Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL260-3 : 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 11:49:30 AM UTC 2026

% Result   : Unsatisfiable 106.81s 14.08s
% Output   : Proof 113.11s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : LCL260-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.45  % Computer : n004.cluster.edu
% 0.21/0.45  % Model    : x86_64 x86_64
% 0.21/0.45  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.45  % Memory   : 8046.5625MB
% 0.21/0.45  % OS       : Linux 6.8.0-71-generic
% 0.21/0.45  % CPULimit : 300
% 0.21/0.45  % WCLimit  : 300
% 0.21/0.45  % DateTime : Sun Sep 27 15:31:36 UTC 2026
% 0.21/0.46  % CPUTime  : 
% 0.21/0.46  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 106.81/14.08  Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 106.81/14.08  
% 106.81/14.08  % SZS status Unsatisfiable
% 106.81/14.08  
% 110.86/14.54  % SZS output start Proof
% 110.86/14.54  Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 110.86/14.54  Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 110.86/14.54  Axiom 3 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 110.86/14.54  Axiom 4 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 110.86/14.54  Axiom 5 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 110.86/14.54  Axiom 6 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 110.86/14.54  Axiom 7 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 110.86/14.54  Axiom 8 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 110.86/14.55  Axiom 9 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 110.86/14.55  
% 110.86/14.55  Goal 1 (prove_this): theorem(implies(or(p, q), implies(or(not(p), q), q))) = true.
% 110.86/14.55  Proof:
% 110.86/14.55    theorem(implies(or(p, q), implies(or(not(p), q), q)))
% 110.86/14.55  = { by axiom 2 (ifeq_axiom) R->L }
% 110.86/14.55    ifeq(true, true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.55  = { by axiom 9 (rule_2) R->L }
% 110.86/14.55    ifeq(ifeq(theorem(implies(or(implies(or(p, q), implies(or(not(p), q), q)), p), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p)))), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.56  = { by axiom 1 (implies_definition) }
% 110.86/14.56    ifeq(ifeq(theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p)))), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.56  = { by axiom 2 (ifeq_axiom) R->L }
% 110.86/14.56    ifeq(ifeq(ifeq(true, true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.56  = { by axiom 5 (rule_1) R->L }
% 110.86/14.56    ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(p), or(not(or(p, q)), p))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))))), true, theorem(or(not(or(not(p), or(not(or(p, q)), p))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.56  = { by axiom 1 (implies_definition) R->L }
% 110.86/14.57    ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(p), or(not(or(p, q)), p))), implies(or(implies(or(p, q), implies(or(not(p), q), q)), p), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))))), true, theorem(or(not(or(not(p), or(not(or(p, q)), p))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.57  = { by axiom 1 (implies_definition) R->L }
% 110.86/14.57    ifeq(ifeq(ifeq(ifeq(axiom(or(not(implies(p, or(not(or(p, q)), p))), implies(or(implies(or(p, q), implies(or(not(p), q), q)), p), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))))), true, theorem(or(not(or(not(p), or(not(or(p, q)), p))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.57  = { by axiom 1 (implies_definition) R->L }
% 110.86/14.57    ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(p, or(not(or(p, q)), p)), implies(or(implies(or(p, q), implies(or(not(p), q), q)), p), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))))), true, theorem(or(not(or(not(p), or(not(or(p, q)), p))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.57  = { by axiom 7 (axiom_1_6) }
% 110.86/14.57    ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(p), or(not(or(p, q)), p))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.57  = { by axiom 2 (ifeq_axiom) }
% 110.86/14.57    ifeq(ifeq(ifeq(theorem(or(not(or(not(p), or(not(or(p, q)), p))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.57  = { by axiom 2 (ifeq_axiom) R->L }
% 110.86/14.57    ifeq(ifeq(ifeq(theorem(or(not(or(not(p), or(not(or(p, q)), p))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))))), true, ifeq(true, true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.57  = { by axiom 5 (rule_1) R->L }
% 110.86/14.58    ifeq(ifeq(ifeq(theorem(or(not(or(not(p), or(not(or(p, q)), p))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))))), true, ifeq(ifeq(axiom(or(not(p), or(not(or(p, q)), p))), true, theorem(or(not(p), or(not(or(p, q)), p))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.58  = { by axiom 1 (implies_definition) R->L }
% 110.86/14.58    ifeq(ifeq(ifeq(theorem(or(not(or(not(p), or(not(or(p, q)), p))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))))), true, ifeq(ifeq(axiom(implies(p, or(not(or(p, q)), p))), true, theorem(or(not(p), or(not(or(p, q)), p))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.58  = { by axiom 3 (axiom_1_3) }
