Twee---2.7.TMO-Non.f

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL215-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n004.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 11:49:22 AM UTC 2026

% Result   : Timeout 287.66s 41.90s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL215-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.05  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.40  % Computer : n004.cluster.edu
% 0.12/0.40  % Model    : x86_64 x86_64
% 0.12/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40  % Memory   : 8046.5625MB
% 0.12/0.40  % OS       : Linux 6.8.0-71-generic
% 0.12/0.40  % CPULimit : 300
% 0.12/0.40  % WCLimit  : 300
% 0.12/0.40  % DateTime : Sun Sep 27 15:27:06 UTC 2026
% 0.12/0.40  % CPUTime  : 
% 0.12/0.40  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 287.66/41.90  Command-line arguments: --flatten-regeneralise
% 287.66/41.90  
% 287.66/41.90  % SZS status Unsatisfiable
% 287.66/41.90  
% 290.01/42.15  % SZS output start Proof
% 290.01/42.15  Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 290.01/42.15  Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 290.01/42.15  Axiom 3 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 290.01/42.15  Axiom 4 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 290.01/42.15  Axiom 5 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 290.01/42.15  Axiom 6 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 290.01/42.15  Axiom 7 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 290.01/42.15  Axiom 8 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 290.01/42.16  Axiom 9 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 290.01/42.16  
% 290.01/42.16  Goal 1 (prove_this): theorem(implies(implies(p, q), implies(or(p, q), q))) = true.
% 290.01/42.16  Proof:
% 290.01/42.16    theorem(implies(implies(p, q), implies(or(p, q), q)))
% 290.01/42.16  = { by axiom 2 (ifeq_axiom) R->L }
% 290.01/42.16    ifeq(true, true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.16  = { by axiom 7 (rule_2) R->L }
% 290.01/42.16    ifeq(ifeq(theorem(implies(or(p, implies(implies(p, q), implies(or(p, q), q))), or(implies(implies(p, q), implies(or(p, q), q)), p))), true, ifeq(theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.16  = { by axiom 2 (ifeq_axiom) R->L }
% 290.01/42.16    ifeq(ifeq(ifeq(true, true, theorem(implies(or(p, implies(implies(p, q), implies(or(p, q), q))), or(implies(implies(p, q), implies(or(p, q), q)), p))), true), true, ifeq(theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.16  = { by axiom 6 (axiom_1_4) R->L }
% 290.01/42.16    ifeq(ifeq(ifeq(axiom(implies(or(p, implies(implies(p, q), implies(or(p, q), q))), or(implies(implies(p, q), implies(or(p, q), q)), p))), true, theorem(implies(or(p, implies(implies(p, q), implies(or(p, q), q))), or(implies(implies(p, q), implies(or(p, q), q)), p))), true), true, ifeq(theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.16  = { by axiom 3 (rule_1) }
% 290.01/42.16    ifeq(ifeq(true, true, ifeq(theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.16  = { by axiom 2 (ifeq_axiom) }
% 290.01/42.16    ifeq(ifeq(theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.16  = { by axiom 2 (ifeq_axiom) R->L }
% 290.01/42.16    ifeq(ifeq(ifeq(true, true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.16  = { by axiom 7 (rule_2) R->L }
% 290.01/42.17    ifeq(ifeq(ifeq(ifeq(theorem(implies(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))), or(p, implies(or(p, q), q)))), true, ifeq(theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true, theorem(or(p, implies(or(p, q), q))), true), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.17  = { by axiom 2 (ifeq_axiom) R->L }
% 290.01/42.17    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))), or(p, implies(or(p, q), q)))), true), true, ifeq(theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true, theorem(or(p, implies(or(p, q), q))), true), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.17  = { by axiom 5 (axiom_1_2) R->L }
% 290.01/42.17    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))), or(p, implies(or(p, q), q)))), true, theorem(implies(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))), or(p, implies(or(p, q), q)))), true), true, ifeq(theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true, theorem(or(p, implies(or(p, q), q))), true), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.17  = { by axiom 3 (rule_1) }
% 290.01/42.17    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true, theorem(or(p, implies(or(p, q), q))), true), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.17  = { by axiom 2 (ifeq_axiom) }
% 290.01/42.17    ifeq(ifeq(ifeq(ifeq(theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.17  = { by axiom 2 (ifeq_axiom) R->L }
% 290.01/42.17    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.17  = { by axiom 7 (rule_2) R->L }
% 290.01/42.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q)))), true, ifeq(theorem(implies(X, or(Y, X))), true, theorem(implies(or(p, q), or(p, q))), true), true), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.17  = { by axiom 2 (ifeq_axiom) R->L }
% 290.01/42.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q)))), true, ifeq(ifeq(true, true, theorem(implies(X, or(Y, X))), true), true, theorem(implies(or(p, q), or(p, q))), true), true), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.17  = { by axiom 4 (axiom_1_3) R->L }
