TSTP Solution File: LCL104-1 by Twee---2.4.2
View Problem
- Process Solution
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% File : Twee---2.4.2
% Problem : LCL104-1 : 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 : n008.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 08:17:26 EDT 2023
% Result : Unsatisfiable 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LCL104-1 : 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
% 0.14/0.36 % Computer : n008.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 04:27:32 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.45 Command-line arguments: --no-flatten-goal
% 0.21/0.45
% 0.21/0.45 % SZS status Unsatisfiable
% 0.21/0.45
% 0.21/0.48 % SZS output start Proof
% 0.21/0.48 Take the following subset of the input axioms:
% 0.21/0.48 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 0.21/0.48 fof(p_4, axiom, ![Z, U, X2, Y2]: is_a_theorem(equivalent(X2, equivalent(equivalent(equivalent(equivalent(Y2, Z), equivalent(Y2, U)), equivalent(Z, U)), X2)))).
% 0.21/0.48 fof(prove_p_1, negated_conjecture, ~is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))).
% 0.21/0.48 fof(q_3, axiom, ![X2, Y2, Z2]: is_a_theorem(equivalent(equivalent(equivalent(X2, Y2), equivalent(equivalent(Y2, X2), Z2)), Z2))).
% 0.21/0.48
% 0.21/0.48 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.48 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.48 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.49 fresh(y, y, x1...xn) = u
% 0.21/0.49 C => fresh(s, t, x1...xn) = v
% 0.21/0.49 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.49 variables of u and v.
% 0.21/0.49 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.49 input problem has no model of domain size 1).
% 0.21/0.49
% 0.21/0.49 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.49
% 0.21/0.49 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 0.21/0.49 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 0.21/0.49 Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 0.21/0.49 Axiom 4 (q_3): is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, X), Z)), Z)) = true.
% 0.21/0.49 Axiom 5 (p_4): is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, W)), equivalent(Z, W)), X))) = true.
% 0.21/0.49
% 0.21/0.49 Lemma 6: is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y)))) = true.
% 0.21/0.49 Proof:
% 0.21/0.49 is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 0.21/0.49 = { by axiom 2 (condensed_detachment) R->L }
% 0.21/0.49 fresh(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(Z, Y)), equivalent(X, Y)), equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 0.21/0.49 = { by axiom 4 (q_3) R->L }
% 0.21/0.49 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(Z, Y)), equivalent(X, Y)), equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))), true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(Z, Y)), equivalent(X, Y)), equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 0.21/0.49 = { by axiom 3 (condensed_detachment) }
% 0.21/0.49 fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(Z, Y)), equivalent(X, Y)), equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y)))))), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 0.21/0.49 = { by axiom 5 (p_4) }
% 0.21/0.49 fresh2(true, true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 0.21/0.49 = { by axiom 1 (condensed_detachment) }
% 0.21/0.49 true
% 0.21/0.49
% 0.21/0.49 Lemma 7: fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(equivalent(Z, X), equivalent(Z, Y))) = is_a_theorem(equivalent(equivalent(Z, X), equivalent(Z, Y))).
% 0.21/0.49 Proof:
% 0.21/0.49 fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(equivalent(Z, X), equivalent(Z, Y)))
% 0.21/0.49 = { by axiom 3 (condensed_detachment) R->L }
% 0.21/0.49 fresh(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y)))), true, equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y)))
% 0.21/0.49 = { by lemma 6 }
% 0.21/0.49 fresh(true, true, equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y)))
% 0.21/0.49 = { by axiom 2 (condensed_detachment) }
% 0.21/0.49 is_a_theorem(equivalent(equivalent(Z, X), equivalent(Z, Y)))
% 0.21/0.49
% 0.21/0.49 Lemma 8: is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))) = true.
% 0.21/0.49 Proof:
% 0.21/0.49 is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.21/0.49 = { by axiom 2 (condensed_detachment) R->L }
% 0.21/0.49 fresh(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.21/0.49 = { by axiom 1 (condensed_detachment) R->L }
% 0.21/0.49 fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.21/0.49 = { by axiom 1 (condensed_detachment) R->L }
% 0.21/0.49 fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.21/0.49 = { by axiom 1 (condensed_detachment) R->L }
% 0.21/0.49 fresh(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), equivalent(X, Z))), equivalent(equivalent(Y, Z), W))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.21/0.49 = { by lemma 6 R->L }
% 0.21/0.50 fresh(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), equivalent(X, Z))), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), equivalent(X, Z))), equivalent(equivalent(Y, Z), W))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.21/0.50 = { by lemma 7 }
% 0.21/0.50 fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), equivalent(X, Z))), equivalent(equivalent(Y, Z), W))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.21/0.50 = { by axiom 3 (condensed_detachment) R->L }
% 0.21/0.50 fresh(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), equivalent(X, Z))), equivalent(equivalent(Y, Z), W)))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), equivalent(X, Z))), equivalent(equivalent(Y, Z), W)))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.21/0.50 = { by lemma 7 R->L }
% 0.21/0.50 fresh(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), equivalent(X, Z))), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(Y, Z), W))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), equivalent(X, Z))), equivalent(equivalent(Y, Z), W)))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), equivalent(X, Z))), equivalent(equivalent(Y, Z), W)))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.21/0.50 = { by axiom 4 (q_3) }
% 0.21/0.50 fresh(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), equivalent(X, Z))), equivalent(equivalent(Y, Z), W)))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), equivalent(X, Z))), equivalent(equivalent(Y, Z), W)))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.21/0.50 = { by axiom 1 (condensed_detachment) }
% 0.21/0.50 fresh(fresh2(fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), equivalent(X, Z))), equivalent(equivalent(Y, Z), W)))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.21/0.50 = { by axiom 2 (condensed_detachment) }
% 0.21/0.50 fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.21/0.50 = { by lemma 7 }
% 0.21/0.50 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.21/0.50 = { by axiom 3 (condensed_detachment) }
% 0.21/0.50 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.21/0.50 = { by axiom 5 (p_4) }
% 0.21/0.50 fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.21/0.50 = { by axiom 1 (condensed_detachment) }
% 0.21/0.50 true
% 0.21/0.50
% 0.21/0.50 Goal 1 (prove_p_1): is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))) = true.
% 0.21/0.50 Proof:
% 0.21/0.50 is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))
% 0.21/0.50 = { by axiom 2 (condensed_detachment) R->L }
% 0.21/0.50 fresh(true, true, equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))
% 0.21/0.50 = { by lemma 8 R->L }
% 0.21/0.50 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))
% 0.21/0.50 = { by axiom 3 (condensed_detachment) }
% 0.21/0.50 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))
% 0.21/0.50 = { by lemma 8 }
% 0.21/0.50 fresh2(true, true, equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))
% 0.21/0.50 = { by axiom 1 (condensed_detachment) }
% 0.21/0.50 true
% 0.21/0.50 % SZS output end Proof
% 0.21/0.50
% 0.21/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------