%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL241-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:49:27 AM UTC 2026
% Result : Unsatisfiable 219.15s 28.10s
% Output : Proof 225.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL241-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.42 % Computer : n015.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sun Sep 27 15:33:45 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 219.15/28.10 Command-line arguments: --flatten-regeneralise
% 219.15/28.10
% 219.15/28.10 % SZS status Unsatisfiable
% 219.15/28.10
% 223.06/28.69 % SZS output start Proof
% 223.06/28.69 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 223.06/28.69 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 223.06/28.69 Axiom 3 (and_defn): and(X, Y) = not(or(not(X), not(Y))).
% 223.06/28.69 Axiom 4 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 223.06/28.69 Axiom 5 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 223.06/28.69 Axiom 6 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 223.06/28.69 Axiom 7 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 223.06/28.69 Axiom 8 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 223.06/28.69 Axiom 9 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 223.86/28.71 Axiom 10 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 223.86/28.71
% 223.86/28.71 Goal 1 (prove_this): theorem(implies(and(p, q), q)) = true.
% 223.86/28.71 Proof:
% 223.86/28.71 theorem(implies(and(p, q), q))
% 223.86/28.71 = { by axiom 2 (ifeq_axiom) R->L }
% 223.86/28.71 ifeq(true, true, theorem(implies(and(p, q), q)), true)
% 223.86/28.71 = { by axiom 2 (ifeq_axiom) R->L }
% 223.86/28.71 ifeq(true, true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.71 = { by axiom 8 (rule_2) R->L }
% 223.86/28.71 ifeq(ifeq(theorem(implies(implies(not(not(q)), q), implies(implies(and(p, q), not(not(q))), implies(and(p, q), q)))), true, ifeq(theorem(implies(not(not(q)), q)), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.71 = { by axiom 2 (ifeq_axiom) R->L }
% 223.86/28.71 ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(not(q)), q), implies(implies(and(p, q), not(not(q))), implies(and(p, q), q)))), true), true, ifeq(theorem(implies(not(not(q)), q)), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.71 = { by axiom 9 (axiom_1_6) R->L }
% 223.86/28.71 ifeq(ifeq(ifeq(axiom(implies(implies(not(not(q)), q), implies(or(not(and(p, q)), not(not(q))), or(not(and(p, q)), q)))), true, theorem(implies(implies(not(not(q)), q), implies(implies(and(p, q), not(not(q))), implies(and(p, q), q)))), true), true, ifeq(theorem(implies(not(not(q)), q)), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.71 = { by axiom 1 (implies_definition) R->L }
% 223.86/28.71 ifeq(ifeq(ifeq(axiom(implies(implies(not(not(q)), q), implies(implies(and(p, q), not(not(q))), or(not(and(p, q)), q)))), true, theorem(implies(implies(not(not(q)), q), implies(implies(and(p, q), not(not(q))), implies(and(p, q), q)))), true), true, ifeq(theorem(implies(not(not(q)), q)), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.71 = { by axiom 1 (implies_definition) R->L }
% 223.86/28.71 ifeq(ifeq(ifeq(axiom(implies(implies(not(not(q)), q), implies(implies(and(p, q), not(not(q))), implies(and(p, q), q)))), true, theorem(implies(implies(not(not(q)), q), implies(implies(and(p, q), not(not(q))), implies(and(p, q), q)))), true), true, ifeq(theorem(implies(not(not(q)), q)), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.71 = { by axiom 4 (rule_1) }
% 223.86/28.71 ifeq(ifeq(true, true, ifeq(theorem(implies(not(not(q)), q)), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.71 = { by axiom 2 (ifeq_axiom) }
% 223.86/28.71 ifeq(ifeq(theorem(implies(not(not(q)), q)), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.71 = { by axiom 2 (ifeq_axiom) R->L }
% 223.86/28.71 ifeq(ifeq(ifeq(true, true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.71 = { by axiom 8 (rule_2) R->L }
% 223.86/28.72 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q)))), true, ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.72 = { by axiom 2 (ifeq_axiom) R->L }
% 223.86/28.72 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q)))), true), true, ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.72 = { by axiom 4 (rule_1) R->L }
% 223.86/28.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(not(not(q)), q), implies(not(not(q)), q)), implies(not(not(q)), q)), implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))))), true, theorem(implies(implies(or(implies(not(not(q)), q), implies(not(not(q)), q)), implies(not(not(q)), q)), implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))))), true), true, theorem(implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q)))), true), true, ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.72 = { by axiom 1 (implies_definition) }
% 223.86/28.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(not(not(q)), q), implies(not(not(q)), q)), implies(not(not(q)), q)), implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), or(not(or(implies(not(not(q)), q), not(q))), implies(not(not(q)), q))))), true, theorem(implies(implies(or(implies(not(not(q)), q), implies(not(not(q)), q)), implies(not(not(q)), q)), implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))))), true), true, theorem(implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q)))), true), true, ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.73 = { by axiom 1 (implies_definition) }
% 223.86/28.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(not(not(q)), q), implies(not(not(q)), q)), implies(not(not(q)), q)), implies(or(not(or(implies(not(not(q)), q), not(q))), or(implies(not(not(q)), q), implies(not(not(q)), q))), or(not(or(implies(not(not(q)), q), not(q))), implies(not(not(q)), q))))), true, theorem(implies(implies(or(implies(not(not(q)), q), implies(not(not(q)), q)), implies(not(not(q)), q)), implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))))), true), true, theorem(implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q)))), true), true, ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.73 = { by axiom 9 (axiom_1_6) }
% 223.86/28.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(implies(not(not(q)), q), implies(not(not(q)), q)), implies(not(not(q)), q)), implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))))), true), true, theorem(implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q)))), true), true, ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.73 = { by axiom 2 (ifeq_axiom) }