% 290.01/42.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q)))), true, ifeq(ifeq(axiom(implies(X, or(Y, X))), true, theorem(implies(X, or(Y, X))), true), true, theorem(implies(or(p, q), or(p, q))), true), true), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.17  = { by axiom 3 (rule_1) }
% 290.01/42.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q)))), true, ifeq(true, true, theorem(implies(or(p, q), or(p, q))), true), true), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.17  = { by axiom 2 (ifeq_axiom) }
% 290.01/42.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q)))), true, theorem(implies(or(p, q), or(p, q))), true), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.17  = { by axiom 2 (ifeq_axiom) R->L }
% 290.01/42.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q)))), true), true, theorem(implies(or(p, q), or(p, q))), true), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.18  = { by axiom 3 (rule_1) R->L }
% 290.01/42.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q)))), true, theorem(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q)))), true), true, theorem(implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q)))), true), true, theorem(implies(or(p, q), or(p, q))), true), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.18  = { by axiom 1 (implies_definition) }
% 290.01/42.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(p, q), or(not(implies(X, or(Y, X))), or(p, q)))), true, theorem(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q)))), true), true, theorem(implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q)))), true), true, theorem(implies(or(p, q), or(p, q))), true), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.18  = { by axiom 4 (axiom_1_3) }
% 290.01/42.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q)))), true), true, theorem(implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q)))), true), true, theorem(implies(or(p, q), or(p, q))), true), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.18  = { by axiom 2 (ifeq_axiom) }
% 290.01/42.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q)))), true, theorem(implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q)))), true), true, theorem(implies(or(p, q), or(p, q))), true), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.18  = { by axiom 2 (ifeq_axiom) R->L }
% 290.01/42.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q)))), true, theorem(implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q)))), true), true), true, theorem(implies(or(p, q), or(p, q))), true), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.18  = { by axiom 3 (rule_1) R->L }
% 290.01/42.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q))), implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q))))), true, theorem(implies(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q))), implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q))))), true), true, ifeq(theorem(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q)))), true, theorem(implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q)))), true), true), true, theorem(implies(or(p, q), or(p, q))), true), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.18  = { by axiom 1 (implies_definition) }
% 290.01/42.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q))), or(not(implies(X, or(Y, X))), implies(or(p, q), or(p, q))))), true, theorem(implies(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q))), implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q))))), true), true, ifeq(theorem(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q)))), true, theorem(implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q)))), true), true), true, theorem(implies(or(p, q), or(p, q))), true), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.19  = { by axiom 1 (implies_definition) }
% 290.01/42.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, q), or(not(implies(X, or(Y, X))), or(p, q))), or(not(implies(X, or(Y, X))), implies(or(p, q), or(p, q))))), true, theorem(implies(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q))), implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q))))), true), true, ifeq(theorem(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q)))), true, theorem(implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q)))), true), true), true, theorem(implies(or(p, q), or(p, q))), true), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.19  = { by axiom 1 (implies_definition) }
% 290.01/42.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, q), or(not(implies(X, or(Y, X))), or(p, q))), or(not(implies(X, or(Y, X))), or(not(or(p, q)), or(p, q))))), true, theorem(implies(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q))), implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q))))), true), true, ifeq(theorem(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q)))), true, theorem(implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q)))), true), true), true, theorem(implies(or(p, q), or(p, q))), true), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.19  = { by axiom 1 (implies_definition) }
