%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL181-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 11:49:14 AM UTC 2026
% Result : Unsatisfiable 235.28s 30.13s
% Output : Proof 240.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL181-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 15:24:37 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 235.28/30.13 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
% 235.28/30.13
% 235.28/30.13 % SZS status Unsatisfiable
% 235.28/30.13
% 238.98/30.51 % SZS output start Proof
% 238.98/30.51 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 238.98/30.51 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 238.98/30.51 Axiom 3 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 238.98/30.51 Axiom 4 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 238.98/30.51 Axiom 5 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 238.98/30.51 Axiom 6 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 238.98/30.51 Axiom 7 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 238.98/30.51 Axiom 8 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 238.98/30.51 Axiom 9 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 238.98/30.51
% 238.98/30.51 Goal 1 (prove_this): theorem(implies(implies(not(p), q), implies(not(q), p))) = true.
% 238.98/30.51 Proof:
% 238.98/30.51 theorem(implies(implies(not(p), q), implies(not(q), p)))
% 238.98/30.52 = { by axiom 2 (ifeq_axiom) R->L }
% 238.98/30.52 ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true)
% 238.98/30.52 = { by axiom 2 (ifeq_axiom) R->L }
% 238.98/30.52 ifeq(true, true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.52 = { by axiom 9 (rule_2) R->L }
% 238.98/30.52 ifeq(ifeq(theorem(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p))))), true, ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.52 = { by axiom 2 (ifeq_axiom) R->L }
% 238.98/30.52 ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p))))), true), true, ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.52 = { by axiom 5 (rule_1) R->L }
% 238.98/30.52 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))), implies(implies(not(p), q), implies(not(q), p))), implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))))), true, theorem(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))), implies(implies(not(p), q), implies(not(q), p))), implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))))), true), true, theorem(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p))))), true), true, ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.52 = { by axiom 1 (implies_definition) }
% 238.98/30.53 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))), implies(implies(not(p), q), implies(not(q), p))), implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), or(not(or(implies(implies(not(p), q), implies(not(q), p)), q)), implies(implies(not(p), q), implies(not(q), p)))))), true, theorem(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))), implies(implies(not(p), q), implies(not(q), p))), implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))))), true), true, theorem(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p))))), true), true, ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.53 = { by axiom 1 (implies_definition) }
% 238.98/30.53 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))), implies(implies(not(p), q), implies(not(q), p))), implies(or(not(or(implies(implies(not(p), q), implies(not(q), p)), q)), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), or(not(or(implies(implies(not(p), q), implies(not(q), p)), q)), implies(implies(not(p), q), implies(not(q), p)))))), true, theorem(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))), implies(implies(not(p), q), implies(not(q), p))), implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))))), true), true, theorem(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p))))), true), true, ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.53 = { by axiom 7 (axiom_1_6) }
% 238.98/30.53 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))), implies(implies(not(p), q), implies(not(q), p))), implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))))), true), true, theorem(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p))))), true), true, ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.53 = { by axiom 2 (ifeq_axiom) }
% 238.98/30.53 ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))), implies(implies(not(p), q), implies(not(q), p))), implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))))), true, theorem(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p))))), true), true, ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.54 = { by axiom 2 (ifeq_axiom) R->L }
% 238.98/30.54 ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))), implies(implies(not(p), q), implies(not(q), p))), implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))))), true, ifeq(true, true, theorem(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p))))), true), true), true, ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.54 = { by axiom 5 (rule_1) R->L }