% 223.86/28.73 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(not(q)), q), implies(not(not(q)), q)), implies(not(not(q)), q)), implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))))), true, theorem(implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q)))), true), true, ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.73 = { by axiom 2 (ifeq_axiom) R->L }
% 223.86/28.73 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(not(q)), q), implies(not(not(q)), q)), implies(not(not(q)), q)), implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))))), true, ifeq(true, true, theorem(implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q)))), true), true), true, ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.74 = { by axiom 4 (rule_1) R->L }
% 223.86/28.74 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(not(q)), q), implies(not(not(q)), q)), implies(not(not(q)), q)), implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))))), true, ifeq(ifeq(axiom(implies(or(implies(not(not(q)), q), implies(not(not(q)), q)), implies(not(not(q)), q))), true, theorem(implies(or(implies(not(not(q)), q), implies(not(not(q)), q)), implies(not(not(q)), q))), true), true, theorem(implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q)))), true), true), true, ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.74 = { by axiom 6 (axiom_1_2) }
% 223.86/28.74 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(not(q)), q), implies(not(not(q)), q)), implies(not(not(q)), q)), implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))))), true, ifeq(ifeq(true, true, theorem(implies(or(implies(not(not(q)), q), implies(not(not(q)), q)), implies(not(not(q)), q))), true), true, theorem(implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q)))), true), true), true, ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.74 = { by axiom 2 (ifeq_axiom) }
% 223.86/28.74 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(not(q)), q), implies(not(not(q)), q)), implies(not(not(q)), q)), implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))))), true, ifeq(theorem(implies(or(implies(not(not(q)), q), implies(not(not(q)), q)), implies(not(not(q)), q))), true, theorem(implies(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))), implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q)))), true), true), true, ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.74 = { by axiom 8 (rule_2) }
% 223.86/28.74 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.74 = { by axiom 2 (ifeq_axiom) }
% 223.86/28.74 ifeq(ifeq(ifeq(ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.74 = { by axiom 2 (ifeq_axiom) R->L }
% 223.86/28.74 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.74 = { by axiom 8 (rule_2) R->L }
% 223.86/28.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(not(q)), implies(not(q), q)), implies(not(q), implies(not(not(q)), q)))), true, ifeq(theorem(implies(not(not(q)), implies(not(q), q))), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.74 = { by axiom 2 (ifeq_axiom) R->L }
% 223.86/28.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(not(q)), implies(not(q), q)), implies(not(q), implies(not(not(q)), q)))), true), true, ifeq(theorem(implies(not(not(q)), implies(not(q), q))), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.74 = { by axiom 10 (axiom_1_5) R->L }
% 223.86/28.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(not(not(q))), or(not(not(q)), q)), or(not(not(q)), or(not(not(not(q))), q)))), true, theorem(implies(implies(not(not(q)), implies(not(q), q)), implies(not(q), implies(not(not(q)), q)))), true), true, ifeq(theorem(implies(not(not(q)), implies(not(q), q))), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.74 = { by axiom 1 (implies_definition) R->L }
% 223.86/28.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(not(q)), or(not(not(q)), q)), or(not(not(q)), or(not(not(not(q))), q)))), true, theorem(implies(implies(not(not(q)), implies(not(q), q)), implies(not(q), implies(not(not(q)), q)))), true), true, ifeq(theorem(implies(not(not(q)), implies(not(q), q))), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.75 = { by axiom 1 (implies_definition) R->L }
% 223.86/28.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(not(q)), or(not(not(q)), q)), or(not(not(q)), implies(not(not(q)), q)))), true, theorem(implies(implies(not(not(q)), implies(not(q), q)), implies(not(q), implies(not(not(q)), q)))), true), true, ifeq(theorem(implies(not(not(q)), implies(not(q), q))), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.75 = { by axiom 1 (implies_definition) R->L }
% 223.86/28.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(not(q)), implies(not(q), q)), or(not(not(q)), implies(not(not(q)), q)))), true, theorem(implies(implies(not(not(q)), implies(not(q), q)), implies(not(q), implies(not(not(q)), q)))), true), true, ifeq(theorem(implies(not(not(q)), implies(not(q), q))), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.75 = { by axiom 1 (implies_definition) R->L }
% 223.86/28.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(not(q)), implies(not(q), q)), implies(not(q), implies(not(not(q)), q)))), true, theorem(implies(implies(not(not(q)), implies(not(q), q)), implies(not(q), implies(not(not(q)), q)))), true), true, ifeq(theorem(implies(not(not(q)), implies(not(q), q))), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.75 = { by axiom 4 (rule_1) }
% 223.86/28.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(not(not(q)), implies(not(q), q))), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.75 = { by axiom 2 (ifeq_axiom) }
% 223.86/28.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(not(not(q)), implies(not(q), q))), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.75 = { by axiom 2 (ifeq_axiom) R->L }
% 223.86/28.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(not(not(q)), implies(not(q), q))), true), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.75 = { by axiom 8 (rule_2) R->L }
% 223.86/28.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(q, not(not(q))), implies(not(q), q)), implies(or(not(not(not(q))), or(q, not(not(q)))), or(not(not(not(q))), implies(not(q), q))))), true, ifeq(theorem(implies(or(q, not(not(q))), implies(not(q), q))), true, theorem(implies(or(not(not(not(q))), or(q, not(not(q)))), or(not(not(not(q))), implies(not(q), q)))), true), true), true, theorem(implies(not(not(q)), implies(not(q), q))), true), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.75 = { by axiom 2 (ifeq_axiom) R->L }