% 290.01/42.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(or(p, q)), or(not(implies(X, or(Y, X))), or(p, q))), or(not(implies(X, or(Y, X))), or(not(or(p, q)), or(p, q))))), true, theorem(implies(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q))), implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q))))), true), true, ifeq(theorem(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q)))), true, theorem(implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q)))), true), true), true, theorem(implies(or(p, q), or(p, q))), true), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.19  = { by axiom 9 (axiom_1_5) }
% 290.01/42.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q))), implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q))))), true), true, ifeq(theorem(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q)))), true, theorem(implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q)))), true), true), true, theorem(implies(or(p, q), or(p, q))), true), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.19  = { by axiom 2 (ifeq_axiom) }
% 290.01/42.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q))), implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q))))), true, ifeq(theorem(implies(or(p, q), implies(implies(X, or(Y, X)), or(p, q)))), true, theorem(implies(implies(X, or(Y, X)), implies(or(p, q), or(p, q)))), true), true), true, theorem(implies(or(p, q), or(p, q))), true), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.19  = { by axiom 7 (rule_2) }
% 290.01/42.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(p, q), or(p, q))), true), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.19  = { by axiom 2 (ifeq_axiom) }
% 290.01/42.19    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(p, q), or(p, q))), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.19  = { by axiom 2 (ifeq_axiom) R->L }
% 290.01/42.19    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(or(p, q), or(p, q))), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.20  = { by axiom 7 (rule_2) R->L }
% 290.01/42.20    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))))), true, ifeq(theorem(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q)))), true, theorem(implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true), true), true, ifeq(theorem(implies(or(p, q), or(p, q))), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.01/42.20  = { by axiom 2 (ifeq_axiom) R->L }
% 290.01/42.20    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))))), true), true, ifeq(theorem(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q)))), true, theorem(implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true), true), true, ifeq(theorem(implies(or(p, q), or(p, q))), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.20  = { by axiom 3 (rule_1) R->L }
% 290.47/42.20    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, implies(or(p, q), q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))))), true, theorem(implies(implies(or(p, implies(or(p, q), q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))))), true), true, theorem(implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))))), true), true, ifeq(theorem(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q)))), true, theorem(implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true), true), true, ifeq(theorem(implies(or(p, q), or(p, q))), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.20  = { by axiom 1 (implies_definition) }
% 290.47/42.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, implies(or(p, q), q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), or(not(implies(or(p, q), or(p, q))), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))))), true, theorem(implies(implies(or(p, implies(or(p, q), q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))))), true), true, theorem(implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))))), true), true, ifeq(theorem(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q)))), true, theorem(implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true), true), true, ifeq(theorem(implies(or(p, q), or(p, q))), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.21  = { by axiom 1 (implies_definition) }
% 290.47/42.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, implies(or(p, q), q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), implies(or(not(implies(or(p, q), or(p, q))), or(p, implies(or(p, q), q))), or(not(implies(or(p, q), or(p, q))), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))))), true, theorem(implies(implies(or(p, implies(or(p, q), q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))))), true), true, theorem(implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))))), true), true, ifeq(theorem(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q)))), true, theorem(implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true), true), true, ifeq(theorem(implies(or(p, q), or(p, q))), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.21  = { by axiom 8 (axiom_1_6) }
% 290.47/42.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(p, implies(or(p, q), q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))))), true), true, theorem(implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))))), true), true, ifeq(theorem(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q)))), true, theorem(implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true), true), true, ifeq(theorem(implies(or(p, q), or(p, q))), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.21  = { by axiom 2 (ifeq_axiom) }
