TSTP Solution File: LCL113-10 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL113-10 : TPTP v8.1.2. Released v7.3.0.
% 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 08:17:30 EDT 2023
% Result : Unsatisfiable 144.85s 18.92s
% Output : Proof 145.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL113-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Aug 25 05:41:35 EDT 2023
% 0.13/0.34 % CPUTime :
% 144.85/18.92 Command-line arguments: --no-flatten-goal
% 144.85/18.92
% 144.85/18.92 % SZS status Unsatisfiable
% 144.85/18.92
% 145.00/18.93 % SZS output start Proof
% 145.00/18.93 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 145.00/18.93 Axiom 2 (mv_1): is_a_theorem(implies(X, implies(Y, X))) = true.
% 145.00/18.93 Axiom 3 (mv_5): is_a_theorem(implies(implies(not(X), not(Y)), implies(Y, X))) = true.
% 145.00/18.93 Axiom 4 (mv_2): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 145.00/18.93 Axiom 5 (mv_3): is_a_theorem(implies(implies(implies(X, Y), Y), implies(implies(Y, X), X))) = true.
% 145.00/18.93 Axiom 6 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 145.00/18.93
% 145.00/18.93 Lemma 7: ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), Z)), true, is_a_theorem(Z), true) = true.
% 145.00/18.93 Proof:
% 145.00/18.93 ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), Z)), true, is_a_theorem(Z), true)
% 145.00/18.93 = { by axiom 1 (ifeq_axiom) R->L }
% 145.00/18.93 ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), Z)), true, ifeq(true, true, is_a_theorem(Z), true), true)
% 145.00/18.93 = { by axiom 2 (mv_1) R->L }
% 145.00/18.93 ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), Z)), true, ifeq(is_a_theorem(implies(X, implies(Y, X))), true, is_a_theorem(Z), true), true)
% 145.00/18.94 = { by axiom 6 (condensed_detachment) }
% 145.00/18.94 true
% 145.00/18.94
% 145.00/18.94 Lemma 8: ifeq(is_a_theorem(implies(implies(X, Y), Z)), true, is_a_theorem(implies(Y, Z)), true) = true.
% 145.00/18.94 Proof:
% 145.00/18.94 ifeq(is_a_theorem(implies(implies(X, Y), Z)), true, is_a_theorem(implies(Y, Z)), true)
% 145.00/18.94 = { by axiom 1 (ifeq_axiom) R->L }
% 145.00/18.94 ifeq(true, true, ifeq(is_a_theorem(implies(implies(X, Y), Z)), true, is_a_theorem(implies(Y, Z)), true), true)
% 145.00/18.94 = { by lemma 7 R->L }
% 145.00/18.94 ifeq(ifeq(is_a_theorem(implies(implies(Y, implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, is_a_theorem(implies(implies(implies(X, Y), Z), implies(Y, Z))), true), true, ifeq(is_a_theorem(implies(implies(X, Y), Z)), true, is_a_theorem(implies(Y, Z)), true), true)
% 145.00/18.94 = { by axiom 4 (mv_2) }
% 145.00/18.94 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(X, Y), Z), implies(Y, Z))), true), true, ifeq(is_a_theorem(implies(implies(X, Y), Z)), true, is_a_theorem(implies(Y, Z)), true), true)
% 145.00/18.94 = { by axiom 1 (ifeq_axiom) }
% 145.00/18.94 ifeq(is_a_theorem(implies(implies(implies(X, Y), Z), implies(Y, Z))), true, ifeq(is_a_theorem(implies(implies(X, Y), Z)), true, is_a_theorem(implies(Y, Z)), true), true)
% 145.00/18.94 = { by axiom 6 (condensed_detachment) }
% 145.00/18.94 true
% 145.00/18.94
% 145.00/18.94 Lemma 9: ifeq(is_a_theorem(implies(X, Y)), true, is_a_theorem(implies(implies(Y, Z), implies(X, Z))), true) = true.