% 223.86/28.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(q, not(not(q))), implies(not(q), q)), implies(or(not(not(not(q))), or(q, not(not(q)))), or(not(not(not(q))), implies(not(q), q))))), true), true, ifeq(theorem(implies(or(q, not(not(q))), implies(not(q), q))), true, theorem(implies(or(not(not(not(q))), or(q, not(not(q)))), or(not(not(not(q))), implies(not(q), q)))), true), true), true, theorem(implies(not(not(q)), implies(not(q), q))), true), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.75 = { by axiom 9 (axiom_1_6) R->L }
% 223.86/28.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(q, not(not(q))), implies(not(q), q)), implies(or(not(not(not(q))), or(q, not(not(q)))), or(not(not(not(q))), implies(not(q), q))))), true, theorem(implies(implies(or(q, not(not(q))), implies(not(q), q)), implies(or(not(not(not(q))), or(q, not(not(q)))), or(not(not(not(q))), implies(not(q), q))))), true), true, ifeq(theorem(implies(or(q, not(not(q))), implies(not(q), q))), true, theorem(implies(or(not(not(not(q))), or(q, not(not(q)))), or(not(not(not(q))), implies(not(q), q)))), true), true), true, theorem(implies(not(not(q)), implies(not(q), q))), true), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.76 = { by axiom 4 (rule_1) }
% 223.86/28.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(or(q, not(not(q))), implies(not(q), q))), true, theorem(implies(or(not(not(not(q))), or(q, not(not(q)))), or(not(not(not(q))), implies(not(q), q)))), true), true), true, theorem(implies(not(not(q)), implies(not(q), q))), true), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.76 = { by axiom 2 (ifeq_axiom) }
% 223.86/28.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(q, not(not(q))), implies(not(q), q))), true, theorem(implies(or(not(not(not(q))), or(q, not(not(q)))), or(not(not(not(q))), implies(not(q), q)))), true), true, theorem(implies(not(not(q)), implies(not(q), q))), true), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.76 = { by axiom 2 (ifeq_axiom) R->L }
% 223.86/28.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(q, not(not(q))), implies(not(q), q))), true), true, theorem(implies(or(not(not(not(q))), or(q, not(not(q)))), or(not(not(not(q))), implies(not(q), q)))), true), true, theorem(implies(not(not(q)), implies(not(q), q))), true), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.76 = { by axiom 7 (axiom_1_4) R->L }
% 223.86/28.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(q, not(not(q))), or(not(not(q)), q))), true, theorem(implies(or(q, not(not(q))), implies(not(q), q))), true), true, theorem(implies(or(not(not(not(q))), or(q, not(not(q)))), or(not(not(not(q))), implies(not(q), q)))), true), true, theorem(implies(not(not(q)), implies(not(q), q))), true), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.76 = { by axiom 1 (implies_definition) R->L }
% 223.86/28.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(q, not(not(q))), implies(not(q), q))), true, theorem(implies(or(q, not(not(q))), implies(not(q), q))), true), true, theorem(implies(or(not(not(not(q))), or(q, not(not(q)))), or(not(not(not(q))), implies(not(q), q)))), true), true, theorem(implies(not(not(q)), implies(not(q), q))), true), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.76 = { by axiom 4 (rule_1) }
% 223.86/28.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(not(not(q))), or(q, not(not(q)))), or(not(not(not(q))), implies(not(q), q)))), true), true, theorem(implies(not(not(q)), implies(not(q), q))), true), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.76 = { by axiom 2 (ifeq_axiom) }
% 223.86/28.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(not(not(q))), or(q, not(not(q)))), or(not(not(not(q))), implies(not(q), q)))), true, theorem(implies(not(not(q)), implies(not(q), q))), true), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.77 = { by axiom 1 (implies_definition) R->L }
% 223.86/28.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(not(q)), or(q, not(not(q)))), or(not(not(not(q))), implies(not(q), q)))), true, theorem(implies(not(not(q)), implies(not(q), q))), true), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.77 = { by axiom 1 (implies_definition) R->L }
% 223.86/28.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(not(q)), or(q, not(not(q)))), implies(not(not(q)), implies(not(q), q)))), true, theorem(implies(not(not(q)), implies(not(q), q))), true), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.77 = { by axiom 2 (ifeq_axiom) R->L }
% 223.86/28.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(not(q)), or(q, not(not(q)))), implies(not(not(q)), implies(not(q), q)))), true, ifeq(true, true, theorem(implies(not(not(q)), implies(not(q), q))), true), true), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.77 = { by axiom 4 (rule_1) R->L }
% 223.86/28.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(not(q)), or(q, not(not(q)))), implies(not(not(q)), implies(not(q), q)))), true, ifeq(ifeq(axiom(implies(not(not(q)), or(q, not(not(q))))), true, theorem(implies(not(not(q)), or(q, not(not(q))))), true), true, theorem(implies(not(not(q)), implies(not(q), q))), true), true), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.77 = { by axiom 5 (axiom_1_3) }
% 223.86/28.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(not(q)), or(q, not(not(q)))), implies(not(not(q)), implies(not(q), q)))), true, ifeq(ifeq(true, true, theorem(implies(not(not(q)), or(q, not(not(q))))), true), true, theorem(implies(not(not(q)), implies(not(q), q))), true), true), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.77 = { by axiom 2 (ifeq_axiom) }
% 223.86/28.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(not(q)), or(q, not(not(q)))), implies(not(not(q)), implies(not(q), q)))), true, ifeq(theorem(implies(not(not(q)), or(q, not(not(q))))), true, theorem(implies(not(not(q)), implies(not(q), q))), true), true), true, theorem(implies(not(q), implies(not(not(q)), q))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.77 = { by axiom 8 (rule_2) }
% 223.86/28.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(not(q), implies(not(not(q)), q))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.77 = { by axiom 2 (ifeq_axiom) }