% 290.47/42.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, implies(or(p, q), q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))))), true, theorem(implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))))), true), true, ifeq(theorem(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q)))), true, theorem(implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true), true), true, ifeq(theorem(implies(or(p, q), or(p, q))), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.22  = { by axiom 2 (ifeq_axiom) R->L }
% 290.47/42.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, implies(or(p, q), q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))))), true, ifeq(true, true, theorem(implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))))), true), true), true, ifeq(theorem(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q)))), true, theorem(implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true), true), true, ifeq(theorem(implies(or(p, q), or(p, q))), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.22  = { by axiom 3 (rule_1) R->L }
% 290.47/42.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, implies(or(p, q), q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))))), true, ifeq(ifeq(axiom(implies(or(p, implies(or(p, q), q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true, theorem(implies(or(p, implies(or(p, q), q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true), true, theorem(implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))))), true), true), true, ifeq(theorem(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q)))), true, theorem(implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true), true), true, ifeq(theorem(implies(or(p, q), or(p, q))), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.22  = { by axiom 4 (axiom_1_3) }
% 290.47/42.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, implies(or(p, q), q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))))), true, ifeq(ifeq(true, true, theorem(implies(or(p, implies(or(p, q), q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true), true, theorem(implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))))), true), true), true, ifeq(theorem(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q)))), true, theorem(implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true), true), true, ifeq(theorem(implies(or(p, q), or(p, q))), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.22  = { by axiom 2 (ifeq_axiom) }
% 290.47/42.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, implies(or(p, q), q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))))), true, ifeq(theorem(implies(or(p, implies(or(p, q), q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true, theorem(implies(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q))), implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))))), true), true), true, ifeq(theorem(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q)))), true, theorem(implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true), true), true, ifeq(theorem(implies(or(p, q), or(p, q))), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.22  = { by axiom 7 (rule_2) }
% 290.47/42.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q)))), true, theorem(implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true), true), true, ifeq(theorem(implies(or(p, q), or(p, q))), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.23  = { by axiom 2 (ifeq_axiom) }
% 290.47/42.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q)))), true, theorem(implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true), true, ifeq(theorem(implies(or(p, q), or(p, q))), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.23  = { by axiom 2 (ifeq_axiom) R->L }
% 290.47/42.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q)))), true), true, theorem(implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true), true, ifeq(theorem(implies(or(p, q), or(p, q))), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.23  = { by axiom 9 (axiom_1_5) R->L }
% 290.47/42.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(or(p, q)), or(p, q)), or(p, or(not(or(p, q)), q)))), true, theorem(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q)))), true), true, theorem(implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true), true, ifeq(theorem(implies(or(p, q), or(p, q))), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.23  = { by axiom 1 (implies_definition) R->L }
% 290.47/42.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, q), or(p, q)), or(p, or(not(or(p, q)), q)))), true, theorem(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q)))), true), true, theorem(implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true), true, ifeq(theorem(implies(or(p, q), or(p, q))), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.23  = { by axiom 1 (implies_definition) R->L }
% 290.47/42.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q)))), true, theorem(implies(implies(or(p, q), or(p, q)), or(p, implies(or(p, q), q)))), true), true, theorem(implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true), true, ifeq(theorem(implies(or(p, q), or(p, q))), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.23  = { by axiom 3 (rule_1) }
% 290.47/42.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true), true, ifeq(theorem(implies(or(p, q), or(p, q))), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.23  = { by axiom 2 (ifeq_axiom) }