% 145.00/18.94 Proof:
% 145.00/18.94 ifeq(is_a_theorem(implies(X, Y)), true, is_a_theorem(implies(implies(Y, Z), implies(X, Z))), true)
% 145.00/18.94 = { by axiom 1 (ifeq_axiom) R->L }
% 145.00/18.94 ifeq(true, true, ifeq(is_a_theorem(implies(X, Y)), true, is_a_theorem(implies(implies(Y, Z), implies(X, Z))), true), true)
% 145.00/18.94 = { by axiom 4 (mv_2) R->L }
% 145.00/18.94 ifeq(is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))), true, ifeq(is_a_theorem(implies(X, Y)), true, is_a_theorem(implies(implies(Y, Z), implies(X, Z))), true), true)
% 145.00/18.94 = { by axiom 6 (condensed_detachment) }
% 145.00/18.94 true
% 145.00/18.94
% 145.00/18.94 Lemma 10: is_a_theorem(implies(implies(implies(implies(X, Y), Y), Z), implies(X, Z))) = true.
% 145.00/18.94 Proof:
% 145.00/18.94 is_a_theorem(implies(implies(implies(implies(X, Y), Y), Z), implies(X, Z)))
% 145.00/18.94 = { by axiom 1 (ifeq_axiom) R->L }
% 145.00/18.94 ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X, Y), Y), Z), implies(X, Z))), true)
% 145.00/18.94 = { by lemma 8 R->L }
% 145.00/18.94 ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, X), X), implies(implies(X, Y), Y))), true, is_a_theorem(implies(X, implies(implies(X, Y), Y))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Y), Z), implies(X, Z))), true)
% 145.00/18.94 = { by axiom 5 (mv_3) }
% 145.00/18.94 ifeq(ifeq(true, true, is_a_theorem(implies(X, implies(implies(X, Y), Y))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), Y), Z), implies(X, Z))), true)
% 145.00/18.94 = { by axiom 1 (ifeq_axiom) }
% 145.00/18.94 ifeq(is_a_theorem(implies(X, implies(implies(X, Y), Y))), true, is_a_theorem(implies(implies(implies(implies(X, Y), Y), Z), implies(X, Z))), true)
% 145.00/18.94 = { by lemma 9 }
% 145.00/18.94 true
% 145.00/18.94
% 145.00/18.94 Lemma 11: ifeq(is_a_theorem(implies(implies(implies(X, Y), Y), Z)), true, is_a_theorem(implies(X, Z)), true) = true.
% 145.00/18.94 Proof:
% 145.00/18.94 ifeq(is_a_theorem(implies(implies(implies(X, Y), Y), Z)), true, is_a_theorem(implies(X, Z)), true)
% 145.00/18.94 = { by axiom 1 (ifeq_axiom) R->L }
% 145.00/18.94 ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X, Y), Y), Z)), true, is_a_theorem(implies(X, Z)), true), true)
% 145.00/18.94 = { by lemma 10 R->L }
% 145.00/18.94 ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), Y), Z), implies(X, Z))), true, ifeq(is_a_theorem(implies(implies(implies(X, Y), Y), Z)), true, is_a_theorem(implies(X, Z)), true), true)
% 145.00/18.94 = { by axiom 6 (condensed_detachment) }
% 145.00/18.94 true
% 145.00/18.94
% 145.00/18.94 Lemma 12: is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))) = true.
% 145.00/18.94 Proof:
% 145.00/18.94 is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W)))
% 145.00/18.94 = { by axiom 1 (ifeq_axiom) R->L }
% 145.00/18.94 ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))), true)
% 145.00/18.94 = { by axiom 4 (mv_2) R->L }
% 145.00/18.94 ifeq(is_a_theorem(implies(implies(Z, X), implies(implies(X, Y), implies(Z, Y)))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))), true)
% 145.00/18.94 = { by lemma 9 }
% 145.00/18.94 true
% 145.00/18.94
% 145.00/18.94 Lemma 13: ifeq(is_a_theorem(implies(implies(implies(not(X), not(Y)), implies(Y, X)), Z)), true, is_a_theorem(Z), true) = true.
% 145.00/18.94 Proof:
% 145.00/18.94 ifeq(is_a_theorem(implies(implies(implies(not(X), not(Y)), implies(Y, X)), Z)), true, is_a_theorem(Z), true)
% 145.00/18.94 = { by axiom 1 (ifeq_axiom) R->L }
% 145.00/18.94 ifeq(is_a_theorem(implies(implies(implies(not(X), not(Y)), implies(Y, X)), Z)), true, ifeq(true, true, is_a_theorem(Z), true), true)
% 145.00/18.94 = { by axiom 3 (mv_5) R->L }
% 145.00/18.94 ifeq(is_a_theorem(implies(implies(implies(not(X), not(Y)), implies(Y, X)), Z)), true, ifeq(is_a_theorem(implies(implies(not(X), not(Y)), implies(Y, X))), true, is_a_theorem(Z), true), true)
% 145.00/18.94 = { by axiom 6 (condensed_detachment) }
% 145.00/18.94 true
% 145.00/18.94
% 145.00/18.94 Lemma 14: ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), W)), true, is_a_theorem(implies(implies(Z, X), W)), true) = true.
