TSTP Solution File: LCL131-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL131-1 : 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 : n028.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 08:17:35 EDT 2023
% Result : Unsatisfiable 74.19s 9.90s
% Output : Proof 75.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL131-1 : 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 : n028.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 : Thu Aug 24 21:56:05 EDT 2023
% 0.15/0.34 % CPUTime :
% 74.19/9.90 Command-line arguments: --no-flatten-goal
% 74.19/9.90
% 74.19/9.90 % SZS status Unsatisfiable
% 74.19/9.90
% 74.88/9.93 % SZS output start Proof
% 74.88/9.93 Take the following subset of the input axioms:
% 74.88/9.93 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 74.88/9.93 fof(prove_lg_2, negated_conjecture, ~is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))).
% 74.88/9.93 fof(s_6, axiom, ![Z, U, X2, Y2]: is_a_theorem(equivalent(equivalent(X2, equivalent(equivalent(equivalent(Y2, Z), equivalent(U, Z)), equivalent(Y2, U))), X2))).
% 74.88/9.93
% 74.88/9.93 Now clausify the problem and encode Horn clauses using encoding 3 of
% 74.88/9.93 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 74.88/9.93 We repeatedly replace C & s=t => u=v by the two clauses:
% 74.88/9.93 fresh(y, y, x1...xn) = u
% 74.88/9.93 C => fresh(s, t, x1...xn) = v
% 74.88/9.93 where fresh is a fresh function symbol and x1..xn are the free
% 74.88/9.93 variables of u and v.
% 74.88/9.93 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 74.88/9.93 input problem has no model of domain size 1).
% 74.88/9.93
% 74.88/9.93 The encoding turns the above axioms into the following unit equations and goals:
% 74.88/9.93
% 74.88/9.93 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 74.88/9.93 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 74.88/9.93 Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 74.88/9.93 Axiom 4 (s_6): is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), X)) = true.
% 74.88/9.93
% 74.88/9.93 Lemma 5: fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)))), true, X) = is_a_theorem(X).
% 74.88/9.93 Proof:
% 74.88/9.93 fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W)))), true, X)
% 74.88/9.93 = { by axiom 3 (condensed_detachment) R->L }
% 74.88/9.93 fresh(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), X)), true, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), X)
% 74.88/9.93 = { by axiom 4 (s_6) }
% 74.88/9.93 fresh(true, true, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), X)
% 74.88/9.93 = { by axiom 2 (condensed_detachment) }
% 74.88/9.93 is_a_theorem(X)
% 74.88/9.93
% 74.88/9.93 Lemma 6: is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z)), equivalent(equivalent(equivalent(W, V), equivalent(U, V)), equivalent(W, U)))) = true.
% 74.88/9.93 Proof:
% 74.88/9.93 is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z)), equivalent(equivalent(equivalent(W, V), equivalent(U, V)), equivalent(W, U))))
% 74.88/9.93 = { by lemma 5 R->L }
% 74.88/9.93 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z)), equivalent(equivalent(equivalent(W, V), equivalent(U, V)), equivalent(W, U))), equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z)), equivalent(equivalent(equivalent(W, V), equivalent(U, V)), equivalent(W, U))))
% 74.88/9.93 = { by axiom 4 (s_6) }
% 74.88/9.93 fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z)), equivalent(equivalent(equivalent(W, V), equivalent(U, V)), equivalent(W, U))))
% 74.88/9.93 = { by axiom 1 (condensed_detachment) }
% 74.88/9.93 true
% 74.88/9.93
% 74.88/9.93 Lemma 7: is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z))) = true.
% 74.88/9.93 Proof:
% 74.88/9.93 is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z)))
% 74.88/9.93 = { by lemma 5 R->L }
% 74.88/9.93 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z)), equivalent(equivalent(equivalent(W, V), equivalent(U, V)), equivalent(W, U)))), true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z)))
% 74.88/9.93 = { by lemma 6 }
% 74.88/9.93 fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z)))
% 74.88/9.93 = { by axiom 1 (condensed_detachment) }
% 74.88/9.93 true
% 74.88/9.93
% 74.88/9.93 Lemma 8: fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(Z, Y))), true, equivalent(X, Z)) = is_a_theorem(equivalent(X, Z)).
