%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL240-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:49:27 AM UTC 2026
% Result : Unsatisfiable 206.45s 26.50s
% Output : Proof 209.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL240-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 15:30:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.12/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 206.45/26.50 Command-line arguments: --flatten-regeneralise
% 206.45/26.50
% 206.45/26.50 % SZS status Unsatisfiable
% 206.45/26.50
% 208.87/26.70 % SZS output start Proof
% 208.87/26.70 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 208.87/26.70 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 208.87/26.70 Axiom 3 (and_defn): and(X, Y) = not(or(not(X), not(Y))).
% 208.87/26.70 Axiom 4 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 208.87/26.70 Axiom 5 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 208.87/26.70 Axiom 6 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 208.87/26.70 Axiom 7 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 208.87/26.70 Axiom 8 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 208.87/26.70 Axiom 9 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 208.87/26.71 Axiom 10 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 208.87/26.71
% 208.87/26.71 Goal 1 (prove_this): theorem(implies(and(p, q), p)) = true.
% 208.87/26.71 Proof:
% 208.87/26.71 theorem(implies(and(p, q), p))
% 208.87/26.71 = { by axiom 2 (ifeq_axiom) R->L }
% 208.87/26.71 ifeq(true, true, theorem(implies(and(p, q), p)), true)
% 208.87/26.71 = { by axiom 2 (ifeq_axiom) R->L }
% 208.87/26.71 ifeq(true, true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.71 = { by axiom 8 (rule_2) R->L }
% 208.87/26.71 ifeq(ifeq(theorem(implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p)))), true, ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.71 = { by axiom 2 (ifeq_axiom) R->L }
% 208.87/26.71 ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p)))), true), true, ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.71 = { by axiom 4 (rule_1) R->L }
% 208.87/26.71 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(and(p, q), p), implies(and(p, q), p)), implies(and(p, q), p)), implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))))), true, theorem(implies(implies(or(implies(and(p, q), p), implies(and(p, q), p)), implies(and(p, q), p)), implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))))), true), true, theorem(implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p)))), true), true, ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.72 = { by axiom 1 (implies_definition) }
% 208.87/26.72 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(and(p, q), p), implies(and(p, q), p)), implies(and(p, q), p)), implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), or(not(implies(not(p), implies(and(p, q), p))), implies(and(p, q), p))))), true, theorem(implies(implies(or(implies(and(p, q), p), implies(and(p, q), p)), implies(and(p, q), p)), implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))))), true), true, theorem(implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p)))), true), true, ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.72 = { by axiom 1 (implies_definition) }
% 208.87/26.72 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(and(p, q), p), implies(and(p, q), p)), implies(and(p, q), p)), implies(or(not(implies(not(p), implies(and(p, q), p))), or(implies(and(p, q), p), implies(and(p, q), p))), or(not(implies(not(p), implies(and(p, q), p))), implies(and(p, q), p))))), true, theorem(implies(implies(or(implies(and(p, q), p), implies(and(p, q), p)), implies(and(p, q), p)), implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))))), true), true, theorem(implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p)))), true), true, ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.72 = { by axiom 9 (axiom_1_6) }
% 208.87/26.72 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(implies(and(p, q), p), implies(and(p, q), p)), implies(and(p, q), p)), implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))))), true), true, theorem(implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p)))), true), true, ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.72 = { by axiom 2 (ifeq_axiom) }
% 208.87/26.72 ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(and(p, q), p), implies(and(p, q), p)), implies(and(p, q), p)), implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))))), true, theorem(implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p)))), true), true, ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.72 = { by axiom 2 (ifeq_axiom) R->L }
% 208.87/26.72 ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(and(p, q), p), implies(and(p, q), p)), implies(and(p, q), p)), implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))))), true, ifeq(true, true, theorem(implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p)))), true), true), true, ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.72 = { by axiom 4 (rule_1) R->L }
% 208.87/26.72 ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(and(p, q), p), implies(and(p, q), p)), implies(and(p, q), p)), implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))))), true, ifeq(ifeq(axiom(implies(or(implies(and(p, q), p), implies(and(p, q), p)), implies(and(p, q), p))), true, theorem(implies(or(implies(and(p, q), p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, theorem(implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p)))), true), true), true, ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.72 = { by axiom 6 (axiom_1_2) }
% 208.87/26.73 ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(and(p, q), p), implies(and(p, q), p)), implies(and(p, q), p)), implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))))), true, ifeq(ifeq(true, true, theorem(implies(or(implies(and(p, q), p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, theorem(implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p)))), true), true), true, ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.73 = { by axiom 2 (ifeq_axiom) }