% 110.86/14.58    ifeq(ifeq(ifeq(theorem(or(not(or(not(p), or(not(or(p, q)), p))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))))), true, ifeq(ifeq(true, true, theorem(or(not(p), or(not(or(p, q)), p))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.58  = { by axiom 2 (ifeq_axiom) }
% 110.86/14.58    ifeq(ifeq(ifeq(theorem(or(not(or(not(p), or(not(or(p, q)), p))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))))), true, ifeq(theorem(or(not(p), or(not(or(p, q)), p))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.58  = { by axiom 1 (implies_definition) R->L }
% 110.86/14.58    ifeq(ifeq(ifeq(theorem(implies(or(not(p), or(not(or(p, q)), p)), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))))), true, ifeq(theorem(or(not(p), or(not(or(p, q)), p))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.58  = { by axiom 9 (rule_2) }
% 110.86/14.58    ifeq(ifeq(true, true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.58  = { by axiom 2 (ifeq_axiom) }
% 110.86/14.58    ifeq(ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.58  = { by axiom 2 (ifeq_axiom) R->L }
% 110.86/14.58    ifeq(ifeq(ifeq(true, true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.58  = { by axiom 9 (rule_2) R->L }
% 110.86/14.59    ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(or(p, q)), or(p, implies(or(not(p), q), q))), or(p, or(not(or(p, q)), implies(or(not(p), q), q))))), true, ifeq(theorem(or(not(or(p, q)), or(p, implies(or(not(p), q), q)))), true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.59  = { by axiom 1 (implies_definition) }
% 110.86/14.59    ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(or(p, q)), or(p, implies(or(not(p), q), q)))), or(p, or(not(or(p, q)), implies(or(not(p), q), q))))), true, ifeq(theorem(or(not(or(p, q)), or(p, implies(or(not(p), q), q)))), true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.59  = { by axiom 2 (ifeq_axiom) R->L }
% 110.86/14.59    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(or(p, q)), or(p, implies(or(not(p), q), q)))), or(p, or(not(or(p, q)), implies(or(not(p), q), q))))), true), true, ifeq(theorem(or(not(or(p, q)), or(p, implies(or(not(p), q), q)))), true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.59  = { by axiom 8 (axiom_1_5) R->L }
% 110.86/14.59    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(or(p, q)), or(p, implies(or(not(p), q), q))), or(p, or(not(or(p, q)), implies(or(not(p), q), q))))), true, theorem(or(not(or(not(or(p, q)), or(p, implies(or(not(p), q), q)))), or(p, or(not(or(p, q)), implies(or(not(p), q), q))))), true), true, ifeq(theorem(or(not(or(p, q)), or(p, implies(or(not(p), q), q)))), true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.59  = { by axiom 1 (implies_definition) }
% 110.86/14.59    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(or(p, q)), or(p, implies(or(not(p), q), q)))), or(p, or(not(or(p, q)), implies(or(not(p), q), q))))), true, theorem(or(not(or(not(or(p, q)), or(p, implies(or(not(p), q), q)))), or(p, or(not(or(p, q)), implies(or(not(p), q), q))))), true), true, ifeq(theorem(or(not(or(p, q)), or(p, implies(or(not(p), q), q)))), true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.59  = { by axiom 5 (rule_1) }
% 110.86/14.59    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(not(or(p, q)), or(p, implies(or(not(p), q), q)))), true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.59  = { by axiom 2 (ifeq_axiom) }
% 110.86/14.59    ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(p, q)), or(p, implies(or(not(p), q), q)))), true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.59  = { by axiom 1 (implies_definition) }
% 110.86/14.60    ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(p, q)), or(p, or(not(or(not(p), q)), q)))), true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.60  = { by axiom 2 (ifeq_axiom) R->L }
% 110.86/14.60    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(p, q)), or(p, or(not(or(not(p), q)), q)))), true), true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.60  = { by axiom 5 (rule_1) R->L }
% 110.86/14.60    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(q), or(not(or(not(p), q)), q))), or(not(or(p, q)), or(p, or(not(or(not(p), q)), q))))), true, theorem(or(not(or(not(q), or(not(or(not(p), q)), q))), or(not(or(p, q)), or(p, or(not(or(not(p), q)), q))))), true), true, theorem(or(not(or(p, q)), or(p, or(not(or(not(p), q)), q)))), true), true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.60  = { by axiom 1 (implies_definition) R->L }
% 110.86/14.60    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(q), or(not(or(not(p), q)), q))), implies(or(p, q), or(p, or(not(or(not(p), q)), q))))), true, theorem(or(not(or(not(q), or(not(or(not(p), q)), q))), or(not(or(p, q)), or(p, or(not(or(not(p), q)), q))))), true), true, theorem(or(not(or(p, q)), or(p, or(not(or(not(p), q)), q)))), true), true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.60  = { by axiom 1 (implies_definition) R->L }