% 238.98/30.54 ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))), implies(implies(not(p), q), implies(not(q), p))), implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))))), true, ifeq(ifeq(axiom(implies(or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))), implies(implies(not(p), q), implies(not(q), p)))), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p))))), true), true), true, ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.54 = { by axiom 4 (axiom_1_2) }
% 238.98/30.54 ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))), implies(implies(not(p), q), implies(not(q), p))), implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))))), true, ifeq(ifeq(true, true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p))))), true), true), true, ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.54 = { by axiom 2 (ifeq_axiom) }
% 238.98/30.54 ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))), implies(implies(not(p), q), implies(not(q), p))), implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))))), true, ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))), implies(implies(not(p), q), implies(not(q), p)))), true, theorem(implies(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p))))), true), true), true, ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.54 = { by axiom 9 (rule_2) }
% 238.98/30.54 ifeq(ifeq(true, true, ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.54 = { by axiom 2 (ifeq_axiom) }
% 238.98/30.55 ifeq(ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.55 = { by axiom 2 (ifeq_axiom) R->L }
% 238.98/30.55 ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.55 = { by axiom 9 (rule_2) R->L }
% 238.98/30.55 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(not(p), q), or(not(q), implies(not(q), p))), or(not(q), implies(implies(not(p), q), implies(not(q), p))))), true, ifeq(theorem(implies(implies(not(p), q), or(not(q), implies(not(q), p)))), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.55 = { by axiom 2 (ifeq_axiom) R->L }
% 238.98/30.56 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(not(p), q), or(not(q), implies(not(q), p))), or(not(q), implies(implies(not(p), q), implies(not(q), p))))), true), true, ifeq(theorem(implies(implies(not(p), q), or(not(q), implies(not(q), p)))), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.56 = { by axiom 8 (axiom_1_5) R->L }
% 238.98/30.56 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(implies(not(p), q)), or(not(q), implies(not(q), p))), or(not(q), or(not(implies(not(p), q)), implies(not(q), p))))), true, theorem(implies(implies(implies(not(p), q), or(not(q), implies(not(q), p))), or(not(q), implies(implies(not(p), q), implies(not(q), p))))), true), true, ifeq(theorem(implies(implies(not(p), q), or(not(q), implies(not(q), p)))), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.56 = { by axiom 1 (implies_definition) R->L }
% 238.98/30.56 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(not(p), q), or(not(q), implies(not(q), p))), or(not(q), or(not(implies(not(p), q)), implies(not(q), p))))), true, theorem(implies(implies(implies(not(p), q), or(not(q), implies(not(q), p))), or(not(q), implies(implies(not(p), q), implies(not(q), p))))), true), true, ifeq(theorem(implies(implies(not(p), q), or(not(q), implies(not(q), p)))), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.56 = { by axiom 1 (implies_definition) R->L }
% 238.98/30.56 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(not(p), q), or(not(q), implies(not(q), p))), or(not(q), implies(implies(not(p), q), implies(not(q), p))))), true, theorem(implies(implies(implies(not(p), q), or(not(q), implies(not(q), p))), or(not(q), implies(implies(not(p), q), implies(not(q), p))))), true), true, ifeq(theorem(implies(implies(not(p), q), or(not(q), implies(not(q), p)))), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.56 = { by axiom 5 (rule_1) }
% 238.98/30.56 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(implies(not(p), q), or(not(q), implies(not(q), p)))), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.56 = { by axiom 2 (ifeq_axiom) }
% 238.98/30.57 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), q), or(not(q), implies(not(q), p)))), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.57 = { by axiom 1 (implies_definition) R->L }
% 238.98/30.57 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.57 = { by axiom 2 (ifeq_axiom) R->L }
% 238.98/30.57 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.57 = { by axiom 9 (rule_2) R->L }
% 238.98/30.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(q), or(not(q), p)), or(not(q), implies(not(q), p)))), true, ifeq(theorem(implies(not(q), or(not(q), p))), true, theorem(or(not(q), implies(not(q), p))), true), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.57 = { by axiom 2 (ifeq_axiom) R->L }
% 238.98/30.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(q), or(not(q), p)), or(not(q), implies(not(q), p)))), true), true, ifeq(theorem(implies(not(q), or(not(q), p))), true, theorem(or(not(q), implies(not(q), p))), true), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.57 = { by axiom 8 (axiom_1_5) R->L }