% 290.47/42.23    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, q), or(p, q)), or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q))))), true, ifeq(theorem(implies(or(p, q), or(p, q))), true, theorem(or(or(p, implies(or(p, q), q)), or(p, implies(or(p, q), q)))), true), true), true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.23  = { by axiom 7 (rule_2) }
% 290.47/42.23    ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(p, implies(or(p, q), q))), true), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.23  = { by axiom 2 (ifeq_axiom) }
% 290.47/42.23    ifeq(ifeq(ifeq(theorem(or(p, implies(or(p, q), q))), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.23  = { by axiom 2 (ifeq_axiom) R->L }
% 290.47/42.23    ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(p, implies(or(p, q), q))), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.24  = { by axiom 7 (rule_2) R->L }
% 290.47/42.24    ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(p, q), q), or(not(implies(p, q)), implies(or(p, q), q))), implies(or(p, implies(or(p, q), q)), or(p, or(not(implies(p, q)), implies(or(p, q), q)))))), true, ifeq(theorem(implies(implies(or(p, q), q), or(not(implies(p, q)), implies(or(p, q), q)))), true, theorem(implies(or(p, implies(or(p, q), q)), or(p, or(not(implies(p, q)), implies(or(p, q), q))))), true), true), true, ifeq(theorem(or(p, implies(or(p, q), q))), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.24  = { by axiom 2 (ifeq_axiom) R->L }
% 290.47/42.24    ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(p, q), q), or(not(implies(p, q)), implies(or(p, q), q))), implies(or(p, implies(or(p, q), q)), or(p, or(not(implies(p, q)), implies(or(p, q), q)))))), true, ifeq(ifeq(true, true, theorem(implies(implies(or(p, q), q), or(not(implies(p, q)), implies(or(p, q), q)))), true), true, theorem(implies(or(p, implies(or(p, q), q)), or(p, or(not(implies(p, q)), implies(or(p, q), q))))), true), true), true, ifeq(theorem(or(p, implies(or(p, q), q))), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.24  = { by axiom 4 (axiom_1_3) R->L }
% 290.47/42.24    ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(p, q), q), or(not(implies(p, q)), implies(or(p, q), q))), implies(or(p, implies(or(p, q), q)), or(p, or(not(implies(p, q)), implies(or(p, q), q)))))), true, ifeq(ifeq(axiom(implies(implies(or(p, q), q), or(not(implies(p, q)), implies(or(p, q), q)))), true, theorem(implies(implies(or(p, q), q), or(not(implies(p, q)), implies(or(p, q), q)))), true), true, theorem(implies(or(p, implies(or(p, q), q)), or(p, or(not(implies(p, q)), implies(or(p, q), q))))), true), true), true, ifeq(theorem(or(p, implies(or(p, q), q))), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.24  = { by axiom 3 (rule_1) }
% 290.47/42.24    ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(p, q), q), or(not(implies(p, q)), implies(or(p, q), q))), implies(or(p, implies(or(p, q), q)), or(p, or(not(implies(p, q)), implies(or(p, q), q)))))), true, ifeq(true, true, theorem(implies(or(p, implies(or(p, q), q)), or(p, or(not(implies(p, q)), implies(or(p, q), q))))), true), true), true, ifeq(theorem(or(p, implies(or(p, q), q))), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.24  = { by axiom 2 (ifeq_axiom) }
% 290.47/42.24    ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(p, q), q), or(not(implies(p, q)), implies(or(p, q), q))), implies(or(p, implies(or(p, q), q)), or(p, or(not(implies(p, q)), implies(or(p, q), q)))))), true, theorem(implies(or(p, implies(or(p, q), q)), or(p, or(not(implies(p, q)), implies(or(p, q), q))))), true), true, ifeq(theorem(or(p, implies(or(p, q), q))), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.24  = { by axiom 2 (ifeq_axiom) R->L }
% 290.47/42.24    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(or(p, q), q), or(not(implies(p, q)), implies(or(p, q), q))), implies(or(p, implies(or(p, q), q)), or(p, or(not(implies(p, q)), implies(or(p, q), q)))))), true), true, theorem(implies(or(p, implies(or(p, q), q)), or(p, or(not(implies(p, q)), implies(or(p, q), q))))), true), true, ifeq(theorem(or(p, implies(or(p, q), q))), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.24  = { by axiom 8 (axiom_1_6) R->L }
% 290.47/42.24    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(p, q), q), or(not(implies(p, q)), implies(or(p, q), q))), implies(or(p, implies(or(p, q), q)), or(p, or(not(implies(p, q)), implies(or(p, q), q)))))), true, theorem(implies(implies(implies(or(p, q), q), or(not(implies(p, q)), implies(or(p, q), q))), implies(or(p, implies(or(p, q), q)), or(p, or(not(implies(p, q)), implies(or(p, q), q)))))), true), true, theorem(implies(or(p, implies(or(p, q), q)), or(p, or(not(implies(p, q)), implies(or(p, q), q))))), true), true, ifeq(theorem(or(p, implies(or(p, q), q))), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.24  = { by axiom 3 (rule_1) }
% 290.47/42.24    ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(p, implies(or(p, q), q)), or(p, or(not(implies(p, q)), implies(or(p, q), q))))), true), true, ifeq(theorem(or(p, implies(or(p, q), q))), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.24  = { by axiom 2 (ifeq_axiom) }
% 290.47/42.24    ifeq(ifeq(ifeq(theorem(implies(or(p, implies(or(p, q), q)), or(p, or(not(implies(p, q)), implies(or(p, q), q))))), true, ifeq(theorem(or(p, implies(or(p, q), q))), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.24  = { by axiom 1 (implies_definition) R->L }