% 208.87/26.73 ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(and(p, q), p), implies(and(p, q), p)), implies(and(p, q), p)), implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))))), true, ifeq(theorem(implies(or(implies(and(p, q), p), implies(and(p, q), p)), implies(and(p, q), p))), true, theorem(implies(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))), implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p)))), true), true), true, ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.73 = { by axiom 8 (rule_2) }
% 208.87/26.73 ifeq(ifeq(true, true, ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.73 = { by axiom 2 (ifeq_axiom) }
% 208.87/26.73 ifeq(ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.73 = { by axiom 2 (ifeq_axiom) R->L }
% 208.87/26.73 ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.73 = { by axiom 8 (rule_2) R->L }
% 208.87/26.73 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(not(p), implies(and(p, q), p)), implies(or(implies(and(p, q), p), not(p)), or(implies(and(p, q), p), implies(and(p, q), p)))), implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))))), true, ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(or(implies(and(p, q), p), not(p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.73 = { by axiom 2 (ifeq_axiom) R->L }
% 208.87/26.73 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(not(p), implies(and(p, q), p)), implies(or(implies(and(p, q), p), not(p)), or(implies(and(p, q), p), implies(and(p, q), p)))), implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))))), true), true, ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(or(implies(and(p, q), p), not(p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.74 = { by axiom 10 (axiom_1_5) R->L }
% 208.87/26.74 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(implies(not(p), implies(and(p, q), p))), or(not(or(implies(and(p, q), p), not(p))), or(implies(and(p, q), p), implies(and(p, q), p)))), or(not(or(implies(and(p, q), p), not(p))), or(not(implies(not(p), implies(and(p, q), p))), or(implies(and(p, q), p), implies(and(p, q), p)))))), true, theorem(implies(implies(implies(not(p), implies(and(p, q), p)), implies(or(implies(and(p, q), p), not(p)), or(implies(and(p, q), p), implies(and(p, q), p)))), implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))))), true), true, ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(or(implies(and(p, q), p), not(p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.74 = { by axiom 1 (implies_definition) R->L }
% 208.87/26.74 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(not(p), implies(and(p, q), p)), or(not(or(implies(and(p, q), p), not(p))), or(implies(and(p, q), p), implies(and(p, q), p)))), or(not(or(implies(and(p, q), p), not(p))), or(not(implies(not(p), implies(and(p, q), p))), or(implies(and(p, q), p), implies(and(p, q), p)))))), true, theorem(implies(implies(implies(not(p), implies(and(p, q), p)), implies(or(implies(and(p, q), p), not(p)), or(implies(and(p, q), p), implies(and(p, q), p)))), implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))))), true), true, ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(or(implies(and(p, q), p), not(p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.74 = { by axiom 1 (implies_definition) R->L }
% 208.87/26.74 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(not(p), implies(and(p, q), p)), or(not(or(implies(and(p, q), p), not(p))), or(implies(and(p, q), p), implies(and(p, q), p)))), or(not(or(implies(and(p, q), p), not(p))), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))))), true, theorem(implies(implies(implies(not(p), implies(and(p, q), p)), implies(or(implies(and(p, q), p), not(p)), or(implies(and(p, q), p), implies(and(p, q), p)))), implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))))), true), true, ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(or(implies(and(p, q), p), not(p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.74 = { by axiom 1 (implies_definition) R->L }
% 208.87/26.74 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(not(p), implies(and(p, q), p)), implies(or(implies(and(p, q), p), not(p)), or(implies(and(p, q), p), implies(and(p, q), p)))), or(not(or(implies(and(p, q), p), not(p))), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))))), true, theorem(implies(implies(implies(not(p), implies(and(p, q), p)), implies(or(implies(and(p, q), p), not(p)), or(implies(and(p, q), p), implies(and(p, q), p)))), implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))))), true), true, ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(or(implies(and(p, q), p), not(p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.75 = { by axiom 1 (implies_definition) R->L }
% 208.87/26.75 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(not(p), implies(and(p, q), p)), implies(or(implies(and(p, q), p), not(p)), or(implies(and(p, q), p), implies(and(p, q), p)))), implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))))), true, theorem(implies(implies(implies(not(p), implies(and(p, q), p)), implies(or(implies(and(p, q), p), not(p)), or(implies(and(p, q), p), implies(and(p, q), p)))), implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))))), true), true, ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(or(implies(and(p, q), p), not(p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.75 = { by axiom 4 (rule_1) }
% 208.87/26.75 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(or(implies(and(p, q), p), not(p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.75 = { by axiom 2 (ifeq_axiom) }
% 208.87/26.75 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(or(implies(and(p, q), p), not(p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.75 = { by axiom 2 (ifeq_axiom) R->L }
% 208.87/26.75 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(or(implies(and(p, q), p), not(p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true), true, theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.75 = { by axiom 9 (axiom_1_6) R->L }