% 238.98/30.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(not(q)), or(not(q), p)), or(not(q), or(not(not(q)), p)))), true, theorem(implies(implies(not(q), or(not(q), p)), or(not(q), implies(not(q), p)))), true), true, ifeq(theorem(implies(not(q), or(not(q), p))), true, theorem(or(not(q), implies(not(q), p))), true), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.57 = { by axiom 1 (implies_definition) R->L }
% 238.98/30.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(q), or(not(q), p)), or(not(q), or(not(not(q)), p)))), true, theorem(implies(implies(not(q), or(not(q), p)), or(not(q), implies(not(q), p)))), true), true, ifeq(theorem(implies(not(q), or(not(q), p))), true, theorem(or(not(q), implies(not(q), p))), true), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.57 = { by axiom 1 (implies_definition) R->L }
% 238.98/30.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(q), or(not(q), p)), or(not(q), implies(not(q), p)))), true, theorem(implies(implies(not(q), or(not(q), p)), or(not(q), implies(not(q), p)))), true), true, ifeq(theorem(implies(not(q), or(not(q), p))), true, theorem(or(not(q), implies(not(q), p))), true), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.57 = { by axiom 5 (rule_1) }
% 238.98/30.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(not(q), or(not(q), p))), true, theorem(or(not(q), implies(not(q), p))), true), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.58 = { by axiom 2 (ifeq_axiom) }
% 238.98/30.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(not(q), or(not(q), p))), true, theorem(or(not(q), implies(not(q), p))), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.58 = { by axiom 2 (ifeq_axiom) R->L }
% 238.98/30.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(not(q), or(not(q), p))), true), true, theorem(or(not(q), implies(not(q), p))), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.58 = { by axiom 9 (rule_2) R->L }
% 238.98/30.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, not(q)), or(not(q), p)), implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p))))), true, ifeq(theorem(implies(or(p, not(q)), or(not(q), p))), true, theorem(implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p)))), true), true), true, theorem(implies(not(q), or(not(q), p))), true), true, theorem(or(not(q), implies(not(q), p))), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.58 = { by axiom 2 (ifeq_axiom) R->L }
% 238.98/30.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, not(q)), or(not(q), p)), implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p))))), true, ifeq(ifeq(true, true, theorem(implies(or(p, not(q)), or(not(q), p))), true), true, theorem(implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p)))), true), true), true, theorem(implies(not(q), or(not(q), p))), true), true, theorem(or(not(q), implies(not(q), p))), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.58 = { by axiom 6 (axiom_1_4) R->L }
% 238.98/30.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, not(q)), or(not(q), p)), implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p))))), true, ifeq(ifeq(axiom(implies(or(p, not(q)), or(not(q), p))), true, theorem(implies(or(p, not(q)), or(not(q), p))), true), true, theorem(implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p)))), true), true), true, theorem(implies(not(q), or(not(q), p))), true), true, theorem(or(not(q), implies(not(q), p))), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.58 = { by axiom 5 (rule_1) }
% 238.98/30.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, not(q)), or(not(q), p)), implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p))))), true, ifeq(true, true, theorem(implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p)))), true), true), true, theorem(implies(not(q), or(not(q), p))), true), true, theorem(or(not(q), implies(not(q), p))), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.58 = { by axiom 2 (ifeq_axiom) }
% 238.98/30.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, not(q)), or(not(q), p)), implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p))))), true, theorem(implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p)))), true), true, theorem(implies(not(q), or(not(q), p))), true), true, theorem(or(not(q), implies(not(q), p))), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.59 = { by axiom 2 (ifeq_axiom) R->L }
% 238.98/30.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(p, not(q)), or(not(q), p)), implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p))))), true), true, theorem(implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p)))), true), true, theorem(implies(not(q), or(not(q), p))), true), true, theorem(or(not(q), implies(not(q), p))), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.59 = { by axiom 7 (axiom_1_6) R->L }
% 238.98/30.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, not(q)), or(not(q), p)), implies(or(not(not(q)), or(p, not(q))), or(not(not(q)), or(not(q), p))))), true, theorem(implies(implies(or(p, not(q)), or(not(q), p)), implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p))))), true), true, theorem(implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p)))), true), true, theorem(implies(not(q), or(not(q), p))), true), true, theorem(or(not(q), implies(not(q), p))), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.59 = { by axiom 1 (implies_definition) R->L }