% 110.86/14.60    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(implies(q, or(not(or(not(p), q)), q))), implies(or(p, q), or(p, or(not(or(not(p), q)), q))))), true, theorem(or(not(or(not(q), or(not(or(not(p), q)), q))), or(not(or(p, q)), or(p, or(not(or(not(p), q)), q))))), true), true, theorem(or(not(or(p, q)), or(p, or(not(or(not(p), q)), q)))), true), true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 110.86/14.60  = { by axiom 1 (implies_definition) R->L }
% 111.54/14.60    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(q, or(not(or(not(p), q)), q)), implies(or(p, q), or(p, or(not(or(not(p), q)), q))))), true, theorem(or(not(or(not(q), or(not(or(not(p), q)), q))), or(not(or(p, q)), or(p, or(not(or(not(p), q)), q))))), true), true, theorem(or(not(or(p, q)), or(p, or(not(or(not(p), q)), q)))), true), true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 111.54/14.61  = { by axiom 7 (axiom_1_6) }
% 111.54/14.61    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(q), or(not(or(not(p), q)), q))), or(not(or(p, q)), or(p, or(not(or(not(p), q)), q))))), true), true, theorem(or(not(or(p, q)), or(p, or(not(or(not(p), q)), q)))), true), true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 111.54/14.61  = { by axiom 2 (ifeq_axiom) }
% 111.54/14.61    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(q), or(not(or(not(p), q)), q))), or(not(or(p, q)), or(p, or(not(or(not(p), q)), q))))), true, theorem(or(not(or(p, q)), or(p, or(not(or(not(p), q)), q)))), true), true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 111.54/14.61  = { by axiom 2 (ifeq_axiom) R->L }
% 111.54/14.61    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(q), or(not(or(not(p), q)), q))), or(not(or(p, q)), or(p, or(not(or(not(p), q)), q))))), true, ifeq(true, true, theorem(or(not(or(p, q)), or(p, or(not(or(not(p), q)), q)))), true), true), true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 111.54/14.61  = { by axiom 5 (rule_1) R->L }
% 111.54/14.61    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(q), or(not(or(not(p), q)), q))), or(not(or(p, q)), or(p, or(not(or(not(p), q)), q))))), true, ifeq(ifeq(axiom(or(not(q), or(not(or(not(p), q)), q))), true, theorem(or(not(q), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(p, q)), or(p, or(not(or(not(p), q)), q)))), true), true), true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 111.54/14.61  = { by axiom 1 (implies_definition) R->L }
% 111.54/14.61    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(q), or(not(or(not(p), q)), q))), or(not(or(p, q)), or(p, or(not(or(not(p), q)), q))))), true, ifeq(ifeq(axiom(implies(q, or(not(or(not(p), q)), q))), true, theorem(or(not(q), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(p, q)), or(p, or(not(or(not(p), q)), q)))), true), true), true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 111.54/14.61  = { by axiom 3 (axiom_1_3) }
% 111.54/14.62    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(q), or(not(or(not(p), q)), q))), or(not(or(p, q)), or(p, or(not(or(not(p), q)), q))))), true, ifeq(ifeq(true, true, theorem(or(not(q), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(p, q)), or(p, or(not(or(not(p), q)), q)))), true), true), true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 111.54/14.62  = { by axiom 2 (ifeq_axiom) }
% 111.54/14.62    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(q), or(not(or(not(p), q)), q))), or(not(or(p, q)), or(p, or(not(or(not(p), q)), q))))), true, ifeq(theorem(or(not(q), or(not(or(not(p), q)), q))), true, theorem(or(not(or(p, q)), or(p, or(not(or(not(p), q)), q)))), true), true), true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 111.54/14.62  = { by axiom 1 (implies_definition) R->L }
% 111.54/14.62    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(q), or(not(or(not(p), q)), q)), or(not(or(p, q)), or(p, or(not(or(not(p), q)), q))))), true, ifeq(theorem(or(not(q), or(not(or(not(p), q)), q))), true, theorem(or(not(or(p, q)), or(p, or(not(or(not(p), q)), q)))), true), true), true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 111.54/14.62  = { by axiom 9 (rule_2) }
% 111.54/14.62    ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 111.54/14.62  = { by axiom 2 (ifeq_axiom) }
% 111.54/14.62    ifeq(ifeq(ifeq(theorem(or(p, or(not(or(p, q)), implies(or(not(p), q), q)))), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 111.54/14.62  = { by axiom 1 (implies_definition) R->L }
% 111.54/14.62    ifeq(ifeq(ifeq(theorem(or(p, implies(or(p, q), implies(or(not(p), q), q)))), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 111.54/14.62  = { by axiom 2 (ifeq_axiom) R->L }
% 111.54/14.62    ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(p, implies(or(p, q), implies(or(not(p), q), q)))), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 111.54/14.62  = { by axiom 5 (rule_1) R->L }