% 290.47/42.24    ifeq(ifeq(ifeq(theorem(implies(or(p, implies(or(p, q), q)), or(p, implies(implies(p, q), implies(or(p, q), q))))), true, ifeq(theorem(or(p, implies(or(p, q), q))), true, theorem(or(p, implies(implies(p, q), implies(or(p, q), q)))), true), true), true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.24  = { by axiom 7 (rule_2) }
% 290.47/42.24    ifeq(ifeq(true, true, theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.24  = { by axiom 2 (ifeq_axiom) }
% 290.47/42.24    ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true)
% 290.47/42.25  = { by axiom 2 (ifeq_axiom) R->L }
% 290.47/42.25    ifeq(true, true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.25  = { by axiom 7 (rule_2) R->L }
% 290.47/42.25    ifeq(ifeq(theorem(implies(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))), implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q))))), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.25  = { by axiom 1 (implies_definition) }
% 290.47/42.25    ifeq(ifeq(theorem(implies(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))), or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), implies(implies(p, q), implies(or(p, q), q))))), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.25  = { by axiom 1 (implies_definition) }
% 290.47/42.25    ifeq(ifeq(theorem(implies(or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))), or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), implies(implies(p, q), implies(or(p, q), q))))), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.25  = { by axiom 2 (ifeq_axiom) R->L }
% 290.47/42.25    ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))), or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), implies(implies(p, q), implies(or(p, q), q))))), true), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.25  = { by axiom 3 (rule_1) R->L }
% 290.47/42.25    ifeq(ifeq(ifeq(ifeq(axiom(implies(or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))), implies(implies(p, q), implies(or(p, q), q)))), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))), implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(implies(or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))), or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), implies(implies(p, q), implies(or(p, q), q))))), true), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.25  = { by axiom 5 (axiom_1_2) }
% 290.47/42.25    ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))), implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(implies(or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))), or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), implies(implies(p, q), implies(or(p, q), q))))), true), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.25  = { by axiom 2 (ifeq_axiom) }
% 290.47/42.25    ifeq(ifeq(ifeq(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))), implies(implies(p, q), implies(or(p, q), q)))), true, theorem(implies(or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))), or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), implies(implies(p, q), implies(or(p, q), q))))), true), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.26  = { by axiom 2 (ifeq_axiom) R->L }
% 290.47/42.26    ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))), implies(implies(p, q), implies(or(p, q), q)))), true, theorem(implies(or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))), or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), implies(implies(p, q), implies(or(p, q), q))))), true), true), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.26  = { by axiom 3 (rule_1) R->L }
% 290.47/42.26    ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))), implies(implies(p, q), implies(or(p, q), q))), implies(or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))), or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), implies(implies(p, q), implies(or(p, q), q)))))), true, theorem(implies(implies(or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))), implies(implies(p, q), implies(or(p, q), q))), implies(or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))), or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), implies(implies(p, q), implies(or(p, q), q)))))), true), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))), implies(implies(p, q), implies(or(p, q), q)))), true, theorem(implies(or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))), or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), implies(implies(p, q), implies(or(p, q), q))))), true), true), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.26  = { by axiom 8 (axiom_1_6) }
% 290.47/42.26    ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))), implies(implies(p, q), implies(or(p, q), q))), implies(or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))), or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), implies(implies(p, q), implies(or(p, q), q)))))), true), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))), implies(implies(p, q), implies(or(p, q), q)))), true, theorem(implies(or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))), or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), implies(implies(p, q), implies(or(p, q), q))))), true), true), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.26  = { by axiom 2 (ifeq_axiom) }