% 223.86/28.77 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(not(q), implies(not(not(q)), q))), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.77 = { by axiom 2 (ifeq_axiom) R->L }
% 223.86/28.77 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(not(q), implies(not(not(q)), q))), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.77 = { by axiom 4 (rule_1) R->L }
% 223.86/28.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(q), implies(not(not(q)), q)), implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))))), true, theorem(implies(implies(not(q), implies(not(not(q)), q)), implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))))), true), true, ifeq(theorem(implies(not(q), implies(not(not(q)), q))), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.77 = { by axiom 9 (axiom_1_6) }
% 223.86/28.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(q), implies(not(not(q)), q)), implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))))), true), true, ifeq(theorem(implies(not(q), implies(not(not(q)), q))), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.78 = { by axiom 2 (ifeq_axiom) }
% 223.86/28.78 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(q), implies(not(not(q)), q)), implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q))))), true, ifeq(theorem(implies(not(q), implies(not(not(q)), q))), true, theorem(implies(or(implies(not(not(q)), q), not(q)), or(implies(not(not(q)), q), implies(not(not(q)), q)))), true), true), true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.78 = { by axiom 8 (rule_2) }
% 223.86/28.78 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.78 = { by axiom 2 (ifeq_axiom) }
% 223.86/28.78 ifeq(ifeq(ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true, theorem(implies(not(not(q)), q)), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.78 = { by axiom 2 (ifeq_axiom) R->L }
% 223.86/28.78 ifeq(ifeq(ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true, ifeq(true, true, theorem(implies(not(not(q)), q)), true), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.78 = { by axiom 8 (rule_2) R->L }
% 223.86/28.78 ifeq(ifeq(ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true, ifeq(ifeq(theorem(implies(implies(q, implies(not(not(q)), q)), or(implies(not(not(q)), q), not(q)))), true, ifeq(theorem(implies(q, implies(not(not(q)), q))), true, theorem(or(implies(not(not(q)), q), not(q))), true), true), true, theorem(implies(not(not(q)), q)), true), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.78 = { by axiom 2 (ifeq_axiom) R->L }
% 223.86/28.78 ifeq(ifeq(ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(implies(q, implies(not(not(q)), q)), or(implies(not(not(q)), q), not(q)))), true), true, ifeq(theorem(implies(q, implies(not(not(q)), q))), true, theorem(or(implies(not(not(q)), q), not(q))), true), true), true, theorem(implies(not(not(q)), q)), true), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.78 = { by axiom 7 (axiom_1_4) R->L }
% 223.86/28.78 ifeq(ifeq(ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true, ifeq(ifeq(ifeq(axiom(implies(or(not(q), implies(not(not(q)), q)), or(implies(not(not(q)), q), not(q)))), true, theorem(implies(implies(q, implies(not(not(q)), q)), or(implies(not(not(q)), q), not(q)))), true), true, ifeq(theorem(implies(q, implies(not(not(q)), q))), true, theorem(or(implies(not(not(q)), q), not(q))), true), true), true, theorem(implies(not(not(q)), q)), true), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.78 = { by axiom 1 (implies_definition) R->L }
% 223.86/28.78 ifeq(ifeq(ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true, ifeq(ifeq(ifeq(axiom(implies(implies(q, implies(not(not(q)), q)), or(implies(not(not(q)), q), not(q)))), true, theorem(implies(implies(q, implies(not(not(q)), q)), or(implies(not(not(q)), q), not(q)))), true), true, ifeq(theorem(implies(q, implies(not(not(q)), q))), true, theorem(or(implies(not(not(q)), q), not(q))), true), true), true, theorem(implies(not(not(q)), q)), true), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.78 = { by axiom 4 (rule_1) }
% 223.86/28.78 ifeq(ifeq(ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true, ifeq(ifeq(true, true, ifeq(theorem(implies(q, implies(not(not(q)), q))), true, theorem(or(implies(not(not(q)), q), not(q))), true), true), true, theorem(implies(not(not(q)), q)), true), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.78 = { by axiom 2 (ifeq_axiom) }
% 223.86/28.78 ifeq(ifeq(ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true, ifeq(ifeq(theorem(implies(q, implies(not(not(q)), q))), true, theorem(or(implies(not(not(q)), q), not(q))), true), true, theorem(implies(not(not(q)), q)), true), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.78 = { by axiom 2 (ifeq_axiom) R->L }
% 223.86/28.78 ifeq(ifeq(ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(q, implies(not(not(q)), q))), true), true, theorem(or(implies(not(not(q)), q), not(q))), true), true, theorem(implies(not(not(q)), q)), true), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.78 = { by axiom 5 (axiom_1_3) R->L }
% 223.86/28.78 ifeq(ifeq(ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true, ifeq(ifeq(ifeq(axiom(implies(q, or(not(not(not(q))), q))), true, theorem(implies(q, implies(not(not(q)), q))), true), true, theorem(or(implies(not(not(q)), q), not(q))), true), true, theorem(implies(not(not(q)), q)), true), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.78 = { by axiom 1 (implies_definition) R->L }
% 223.86/28.78 ifeq(ifeq(ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true, ifeq(ifeq(ifeq(axiom(implies(q, implies(not(not(q)), q))), true, theorem(implies(q, implies(not(not(q)), q))), true), true, theorem(or(implies(not(not(q)), q), not(q))), true), true, theorem(implies(not(not(q)), q)), true), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.78 = { by axiom 4 (rule_1) }
% 223.86/28.78 ifeq(ifeq(ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true, ifeq(ifeq(true, true, theorem(or(implies(not(not(q)), q), not(q))), true), true, theorem(implies(not(not(q)), q)), true), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.78 = { by axiom 2 (ifeq_axiom) }
% 223.86/28.78 ifeq(ifeq(ifeq(theorem(implies(or(implies(not(not(q)), q), not(q)), implies(not(not(q)), q))), true, ifeq(theorem(or(implies(not(not(q)), q), not(q))), true, theorem(implies(not(not(q)), q)), true), true), true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.78 = { by axiom 8 (rule_2) }