% 145.00/18.94 Proof:
% 145.00/18.94 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), W)), true, is_a_theorem(implies(implies(Z, X), W)), true)
% 145.00/18.94 = { by axiom 1 (ifeq_axiom) R->L }
% 145.00/18.94 ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), W)), true, is_a_theorem(implies(implies(Z, X), W)), true), true)
% 145.00/18.94 = { by lemma 12 R->L }
% 145.00/18.94 ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))), true, ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), W)), true, is_a_theorem(implies(implies(Z, X), W)), true), true)
% 145.00/18.94 = { by axiom 6 (condensed_detachment) }
% 145.00/18.94 true
% 145.00/18.94
% 145.00/18.94 Goal 1 (prove_mv_33): is_a_theorem(implies(implies(not(a), b), implies(not(b), a))) = true.
% 145.00/18.94 Proof:
% 145.00/18.94 is_a_theorem(implies(implies(not(a), b), implies(not(b), a)))
% 145.00/18.94 = { by axiom 1 (ifeq_axiom) R->L }
% 145.00/18.94 ifeq(true, true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true)
% 145.00/18.94 = { by axiom 6 (condensed_detachment) R->L }
% 145.00/18.94 ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), b), implies(implies(b, not(not(b))), implies(not(b), a))), implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a))))), true, ifeq(is_a_theorem(implies(implies(not(a), b), implies(implies(b, not(not(b))), implies(not(b), a)))), true, is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true)
% 145.00/18.94 = { by axiom 1 (ifeq_axiom) R->L }
% 145.00/18.94 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(a), b), implies(implies(b, not(not(b))), implies(not(b), a))), implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(a), b), implies(implies(b, not(not(b))), implies(not(b), a)))), true, is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true)
% 145.00/18.94 = { by lemma 10 R->L }
% 145.00/18.94 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, not(not(b))), implies(not(b), a)), implies(not(b), a)), implies(implies(not(a), b), implies(not(b), a))), implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a))))), true, is_a_theorem(implies(implies(implies(not(a), b), implies(implies(b, not(not(b))), implies(not(b), a))), implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(a), b), implies(implies(b, not(not(b))), implies(not(b), a)))), true, is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true)
% 145.00/18.94 = { by lemma 14 }
% 145.00/18.94 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(a), b), implies(implies(b, not(not(b))), implies(not(b), a)))), true, is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true)
% 145.00/18.94 = { by axiom 1 (ifeq_axiom) }
% 145.00/18.94 ifeq(ifeq(is_a_theorem(implies(implies(not(a), b), implies(implies(b, not(not(b))), implies(not(b), a)))), true, is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true)
% 145.00/18.94 = { by axiom 1 (ifeq_axiom) R->L }
% 145.00/18.94 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(a), b), implies(implies(b, not(not(b))), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true)
% 145.00/18.94 = { by lemma 13 R->L }
% 145.00/18.94 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), not(not(b))), implies(not(b), a)), implies(implies(implies(b, not(not(b))), implies(not(a), not(not(b)))), implies(implies(b, not(not(b))), implies(not(b), a))))), true, is_a_theorem(implies(implies(implies(b, not(not(b))), implies(not(a), not(not(b)))), implies(implies(b, not(not(b))), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(implies(b, not(not(b))), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true)
% 145.00/18.94 = { by axiom 1 (ifeq_axiom) R->L }
% 145.00/18.94 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(a), not(not(b))), implies(not(b), a)), implies(implies(implies(b, not(not(b))), implies(not(a), not(not(b)))), implies(implies(b, not(not(b))), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(implies(b, not(not(b))), implies(not(a), not(not(b)))), implies(implies(b, not(not(b))), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(implies(b, not(not(b))), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true)
% 145.00/18.94 = { by lemma 12 R->L }
% 145.00/18.94 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(a), not(not(b))), implies(not(b), a)), implies(implies(b, not(not(b))), implies(not(b), a))), implies(implies(b, not(not(b))), implies(not(b), a))), implies(implies(implies(b, not(not(b))), implies(not(a), not(not(b)))), implies(implies(b, not(not(b))), implies(not(b), a))))), true, is_a_theorem(implies(implies(implies(not(a), not(not(b))), implies(not(b), a)), implies(implies(implies(b, not(not(b))), implies(not(a), not(not(b)))), implies(implies(b, not(not(b))), implies(not(b), a))))), true), true, is_a_theorem(implies(implies(implies(b, not(not(b))), implies(not(a), not(not(b)))), implies(implies(b, not(not(b))), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(implies(b, not(not(b))), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true)