% 238.98/30.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, not(q)), or(not(q), p)), implies(implies(not(q), or(p, not(q))), or(not(not(q)), or(not(q), p))))), true, theorem(implies(implies(or(p, not(q)), or(not(q), p)), implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p))))), true), true, theorem(implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p)))), true), true, theorem(implies(not(q), or(not(q), p))), true), true, theorem(or(not(q), implies(not(q), p))), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.59 = { by axiom 1 (implies_definition) R->L }
% 238.98/30.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, not(q)), or(not(q), p)), implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p))))), true, theorem(implies(implies(or(p, not(q)), or(not(q), p)), implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p))))), true), true, theorem(implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p)))), true), true, theorem(implies(not(q), or(not(q), p))), true), true, theorem(or(not(q), implies(not(q), p))), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.59 = { by axiom 5 (rule_1) }
% 238.98/30.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p)))), true), true, theorem(implies(not(q), or(not(q), p))), true), true, theorem(or(not(q), implies(not(q), p))), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.59 = { by axiom 2 (ifeq_axiom) }
% 238.98/30.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p)))), true, theorem(implies(not(q), or(not(q), p))), true), true, theorem(or(not(q), implies(not(q), p))), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.60 = { by axiom 2 (ifeq_axiom) R->L }
% 238.98/30.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p)))), true, ifeq(true, true, theorem(implies(not(q), or(not(q), p))), true), true), true, theorem(or(not(q), implies(not(q), p))), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.60 = { by axiom 5 (rule_1) R->L }
% 238.98/30.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p)))), true, ifeq(ifeq(axiom(implies(not(q), or(p, not(q)))), true, theorem(implies(not(q), or(p, not(q)))), true), true, theorem(implies(not(q), or(not(q), p))), true), true), true, theorem(or(not(q), implies(not(q), p))), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.60 = { by axiom 3 (axiom_1_3) }
% 238.98/30.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p)))), true, ifeq(ifeq(true, true, theorem(implies(not(q), or(p, not(q)))), true), true, theorem(implies(not(q), or(not(q), p))), true), true), true, theorem(or(not(q), implies(not(q), p))), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.60 = { by axiom 2 (ifeq_axiom) }
% 238.98/30.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(q), or(p, not(q))), implies(not(q), or(not(q), p)))), true, ifeq(theorem(implies(not(q), or(p, not(q)))), true, theorem(implies(not(q), or(not(q), p))), true), true), true, theorem(or(not(q), implies(not(q), p))), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.60 = { by axiom 9 (rule_2) }
% 238.98/30.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(q), implies(not(q), p))), true), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.60 = { by axiom 2 (ifeq_axiom) }
% 238.98/30.60 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(q), implies(not(q), p))), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.60 = { by axiom 1 (implies_definition) R->L }
% 238.98/30.60 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(q, implies(not(q), p))), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 238.98/30.60 = { by axiom 2 (ifeq_axiom) R->L }
% 239.77/30.60 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(q, implies(not(q), p))), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.60 = { by axiom 5 (rule_1) R->L }
% 239.77/30.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(q, implies(not(q), p)), implies(implies(not(p), q), implies(q, implies(not(q), p))))), true, theorem(implies(implies(q, implies(not(q), p)), implies(implies(not(p), q), implies(q, implies(not(q), p))))), true), true, ifeq(theorem(implies(q, implies(not(q), p))), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.60 = { by axiom 1 (implies_definition) }
% 239.77/30.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(q, implies(not(q), p)), or(not(implies(not(p), q)), implies(q, implies(not(q), p))))), true, theorem(implies(implies(q, implies(not(q), p)), implies(implies(not(p), q), implies(q, implies(not(q), p))))), true), true, ifeq(theorem(implies(q, implies(not(q), p))), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.60 = { by axiom 3 (axiom_1_3) }
% 239.77/30.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(q, implies(not(q), p)), implies(implies(not(p), q), implies(q, implies(not(q), p))))), true), true, ifeq(theorem(implies(q, implies(not(q), p))), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.61 = { by axiom 2 (ifeq_axiom) }
% 239.77/30.61 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(q, implies(not(q), p)), implies(implies(not(p), q), implies(q, implies(not(q), p))))), true, ifeq(theorem(implies(q, implies(not(q), p))), true, theorem(implies(implies(not(p), q), implies(q, implies(not(q), p)))), true), true), true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.61 = { by axiom 9 (rule_2) }