% 223.86/28.78 ifeq(ifeq(true, true, theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.79 = { by axiom 2 (ifeq_axiom) }
% 223.86/28.79 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(true, true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.79 = { by axiom 8 (rule_2) R->L }
% 223.86/28.79 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.79 = { by axiom 2 (ifeq_axiom) R->L }
% 223.86/28.79 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.79 = { by axiom 8 (rule_2) R->L }
% 223.86/28.79 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(not(q)), implies(not(implies(p, not(q))), not(not(q)))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))))), true, ifeq(theorem(implies(not(not(q)), implies(not(implies(p, not(q))), not(not(q))))), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true), true), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.79 = { by axiom 2 (ifeq_axiom) R->L }
% 223.86/28.79 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(not(q)), implies(not(implies(p, not(q))), not(not(q)))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))))), true, ifeq(ifeq(true, true, theorem(implies(not(not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true), true), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.79 = { by axiom 5 (axiom_1_3) R->L }
% 223.86/28.79 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(not(q)), implies(not(implies(p, not(q))), not(not(q)))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))))), true, ifeq(ifeq(axiom(implies(not(not(q)), or(not(not(implies(p, not(q)))), not(not(q))))), true, theorem(implies(not(not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true), true), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.79 = { by axiom 1 (implies_definition) R->L }
% 223.86/28.80 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(not(q)), implies(not(implies(p, not(q))), not(not(q)))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))))), true, ifeq(ifeq(axiom(implies(not(not(q)), implies(not(implies(p, not(q))), not(not(q))))), true, theorem(implies(not(not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true), true), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.80 = { by axiom 4 (rule_1) }
% 223.86/28.80 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(not(q)), implies(not(implies(p, not(q))), not(not(q)))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))))), true, ifeq(true, true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true), true), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.80 = { by axiom 2 (ifeq_axiom) }
% 223.86/28.80 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(not(q)), implies(not(implies(p, not(q))), not(not(q)))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))))), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.80 = { by axiom 2 (ifeq_axiom) R->L }
% 223.86/28.80 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(not(q)), implies(not(implies(p, not(q))), not(not(q)))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))))), true), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.80 = { by axiom 9 (axiom_1_6) R->L }
% 223.86/28.80 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(not(q)), implies(not(implies(p, not(q))), not(not(q)))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))))), true, theorem(implies(implies(not(not(q)), implies(not(implies(p, not(q))), not(not(q)))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))))), true), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 223.86/28.80 = { by axiom 4 (rule_1) }
% 223.86/28.80 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.80 = { by axiom 2 (ifeq_axiom) }
% 224.66/28.80 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.81 = { by axiom 2 (ifeq_axiom) R->L }
% 224.66/28.81 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.81 = { by axiom 8 (rule_2) R->L }
% 224.66/28.81 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))), implies(not(implies(p, not(q))), not(not(q)))), implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))))), true, ifeq(theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))), implies(not(implies(p, not(q))), not(not(q))))), true, theorem(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true), true), true, ifeq(theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.81 = { by axiom 2 (ifeq_axiom) R->L }
% 224.66/28.81 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))), implies(not(implies(p, not(q))), not(not(q)))), implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))))), true, ifeq(ifeq(true, true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true), true), true, ifeq(theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.81 = { by axiom 6 (axiom_1_2) R->L }
% 224.66/28.82 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))), implies(not(implies(p, not(q))), not(not(q)))), implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))))), true, ifeq(ifeq(axiom(implies(or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))), implies(not(implies(p, not(q))), not(not(q))))), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true), true), true, ifeq(theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.82 = { by axiom 4 (rule_1) }
% 224.66/28.82 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))), implies(not(implies(p, not(q))), not(not(q)))), implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))))), true, ifeq(true, true, theorem(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true), true), true, ifeq(theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.82 = { by axiom 2 (ifeq_axiom) }
% 224.66/28.82 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))), implies(not(implies(p, not(q))), not(not(q)))), implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))))), true, theorem(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true), true, ifeq(theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.82 = { by axiom 2 (ifeq_axiom) R->L }
% 224.66/28.82 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))), implies(not(implies(p, not(q))), not(not(q)))), implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))))), true), true, theorem(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true), true, ifeq(theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.82 = { by axiom 9 (axiom_1_6) R->L }