% 74.88/9.93 Proof:
% 74.88/9.93 fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(Z, Y))), true, equivalent(X, Z))
% 74.88/9.93 = { by axiom 3 (condensed_detachment) R->L }
% 74.88/9.93 fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z))), true, equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z))
% 74.88/9.93 = { by lemma 7 }
% 74.88/9.93 fresh(true, true, equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z))
% 74.88/9.93 = { by axiom 2 (condensed_detachment) }
% 74.88/9.94 is_a_theorem(equivalent(X, Z))
% 74.88/9.94
% 74.88/9.94 Lemma 9: fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), W)), true, equivalent(equivalent(X, Z), W)) = is_a_theorem(equivalent(equivalent(X, Z), W)).
% 74.88/9.94 Proof:
% 74.88/9.94 fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), W)), true, equivalent(equivalent(X, Z), W))
% 74.88/9.94 = { by axiom 3 (condensed_detachment) R->L }
% 74.88/9.94 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), W), equivalent(equivalent(X, Z), W))), true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), W), equivalent(equivalent(X, Z), W))
% 74.88/9.94 = { by lemma 5 R->L }
% 74.88/9.94 fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), W), equivalent(equivalent(X, Z), W)), equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), W), equivalent(equivalent(X, Z), W))), true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), W), equivalent(equivalent(X, Z), W))
% 74.88/9.94 = { by lemma 7 }
% 74.88/9.94 fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), W), equivalent(equivalent(X, Z), W))), true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), W), equivalent(equivalent(X, Z), W))
% 74.88/9.94 = { by axiom 1 (condensed_detachment) }
% 74.88/9.94 fresh(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), W), equivalent(equivalent(X, Z), W))
% 74.88/9.94 = { by axiom 2 (condensed_detachment) }
% 74.88/9.94 is_a_theorem(equivalent(equivalent(X, Z), W))
% 74.88/9.94
% 74.88/9.94 Lemma 10: is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, equivalent(W, Z)), equivalent(Y, W)))) = true.
% 74.88/9.94 Proof:
% 74.88/9.94 is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, equivalent(W, Z)), equivalent(Y, W))))
% 74.88/9.94 = { by lemma 9 R->L }
% 74.88/9.94 fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(W, Z)), equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(equivalent(X, equivalent(W, Z)), equivalent(Y, W)))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, equivalent(W, Z)), equivalent(Y, W))))
% 74.88/9.94 = { by lemma 9 R->L }
% 74.88/9.94 fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, equivalent(W, Z)), equivalent(Y, W)), equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))), equivalent(equivalent(X, equivalent(W, Z)), equivalent(Y, W)))), true, equivalent(equivalent(equivalent(X, equivalent(W, Z)), equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(equivalent(X, equivalent(W, Z)), equivalent(Y, W)))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, equivalent(W, Z)), equivalent(Y, W))))
% 74.88/9.94 = { by axiom 4 (s_6) }
% 74.88/9.94 fresh2(fresh2(true, true, equivalent(equivalent(equivalent(X, equivalent(W, Z)), equivalent(equivalent(Y, Z), equivalent(W, Z))), equivalent(equivalent(X, equivalent(W, Z)), equivalent(Y, W)))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, equivalent(W, Z)), equivalent(Y, W))))
% 74.88/9.94 = { by axiom 1 (condensed_detachment) }
% 74.88/9.94 fresh2(true, true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, equivalent(W, Z)), equivalent(Y, W))))
% 74.88/9.94 = { by axiom 1 (condensed_detachment) }
% 74.88/9.94 true
% 74.88/9.94
% 74.88/9.94 Lemma 11: is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W)))) = true.