% 239.77/30.61 ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.61 = { by axiom 2 (ifeq_axiom) }
% 239.77/30.61 ifeq(ifeq(ifeq(theorem(or(not(q), implies(implies(not(p), q), implies(not(q), p)))), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.61 = { by axiom 1 (implies_definition) R->L }
% 239.77/30.61 ifeq(ifeq(ifeq(theorem(implies(q, implies(implies(not(p), q), implies(not(q), p)))), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.61 = { by axiom 2 (ifeq_axiom) R->L }
% 239.77/30.61 ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(q, implies(implies(not(p), q), implies(not(q), p)))), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.61 = { by axiom 5 (rule_1) R->L }
% 239.77/30.61 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(q, implies(implies(not(p), q), implies(not(q), p))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))))), true, theorem(implies(implies(q, implies(implies(not(p), q), implies(not(q), p))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))))), true), true, ifeq(theorem(implies(q, implies(implies(not(p), q), implies(not(q), p)))), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.61 = { by axiom 7 (axiom_1_6) }
% 239.77/30.61 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(q, implies(implies(not(p), q), implies(not(q), p))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))))), true), true, ifeq(theorem(implies(q, implies(implies(not(p), q), implies(not(q), p)))), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.61 = { by axiom 2 (ifeq_axiom) }
% 239.77/30.61 ifeq(ifeq(ifeq(theorem(implies(implies(q, implies(implies(not(p), q), implies(not(q), p))), implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p)))))), true, ifeq(theorem(implies(q, implies(implies(not(p), q), implies(not(q), p)))), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), or(implies(implies(not(p), q), implies(not(q), p)), implies(implies(not(p), q), implies(not(q), p))))), true), true), true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.61 = { by axiom 9 (rule_2) }
% 239.77/30.61 ifeq(ifeq(true, true, theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.61 = { by axiom 2 (ifeq_axiom) }
% 239.77/30.61 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.61 = { by axiom 9 (rule_2) R->L }
% 239.77/30.61 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(theorem(implies(or(q, implies(implies(not(p), q), implies(not(q), p))), or(implies(implies(not(p), q), implies(not(q), p)), q))), true, ifeq(theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.61 = { by axiom 2 (ifeq_axiom) R->L }
% 239.77/30.61 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(or(q, implies(implies(not(p), q), implies(not(q), p))), or(implies(implies(not(p), q), implies(not(q), p)), q))), true), true, ifeq(theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.61 = { by axiom 6 (axiom_1_4) R->L }
% 239.77/30.61 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(axiom(implies(or(q, implies(implies(not(p), q), implies(not(q), p))), or(implies(implies(not(p), q), implies(not(q), p)), q))), true, theorem(implies(or(q, implies(implies(not(p), q), implies(not(q), p))), or(implies(implies(not(p), q), implies(not(q), p)), q))), true), true, ifeq(theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.61 = { by axiom 5 (rule_1) }
% 239.77/30.61 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(true, true, ifeq(theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.62 = { by axiom 2 (ifeq_axiom) }
% 239.77/30.62 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.62 = { by axiom 2 (ifeq_axiom) R->L }
% 239.77/30.62 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(true, true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.62 = { by axiom 9 (rule_2) R->L }
% 239.77/30.62 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true, ifeq(theorem(or(implies(not(q), p), not(p))), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.62 = { by axiom 1 (implies_definition) }
% 239.77/30.62 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true, ifeq(theorem(or(or(not(not(q)), p), not(p))), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.62 = { by axiom 2 (ifeq_axiom) R->L }
% 239.77/30.62 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true, ifeq(ifeq(true, true, theorem(or(or(not(not(q)), p), not(p))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.62 = { by axiom 5 (rule_1) R->L }
% 239.77/30.62 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true, ifeq(ifeq(ifeq(axiom(implies(or(not(p), or(not(not(q)), p)), or(or(not(not(q)), p), not(p)))), true, theorem(implies(or(not(p), or(not(not(q)), p)), or(or(not(not(q)), p), not(p)))), true), true, theorem(or(or(not(not(q)), p), not(p))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.62 = { by axiom 6 (axiom_1_4) }
% 239.77/30.62 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(p), or(not(not(q)), p)), or(or(not(not(q)), p), not(p)))), true), true, theorem(or(or(not(not(q)), p), not(p))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.62 = { by axiom 2 (ifeq_axiom) }