% 224.66/28.83 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))), implies(not(implies(p, not(q))), not(not(q)))), implies(or(not(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), or(not(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), implies(not(implies(p, not(q))), not(not(q))))))), true, theorem(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))), implies(not(implies(p, not(q))), not(not(q)))), implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))))), true), true, theorem(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true), true, ifeq(theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.83 = { by axiom 1 (implies_definition) R->L }
% 224.66/28.83 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))), implies(not(implies(p, not(q))), not(not(q)))), implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), or(not(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), implies(not(implies(p, not(q))), not(not(q))))))), true, theorem(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))), implies(not(implies(p, not(q))), not(not(q)))), implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))))), true), true, theorem(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true), true, ifeq(theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.83 = { by axiom 1 (implies_definition) R->L }
% 224.66/28.83 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))), implies(not(implies(p, not(q))), not(not(q)))), implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))))), true, theorem(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))), implies(not(implies(p, not(q))), not(not(q)))), implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))))), true), true, theorem(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true), true, ifeq(theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.83 = { by axiom 4 (rule_1) }
% 224.66/28.83 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true), true, ifeq(theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.83 = { by axiom 2 (ifeq_axiom) }
% 224.66/28.83 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true, ifeq(theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), or(implies(not(implies(p, not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true, theorem(implies(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.84 = { by axiom 8 (rule_2) }
% 224.66/28.84 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(true, true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.84 = { by axiom 2 (ifeq_axiom) }
% 224.66/28.84 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.84 = { by axiom 2 (ifeq_axiom) R->L }
% 224.66/28.84 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(true, true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.84 = { by axiom 8 (rule_2) R->L }
% 224.66/28.84 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true, ifeq(theorem(implies(not(q), implies(p, not(q)))), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.84 = { by axiom 2 (ifeq_axiom) R->L }
% 224.66/28.84 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true, ifeq(ifeq(true, true, theorem(implies(not(q), implies(p, not(q)))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.84 = { by axiom 5 (axiom_1_3) R->L }
% 224.66/28.84 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true, ifeq(ifeq(axiom(implies(not(q), or(not(p), not(q)))), true, theorem(implies(not(q), implies(p, not(q)))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.84 = { by axiom 1 (implies_definition) R->L }
% 224.66/28.84 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true, ifeq(ifeq(axiom(implies(not(q), implies(p, not(q)))), true, theorem(implies(not(q), implies(p, not(q)))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.84 = { by axiom 4 (rule_1) }
% 224.66/28.84 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true, ifeq(true, true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.84 = { by axiom 2 (ifeq_axiom) }
% 224.66/28.84 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.84 = { by axiom 2 (ifeq_axiom) R->L }
% 224.66/28.84 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.85 = { by axiom 8 (rule_2) R->L }
% 224.66/28.85 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q)))), implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q)))))), true, ifeq(theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.85 = { by axiom 2 (ifeq_axiom) R->L }
% 224.66/28.85 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q)))), implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q)))))), true), true, ifeq(theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.85 = { by axiom 10 (axiom_1_5) R->L }
% 224.66/28.85 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(not(implies(p, not(q)))), or(not(implies(p, not(q))), not(not(q)))), or(not(implies(p, not(q))), or(not(not(implies(p, not(q)))), not(not(q)))))), true, theorem(implies(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q)))), implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q)))))), true), true, ifeq(theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.85 = { by axiom 1 (implies_definition) R->L }
% 224.66/28.85 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(implies(p, not(q))), or(not(implies(p, not(q))), not(not(q)))), or(not(implies(p, not(q))), or(not(not(implies(p, not(q)))), not(not(q)))))), true, theorem(implies(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q)))), implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q)))))), true), true, ifeq(theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.85 = { by axiom 1 (implies_definition) R->L }
% 224.66/28.85 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(implies(p, not(q))), or(not(implies(p, not(q))), not(not(q)))), or(not(implies(p, not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true, theorem(implies(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q)))), implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q)))))), true), true, ifeq(theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.85 = { by axiom 1 (implies_definition) R->L }
% 224.66/28.85 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q)))), or(not(implies(p, not(q))), implies(not(implies(p, not(q))), not(not(q)))))), true, theorem(implies(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q)))), implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q)))))), true), true, ifeq(theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.86 = { by axiom 1 (implies_definition) R->L }