% 74.88/9.94 Proof:
% 74.88/9.94 is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W))))
% 74.88/9.94 = { by lemma 8 R->L }
% 74.88/9.94 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(X, Z)), equivalent(equivalent(equivalent(X, W), equivalent(Z, W)), equivalent(X, Z)))), true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W))))
% 74.88/9.94 = { by lemma 6 }
% 74.88/9.94 fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W))))
% 74.88/9.94 = { by axiom 1 (condensed_detachment) }
% 74.88/9.94 true
% 74.88/9.94
% 74.88/9.94 Lemma 12: fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(Z, Y))), true, equivalent(equivalent(X, W), equivalent(Z, W))) = is_a_theorem(equivalent(equivalent(X, W), equivalent(Z, W))).
% 74.88/9.94 Proof:
% 74.88/9.94 fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(Z, Y))), true, equivalent(equivalent(X, W), equivalent(Z, W)))
% 74.88/9.94 = { by axiom 3 (condensed_detachment) R->L }
% 74.88/9.94 fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W)))), true, equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W)))
% 74.88/9.94 = { by lemma 11 }
% 74.88/9.94 fresh(true, true, equivalent(equivalent(X, Y), equivalent(Z, Y)), equivalent(equivalent(X, W), equivalent(Z, W)))
% 74.88/9.94 = { by axiom 2 (condensed_detachment) }
% 74.88/9.94 is_a_theorem(equivalent(equivalent(X, W), equivalent(Z, W)))
% 74.88/9.94
% 74.88/9.94 Goal 1 (prove_lg_2): is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))) = true.
% 74.88/9.94 Proof:
% 74.88/9.94 is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 74.88/9.94 = { by axiom 2 (condensed_detachment) R->L }
% 74.88/9.94 fresh(true, true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 74.88/9.94 = { by axiom 1 (condensed_detachment) R->L }
% 74.88/9.94 fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 74.88/9.94 = { by axiom 1 (condensed_detachment) R->L }
% 74.88/9.94 fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 74.88/9.94 = { by lemma 7 R->L }
% 74.88/9.94 fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 74.88/9.95 = { by axiom 3 (condensed_detachment) R->L }
% 74.88/9.95 fresh(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 74.88/9.95 = { by axiom 2 (condensed_detachment) R->L }
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% 74.88/9.96 = { by lemma 11 R->L }
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% 74.88/9.96 = { by lemma 9 }
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% 74.88/9.96 = { by axiom 3 (condensed_detachment) }
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% 74.88/9.97 = { by lemma 8 R->L }
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% 74.88/9.97 = { by lemma 10 }
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% 74.88/9.97 = { by axiom 1 (condensed_detachment) }
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% 74.88/9.97 = { by axiom 1 (condensed_detachment) }
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% 74.88/9.97 = { by axiom 2 (condensed_detachment) }
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% 74.88/9.97 = { by lemma 12 }
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% 74.88/9.97 = { by axiom 3 (condensed_detachment) }
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% 74.88/9.98 = { by axiom 2 (condensed_detachment) R->L }
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% 74.88/9.98 = { by axiom 1 (condensed_detachment) R->L }
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% 74.88/9.98 = { by axiom 1 (condensed_detachment) R->L }
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% 75.45/9.98 = { by lemma 7 R->L }
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% 75.45/9.99 = { by axiom 3 (condensed_detachment) R->L }
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% 75.45/9.99 = { by lemma 12 R->L }
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% 75.45/10.00 = { by axiom 1 (condensed_detachment) }
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% 75.45/10.01 = { by axiom 2 (condensed_detachment) }
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% 75.45/10.01 = { by axiom 3 (condensed_detachment) R->L }
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% 75.45/10.01 = { by lemma 10 }
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% 75.45/10.01 = { by axiom 2 (condensed_detachment) }
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% 75.45/10.02 = { by axiom 3 (condensed_detachment) }
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% 75.45/10.02 = { by axiom 4 (s_6) }
% 75.45/10.02 fresh2(fresh2(true, true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 75.45/10.02 = { by axiom 1 (condensed_detachment) }
% 75.45/10.02 fresh2(true, true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 75.45/10.02 = { by axiom 1 (condensed_detachment) }
% 75.45/10.02 true
% 75.45/10.02 % SZS output end Proof
% 75.45/10.02
% 75.45/10.02 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------