TSTP Solution File: LCL011-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL011-1 : 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 : n026.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 08:17:01 EDT 2023
% Result : Unsatisfiable 0.20s 0.61s
% 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
% 0.00/0.13 % Problem : LCL011-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 02:39:17 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.61 Command-line arguments: --no-flatten-goal
% 0.20/0.61
% 0.20/0.61 % SZS status Unsatisfiable
% 0.20/0.61
% 0.20/0.62 % SZS output start Proof
% 0.20/0.62 Take the following subset of the input axioms:
% 0.20/0.62 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 0.20/0.62 fof(prove_yqf, negated_conjecture, ~is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))).
% 0.20/0.62 fof(yqj, axiom, ![Z, X2, Y2]: is_a_theorem(equivalent(equivalent(X2, Y2), equivalent(equivalent(Z, X2), equivalent(Y2, Z))))).
% 0.20/0.62
% 0.20/0.62 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.62 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.62 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.62 fresh(y, y, x1...xn) = u
% 0.20/0.62 C => fresh(s, t, x1...xn) = v
% 0.20/0.62 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.62 variables of u and v.
% 0.20/0.62 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.62 input problem has no model of domain size 1).
% 0.20/0.62
% 0.20/0.62 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.62
% 0.20/0.62 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 0.20/0.62 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 0.20/0.62 Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 0.20/0.62 Axiom 4 (yqj): is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Y, Z)))) = true.
% 0.20/0.62
% 0.20/0.62 Lemma 5: fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(equivalent(Z, X), equivalent(Y, Z))) = is_a_theorem(equivalent(equivalent(Z, X), equivalent(Y, Z))).
% 0.20/0.62 Proof:
% 0.20/0.62 fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(equivalent(Z, X), equivalent(Y, Z)))
% 0.20/0.62 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.62 fresh(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Y, Z)))), true, equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Y, Z)))
% 0.20/0.62 = { by axiom 4 (yqj) }
% 0.20/0.62 fresh(true, true, equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Y, Z)))
% 0.20/0.62 = { by axiom 2 (condensed_detachment) }
% 0.20/0.62 is_a_theorem(equivalent(equivalent(Z, X), equivalent(Y, Z)))
% 0.20/0.62
% 0.20/0.62 Lemma 6: is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(equivalent(W, Y), equivalent(Z, W)), X))) = true.
% 0.20/0.62 Proof:
% 0.20/0.62 is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(equivalent(W, Y), equivalent(Z, W)), X)))
% 0.20/0.62 = { by lemma 5 R->L }
% 0.20/0.62 fresh2(is_a_theorem(equivalent(equivalent(Y, Z), equivalent(equivalent(W, Y), equivalent(Z, W)))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(equivalent(W, Y), equivalent(Z, W)), X)))
% 0.20/0.62 = { by axiom 4 (yqj) }
% 0.20/0.62 fresh2(true, true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(equivalent(W, Y), equivalent(Z, W)), X)))
% 0.20/0.62 = { by axiom 1 (condensed_detachment) }
% 0.20/0.62 true
% 0.20/0.62
% 0.20/0.62 Lemma 7: fresh2(is_a_theorem(equivalent(X, equivalent(Y, Z))), true, equivalent(equivalent(equivalent(W, Y), equivalent(Z, W)), X)) = is_a_theorem(equivalent(equivalent(equivalent(W, Y), equivalent(Z, W)), X)).
% 0.20/0.62 Proof:
% 0.20/0.62 fresh2(is_a_theorem(equivalent(X, equivalent(Y, Z))), true, equivalent(equivalent(equivalent(W, Y), equivalent(Z, W)), X))
% 0.20/0.62 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.62 fresh(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(equivalent(W, Y), equivalent(Z, W)), X))), true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(equivalent(W, Y), equivalent(Z, W)), X))
% 0.20/0.62 = { by lemma 6 }
% 0.20/0.62 fresh(true, true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(equivalent(W, Y), equivalent(Z, W)), X))
% 0.20/0.62 = { by axiom 2 (condensed_detachment) }
% 0.20/0.62 is_a_theorem(equivalent(equivalent(equivalent(W, Y), equivalent(Z, W)), X))
% 0.20/0.62
% 0.20/0.62 Lemma 8: fresh2(is_a_theorem(equivalent(X, equivalent(Y, Z))), true, equivalent(equivalent(Z, Y), X)) = is_a_theorem(equivalent(equivalent(Z, Y), X)).