% 111.54/14.62    ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(p, implies(or(p, q), implies(or(not(p), q), q)))), or(implies(or(p, q), implies(or(not(p), q), q)), p))), true, theorem(or(not(or(p, implies(or(p, q), implies(or(not(p), q), q)))), or(implies(or(p, q), implies(or(not(p), q), q)), p))), true), true, ifeq(theorem(or(p, implies(or(p, q), implies(or(not(p), q), q)))), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 111.54/14.62  = { by axiom 1 (implies_definition) R->L }
% 111.54/14.62    ifeq(ifeq(ifeq(ifeq(axiom(implies(or(p, implies(or(p, q), implies(or(not(p), q), q))), or(implies(or(p, q), implies(or(not(p), q), q)), p))), true, theorem(or(not(or(p, implies(or(p, q), implies(or(not(p), q), q)))), or(implies(or(p, q), implies(or(not(p), q), q)), p))), true), true, ifeq(theorem(or(p, implies(or(p, q), implies(or(not(p), q), q)))), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 111.54/14.62  = { by axiom 6 (axiom_1_4) }
% 111.54/14.63    ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(p, implies(or(p, q), implies(or(not(p), q), q)))), or(implies(or(p, q), implies(or(not(p), q), q)), p))), true), true, ifeq(theorem(or(p, implies(or(p, q), implies(or(not(p), q), q)))), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 111.54/14.63  = { by axiom 2 (ifeq_axiom) }
% 111.54/14.63    ifeq(ifeq(ifeq(theorem(or(not(or(p, implies(or(p, q), implies(or(not(p), q), q)))), or(implies(or(p, q), implies(or(not(p), q), q)), p))), true, ifeq(theorem(or(p, implies(or(p, q), implies(or(not(p), q), q)))), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 111.54/14.63  = { by axiom 1 (implies_definition) R->L }
% 111.54/14.63    ifeq(ifeq(ifeq(theorem(implies(or(p, implies(or(p, q), implies(or(not(p), q), q))), or(implies(or(p, q), implies(or(not(p), q), q)), p))), true, ifeq(theorem(or(p, implies(or(p, q), implies(or(not(p), q), q)))), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), p)), true), true), true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 111.54/14.63  = { by axiom 9 (rule_2) }
% 111.54/14.63    ifeq(ifeq(true, true, theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 111.54/14.63  = { by axiom 2 (ifeq_axiom) }
% 111.54/14.63    ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true)
% 111.54/14.63  = { by axiom 2 (ifeq_axiom) R->L }
% 111.54/14.63    ifeq(true, true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 111.54/14.63  = { by axiom 9 (rule_2) R->L }
% 111.54/14.63    ifeq(ifeq(theorem(implies(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q))))), true, ifeq(theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 111.54/14.63  = { by axiom 1 (implies_definition) }
% 111.54/14.64    ifeq(ifeq(theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q))))), true, ifeq(theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 111.54/14.64  = { by axiom 2 (ifeq_axiom) R->L }
% 111.54/14.64    ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q))))), true), true, ifeq(theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 111.54/14.64  = { by axiom 5 (rule_1) R->L }
% 111.54/14.65    ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))))), true, theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))))), true), true, theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q))))), true), true, ifeq(theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 111.54/14.65  = { by axiom 1 (implies_definition) R->L }
% 111.54/14.65    ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))))), true, theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))))), true), true, theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q))))), true), true, ifeq(theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 111.54/14.65  = { by axiom 1 (implies_definition) R->L }
% 111.54/14.66    ifeq(ifeq(ifeq(ifeq(axiom(or(not(implies(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))))), true, theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))))), true), true, theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q))))), true), true, ifeq(theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 111.54/14.66  = { by axiom 1 (implies_definition) R->L }
% 111.54/14.66    ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))), implies(or(p, q), implies(or(not(p), q), q))), implies(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))))), true, theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))))), true), true, theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q))))), true), true, ifeq(theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 111.54/14.67  = { by axiom 7 (axiom_1_6) }
% 111.54/14.67    ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))))), true), true, theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q))))), true), true, ifeq(theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 111.54/14.67  = { by axiom 2 (ifeq_axiom) }
% 111.54/14.67    ifeq(ifeq(ifeq(theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))))), true, theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q))))), true), true, ifeq(theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 111.54/14.68  = { by axiom 2 (ifeq_axiom) R->L }