% 224.66/28.86 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q)))), implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q)))))), true, theorem(implies(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q)))), implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q)))))), true), true, ifeq(theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.86 = { by axiom 4 (rule_1) }
% 224.66/28.86 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.86 = { by axiom 2 (ifeq_axiom) }
% 224.66/28.86 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.86 = { by axiom 2 (ifeq_axiom) R->L }
% 224.66/28.86 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.86 = { by axiom 8 (rule_2) R->L }
% 224.66/28.86 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(not(q)), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q)))), implies(or(not(not(implies(p, not(q)))), or(not(not(q)), not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q))))))), true, ifeq(theorem(implies(or(not(not(q)), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q))))), true, theorem(implies(or(not(not(implies(p, not(q)))), or(not(not(q)), not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q)))))), true), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.86 = { by axiom 2 (ifeq_axiom) R->L }
% 224.66/28.87 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(not(not(q)), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q)))), implies(or(not(not(implies(p, not(q)))), or(not(not(q)), not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q))))))), true), true, ifeq(theorem(implies(or(not(not(q)), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q))))), true, theorem(implies(or(not(not(implies(p, not(q)))), or(not(not(q)), not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q)))))), true), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.87 = { by axiom 9 (axiom_1_6) R->L }
% 224.66/28.87 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(not(not(q)), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q)))), implies(or(not(not(implies(p, not(q)))), or(not(not(q)), not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q))))))), true, theorem(implies(implies(or(not(not(q)), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q)))), implies(or(not(not(implies(p, not(q)))), or(not(not(q)), not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q))))))), true), true, ifeq(theorem(implies(or(not(not(q)), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q))))), true, theorem(implies(or(not(not(implies(p, not(q)))), or(not(not(q)), not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q)))))), true), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.87 = { by axiom 4 (rule_1) }
% 224.66/28.87 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(or(not(not(q)), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q))))), true, theorem(implies(or(not(not(implies(p, not(q)))), or(not(not(q)), not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q)))))), true), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.87 = { by axiom 2 (ifeq_axiom) }
% 224.66/28.87 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(not(q)), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q))))), true, theorem(implies(or(not(not(implies(p, not(q)))), or(not(not(q)), not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q)))))), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.87 = { by axiom 2 (ifeq_axiom) R->L }
% 224.66/28.87 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(not(q)), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q))))), true), true, theorem(implies(or(not(not(implies(p, not(q)))), or(not(not(q)), not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q)))))), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.88 = { by axiom 7 (axiom_1_4) R->L }
% 224.66/28.88 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(not(q)), not(implies(p, not(q)))), or(not(implies(p, not(q))), not(not(q))))), true, theorem(implies(or(not(not(q)), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q))))), true), true, theorem(implies(or(not(not(implies(p, not(q)))), or(not(not(q)), not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q)))))), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.88 = { by axiom 1 (implies_definition) R->L }
% 224.66/28.88 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(not(q)), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q))))), true, theorem(implies(or(not(not(q)), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q))))), true), true, theorem(implies(or(not(not(implies(p, not(q)))), or(not(not(q)), not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q)))))), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.88 = { by axiom 4 (rule_1) }
% 224.66/28.88 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(not(implies(p, not(q)))), or(not(not(q)), not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q)))))), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.88 = { by axiom 2 (ifeq_axiom) }
% 224.66/28.88 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(not(implies(p, not(q)))), or(not(not(q)), not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q)))))), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.88 = { by axiom 1 (implies_definition) R->L }
% 224.66/28.88 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(q))), or(not(not(q)), not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(q)))))), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.88 = { by axiom 1 (implies_definition) R->L }
% 224.66/28.89 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(q))), or(not(not(q)), not(implies(p, not(q))))), implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q)))))), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.89 = { by axiom 2 (ifeq_axiom) R->L }
% 224.66/28.89 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(q))), or(not(not(q)), not(implies(p, not(q))))), implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q)))))), true, ifeq(true, true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.89 = { by axiom 4 (rule_1) R->L }
% 224.66/28.89 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(q))), or(not(not(q)), not(implies(p, not(q))))), implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q)))))), true, ifeq(ifeq(axiom(implies(not(implies(p, not(q))), or(not(not(q)), not(implies(p, not(q)))))), true, theorem(implies(not(implies(p, not(q))), or(not(not(q)), not(implies(p, not(q)))))), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.89 = { by axiom 5 (axiom_1_3) }