% 239.77/30.62 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true, ifeq(ifeq(theorem(implies(or(not(p), or(not(not(q)), p)), or(or(not(not(q)), p), not(p)))), true, theorem(or(or(not(not(q)), p), not(p))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.62 = { by axiom 1 (implies_definition) R->L }
% 239.77/30.63 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true, ifeq(ifeq(theorem(implies(implies(p, or(not(not(q)), p)), or(or(not(not(q)), p), not(p)))), true, theorem(or(or(not(not(q)), p), not(p))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.63 = { by axiom 2 (ifeq_axiom) R->L }
% 239.77/30.63 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true, ifeq(ifeq(theorem(implies(implies(p, or(not(not(q)), p)), or(or(not(not(q)), p), not(p)))), true, ifeq(true, true, theorem(or(or(not(not(q)), p), not(p))), true), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.63 = { by axiom 5 (rule_1) R->L }
% 239.77/30.63 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true, ifeq(ifeq(theorem(implies(implies(p, or(not(not(q)), p)), or(or(not(not(q)), p), not(p)))), true, ifeq(ifeq(axiom(implies(p, or(not(not(q)), p))), true, theorem(implies(p, or(not(not(q)), p))), true), true, theorem(or(or(not(not(q)), p), not(p))), true), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.63 = { by axiom 3 (axiom_1_3) }
% 239.77/30.63 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true, ifeq(ifeq(theorem(implies(implies(p, or(not(not(q)), p)), or(or(not(not(q)), p), not(p)))), true, ifeq(ifeq(true, true, theorem(implies(p, or(not(not(q)), p))), true), true, theorem(or(or(not(not(q)), p), not(p))), true), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.63 = { by axiom 2 (ifeq_axiom) }
% 239.77/30.63 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true, ifeq(ifeq(theorem(implies(implies(p, or(not(not(q)), p)), or(or(not(not(q)), p), not(p)))), true, ifeq(theorem(implies(p, or(not(not(q)), p))), true, theorem(or(or(not(not(q)), p), not(p))), true), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.63 = { by axiom 9 (rule_2) }
% 239.77/30.63 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true, ifeq(true, true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.63 = { by axiom 2 (ifeq_axiom) }
% 239.77/30.63 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.64 = { by axiom 2 (ifeq_axiom) R->L }
% 239.77/30.64 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.64 = { by axiom 9 (rule_2) R->L }
% 239.77/30.64 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true, ifeq(theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)))), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.64 = { by axiom 2 (ifeq_axiom) R->L }
% 239.77/30.64 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true, ifeq(ifeq(true, true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)))), true), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.64 = { by axiom 7 (axiom_1_6) R->L }
% 239.77/30.64 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true, ifeq(ifeq(axiom(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)))), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)))), true), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.65 = { by axiom 5 (rule_1) }
% 239.77/30.65 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.65 = { by axiom 2 (ifeq_axiom) }
% 239.77/30.65 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.66 = { by axiom 2 (ifeq_axiom) R->L }
% 239.77/30.66 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.66 = { by axiom 9 (rule_2) R->L }
% 239.77/30.66 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(q), p), q), or(q, implies(not(q), p))), implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true, ifeq(theorem(implies(or(implies(not(q), p), q), or(q, implies(not(q), p)))), true, theorem(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.66 = { by axiom 2 (ifeq_axiom) R->L }
% 239.77/30.66 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(q), p), q), or(q, implies(not(q), p))), implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true, ifeq(ifeq(true, true, theorem(implies(or(implies(not(q), p), q), or(q, implies(not(q), p)))), true), true, theorem(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.67 = { by axiom 6 (axiom_1_4) R->L }
% 239.77/30.67 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(q), p), q), or(q, implies(not(q), p))), implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true, ifeq(ifeq(axiom(implies(or(implies(not(q), p), q), or(q, implies(not(q), p)))), true, theorem(implies(or(implies(not(q), p), q), or(q, implies(not(q), p)))), true), true, theorem(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.67 = { by axiom 5 (rule_1) }
% 239.77/30.67 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(q), p), q), or(q, implies(not(q), p))), implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true, ifeq(true, true, theorem(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.67 = { by axiom 2 (ifeq_axiom) }
% 239.77/30.67 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(q), p), q), or(q, implies(not(q), p))), implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true, theorem(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.67 = { by axiom 2 (ifeq_axiom) R->L }
