%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL217-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 11:49:23 AM UTC 2026
% Result : Unsatisfiable 43.50s 6.00s
% Output : Proof 47.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL217-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n018.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 27 15:29:23 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.50/6.00 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
% 43.50/6.00
% 43.50/6.00 % SZS status Unsatisfiable
% 43.50/6.00
% 45.93/6.33 % SZS output start Proof
% 45.93/6.34 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 45.93/6.34 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 45.93/6.34 Axiom 3 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 45.93/6.34 Axiom 4 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 45.93/6.34 Axiom 5 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 45.93/6.34 Axiom 6 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 45.93/6.34 Axiom 7 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 45.93/6.34 Axiom 8 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 45.93/6.35 Axiom 9 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 45.93/6.35
% 45.93/6.35 Goal 1 (prove_this): theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))) = true.
% 45.93/6.35 Proof:
% 45.93/6.35 theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p))))
% 45.93/6.35 = { by axiom 2 (ifeq_axiom) R->L }
% 45.93/6.35 ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true)
% 45.93/6.35 = { by axiom 2 (ifeq_axiom) R->L }
% 45.93/6.35 ifeq(true, true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 45.93/6.35 = { by axiom 9 (rule_2) R->L }
% 45.93/6.35 ifeq(ifeq(theorem(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 45.93/6.36 = { by axiom 2 (ifeq_axiom) R->L }
% 45.93/6.36 ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 45.93/6.37 = { by axiom 5 (rule_1) R->L }
% 45.93/6.37 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))))), true, theorem(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))))), true), true, theorem(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 45.93/6.37 = { by axiom 1 (implies_definition) }
% 45.93/6.37 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), or(not(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))))), true, theorem(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))))), true), true, theorem(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 45.93/6.38 = { by axiom 1 (implies_definition) }
% 45.93/6.38 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(or(not(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), or(not(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))))), true, theorem(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))))), true), true, theorem(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 45.93/6.38 = { by axiom 7 (axiom_1_6) }
% 45.93/6.39 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))))), true), true, theorem(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 45.93/6.39 = { by axiom 2 (ifeq_axiom) }
% 45.93/6.39 ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))))), true, theorem(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 45.93/6.39 = { by axiom 2 (ifeq_axiom) R->L }
% 45.93/6.40 ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))))), true, ifeq(true, true, theorem(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true), true), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 45.93/6.40 = { by axiom 5 (rule_1) R->L }
% 46.69/6.40 ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))))), true, ifeq(ifeq(axiom(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true), true), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.40 = { by axiom 4 (axiom_1_2) }
% 46.69/6.40 ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))))), true, ifeq(ifeq(true, true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true), true), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.41 = { by axiom 2 (ifeq_axiom) }
% 46.69/6.41 ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))))), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, theorem(implies(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true), true), true, ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.41 = { by axiom 9 (rule_2) }
% 46.69/6.41 ifeq(ifeq(true, true, ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.41 = { by axiom 2 (ifeq_axiom) }
% 46.69/6.41 ifeq(ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.41 = { by axiom 1 (implies_definition) }
% 46.69/6.41 ifeq(ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), or(not(implies(p, q)), implies(implies(p, not(q)), not(p)))))), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.41 = { by axiom 2 (ifeq_axiom) R->L }
% 46.69/6.42 ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), or(not(implies(p, q)), implies(implies(p, not(q)), not(p)))))), true), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.42 = { by axiom 5 (rule_1) R->L }
% 46.69/6.42 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(p, not(q)), not(p)), or(not(implies(p, q)), implies(implies(p, not(q)), not(p)))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), or(not(implies(p, q)), implies(implies(p, not(q)), not(p))))))), true, theorem(implies(implies(implies(implies(p, not(q)), not(p)), or(not(implies(p, q)), implies(implies(p, not(q)), not(p)))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), or(not(implies(p, q)), implies(implies(p, not(q)), not(p))))))), true), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), or(not(implies(p, q)), implies(implies(p, not(q)), not(p)))))), true), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.42 = { by axiom 7 (axiom_1_6) }
% 46.69/6.42 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(implies(p, not(q)), not(p)), or(not(implies(p, q)), implies(implies(p, not(q)), not(p)))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), or(not(implies(p, q)), implies(implies(p, not(q)), not(p))))))), true), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), or(not(implies(p, q)), implies(implies(p, not(q)), not(p)))))), true), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.42 = { by axiom 2 (ifeq_axiom) }