% 111.54/14.68    ifeq(ifeq(ifeq(theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))))), true, ifeq(true, true, theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q))))), true), true), true, ifeq(theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 111.54/14.68  = { by axiom 5 (rule_1) R->L }
% 111.54/14.68    ifeq(ifeq(ifeq(theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))))), true, ifeq(ifeq(axiom(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(p, q), implies(or(not(p), q), q)))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q))))), true), true), true, ifeq(theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 111.54/14.69  = { by axiom 1 (implies_definition) R->L }
% 111.54/14.69    ifeq(ifeq(ifeq(theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))))), true, ifeq(ifeq(axiom(implies(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))), implies(or(p, q), implies(or(not(p), q), q)))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q))))), true), true), true, ifeq(theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 111.54/14.69  = { by axiom 4 (axiom_1_2) }
% 111.54/14.69    ifeq(ifeq(ifeq(theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))))), true, ifeq(ifeq(true, true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q))))), true), true), true, ifeq(theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 111.54/14.69  = { by axiom 2 (ifeq_axiom) }
% 111.54/14.70    ifeq(ifeq(ifeq(theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))))), true, ifeq(theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(p, q), implies(or(not(p), q), q)))), true, theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q))))), true), true), true, ifeq(theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 111.54/14.70  = { by axiom 1 (implies_definition) R->L }
% 111.54/14.70    ifeq(ifeq(ifeq(theorem(implies(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(p, q), implies(or(not(p), q), q))), or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))))), true, ifeq(theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(p, q), implies(or(not(p), q), q)))), true, theorem(or(not(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q))))), true), true), true, ifeq(theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 111.54/14.70  = { by axiom 9 (rule_2) }
% 112.31/14.70    ifeq(ifeq(true, true, ifeq(theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.70  = { by axiom 2 (ifeq_axiom) }
% 112.31/14.70    ifeq(ifeq(theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.71  = { by axiom 2 (ifeq_axiom) R->L }
% 112.31/14.71    ifeq(ifeq(ifeq(true, true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.71  = { by axiom 9 (rule_2) R->L }
% 112.31/14.71    ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(p), implies(or(not(p), q), q)), or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q))))), true, ifeq(theorem(or(not(p), implies(or(not(p), q), q))), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.71  = { by axiom 1 (implies_definition) }
% 112.31/14.71    ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(p), implies(or(not(p), q), q))), or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q))))), true, ifeq(theorem(or(not(p), implies(or(not(p), q), q))), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.71  = { by axiom 2 (ifeq_axiom) R->L }
% 112.31/14.71    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(p), implies(or(not(p), q), q))), or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, ifeq(theorem(or(not(p), implies(or(not(p), q), q))), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.71  = { by axiom 7 (axiom_1_6) R->L }
% 112.31/14.72    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(p, implies(or(not(p), q), q)), implies(or(not(or(p, q)), p), or(not(or(p, q)), implies(or(not(p), q), q))))), true, theorem(or(not(or(not(p), implies(or(not(p), q), q))), or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, ifeq(theorem(or(not(p), implies(or(not(p), q), q))), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.72  = { by axiom 1 (implies_definition) }
% 112.31/14.72    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(implies(p, implies(or(not(p), q), q))), implies(or(not(or(p, q)), p), or(not(or(p, q)), implies(or(not(p), q), q))))), true, theorem(or(not(or(not(p), implies(or(not(p), q), q))), or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, ifeq(theorem(or(not(p), implies(or(not(p), q), q))), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.72  = { by axiom 1 (implies_definition) }
% 112.31/14.72    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(p), implies(or(not(p), q), q))), implies(or(not(or(p, q)), p), or(not(or(p, q)), implies(or(not(p), q), q))))), true, theorem(or(not(or(not(p), implies(or(not(p), q), q))), or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, ifeq(theorem(or(not(p), implies(or(not(p), q), q))), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.73  = { by axiom 1 (implies_definition) }