% 239.77/30.67 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(implies(not(q), p), q), or(q, implies(not(q), p))), implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true, theorem(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.68 = { by axiom 7 (axiom_1_6) R->L }
% 239.77/30.68 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(not(q), p), q), or(q, implies(not(q), p))), implies(or(not(or(implies(not(q), p), not(p))), or(implies(not(q), p), q)), or(not(or(implies(not(q), p), not(p))), or(q, implies(not(q), p)))))), true, theorem(implies(implies(or(implies(not(q), p), q), or(q, implies(not(q), p))), implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true, theorem(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.68 = { by axiom 1 (implies_definition) R->L }
% 239.77/30.68 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(not(q), p), q), or(q, implies(not(q), p))), implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), or(not(or(implies(not(q), p), not(p))), or(q, implies(not(q), p)))))), true, theorem(implies(implies(or(implies(not(q), p), q), or(q, implies(not(q), p))), implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true, theorem(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.68 = { by axiom 1 (implies_definition) R->L }
% 239.77/30.68 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(not(q), p), q), or(q, implies(not(q), p))), implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true, theorem(implies(implies(or(implies(not(q), p), q), or(q, implies(not(q), p))), implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true, theorem(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.68 = { by axiom 5 (rule_1) }
% 239.77/30.68 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.69 = { by axiom 2 (ifeq_axiom) }
% 239.77/30.69 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.69 = { by axiom 2 (ifeq_axiom) R->L }
% 239.77/30.69 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.69 = { by axiom 5 (rule_1) R->L }
% 239.77/30.69 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))), implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))))), true, theorem(implies(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))), implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))))), true), true, ifeq(theorem(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.70 = { by axiom 1 (implies_definition) }
% 239.77/30.70 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))), implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), or(not(implies(not(p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))))), true, theorem(implies(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))), implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))))), true), true, ifeq(theorem(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 239.77/30.70 = { by axiom 1 (implies_definition) }
% 240.52/30.70 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))), implies(or(not(implies(not(p), q)), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), or(not(implies(not(p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))))), true, theorem(implies(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))), implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))))), true), true, ifeq(theorem(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.70 = { by axiom 7 (axiom_1_6) }
% 240.52/30.70 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))), implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))))), true), true, ifeq(theorem(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.70 = { by axiom 2 (ifeq_axiom) }
% 240.52/30.71 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))), implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))))), true, ifeq(theorem(implies(implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q)), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(implies(not(q), p), q))), implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))))), true), true), true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.71 = { by axiom 9 (rule_2) }
% 240.52/30.71 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.71 = { by axiom 2 (ifeq_axiom) }
% 240.52/30.71 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.71 = { by axiom 2 (ifeq_axiom) R->L }
% 240.52/30.71 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.71 = { by axiom 5 (rule_1) R->L }
% 240.52/30.71 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))), implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p)))))), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))), implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p)))))), true), true, ifeq(theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.71 = { by axiom 1 (implies_definition) }
% 240.52/30.71 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))), or(not(or(implies(not(q), p), not(p))), implies(implies(not(p), q), or(q, implies(not(q), p)))))), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))), implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p)))))), true), true, ifeq(theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.72 = { by axiom 1 (implies_definition) }