% 46.69/6.43 ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, not(q)), not(p)), or(not(implies(p, q)), implies(implies(p, not(q)), not(p)))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), or(not(implies(p, q)), implies(implies(p, not(q)), not(p))))))), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), or(not(implies(p, q)), implies(implies(p, not(q)), not(p)))))), true), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.43 = { by axiom 2 (ifeq_axiom) R->L }
% 46.69/6.43 ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, not(q)), not(p)), or(not(implies(p, q)), implies(implies(p, not(q)), not(p)))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), or(not(implies(p, q)), implies(implies(p, not(q)), not(p))))))), true, ifeq(true, true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), or(not(implies(p, q)), implies(implies(p, not(q)), not(p)))))), true), true), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.43 = { by axiom 5 (rule_1) R->L }
% 46.69/6.44 ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, not(q)), not(p)), or(not(implies(p, q)), implies(implies(p, not(q)), not(p)))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), or(not(implies(p, q)), implies(implies(p, not(q)), not(p))))))), true, ifeq(ifeq(axiom(implies(implies(implies(p, not(q)), not(p)), or(not(implies(p, q)), implies(implies(p, not(q)), not(p))))), true, theorem(implies(implies(implies(p, not(q)), not(p)), or(not(implies(p, q)), implies(implies(p, not(q)), not(p))))), true), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), or(not(implies(p, q)), implies(implies(p, not(q)), not(p)))))), true), true), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.44 = { by axiom 3 (axiom_1_3) }
% 46.69/6.44 ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, not(q)), not(p)), or(not(implies(p, q)), implies(implies(p, not(q)), not(p)))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), or(not(implies(p, q)), implies(implies(p, not(q)), not(p))))))), true, ifeq(ifeq(true, true, theorem(implies(implies(implies(p, not(q)), not(p)), or(not(implies(p, q)), implies(implies(p, not(q)), not(p))))), true), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), or(not(implies(p, q)), implies(implies(p, not(q)), not(p)))))), true), true), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.44 = { by axiom 2 (ifeq_axiom) }
% 46.69/6.44 ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, not(q)), not(p)), or(not(implies(p, q)), implies(implies(p, not(q)), not(p)))), implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), or(not(implies(p, q)), implies(implies(p, not(q)), not(p))))))), true, ifeq(theorem(implies(implies(implies(p, not(q)), not(p)), or(not(implies(p, q)), implies(implies(p, not(q)), not(p))))), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), or(not(implies(p, q)), implies(implies(p, not(q)), not(p)))))), true), true), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.44 = { by axiom 9 (rule_2) }
% 46.69/6.44 ifeq(ifeq(true, true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.44 = { by axiom 2 (ifeq_axiom) }
% 46.69/6.44 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.44 = { by axiom 9 (rule_2) R->L }
% 46.69/6.44 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(theorem(implies(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))))), true, ifeq(theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.45 = { by axiom 2 (ifeq_axiom) R->L }
% 46.69/6.45 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))))), true), true, ifeq(theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.45 = { by axiom 8 (axiom_1_5) R->L }
% 46.69/6.45 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(axiom(implies(or(not(implies(p, not(q))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), or(not(implies(p, not(q))), not(p))))), true, theorem(implies(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))))), true), true, ifeq(theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.45 = { by axiom 1 (implies_definition) R->L }
% 46.69/6.45 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), or(not(implies(p, not(q))), not(p))))), true, theorem(implies(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))))), true), true, ifeq(theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.45 = { by axiom 1 (implies_definition) R->L }
% 46.69/6.45 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))))), true, theorem(implies(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))))), true), true, ifeq(theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.45 = { by axiom 5 (rule_1) }
% 46.69/6.45 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(true, true, ifeq(theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.45 = { by axiom 2 (ifeq_axiom) }
% 46.69/6.46 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.46 = { by axiom 2 (ifeq_axiom) R->L }
% 46.69/6.46 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.46 = { by axiom 9 (rule_2) R->L }
% 46.69/6.46 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(p, implies(implies(p, q), implies(implies(p, not(q)), not(p)))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true, ifeq(theorem(implies(p, implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.46 = { by axiom 1 (implies_definition) }
% 46.69/6.46 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true, ifeq(theorem(implies(p, implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.46 = { by axiom 2 (ifeq_axiom) R->L }
% 46.69/6.46 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, ifeq(theorem(implies(p, implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.47 = { by axiom 6 (axiom_1_4) R->L }
% 46.69/6.47 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true, theorem(implies(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p)))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, ifeq(theorem(implies(p, implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.47 = { by axiom 5 (rule_1) }
