TSTP Solution File: LCL257-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL257-1 : TPTP v8.1.2. Released v2.0.0.
% 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 : n027.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 08:18:19 EDT 2023
% Result : Unsatisfiable 0.20s 0.70s
% Output : Proof 0.20s
% 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 : LCL257-1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.17/0.34 % Computer : n027.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Thu Aug 24 18:14:03 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.20/0.70 Command-line arguments: --no-flatten-goal
% 0.20/0.70
% 0.20/0.70 % SZS status Unsatisfiable
% 0.20/0.70
% 0.20/0.71 % SZS output start Proof
% 0.20/0.71 Take the following subset of the input axioms:
% 0.20/0.71 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 0.20/0.71 fof(prove_xhn, negated_conjecture, ~is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))).
% 0.20/0.71 fof(yql, axiom, ![Z, X2, Y2]: is_a_theorem(equivalent(equivalent(X2, Y2), equivalent(equivalent(Z, Y2), equivalent(X2, Z))))).
% 0.20/0.71
% 0.20/0.71 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.71 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.71 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.71 fresh(y, y, x1...xn) = u
% 0.20/0.71 C => fresh(s, t, x1...xn) = v
% 0.20/0.71 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.71 variables of u and v.
% 0.20/0.71 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.71 input problem has no model of domain size 1).
% 0.20/0.71
% 0.20/0.71 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.71
% 0.20/0.71 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 0.20/0.71 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 0.20/0.71 Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 0.20/0.71 Axiom 4 (yql): is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, Y), equivalent(X, Z)))) = true.
% 0.20/0.71
% 0.20/0.71 Lemma 5: fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(equivalent(Z, Y), equivalent(X, Z))) = is_a_theorem(equivalent(equivalent(Z, Y), equivalent(X, Z))).
% 0.20/0.71 Proof:
% 0.20/0.71 fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(equivalent(Z, Y), equivalent(X, Z)))
% 0.20/0.71 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.71 fresh(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, Y), equivalent(X, Z)))), true, equivalent(X, Y), equivalent(equivalent(Z, Y), equivalent(X, Z)))
% 0.20/0.71 = { by axiom 4 (yql) }
% 0.20/0.71 fresh(true, true, equivalent(X, Y), equivalent(equivalent(Z, Y), equivalent(X, Z)))
% 0.20/0.71 = { by axiom 2 (condensed_detachment) }
% 0.20/0.71 is_a_theorem(equivalent(equivalent(Z, Y), equivalent(X, Z)))
% 0.20/0.71
% 0.20/0.71 Lemma 6: is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Y))), equivalent(equivalent(W, Z), X))) = true.
% 0.20/0.71 Proof:
% 0.20/0.71 is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Y))), equivalent(equivalent(W, Z), X)))
% 0.20/0.71 = { by lemma 5 R->L }
% 0.20/0.71 fresh2(is_a_theorem(equivalent(equivalent(W, Z), equivalent(equivalent(Y, Z), equivalent(W, Y)))), true, equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Y))), equivalent(equivalent(W, Z), X)))
% 0.20/0.71 = { by axiom 4 (yql) }
% 0.20/0.71 fresh2(true, true, equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Y))), equivalent(equivalent(W, Z), X)))
% 0.20/0.71 = { by axiom 1 (condensed_detachment) }
% 0.20/0.71 true
% 0.20/0.71
% 0.20/0.71 Lemma 7: fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Y)))), true, equivalent(equivalent(W, Z), X)) = is_a_theorem(equivalent(equivalent(W, Z), X)).
% 0.20/0.71 Proof:
% 0.20/0.71 fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Y)))), true, equivalent(equivalent(W, Z), X))
% 0.20/0.71 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.71 fresh(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Y))), equivalent(equivalent(W, Z), X))), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Y))), equivalent(equivalent(W, Z), X))
% 0.20/0.71 = { by lemma 6 }
% 0.20/0.71 fresh(true, true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(W, Y))), equivalent(equivalent(W, Z), X))
% 0.20/0.71 = { by axiom 2 (condensed_detachment) }
% 0.20/0.71 is_a_theorem(equivalent(equivalent(W, Z), X))
% 0.20/0.71
% 0.20/0.71 Lemma 8: is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Y, Z), X))) = true.
% 0.20/0.71 Proof:
% 0.20/0.71 is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Y, Z), X)))
% 0.20/0.71 = { by lemma 5 R->L }
% 0.20/0.71 fresh2(is_a_theorem(equivalent(equivalent(Y, Z), equivalent(Y, Z))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Y, Z), X)))
% 0.20/0.71 = { by lemma 7 R->L }
% 0.20/0.71 fresh2(fresh2(is_a_theorem(equivalent(equivalent(Y, Z), equivalent(equivalent(W, Z), equivalent(Y, W)))), true, equivalent(equivalent(Y, Z), equivalent(Y, Z))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Y, Z), X)))
% 0.20/0.71 = { by axiom 4 (yql) }
% 0.20/0.71 fresh2(fresh2(true, true, equivalent(equivalent(Y, Z), equivalent(Y, Z))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Y, Z), X)))
% 0.20/0.71 = { by axiom 1 (condensed_detachment) }
% 0.20/0.71 fresh2(true, true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Y, Z), X)))
% 0.20/0.71 = { by axiom 1 (condensed_detachment) }
% 0.20/0.71 true
% 0.20/0.71
% 0.20/0.71 Lemma 9: fresh2(is_a_theorem(equivalent(equivalent(X, Y), Z)), true, equivalent(equivalent(Z, X), Y)) = is_a_theorem(equivalent(equivalent(Z, X), Y)).