% 145.00/18.94 = { by lemma 11 }
% 145.00/18.94 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, not(not(b))), implies(not(a), not(not(b)))), implies(implies(b, not(not(b))), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(implies(b, not(not(b))), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true)
% 145.00/18.94 = { by axiom 1 (ifeq_axiom) }
% 145.00/18.95 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, not(not(b))), implies(not(a), not(not(b)))), implies(implies(b, not(not(b))), implies(not(b), a)))), true, is_a_theorem(implies(implies(not(a), b), implies(implies(b, not(not(b))), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true)
% 145.00/18.95 = { by lemma 14 }
% 145.00/18.95 ifeq(ifeq(true, true, is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true)
% 145.00/18.95 = { by axiom 1 (ifeq_axiom) }
% 145.00/18.95 ifeq(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true)
% 145.00/18.95 = { by axiom 1 (ifeq_axiom) R->L }
% 145.00/18.95 ifeq(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true, ifeq(true, true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true), true)
% 145.00/18.95 = { by axiom 6 (condensed_detachment) R->L }
% 145.00/18.95 ifeq(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(b))), not(b)), implies(b, not(not(b))))), true, ifeq(is_a_theorem(implies(not(not(not(b))), not(b))), true, is_a_theorem(implies(b, not(not(b)))), true), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true), true)
% 145.00/18.95 = { by axiom 3 (mv_5) }
% 145.00/18.95 ifeq(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(not(b))), not(b))), true, is_a_theorem(implies(b, not(not(b)))), true), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true), true)
% 145.00/18.95 = { by axiom 1 (ifeq_axiom) }
% 145.00/18.95 ifeq(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true, ifeq(ifeq(is_a_theorem(implies(not(not(not(b))), not(b))), true, is_a_theorem(implies(b, not(not(b)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true), true)
% 145.00/18.95 = { by axiom 1 (ifeq_axiom) R->L }
% 145.00/18.95 ifeq(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(not(b))), not(b))), true), true, is_a_theorem(implies(b, not(not(b)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true), true)
% 145.00/18.95 = { by lemma 11 R->L }
% 145.00/18.95 ifeq(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(b)), not(b)), implies(not(not(not(b))), not(b)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(b))), not(b)))), true), true, is_a_theorem(implies(not(not(not(b))), not(b))), true), true, is_a_theorem(implies(b, not(not(b)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true), true)
% 145.00/18.95 = { by axiom 1 (ifeq_axiom) R->L }
% 145.00/18.95 ifeq(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(b)), not(b)), implies(not(not(not(b))), not(b)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(b))), not(b)))), true), true, is_a_theorem(implies(not(not(not(b))), not(b))), true), true, is_a_theorem(implies(b, not(not(b)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true), true)
% 145.00/18.95 = { by lemma 13 R->L }
% 145.00/18.95 ifeq(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(b))), implies(not(not(not(b))), implies(implies(X, implies(Y, X)), not(b))))), true, is_a_theorem(implies(not(not(not(b))), implies(implies(X, implies(Y, X)), not(b)))), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(b)), not(b)), implies(not(not(not(b))), not(b)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(b))), not(b)))), true), true, is_a_theorem(implies(not(not(not(b))), not(b))), true), true, is_a_theorem(implies(b, not(not(b)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true), true)
% 145.00/18.95 = { by axiom 1 (ifeq_axiom) R->L }
% 145.00/18.95 ifeq(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(b))), implies(not(not(not(b))), implies(implies(X, implies(Y, X)), not(b))))), true), true, is_a_theorem(implies(not(not(not(b))), implies(implies(X, implies(Y, X)), not(b)))), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(b)), not(b)), implies(not(not(not(b))), not(b)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(b))), not(b)))), true), true, is_a_theorem(implies(not(not(not(b))), not(b))), true), true, is_a_theorem(implies(b, not(not(b)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true), true)