% 112.31/14.73    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(p), implies(or(not(p), q), q))), or(not(or(not(or(p, q)), p)), or(not(or(p, q)), implies(or(not(p), q), q))))), true, theorem(or(not(or(not(p), implies(or(not(p), q), q))), or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, ifeq(theorem(or(not(p), implies(or(not(p), q), q))), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.73  = { by axiom 1 (implies_definition) R->L }
% 112.31/14.73    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(p), implies(or(not(p), q), q))), or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q))))), true, theorem(or(not(or(not(p), implies(or(not(p), q), q))), or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, ifeq(theorem(or(not(p), implies(or(not(p), q), q))), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.73  = { by axiom 5 (rule_1) }
% 112.31/14.73    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(not(p), implies(or(not(p), q), q))), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.73  = { by axiom 2 (ifeq_axiom) }
% 112.31/14.73    ifeq(ifeq(ifeq(ifeq(theorem(or(not(p), implies(or(not(p), q), q))), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.73  = { by axiom 1 (implies_definition) }
% 112.31/14.73    ifeq(ifeq(ifeq(ifeq(theorem(or(not(p), or(not(or(not(p), q)), q))), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.74  = { by axiom 2 (ifeq_axiom) R->L }
% 112.31/14.74    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.74  = { by axiom 9 (rule_2) R->L }
% 112.31/14.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q))), or(not(or(not(p), q)), or(not(p), q)))), true, ifeq(theorem(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), true, theorem(or(not(or(not(p), q)), or(not(p), q))), true), true), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.74  = { by axiom 1 (implies_definition) }
% 112.31/14.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), or(not(or(not(p), q)), or(not(p), q)))), true, ifeq(theorem(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), true, theorem(or(not(or(not(p), q)), or(not(p), q))), true), true), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.74  = { by axiom 2 (ifeq_axiom) R->L }
% 112.31/14.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), or(not(or(not(p), q)), or(not(p), q)))), true), true, ifeq(theorem(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), true, theorem(or(not(or(not(p), q)), or(not(p), q))), true), true), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.75  = { by axiom 4 (axiom_1_2) R->L }
% 112.31/14.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q))), or(not(or(not(p), q)), or(not(p), q)))), true, theorem(or(not(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), or(not(or(not(p), q)), or(not(p), q)))), true), true, ifeq(theorem(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), true, theorem(or(not(or(not(p), q)), or(not(p), q))), true), true), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.75  = { by axiom 1 (implies_definition) }
% 112.31/14.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), or(not(or(not(p), q)), or(not(p), q)))), true, theorem(or(not(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), or(not(or(not(p), q)), or(not(p), q)))), true), true, ifeq(theorem(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), true, theorem(or(not(or(not(p), q)), or(not(p), q))), true), true), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.75  = { by axiom 5 (rule_1) }
% 112.31/14.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), true, theorem(or(not(or(not(p), q)), or(not(p), q))), true), true), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.76  = { by axiom 2 (ifeq_axiom) }
% 112.31/14.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), true, theorem(or(not(or(not(p), q)), or(not(p), q))), true), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.76  = { by axiom 2 (ifeq_axiom) R->L }
% 112.31/14.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), true), true, theorem(or(not(or(not(p), q)), or(not(p), q))), true), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.76  = { by axiom 5 (rule_1) R->L }
% 112.31/14.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(p), q)), or(or(not(or(not(p), q)), or(not(p), q)), or(not(p), q)))), true, theorem(or(not(or(not(p), q)), or(or(not(or(not(p), q)), or(not(p), q)), or(not(p), q)))), true), true, theorem(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), true), true, theorem(or(not(or(not(p), q)), or(not(p), q))), true), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.76  = { by axiom 1 (implies_definition) R->L }
% 112.31/14.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(p), q), or(or(not(or(not(p), q)), or(not(p), q)), or(not(p), q)))), true, theorem(or(not(or(not(p), q)), or(or(not(or(not(p), q)), or(not(p), q)), or(not(p), q)))), true), true, theorem(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), true), true, theorem(or(not(or(not(p), q)), or(not(p), q))), true), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.77  = { by axiom 3 (axiom_1_3) }