% 46.69/6.47 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(p, implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.47 = { by axiom 2 (ifeq_axiom) }
% 46.69/6.47 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(p, implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.47 = { by axiom 1 (implies_definition) }
% 46.69/6.47 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.47 = { by axiom 2 (ifeq_axiom) R->L }
% 46.69/6.47 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.47 = { by axiom 9 (rule_2) R->L }
% 46.69/6.48 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(q, implies(implies(p, not(q)), not(p))), implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p)))))), true, ifeq(theorem(implies(q, implies(implies(p, not(q)), not(p)))), true, theorem(implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p))))), true), true), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.48 = { by axiom 2 (ifeq_axiom) R->L }
% 46.69/6.48 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(q, implies(implies(p, not(q)), not(p))), implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p)))))), true), true, ifeq(theorem(implies(q, implies(implies(p, not(q)), not(p)))), true, theorem(implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p))))), true), true), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.48 = { by axiom 7 (axiom_1_6) R->L }
% 46.69/6.48 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(q, implies(implies(p, not(q)), not(p))), implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p)))))), true, theorem(implies(implies(q, implies(implies(p, not(q)), not(p))), implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p)))))), true), true, ifeq(theorem(implies(q, implies(implies(p, not(q)), not(p)))), true, theorem(implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p))))), true), true), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.48 = { by axiom 5 (rule_1) }
% 46.69/6.48 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(q, implies(implies(p, not(q)), not(p)))), true, theorem(implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p))))), true), true), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.48 = { by axiom 2 (ifeq_axiom) }
% 46.69/6.48 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(q, implies(implies(p, not(q)), not(p)))), true, theorem(implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.49 = { by axiom 1 (implies_definition) }
% 46.69/6.49 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(q), implies(implies(p, not(q)), not(p)))), true, theorem(implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.49 = { by axiom 1 (implies_definition) }
% 46.69/6.49 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(q), implies(or(not(p), not(q)), not(p)))), true, theorem(implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.49 = { by axiom 2 (ifeq_axiom) R->L }
% 46.69/6.49 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(q), implies(or(not(p), not(q)), not(p)))), true), true, theorem(implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.49 = { by axiom 5 (rule_1) R->L }
% 46.69/6.50 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(not(p), not(q)), or(not(q), not(p))), or(not(q), implies(or(not(p), not(q)), not(p))))), true, theorem(implies(implies(or(not(p), not(q)), or(not(q), not(p))), or(not(q), implies(or(not(p), not(q)), not(p))))), true), true, theorem(or(not(q), implies(or(not(p), not(q)), not(p)))), true), true, theorem(implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.50 = { by axiom 1 (implies_definition) }
% 46.69/6.50 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(not(p), not(q)), or(not(q), not(p))), or(not(q), or(not(or(not(p), not(q))), not(p))))), true, theorem(implies(implies(or(not(p), not(q)), or(not(q), not(p))), or(not(q), implies(or(not(p), not(q)), not(p))))), true), true, theorem(or(not(q), implies(or(not(p), not(q)), not(p)))), true), true, theorem(implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 46.69/6.50 = { by axiom 1 (implies_definition) }
% 46.69/6.50 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(or(not(p), not(q))), or(not(q), not(p))), or(not(q), or(not(or(not(p), not(q))), not(p))))), true, theorem(implies(implies(or(not(p), not(q)), or(not(q), not(p))), or(not(q), implies(or(not(p), not(q)), not(p))))), true), true, theorem(or(not(q), implies(or(not(p), not(q)), not(p)))), true), true, theorem(implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.50 = { by axiom 8 (axiom_1_5) }
% 47.51/6.51 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(not(p), not(q)), or(not(q), not(p))), or(not(q), implies(or(not(p), not(q)), not(p))))), true), true, theorem(or(not(q), implies(or(not(p), not(q)), not(p)))), true), true, theorem(implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.51 = { by axiom 2 (ifeq_axiom) }
% 47.51/6.51 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(p), not(q)), or(not(q), not(p))), or(not(q), implies(or(not(p), not(q)), not(p))))), true, theorem(or(not(q), implies(or(not(p), not(q)), not(p)))), true), true, theorem(implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.51 = { by axiom 2 (ifeq_axiom) R->L }
% 47.51/6.51 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(p), not(q)), or(not(q), not(p))), or(not(q), implies(or(not(p), not(q)), not(p))))), true, ifeq(true, true, theorem(or(not(q), implies(or(not(p), not(q)), not(p)))), true), true), true, theorem(implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.51 = { by axiom 5 (rule_1) R->L }
% 47.51/6.51 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(p), not(q)), or(not(q), not(p))), or(not(q), implies(or(not(p), not(q)), not(p))))), true, ifeq(ifeq(axiom(implies(or(not(p), not(q)), or(not(q), not(p)))), true, theorem(implies(or(not(p), not(q)), or(not(q), not(p)))), true), true, theorem(or(not(q), implies(or(not(p), not(q)), not(p)))), true), true), true, theorem(implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.52 = { by axiom 6 (axiom_1_4) }