% 0.20/0.62 Proof:
% 0.20/0.62 fresh2(is_a_theorem(equivalent(X, equivalent(Y, Z))), true, equivalent(equivalent(Z, Y), X))
% 0.20/0.62 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.62 fresh(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))), true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))
% 0.20/0.62 = { by lemma 5 R->L }
% 0.20/0.62 fresh(fresh2(is_a_theorem(equivalent(equivalent(Y, Z), equivalent(Z, Y))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))), true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))
% 0.20/0.62 = { by lemma 5 R->L }
% 0.20/0.63 fresh(fresh2(fresh2(is_a_theorem(equivalent(Z, Z)), true, equivalent(equivalent(Y, Z), equivalent(Z, Y))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))), true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))
% 0.20/0.63 = { by axiom 2 (condensed_detachment) R->L }
% 0.20/0.63 fresh(fresh2(fresh2(fresh(true, true, equivalent(equivalent(W, equivalent(Z, Z)), equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), W)), equivalent(Z, Z)), true, equivalent(equivalent(Y, Z), equivalent(Z, Y))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))), true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))
% 0.20/0.63 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.63 fresh(fresh2(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(W, equivalent(Z, Z)), equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), W)), equivalent(Z, Z))), true, equivalent(equivalent(W, equivalent(Z, Z)), equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), W)), equivalent(Z, Z)), true, equivalent(equivalent(Y, Z), equivalent(Z, Y))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))), true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))
% 0.20/0.63 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.63 fresh(fresh2(fresh2(fresh(fresh2(fresh2(true, true, equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(Z, Z))))), true, equivalent(equivalent(equivalent(W, equivalent(Z, Z)), equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), W)), equivalent(Z, Z))), true, equivalent(equivalent(W, equivalent(Z, Z)), equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), W)), equivalent(Z, Z)), true, equivalent(equivalent(Y, Z), equivalent(Z, Y))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))), true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))
% 0.20/0.63 = { by lemma 6 R->L }
% 0.20/0.63 fresh(fresh2(fresh2(fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(V, equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), equivalent(Z, Z))), equivalent(equivalent(equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(Z, Z))), equivalent(equivalent(Z, Z), equivalent(Z, Z))), V))), true, equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(Z, Z))))), true, equivalent(equivalent(equivalent(W, equivalent(Z, Z)), equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), W)), equivalent(Z, Z))), true, equivalent(equivalent(W, equivalent(Z, Z)), equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), W)), equivalent(Z, Z)), true, equivalent(equivalent(Y, Z), equivalent(Z, Y))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))), true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))
% 0.20/0.63 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.63 fresh(fresh2(fresh2(fresh(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(V, equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), equivalent(Z, Z))), equivalent(equivalent(equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(Z, Z))), equivalent(equivalent(Z, Z), equivalent(Z, Z))), V)), equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(Z, Z)))))), true, equivalent(equivalent(V, equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), equivalent(Z, Z))), equivalent(equivalent(equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(Z, Z))), equivalent(equivalent(Z, Z), equivalent(Z, Z))), V)), equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(Z, Z))))), true, equivalent(equivalent(equivalent(W, equivalent(Z, Z)), equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), W)), equivalent(Z, Z))), true, equivalent(equivalent(W, equivalent(Z, Z)), equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), W)), equivalent(Z, Z)), true, equivalent(equivalent(Y, Z), equivalent(Z, Y))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))), true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))
% 0.20/0.63 = { by lemma 7 R->L }
% 0.20/0.63 fresh(fresh2(fresh2(fresh(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(Z, Z)))), equivalent(equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), equivalent(Z, Z)), equivalent(equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(Z, Z))), equivalent(equivalent(Z, Z), equivalent(Z, Z)))))), true, equivalent(equivalent(equivalent(V, equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), equivalent(Z, Z))), equivalent(equivalent(equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(Z, Z))), equivalent(equivalent(Z, Z), equivalent(Z, Z))), V)), equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(Z, Z)))))), true, equivalent(equivalent(V, equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), equivalent(Z, Z))), equivalent(equivalent(equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(Z, Z))), equivalent(equivalent(Z, Z), equivalent(Z, Z))), V)), equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(Z, Z))))), true, equivalent(equivalent(equivalent(W, equivalent(Z, Z)), equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), W)), equivalent(Z, Z))), true, equivalent(equivalent(W, equivalent(Z, Z)), equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), W)), equivalent(Z, Z)), true, equivalent(equivalent(Y, Z), equivalent(Z, Y))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))), true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))