% 112.31/14.77    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(p), q)), or(or(not(or(not(p), q)), or(not(p), q)), or(not(p), q)))), true), true, theorem(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), true), true, theorem(or(not(or(not(p), q)), or(not(p), q))), true), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.77  = { by axiom 2 (ifeq_axiom) }
% 112.31/14.77    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(p), q)), or(or(not(or(not(p), q)), or(not(p), q)), or(not(p), q)))), true, theorem(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), true), true, theorem(or(not(or(not(p), q)), or(not(p), q))), true), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.77  = { by axiom 2 (ifeq_axiom) R->L }
% 112.31/14.77    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(not(or(not(p), q)), or(or(not(or(not(p), q)), or(not(p), q)), or(not(p), q)))), true, theorem(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), true), true), true, theorem(or(not(or(not(p), q)), or(not(p), q))), true), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.78  = { by axiom 5 (rule_1) R->L }
% 112.31/14.78    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(or(not(p), q)), or(or(not(or(not(p), q)), or(not(p), q)), or(not(p), q)))), or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q))))), true, theorem(or(not(or(not(or(not(p), q)), or(or(not(or(not(p), q)), or(not(p), q)), or(not(p), q)))), or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q))))), true), true, ifeq(theorem(or(not(or(not(p), q)), or(or(not(or(not(p), q)), or(not(p), q)), or(not(p), q)))), true, theorem(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), true), true), true, theorem(or(not(or(not(p), q)), or(not(p), q))), true), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.78  = { by axiom 1 (implies_definition) R->L }
% 112.31/14.78    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(or(not(p), q)), or(or(not(or(not(p), q)), or(not(p), q)), or(not(p), q))), or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q))))), true, theorem(or(not(or(not(or(not(p), q)), or(or(not(or(not(p), q)), or(not(p), q)), or(not(p), q)))), or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q))))), true), true, ifeq(theorem(or(not(or(not(p), q)), or(or(not(or(not(p), q)), or(not(p), q)), or(not(p), q)))), true, theorem(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), true), true), true, theorem(or(not(or(not(p), q)), or(not(p), q))), true), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.78  = { by axiom 8 (axiom_1_5) }
% 112.31/14.79    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(or(not(p), q)), or(or(not(or(not(p), q)), or(not(p), q)), or(not(p), q)))), or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q))))), true), true, ifeq(theorem(or(not(or(not(p), q)), or(or(not(or(not(p), q)), or(not(p), q)), or(not(p), q)))), true, theorem(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), true), true), true, theorem(or(not(or(not(p), q)), or(not(p), q))), true), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.79  = { by axiom 2 (ifeq_axiom) }
% 112.31/14.79    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(or(not(p), q)), or(or(not(or(not(p), q)), or(not(p), q)), or(not(p), q)))), or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q))))), true, ifeq(theorem(or(not(or(not(p), q)), or(or(not(or(not(p), q)), or(not(p), q)), or(not(p), q)))), true, theorem(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), true), true), true, theorem(or(not(or(not(p), q)), or(not(p), q))), true), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.79  = { by axiom 1 (implies_definition) R->L }
% 112.31/14.79    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(or(not(p), q)), or(or(not(or(not(p), q)), or(not(p), q)), or(not(p), q))), or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q))))), true, ifeq(theorem(or(not(or(not(p), q)), or(or(not(or(not(p), q)), or(not(p), q)), or(not(p), q)))), true, theorem(or(or(not(or(not(p), q)), or(not(p), q)), or(not(or(not(p), q)), or(not(p), q)))), true), true), true, theorem(or(not(or(not(p), q)), or(not(p), q))), true), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.79  = { by axiom 9 (rule_2) }
% 112.31/14.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(p), q)), or(not(p), q))), true), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.80  = { by axiom 2 (ifeq_axiom) }
% 112.31/14.80    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(p), q)), or(not(p), q))), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.80  = { by axiom 2 (ifeq_axiom) R->L }
% 112.31/14.80    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(not(or(not(p), q)), or(not(p), q))), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.80  = { by axiom 5 (rule_1) R->L }
% 112.31/14.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(or(not(p), q)), or(not(p), q))), or(not(p), or(not(or(not(p), q)), q)))), true, theorem(or(not(or(not(or(not(p), q)), or(not(p), q))), or(not(p), or(not(or(not(p), q)), q)))), true), true, ifeq(theorem(or(not(or(not(p), q)), or(not(p), q))), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.80  = { by axiom 1 (implies_definition) R->L }
