57 C => fresh(s, t, x1...xn) = v
% 0.19/0.57 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.57 variables of u and v.
% 0.19/0.57 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.57 input problem has no model of domain size 1).
% 0.19/0.57
% 0.19/0.57 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.57
% 0.19/0.57 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 0.19/0.57 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 0.19/0.57 Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 0.19/0.57 Axiom 4 (wo): is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, equivalent(Y, X)))) = true.
% 0.19/0.57
% 0.19/0.57 Lemma 5: fresh2(is_a_theorem(equivalent(X, equivalent(Y, Z))), true, equivalent(Z, equivalent(Y, X))) = is_a_theorem(equivalent(Z, equivalent(Y, X))).
% 0.19/0.57 Proof:
% 0.19/0.57 fresh2(is_a_theorem(equivalent(X, equivalent(Y, Z))), true, equivalent(Z, equivalent(Y, X)))
% 0.19/0.57 = { by axiom 3 (condensed_detachment) R->L }
% 0.19/0.57 fresh(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, equivalent(Y, X)))), true, equivalent(X, equivalent(Y, Z)), equivalent(Z, equivalent(Y, X)))
% 0.19/0.57 = { by axiom 4 (wo) }
% 0.19/0.57 fresh(true, true, equivalent(X, equivalent(Y, Z)), equivalent(Z, equivalent(Y, X)))
% 0.19/0.57 = { by axiom 2 (condensed_detachment) }
% 0.19/0.57 is_a_theorem(equivalent(Z, equivalent(Y, X)))
% 0.19/0.57
% 0.19/0.57 Lemma 6: is_a_theorem(equivalent(equivalent(X, Y), equivalent(Z, equivalent(Y, equivalent(X, Z))))) = true.
% 0.19/0.57 Proof:
% 0.19/0.57 is_a_theorem(equivalent(equivalent(X, Y), equivalent(Z, equivalent(Y, equivalent(X, Z)))))
% 0.19/0.57 = { by lemma 5 R->L }
% 0.19/0.57 fresh2(is_a_theorem(equivalent(equivalent(Y, equivalent(X, Z)), equivalent(Z, equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(Z, equivalent(Y, equivalent(X, Z)))))
% 0.19/0.57 = { by axiom 4 (wo) }
% 0.19/0.57 fresh2(true, true, equivalent(equivalent(X, Y), equivalent(Z, equivalent(Y, equivalent(X, Z)))))
% 0.19/0.57 = { by axiom 1 (condensed_detachment) }
% 0.19/0.57 true
% 0.19/0.57
% 0.19/0.57 Goal 1 (prove_yqm): is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a)))) = true.
% 0.19/0.57 Proof:
% 0.19/0.57 is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))
% 0.19/0.57 = { by lemma 5 R->L }
% 0.19/0.57 fresh2(is_a_theorem(equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))
% 0.19/0.57 = { by axiom 2 (condensed_detachment) R->L }
% 0.19/0.57 fresh2(fresh(true, true, equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))
% 0.19/0.57 = { by axiom 1 (condensed_detachment) R->L }
% 0.19/0.57 fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true, equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))
% 0.19/0.57 = { by axiom 1 (condensed_detachment) R->L }
% 0.19/0.57 fresh2(fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true, equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true, equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))
% 0.19/0.57 = { by lemma 6 R->L }
% 0.19/0.57 fresh2(fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true, equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true, equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true, equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))
% 0.19/0.57 = { by axiom 3 (condensed_detachment) R->L }
% 0.19/0.57 fresh2(fresh(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true, equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true, equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true, equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))
% 0.19/0.57 = { by lemma 5 R->L }
% 0.19/0.58 fresh2(fresh(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))))), true, equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true, equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true, equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true, equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))
% 0.19/0.58 = { by axiom 2 (condensed_detachment) R->L }
% 0.19/0.58 fresh2(fresh(fresh2(fresh(fresh2(fresh(true, true, equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, b), equivalent(a, b))), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))))), true, equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true, equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true, equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true, equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))
% 0.19/0.58 = { by lemma 6 R->L }
% 0.19/0.58 fresh2(fresh(fresh2(fresh(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, b), equivalent(a, b))), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))))), true, equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, b), equivalent(a, b))), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))))), true, equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true, equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true, equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true, equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))
% 0.19/0.58 = { by axiom 3 (condensed_detachment) }
% 0.19/0.58 fresh2(fresh(fresh2(fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, b), equivalent(a, b)))), true, equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))))), true, equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true, equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true, equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true, equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))
% 0.19/0.58 = { by axiom 4 (wo) }
% 0.19/0.58 fresh2(fresh(fresh2(fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))))), true, equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true, equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true, equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true, equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))
% 0.19/0.58 = { by axiom 1 (condensed_detachment) }
% 0.19/0.58 fresh2(fresh(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))))), true, equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true, equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true, equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))
% 0.19/0.58 = { by axiom 1 (condensed_detachment) }
% 0.19/0.58 fresh2(fresh(fresh2(fresh(true, true, equivalent(equivalent(b, equivalent(a, equivalent(c, b))), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))))), equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true, equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true, equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))
% 0.19/0.58 = { by axiom 2 (condensed_detachment) }
% 0.19/0.58 fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(a, b)), equivalent(equivalent(c, a), equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))))), true, equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true, equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))
% 0.19/0.58 = { by lemma 5 }
% 0.19/0.58 fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b))))), true, equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a))), equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))
% 0.19/0.58 = { by axiom 3 (condensed_detachment) }
% 0.19/0.58 fresh2(fresh2(is_a_theorem(equivalent(equivalent(a, equivalent(c, b)), equivalent(b, equivalent(c, a)))), true, equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))
% 0.19/0.58 = { by axiom 4 (wo) }
% 0.19/0.58 fresh2(fresh2(true, true, equivalent(equivalent(c, a), equivalent(equivalent(c, b), equivalent(a, b)))), true, equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))
% 0.19/0.58 = { by axiom 1 (condensed_detachment) }
% 0.19/0.58 fresh2(true, true, equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(c, a))))
% 0.19/0.58 = { by axiom 1 (condensed_detachment) }
% 0.19/0.58 true
% 0.19/0.58 % SZS output end Proof
% 0.19/0.58
% 0.19/0.58 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------