% 0.20/0.63 = { by axiom 4 (yqj) }
% 0.20/0.63 fresh(fresh2(fresh2(fresh(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(V, equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), equivalent(Z, Z))), equivalent(equivalent(equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(Z, Z))), equivalent(equivalent(Z, Z), equivalent(Z, Z))), V)), equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(Z, Z)))))), true, equivalent(equivalent(V, equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), equivalent(Z, Z))), equivalent(equivalent(equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(Z, Z))), equivalent(equivalent(Z, Z), equivalent(Z, Z))), V)), equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(Z, Z))))), true, equivalent(equivalent(equivalent(W, equivalent(Z, Z)), equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), W)), equivalent(Z, Z))), true, equivalent(equivalent(W, equivalent(Z, Z)), equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), W)), equivalent(Z, Z)), true, equivalent(equivalent(Y, Z), equivalent(Z, Y))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))), true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))
% 0.20/0.63 = { by axiom 1 (condensed_detachment) }
% 0.20/0.63 fresh(fresh2(fresh2(fresh(fresh2(fresh(true, true, equivalent(equivalent(V, equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), equivalent(Z, Z))), equivalent(equivalent(equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(Z, Z))), equivalent(equivalent(Z, Z), equivalent(Z, Z))), V)), equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(Z, Z))))), true, equivalent(equivalent(equivalent(W, equivalent(Z, Z)), equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), W)), equivalent(Z, Z))), true, equivalent(equivalent(W, equivalent(Z, Z)), equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), W)), equivalent(Z, Z)), true, equivalent(equivalent(Y, Z), equivalent(Z, Y))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))), true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))
% 0.20/0.63 = { by axiom 2 (condensed_detachment) }
% 0.20/0.63 fresh(fresh2(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(equivalent(Z, Z), equivalent(Z, Z))))), true, equivalent(equivalent(equivalent(W, equivalent(Z, Z)), equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), W)), equivalent(Z, Z))), true, equivalent(equivalent(W, equivalent(Z, Z)), equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), W)), equivalent(Z, Z)), true, equivalent(equivalent(Y, Z), equivalent(Z, Y))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))), true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))
% 0.20/0.63 = { by lemma 7 }
% 0.20/0.63 fresh(fresh2(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(Z, Z)), equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), W)), equivalent(Z, Z))), true, equivalent(equivalent(W, equivalent(Z, Z)), equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), W)), equivalent(Z, Z)), true, equivalent(equivalent(Y, Z), equivalent(Z, Y))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))), true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))
% 0.20/0.63 = { by axiom 3 (condensed_detachment) }
% 0.20/0.63 fresh(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(W, equivalent(Z, Z)), equivalent(equivalent(equivalent(Z, Z), equivalent(Z, Z)), W))), true, equivalent(Z, Z)), true, equivalent(equivalent(Y, Z), equivalent(Z, Y))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))), true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))
% 0.20/0.63 = { by lemma 6 }
% 0.20/0.63 fresh(fresh2(fresh2(fresh2(true, true, equivalent(Z, Z)), true, equivalent(equivalent(Y, Z), equivalent(Z, Y))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))), true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))
% 0.20/0.63 = { by axiom 1 (condensed_detachment) }
% 0.20/0.63 fresh(fresh2(fresh2(true, true, equivalent(equivalent(Y, Z), equivalent(Z, Y))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))), true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))
% 0.20/0.63 = { by axiom 1 (condensed_detachment) }
% 0.20/0.63 fresh(fresh2(true, true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))), true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))
% 0.20/0.63 = { by axiom 1 (condensed_detachment) }
% 0.20/0.63 fresh(true, true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, Y), X))
% 0.20/0.63 = { by axiom 2 (condensed_detachment) }
% 0.20/0.63 is_a_theorem(equivalent(equivalent(Z, Y), X))
% 0.20/0.63
% 0.20/0.63 Goal 1 (prove_yqf): is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))) = true.
% 0.20/0.63 Proof:
% 0.20/0.63 is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))
% 0.20/0.63 = { by lemma 8 R->L }
% 0.20/0.63 fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))
% 0.20/0.63 = { by lemma 8 R->L }
% 0.20/0.63 fresh2(fresh2(is_a_theorem(equivalent(equivalent(b, a), equivalent(equivalent(c, b), equivalent(a, c)))), true, equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))
% 0.20/0.63 = { by axiom 4 (yqj) }
% 0.20/0.63 fresh2(fresh2(true, true, equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(b, a))), true, equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))
% 0.20/0.63 = { by axiom 1 (condensed_detachment) }
% 0.20/0.63 fresh2(true, true, equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))))
% 0.20/0.63 = { by axiom 1 (condensed_detachment) }
% 0.20/0.63 true
% 0.20/0.63 % SZS output end Proof
% 0.20/0.63
% 0.20/0.63 RESULT: Unsatisfiable (the axioms are contradictory).
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