% 112.31/14.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(or(not(p), q)), or(not(p), q)), or(not(p), or(not(or(not(p), q)), q)))), true, theorem(or(not(or(not(or(not(p), q)), or(not(p), q))), or(not(p), or(not(or(not(p), q)), q)))), true), true, ifeq(theorem(or(not(or(not(p), q)), or(not(p), q))), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 112.31/14.80  = { by axiom 8 (axiom_1_5) }
% 113.11/14.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(or(not(p), q)), or(not(p), q))), or(not(p), or(not(or(not(p), q)), q)))), true), true, ifeq(theorem(or(not(or(not(p), q)), or(not(p), q))), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 113.11/14.80  = { by axiom 2 (ifeq_axiom) }
% 113.11/14.80    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(or(not(p), q)), or(not(p), q))), or(not(p), or(not(or(not(p), q)), q)))), true, ifeq(theorem(or(not(or(not(p), q)), or(not(p), q))), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 113.11/14.81  = { by axiom 1 (implies_definition) R->L }
% 113.11/14.81    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(or(not(p), q)), or(not(p), q)), or(not(p), or(not(or(not(p), q)), q)))), true, ifeq(theorem(or(not(or(not(p), q)), or(not(p), q))), true, theorem(or(not(p), or(not(or(not(p), q)), q))), true), true), true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 113.11/14.81  = { by axiom 9 (rule_2) }
% 113.11/14.81    ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 113.11/14.81  = { by axiom 2 (ifeq_axiom) }
% 113.11/14.81    ifeq(ifeq(ifeq(theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 113.11/14.81  = { by axiom 2 (ifeq_axiom) R->L }
% 113.11/14.81    ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 113.11/14.81  = { by axiom 5 (rule_1) R->L }
% 113.11/14.81    ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))))), true, theorem(or(not(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))))), true), true, ifeq(theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 113.11/14.82  = { by axiom 1 (implies_definition) R->L }
% 113.11/14.82    ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))))), true, theorem(or(not(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))))), true), true, ifeq(theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 113.11/14.82  = { by axiom 1 (implies_definition) R->L }
% 113.11/14.82    ifeq(ifeq(ifeq(ifeq(axiom(or(not(implies(or(not(or(p, q)), p), implies(or(p, q), implies(or(not(p), q), q)))), implies(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))))), true, theorem(or(not(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))))), true), true, ifeq(theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 113.11/14.82  = { by axiom 1 (implies_definition) R->L }
% 113.11/14.82    ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(not(or(p, q)), p), implies(or(p, q), implies(or(not(p), q), q))), implies(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p)), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))))), true, theorem(or(not(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))))), true), true, ifeq(theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 113.11/14.82  = { by axiom 7 (axiom_1_6) }
% 113.11/14.82    ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))))), true), true, ifeq(theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 113.11/14.82  = { by axiom 2 (ifeq_axiom) }
% 113.11/14.83    ifeq(ifeq(ifeq(theorem(or(not(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))))), true, ifeq(theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 113.11/14.83  = { by axiom 1 (implies_definition) R->L }
% 113.11/14.83    ifeq(ifeq(ifeq(theorem(implies(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q))), or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q)))))), true, ifeq(theorem(or(not(or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), or(implies(or(p, q), implies(or(not(p), q), q)), implies(or(p, q), implies(or(not(p), q), q))))), true), true), true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 113.11/14.83  = { by axiom 9 (rule_2) }
% 113.11/14.83    ifeq(ifeq(true, true, theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 113.11/14.83  = { by axiom 2 (ifeq_axiom) }
% 113.11/14.83    ifeq(theorem(or(not(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), implies(or(p, q), implies(or(not(p), q), q)))), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 113.11/14.83  = { by axiom 1 (implies_definition) R->L }
% 113.11/14.83    ifeq(theorem(implies(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p)), implies(or(p, q), implies(or(not(p), q), q)))), true, ifeq(theorem(or(implies(or(p, q), implies(or(not(p), q), q)), or(not(or(p, q)), p))), true, theorem(implies(or(p, q), implies(or(not(p), q), q))), true), true)
% 113.11/14.83  = { by axiom 9 (rule_2) }
% 113.11/14.83    true
% 113.11/14.83  % SZS output end Proof
% 113.11/14.83  
% 113.11/14.83  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------