% 240.52/30.72 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(not(p), q), or(not(or(implies(not(q), p), not(p))), or(q, implies(not(q), p)))), or(not(or(implies(not(q), p), not(p))), implies(implies(not(p), q), or(q, implies(not(q), p)))))), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))), implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p)))))), true), true, ifeq(theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.72 = { by axiom 1 (implies_definition) }
% 240.52/30.72 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(not(p), q), or(not(or(implies(not(q), p), not(p))), or(q, implies(not(q), p)))), or(not(or(implies(not(q), p), not(p))), or(not(implies(not(p), q)), or(q, implies(not(q), p)))))), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))), implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p)))))), true), true, ifeq(theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.72 = { by axiom 1 (implies_definition) }
% 240.52/30.72 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(implies(not(p), q)), or(not(or(implies(not(q), p), not(p))), or(q, implies(not(q), p)))), or(not(or(implies(not(q), p), not(p))), or(not(implies(not(p), q)), or(q, implies(not(q), p)))))), true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))), implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p)))))), true), true, ifeq(theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.72 = { by axiom 8 (axiom_1_5) }
% 240.52/30.72 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))), implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p)))))), true), true, ifeq(theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.72 = { by axiom 2 (ifeq_axiom) }
% 240.52/30.72 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p)))), implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p)))))), true, ifeq(theorem(implies(implies(not(p), q), implies(or(implies(not(q), p), not(p)), or(q, implies(not(q), p))))), true, theorem(implies(or(implies(not(q), p), not(p)), implies(implies(not(p), q), or(q, implies(not(q), p))))), true), true), true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.72 = { by axiom 9 (rule_2) }
% 240.52/30.72 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.72 = { by axiom 2 (ifeq_axiom) }
% 240.52/30.72 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.72 = { by axiom 2 (ifeq_axiom) R->L }
% 240.52/30.72 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.73 = { by axiom 5 (rule_1) R->L }
% 240.52/30.73 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(not(p), q), or(q, implies(not(q), p))), or(q, implies(implies(not(p), q), implies(not(q), p))))), true, theorem(implies(implies(implies(not(p), q), or(q, implies(not(q), p))), or(q, implies(implies(not(p), q), implies(not(q), p))))), true), true, ifeq(theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.73 = { by axiom 1 (implies_definition) }
% 240.52/30.73 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(not(p), q), or(q, implies(not(q), p))), or(q, or(not(implies(not(p), q)), implies(not(q), p))))), true, theorem(implies(implies(implies(not(p), q), or(q, implies(not(q), p))), or(q, implies(implies(not(p), q), implies(not(q), p))))), true), true, ifeq(theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.73 = { by axiom 1 (implies_definition) }
% 240.52/30.73 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(implies(not(p), q)), or(q, implies(not(q), p))), or(q, or(not(implies(not(p), q)), implies(not(q), p))))), true, theorem(implies(implies(implies(not(p), q), or(q, implies(not(q), p))), or(q, implies(implies(not(p), q), implies(not(q), p))))), true), true, ifeq(theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.73 = { by axiom 8 (axiom_1_5) }
% 240.52/30.73 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(not(p), q), or(q, implies(not(q), p))), or(q, implies(implies(not(p), q), implies(not(q), p))))), true), true, ifeq(theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.73 = { by axiom 2 (ifeq_axiom) }
% 240.52/30.73 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(ifeq(theorem(implies(implies(implies(not(p), q), or(q, implies(not(q), p))), or(q, implies(implies(not(p), q), implies(not(q), p))))), true, ifeq(theorem(implies(implies(not(p), q), or(q, implies(not(q), p)))), true, theorem(or(q, implies(implies(not(p), q), implies(not(q), p)))), true), true), true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.73 = { by axiom 9 (rule_2) }
% 240.52/30.73 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(ifeq(true, true, theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.73 = { by axiom 2 (ifeq_axiom) }
% 240.52/30.73 ifeq(theorem(implies(or(implies(implies(not(p), q), implies(not(q), p)), q), implies(implies(not(p), q), implies(not(q), p)))), true, ifeq(theorem(or(implies(implies(not(p), q), implies(not(q), p)), q)), true, theorem(implies(implies(not(p), q), implies(not(q), p))), true), true)
% 240.52/30.73 = { by axiom 9 (rule_2) }
% 240.52/30.73 true
% 240.52/30.73 % SZS output end Proof
% 240.52/30.73
% 240.52/30.73 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------