% 145.00/18.95 = { by lemma 8 R->L }
% 145.00/18.95 ifeq(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(b)))), implies(not(not(b)), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(not(not(not(b))), implies(not(not(b)), not(implies(X, implies(Y, X)))))), true), true, is_a_theorem(implies(implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(b))), implies(not(not(not(b))), implies(implies(X, implies(Y, X)), not(b))))), true), true, is_a_theorem(implies(not(not(not(b))), implies(implies(X, implies(Y, X)), not(b)))), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(b)), not(b)), implies(not(not(not(b))), not(b)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(b))), not(b)))), true), true, is_a_theorem(implies(not(not(not(b))), not(b))), true), true, is_a_theorem(implies(b, not(not(b)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true), true)
% 145.00/18.95 = { by axiom 3 (mv_5) }
% 145.00/18.95 ifeq(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(not(b))), implies(not(not(b)), not(implies(X, implies(Y, X)))))), true), true, is_a_theorem(implies(implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(b))), implies(not(not(not(b))), implies(implies(X, implies(Y, X)), not(b))))), true), true, is_a_theorem(implies(not(not(not(b))), implies(implies(X, implies(Y, X)), not(b)))), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(b)), not(b)), implies(not(not(not(b))), not(b)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(b))), not(b)))), true), true, is_a_theorem(implies(not(not(not(b))), not(b))), true), true, is_a_theorem(implies(b, not(not(b)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true), true)
% 145.00/18.95 = { by axiom 1 (ifeq_axiom) }
% 145.00/18.95 ifeq(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(not(b))), implies(not(not(b)), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(b))), implies(not(not(not(b))), implies(implies(X, implies(Y, X)), not(b))))), true), true, is_a_theorem(implies(not(not(not(b))), implies(implies(X, implies(Y, X)), not(b)))), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(b)), not(b)), implies(not(not(not(b))), not(b)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(b))), not(b)))), true), true, is_a_theorem(implies(not(not(not(b))), not(b))), true), true, is_a_theorem(implies(b, not(not(b)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true), true)
% 145.00/18.95 = { by lemma 9 }
% 145.00/18.95 ifeq(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(not(b))), implies(implies(X, implies(Y, X)), not(b)))), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(b)), not(b)), implies(not(not(not(b))), not(b)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(b))), not(b)))), true), true, is_a_theorem(implies(not(not(not(b))), not(b))), true), true, is_a_theorem(implies(b, not(not(b)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true), true)
% 145.00/18.95 = { by axiom 1 (ifeq_axiom) }
% 145.00/18.95 ifeq(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(not(b))), implies(implies(X, implies(Y, X)), not(b)))), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(b)), not(b)), implies(not(not(not(b))), not(b)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(b))), not(b)))), true), true, is_a_theorem(implies(not(not(not(b))), not(b))), true), true, is_a_theorem(implies(b, not(not(b)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true), true)
% 145.00/18.95 = { by lemma 9 }
% 145.00/18.95 ifeq(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(b))), not(b)))), true), true, is_a_theorem(implies(not(not(not(b))), not(b))), true), true, is_a_theorem(implies(b, not(not(b)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true), true)
% 145.00/18.95 = { by axiom 1 (ifeq_axiom) }
% 145.00/18.95 ifeq(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(b))), not(b)))), true, is_a_theorem(implies(not(not(not(b))), not(b))), true), true, is_a_theorem(implies(b, not(not(b)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true), true)
% 145.00/18.95 = { by lemma 7 }
% 145.00/18.95 ifeq(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(b, not(not(b)))), true), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true), true)
% 145.00/18.95 = { by axiom 1 (ifeq_axiom) }
% 145.00/18.95 ifeq(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(b), a)))), true, ifeq(is_a_theorem(implies(b, not(not(b)))), true, is_a_theorem(implies(implies(not(a), b), implies(not(b), a))), true), true)
% 145.00/18.95 = { by axiom 6 (condensed_detachment) }
% 145.00/18.95 true
% 145.00/18.95 % SZS output end Proof
% 145.00/18.95
% 145.00/18.95 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------