% 290.47/42.26    ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))), implies(implies(p, q), implies(or(p, q), q))), implies(or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))), or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), implies(implies(p, q), implies(or(p, q), q)))))), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))), implies(implies(p, q), implies(or(p, q), q)))), true, theorem(implies(or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))), or(not(or(implies(implies(p, q), implies(or(p, q), q)), p)), implies(implies(p, q), implies(or(p, q), q))))), true), true), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.26  = { by axiom 7 (rule_2) }
% 290.47/42.26    ifeq(ifeq(true, true, ifeq(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.26  = { by axiom 2 (ifeq_axiom) }
% 290.47/42.26    ifeq(ifeq(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.26  = { by axiom 2 (ifeq_axiom) R->L }
% 290.47/42.27    ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.27  = { by axiom 7 (rule_2) R->L }
% 290.47/42.27    ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, q), implies(p, implies(or(p, q), q))), implies(p, implies(implies(p, q), implies(or(p, q), q))))), true, ifeq(theorem(implies(implies(p, q), implies(p, implies(or(p, q), q)))), true, theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.27  = { by axiom 2 (ifeq_axiom) R->L }
% 290.47/42.27    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(p, q), implies(p, implies(or(p, q), q))), implies(p, implies(implies(p, q), implies(or(p, q), q))))), true), true, ifeq(theorem(implies(implies(p, q), implies(p, implies(or(p, q), q)))), true, theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.27  = { by axiom 9 (axiom_1_5) R->L }
% 290.47/42.27    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(implies(p, q)), or(not(p), implies(or(p, q), q))), or(not(p), or(not(implies(p, q)), implies(or(p, q), q))))), true, theorem(implies(implies(implies(p, q), implies(p, implies(or(p, q), q))), implies(p, implies(implies(p, q), implies(or(p, q), q))))), true), true, ifeq(theorem(implies(implies(p, q), implies(p, implies(or(p, q), q)))), true, theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.27  = { by axiom 1 (implies_definition) R->L }
% 290.47/42.27    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, q), or(not(p), implies(or(p, q), q))), or(not(p), or(not(implies(p, q)), implies(or(p, q), q))))), true, theorem(implies(implies(implies(p, q), implies(p, implies(or(p, q), q))), implies(p, implies(implies(p, q), implies(or(p, q), q))))), true), true, ifeq(theorem(implies(implies(p, q), implies(p, implies(or(p, q), q)))), true, theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.27  = { by axiom 1 (implies_definition) R->L }
% 290.47/42.27    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, q), or(not(p), implies(or(p, q), q))), or(not(p), implies(implies(p, q), implies(or(p, q), q))))), true, theorem(implies(implies(implies(p, q), implies(p, implies(or(p, q), q))), implies(p, implies(implies(p, q), implies(or(p, q), q))))), true), true, ifeq(theorem(implies(implies(p, q), implies(p, implies(or(p, q), q)))), true, theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.27  = { by axiom 1 (implies_definition) R->L }
% 290.47/42.27    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, q), implies(p, implies(or(p, q), q))), or(not(p), implies(implies(p, q), implies(or(p, q), q))))), true, theorem(implies(implies(implies(p, q), implies(p, implies(or(p, q), q))), implies(p, implies(implies(p, q), implies(or(p, q), q))))), true), true, ifeq(theorem(implies(implies(p, q), implies(p, implies(or(p, q), q)))), true, theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.27  = { by axiom 1 (implies_definition) R->L }
% 290.47/42.27    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, q), implies(p, implies(or(p, q), q))), implies(p, implies(implies(p, q), implies(or(p, q), q))))), true, theorem(implies(implies(implies(p, q), implies(p, implies(or(p, q), q))), implies(p, implies(implies(p, q), implies(or(p, q), q))))), true), true, ifeq(theorem(implies(implies(p, q), implies(p, implies(or(p, q), q)))), true, theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.27  = { by axiom 3 (rule_1) }
% 290.47/42.28    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(implies(p, q), implies(p, implies(or(p, q), q)))), true, theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.28  = { by axiom 2 (ifeq_axiom) }
% 290.47/42.28    ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(p, q), implies(p, implies(or(p, q), q)))), true, theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.28  = { by axiom 1 (implies_definition) }
% 290.47/42.28    ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(p, q), implies(p, or(not(or(p, q)), q)))), true, theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.28  = { by axiom 2 (ifeq_axiom) R->L }
% 290.47/42.28    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(p, q), implies(p, or(not(or(p, q)), q)))), true), true, theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.28  = { by axiom 3 (rule_1) R->L }
% 290.47/42.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(q, or(not(or(p, q)), q)), implies(implies(p, q), implies(p, or(not(or(p, q)), q))))), true, theorem(implies(implies(q, or(not(or(p, q)), q)), implies(implies(p, q), implies(p, or(not(or(p, q)), q))))), true), true, theorem(implies(implies(p, q), implies(p, or(not(or(p, q)), q)))), true), true, theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.28  = { by axiom 1 (implies_definition) }