% 47.51/6.52 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(p), not(q)), or(not(q), not(p))), or(not(q), implies(or(not(p), not(q)), not(p))))), true, ifeq(ifeq(true, true, theorem(implies(or(not(p), not(q)), or(not(q), not(p)))), true), true, theorem(or(not(q), implies(or(not(p), not(q)), not(p)))), true), true), true, theorem(implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.52 = { by axiom 2 (ifeq_axiom) }
% 47.51/6.52 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(p), not(q)), or(not(q), not(p))), or(not(q), implies(or(not(p), not(q)), not(p))))), true, ifeq(theorem(implies(or(not(p), not(q)), or(not(q), not(p)))), true, theorem(or(not(q), implies(or(not(p), not(q)), not(p)))), true), true), true, theorem(implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.53 = { by axiom 9 (rule_2) }
% 47.51/6.53 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.53 = { by axiom 2 (ifeq_axiom) }
% 47.51/6.53 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(p), q), or(not(p), implies(implies(p, not(q)), not(p))))), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.53 = { by axiom 1 (implies_definition) R->L }
% 47.51/6.53 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(p, q), or(not(p), implies(implies(p, not(q)), not(p))))), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.53 = { by axiom 2 (ifeq_axiom) R->L }
% 47.51/6.53 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(implies(p, q), or(not(p), implies(implies(p, not(q)), not(p))))), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.53 = { by axiom 5 (rule_1) R->L }
% 47.51/6.53 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, q), or(not(p), implies(implies(p, not(q)), not(p)))), or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true, theorem(implies(implies(implies(p, q), or(not(p), implies(implies(p, not(q)), not(p)))), or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true), true, ifeq(theorem(implies(implies(p, q), or(not(p), implies(implies(p, not(q)), not(p))))), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.53 = { by axiom 1 (implies_definition) }
% 47.51/6.53 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, q), or(not(p), implies(implies(p, not(q)), not(p)))), or(not(p), or(not(implies(p, q)), implies(implies(p, not(q)), not(p)))))), true, theorem(implies(implies(implies(p, q), or(not(p), implies(implies(p, not(q)), not(p)))), or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true), true, ifeq(theorem(implies(implies(p, q), or(not(p), implies(implies(p, not(q)), not(p))))), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.54 = { by axiom 1 (implies_definition) }
% 47.51/6.54 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(implies(p, q)), or(not(p), implies(implies(p, not(q)), not(p)))), or(not(p), or(not(implies(p, q)), implies(implies(p, not(q)), not(p)))))), true, theorem(implies(implies(implies(p, q), or(not(p), implies(implies(p, not(q)), not(p)))), or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true), true, ifeq(theorem(implies(implies(p, q), or(not(p), implies(implies(p, not(q)), not(p))))), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.54 = { by axiom 8 (axiom_1_5) }
% 47.51/6.54 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(p, q), or(not(p), implies(implies(p, not(q)), not(p)))), or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true), true, ifeq(theorem(implies(implies(p, q), or(not(p), implies(implies(p, not(q)), not(p))))), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.54 = { by axiom 2 (ifeq_axiom) }
% 47.51/6.54 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, q), or(not(p), implies(implies(p, not(q)), not(p)))), or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p)))))), true, ifeq(theorem(implies(implies(p, q), or(not(p), implies(implies(p, not(q)), not(p))))), true, theorem(or(not(p), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.54 = { by axiom 9 (rule_2) }
% 47.51/6.54 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.54 = { by axiom 2 (ifeq_axiom) }
% 47.51/6.55 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.55 = { by axiom 2 (ifeq_axiom) R->L }
% 47.51/6.55 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.55 = { by axiom 5 (rule_1) R->L }
% 47.51/6.55 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)), implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))))), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)), implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.55 = { by axiom 1 (implies_definition) }
% 47.51/6.55 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)), or(not(implies(p, not(q))), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))))), true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)), implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.55 = { by axiom 3 (axiom_1_3) }
% 47.51/6.55 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)), implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))))), true), true, ifeq(theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.55 = { by axiom 2 (ifeq_axiom) }
% 47.51/6.55 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)), implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))))), true, ifeq(theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p))), true, theorem(implies(implies(p, not(q)), or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), not(p)))), true), true), true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.56 = { by axiom 9 (rule_2) }
% 47.51/6.56 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(ifeq(true, true, theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.56 = { by axiom 2 (ifeq_axiom) }
% 47.51/6.56 ifeq(theorem(implies(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p))), implies(implies(p, q), implies(implies(p, not(q)), not(p))))), true, ifeq(theorem(or(implies(implies(p, q), implies(implies(p, not(q)), not(p))), implies(implies(p, not(q)), not(p)))), true, theorem(implies(implies(p, q), implies(implies(p, not(q)), not(p)))), true), true)
% 47.51/6.56 = { by axiom 9 (rule_2) }
% 47.51/6.56 true
% 47.51/6.56 % SZS output end Proof
% 47.51/6.56
% 47.51/6.56 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------