% 224.66/28.89 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(q))), or(not(not(q)), not(implies(p, not(q))))), implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q)))))), true, ifeq(ifeq(true, true, theorem(implies(not(implies(p, not(q))), or(not(not(q)), not(implies(p, not(q)))))), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.89 = { by axiom 2 (ifeq_axiom) }
% 224.66/28.89 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(q))), or(not(not(q)), not(implies(p, not(q))))), implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q)))))), true, ifeq(theorem(implies(not(implies(p, not(q))), or(not(not(q)), not(implies(p, not(q)))))), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), not(not(q))))), true), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.90 = { by axiom 8 (rule_2) }
% 224.66/28.90 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.90 = { by axiom 2 (ifeq_axiom) }
% 224.66/28.90 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.90 = { by axiom 2 (ifeq_axiom) R->L }
% 224.66/28.90 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.90 = { by axiom 4 (rule_1) R->L }
% 224.66/28.90 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q)))), implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q))))))), true, theorem(implies(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q)))), implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q))))))), true), true, ifeq(theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.90 = { by axiom 1 (implies_definition) }
% 224.66/28.90 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q)))), implies(implies(not(q), implies(p, not(q))), or(not(not(q)), implies(not(implies(p, not(q))), not(not(q))))))), true, theorem(implies(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q)))), implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q))))))), true), true, ifeq(theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.90 = { by axiom 1 (implies_definition) }
% 224.66/28.90 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q)))), implies(or(not(not(q)), implies(p, not(q))), or(not(not(q)), implies(not(implies(p, not(q))), not(not(q))))))), true, theorem(implies(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q)))), implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q))))))), true), true, ifeq(theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.90 = { by axiom 9 (axiom_1_6) }
% 224.66/28.90 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q)))), implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q))))))), true), true, ifeq(theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.90 = { by axiom 2 (ifeq_axiom) }
% 224.66/28.90 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q)))), implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q))))))), true, ifeq(theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), not(not(q))))), true, theorem(implies(implies(not(q), implies(p, not(q))), implies(not(q), implies(not(implies(p, not(q))), not(not(q)))))), true), true), true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.90 = { by axiom 8 (rule_2) }
% 224.66/28.90 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.91 = { by axiom 2 (ifeq_axiom) }
% 224.66/28.91 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 224.66/28.91 = { by axiom 2 (ifeq_axiom) R->L }
% 225.48/28.91 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 225.48/28.91 = { by axiom 4 (rule_1) R->L }
% 225.48/28.91 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(q), implies(not(implies(p, not(q))), not(not(q)))), or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))))), true, theorem(implies(implies(not(q), implies(not(implies(p, not(q))), not(not(q)))), or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))))), true), true, ifeq(theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 225.48/28.91 = { by axiom 1 (implies_definition) }
% 225.48/28.91 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(not(q)), implies(not(implies(p, not(q))), not(not(q)))), or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))))), true, theorem(implies(implies(not(q), implies(not(implies(p, not(q))), not(not(q)))), or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))))), true), true, ifeq(theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 225.48/28.91 = { by axiom 7 (axiom_1_4) }
% 225.48/28.91 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(q), implies(not(implies(p, not(q))), not(not(q)))), or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))))), true), true, ifeq(theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 225.48/28.91 = { by axiom 2 (ifeq_axiom) }
% 225.48/28.91 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(ifeq(theorem(implies(implies(not(q), implies(not(implies(p, not(q))), not(not(q)))), or(implies(not(implies(p, not(q))), not(not(q))), not(not(q))))), true, ifeq(theorem(implies(not(q), implies(not(implies(p, not(q))), not(not(q))))), true, theorem(or(implies(not(implies(p, not(q))), not(not(q))), not(not(q)))), true), true), true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 225.48/28.91 = { by axiom 8 (rule_2) }
% 225.48/28.91 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(ifeq(true, true, theorem(implies(not(implies(p, not(q))), not(not(q)))), true), true, theorem(implies(and(p, q), q)), true), true)
% 225.48/28.91 = { by axiom 2 (ifeq_axiom) }
% 225.48/28.91 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(theorem(implies(not(implies(p, not(q))), not(not(q)))), true, theorem(implies(and(p, q), q)), true), true)
% 225.48/28.91 = { by axiom 1 (implies_definition) }
% 225.48/28.91 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(theorem(implies(not(or(not(p), not(q))), not(not(q)))), true, theorem(implies(and(p, q), q)), true), true)
% 225.48/28.91 = { by axiom 3 (and_defn) R->L }
% 225.48/28.91 ifeq(theorem(implies(implies(and(p, q), not(not(q))), implies(and(p, q), q))), true, ifeq(theorem(implies(and(p, q), not(not(q)))), true, theorem(implies(and(p, q), q)), true), true)
% 225.48/28.91 = { by axiom 8 (rule_2) }
% 225.48/28.91 true
% 225.48/28.91 % SZS output end Proof
% 225.48/28.91
% 225.48/28.91 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------