% 290.47/42.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(q, or(not(or(p, q)), q)), implies(implies(p, q), or(not(p), or(not(or(p, q)), q))))), true, theorem(implies(implies(q, or(not(or(p, q)), q)), implies(implies(p, q), implies(p, or(not(or(p, q)), q))))), true), true, theorem(implies(implies(p, q), implies(p, or(not(or(p, q)), q)))), true), true, theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.28  = { by axiom 1 (implies_definition) }
% 290.47/42.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(q, or(not(or(p, q)), q)), implies(or(not(p), q), or(not(p), or(not(or(p, q)), q))))), true, theorem(implies(implies(q, or(not(or(p, q)), q)), implies(implies(p, q), implies(p, or(not(or(p, q)), q))))), true), true, theorem(implies(implies(p, q), implies(p, or(not(or(p, q)), q)))), true), true, theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.28  = { by axiom 8 (axiom_1_6) }
% 290.47/42.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(q, or(not(or(p, q)), q)), implies(implies(p, q), implies(p, or(not(or(p, q)), q))))), true), true, theorem(implies(implies(p, q), implies(p, or(not(or(p, q)), q)))), true), true, theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.28  = { by axiom 2 (ifeq_axiom) }
% 290.47/42.28    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(q, or(not(or(p, q)), q)), implies(implies(p, q), implies(p, or(not(or(p, q)), q))))), true, theorem(implies(implies(p, q), implies(p, or(not(or(p, q)), q)))), true), true, theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.29  = { by axiom 2 (ifeq_axiom) R->L }
% 290.47/42.29    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(q, or(not(or(p, q)), q)), implies(implies(p, q), implies(p, or(not(or(p, q)), q))))), true, ifeq(true, true, theorem(implies(implies(p, q), implies(p, or(not(or(p, q)), q)))), true), true), true, theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.29  = { by axiom 3 (rule_1) R->L }
% 290.47/42.29    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(q, or(not(or(p, q)), q)), implies(implies(p, q), implies(p, or(not(or(p, q)), q))))), true, ifeq(ifeq(axiom(implies(q, or(not(or(p, q)), q))), true, theorem(implies(q, or(not(or(p, q)), q))), true), true, theorem(implies(implies(p, q), implies(p, or(not(or(p, q)), q)))), true), true), true, theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.29  = { by axiom 4 (axiom_1_3) }
% 290.47/42.29    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(q, or(not(or(p, q)), q)), implies(implies(p, q), implies(p, or(not(or(p, q)), q))))), true, ifeq(ifeq(true, true, theorem(implies(q, or(not(or(p, q)), q))), true), true, theorem(implies(implies(p, q), implies(p, or(not(or(p, q)), q)))), true), true), true, theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.29  = { by axiom 2 (ifeq_axiom) }
% 290.47/42.29    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(q, or(not(or(p, q)), q)), implies(implies(p, q), implies(p, or(not(or(p, q)), q))))), true, ifeq(theorem(implies(q, or(not(or(p, q)), q))), true, theorem(implies(implies(p, q), implies(p, or(not(or(p, q)), q)))), true), true), true, theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.29  = { by axiom 7 (rule_2) }
% 290.47/42.29    ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.29  = { by axiom 2 (ifeq_axiom) }
% 290.47/42.29    ifeq(ifeq(ifeq(theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.29  = { by axiom 2 (ifeq_axiom) R->L }
% 290.47/42.29    ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.29  = { by axiom 3 (rule_1) R->L }
% 290.47/42.29    ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(p, implies(implies(p, q), implies(or(p, q), q))), implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))))), true, theorem(implies(implies(p, implies(implies(p, q), implies(or(p, q), q))), implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))))), true), true, ifeq(theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.29  = { by axiom 8 (axiom_1_6) }
% 290.47/42.29    ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(p, implies(implies(p, q), implies(or(p, q), q))), implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))))), true), true, ifeq(theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.29  = { by axiom 2 (ifeq_axiom) }
% 290.47/42.30    ifeq(ifeq(ifeq(theorem(implies(implies(p, implies(implies(p, q), implies(or(p, q), q))), implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q)))))), true, ifeq(theorem(implies(p, implies(implies(p, q), implies(or(p, q), q)))), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), or(implies(implies(p, q), implies(or(p, q), q)), implies(implies(p, q), implies(or(p, q), q))))), true), true), true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.30  = { by axiom 7 (rule_2) }
% 290.47/42.30    ifeq(ifeq(true, true, theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.30  = { by axiom 2 (ifeq_axiom) }
% 290.47/42.30    ifeq(theorem(implies(or(implies(implies(p, q), implies(or(p, q), q)), p), implies(implies(p, q), implies(or(p, q), q)))), true, ifeq(theorem(or(implies(implies(p, q), implies(or(p, q), q)), p)), true, theorem(implies(implies(p, q), implies(or(p, q), q))), true), true)
% 290.47/42.30  = { by axiom 7 (rule_2) }
% 290.47/42.30    true
% 290.47/42.30  % SZS output end Proof
% 290.47/42.30  
% 290.47/42.30  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------