% 0.20/0.71 Proof:
% 0.20/0.71 fresh2(is_a_theorem(equivalent(equivalent(X, Y), Z)), true, equivalent(equivalent(Z, X), Y))
% 0.20/0.71 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.71 fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, X), Y))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, X), Y))
% 0.20/0.71 = { by lemma 7 R->L }
% 0.20/0.71 fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(Z, X), Y), equivalent(equivalent(equivalent(Z, X), Z), equivalent(equivalent(X, Y), equivalent(Z, X))))), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, X), Y))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, X), Y))
% 0.20/0.71 = { by lemma 7 R->L }
% 0.20/0.71 fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z, X), Z), equivalent(equivalent(X, Y), equivalent(Z, X))), equivalent(equivalent(Z, Y), equivalent(equivalent(Z, X), Z)))), true, equivalent(equivalent(equivalent(Z, X), Y), equivalent(equivalent(equivalent(Z, X), Z), equivalent(equivalent(X, Y), equivalent(Z, X))))), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, X), Y))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, X), Y))
% 0.20/0.71 = { by lemma 6 }
% 0.20/0.71 fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(Z, X), Y), equivalent(equivalent(equivalent(Z, X), Z), equivalent(equivalent(X, Y), equivalent(Z, X))))), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, X), Y))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, X), Y))
% 0.20/0.71 = { by axiom 1 (condensed_detachment) }
% 0.20/0.71 fresh(fresh2(true, true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, X), Y))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, X), Y))
% 0.20/0.71 = { by axiom 1 (condensed_detachment) }
% 0.20/0.71 fresh(true, true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, X), Y))
% 0.20/0.71 = { by axiom 2 (condensed_detachment) }
% 0.20/0.72 is_a_theorem(equivalent(equivalent(Z, X), Y))
% 0.20/0.72
% 0.20/0.72 Goal 1 (prove_xhn): is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))) = true.
% 0.20/0.72 Proof:
% 0.20/0.72 is_a_theorem(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))
% 0.20/0.72 = { by axiom 2 (condensed_detachment) R->L }
% 0.20/0.72 fresh(true, true, equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x)), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))
% 0.20/0.72 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.72 fresh(fresh2(true, true, equivalent(equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x)), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x)), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))
% 0.20/0.72 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.72 fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(z, x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, equivalent(equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x)), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x)), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))
% 0.20/0.72 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.72 fresh(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(z, x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true, equivalent(equivalent(equivalent(z, x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, equivalent(equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x)), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x)), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))
% 0.20/0.72 = { by lemma 8 R->L }
% 0.20/0.72 fresh(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(z, x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x)))), true, equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(z, x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true, equivalent(equivalent(equivalent(z, x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, equivalent(equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x)), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x)), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))
% 0.20/0.72 = { by lemma 7 }
% 0.20/0.72 fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(z, x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true, equivalent(equivalent(equivalent(z, x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, equivalent(equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x)), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x)), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))
% 0.20/0.72 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.72 fresh(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(z, x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(z, x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))))), true, equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(z, x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(z, x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, equivalent(equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x)), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x)), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))
% 0.20/0.72 = { by lemma 8 }
% 0.20/0.72 fresh(fresh2(fresh(true, true, equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(equivalent(z, x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), equivalent(equivalent(equivalent(z, x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, equivalent(equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x)), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x)), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))
% 0.20/0.72 = { by axiom 2 (condensed_detachment) }
% 0.20/0.72 fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(z, x), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, equivalent(equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x)), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x)), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))
% 0.20/0.72 = { by lemma 9 }
% 0.20/0.72 fresh(is_a_theorem(equivalent(equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x)), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))), true, equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x)), equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))
% 0.20/0.72 = { by axiom 3 (condensed_detachment) }
% 0.20/0.72 fresh2(is_a_theorem(equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x))), true, equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))
% 0.20/0.72 = { by lemma 9 R->L }
% 0.20/0.72 fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), equivalent(z, x)), z)), true, equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x))), true, equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))
% 0.20/0.72 = { by lemma 9 R->L }
% 0.20/0.72 fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(z, x), z), equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)))), true, equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), equivalent(z, x)), z)), true, equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x))), true, equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))
% 0.20/0.72 = { by axiom 4 (yql) }
% 0.20/0.72 fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(y, z), equivalent(equivalent(z, x), y)), equivalent(z, x)), z)), true, equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x))), true, equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))
% 0.20/0.72 = { by axiom 1 (condensed_detachment) }
% 0.20/0.72 fresh2(fresh2(true, true, equivalent(equivalent(z, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))), equivalent(z, x))), true, equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))
% 0.20/0.72 = { by axiom 1 (condensed_detachment) }
% 0.20/0.72 fresh2(true, true, equivalent(x, equivalent(equivalent(y, z), equivalent(equivalent(z, x), y))))
% 0.20/0.72 = { by axiom 1 (condensed_detachment) }
% 0.20/0.72 true
% 0.20/0.72 % SZS output end Proof
% 0.20/0.72
% 0.20/0.72 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------