% 208.87/26.75 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(p), implies(and(p, q), p)), implies(or(implies(and(p, q), p), not(p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(or(implies(and(p, q), p), not(p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true), true, theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.75 = { by axiom 4 (rule_1) }
% 208.87/26.75 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.75 = { by axiom 2 (ifeq_axiom) }
% 208.87/26.75 ifeq(ifeq(ifeq(theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.75 = { by axiom 2 (ifeq_axiom) R->L }
% 208.87/26.76 ifeq(ifeq(ifeq(theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, ifeq(true, true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.76 = { by axiom 8 (rule_2) R->L }
% 208.87/26.76 ifeq(ifeq(ifeq(theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, ifeq(ifeq(theorem(implies(implies(p, implies(and(p, q), p)), or(implies(and(p, q), p), not(p)))), true, ifeq(theorem(implies(p, implies(and(p, q), p))), true, theorem(or(implies(and(p, q), p), not(p))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.76 = { by axiom 2 (ifeq_axiom) R->L }
% 208.87/26.76 ifeq(ifeq(ifeq(theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(implies(p, implies(and(p, q), p)), or(implies(and(p, q), p), not(p)))), true), true, ifeq(theorem(implies(p, implies(and(p, q), p))), true, theorem(or(implies(and(p, q), p), not(p))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.76 = { by axiom 7 (axiom_1_4) R->L }
% 208.87/26.76 ifeq(ifeq(ifeq(theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, ifeq(ifeq(ifeq(axiom(implies(or(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), not(p)))), true, theorem(implies(implies(p, implies(and(p, q), p)), or(implies(and(p, q), p), not(p)))), true), true, ifeq(theorem(implies(p, implies(and(p, q), p))), true, theorem(or(implies(and(p, q), p), not(p))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.76 = { by axiom 1 (implies_definition) R->L }
% 208.87/26.76 ifeq(ifeq(ifeq(theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, ifeq(ifeq(ifeq(axiom(implies(implies(p, implies(and(p, q), p)), or(implies(and(p, q), p), not(p)))), true, theorem(implies(implies(p, implies(and(p, q), p)), or(implies(and(p, q), p), not(p)))), true), true, ifeq(theorem(implies(p, implies(and(p, q), p))), true, theorem(or(implies(and(p, q), p), not(p))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.76 = { by axiom 4 (rule_1) }
% 208.87/26.76 ifeq(ifeq(ifeq(theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, ifeq(ifeq(true, true, ifeq(theorem(implies(p, implies(and(p, q), p))), true, theorem(or(implies(and(p, q), p), not(p))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.76 = { by axiom 2 (ifeq_axiom) }
% 208.87/26.76 ifeq(ifeq(ifeq(theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, ifeq(ifeq(theorem(implies(p, implies(and(p, q), p))), true, theorem(or(implies(and(p, q), p), not(p))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.76 = { by axiom 2 (ifeq_axiom) R->L }
% 208.87/26.76 ifeq(ifeq(ifeq(theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(p, implies(and(p, q), p))), true), true, theorem(or(implies(and(p, q), p), not(p))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.77 = { by axiom 5 (axiom_1_3) R->L }
% 208.87/26.77 ifeq(ifeq(ifeq(theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, ifeq(ifeq(ifeq(axiom(implies(p, or(not(and(p, q)), p))), true, theorem(implies(p, implies(and(p, q), p))), true), true, theorem(or(implies(and(p, q), p), not(p))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.77 = { by axiom 1 (implies_definition) R->L }
% 208.87/26.77 ifeq(ifeq(ifeq(theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, ifeq(ifeq(ifeq(axiom(implies(p, implies(and(p, q), p))), true, theorem(implies(p, implies(and(p, q), p))), true), true, theorem(or(implies(and(p, q), p), not(p))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.77 = { by axiom 4 (rule_1) }
% 208.87/26.77 ifeq(ifeq(ifeq(theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, ifeq(ifeq(true, true, theorem(or(implies(and(p, q), p), not(p))), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.77 = { by axiom 2 (ifeq_axiom) }
% 208.87/26.77 ifeq(ifeq(ifeq(theorem(implies(or(implies(and(p, q), p), not(p)), implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p))))), true, ifeq(theorem(or(implies(and(p, q), p), not(p))), true, theorem(implies(implies(not(p), implies(and(p, q), p)), or(implies(and(p, q), p), implies(and(p, q), p)))), true), true), true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.77 = { by axiom 8 (rule_2) }
% 208.87/26.77 ifeq(ifeq(true, true, theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.77 = { by axiom 2 (ifeq_axiom) }
% 208.87/26.77 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(true, true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.77 = { by axiom 8 (rule_2) R->L }
% 208.87/26.77 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true, ifeq(theorem(implies(not(p), implies(p, not(q)))), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.77 = { by axiom 2 (ifeq_axiom) R->L }
% 208.87/26.77 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true, ifeq(ifeq(true, true, theorem(implies(not(p), implies(p, not(q)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.77 = { by axiom 8 (rule_2) R->L }
% 208.87/26.77 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true, ifeq(ifeq(ifeq(theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(not(p)), or(not(q), not(p))), or(not(not(p)), implies(p, not(q)))))), true, ifeq(theorem(implies(or(not(q), not(p)), implies(p, not(q)))), true, theorem(implies(or(not(not(p)), or(not(q), not(p))), or(not(not(p)), implies(p, not(q))))), true), true), true, theorem(implies(not(p), implies(p, not(q)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.77 = { by axiom 2 (ifeq_axiom) R->L }
% 208.87/26.78 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(not(p)), or(not(q), not(p))), or(not(not(p)), implies(p, not(q)))))), true), true, ifeq(theorem(implies(or(not(q), not(p)), implies(p, not(q)))), true, theorem(implies(or(not(not(p)), or(not(q), not(p))), or(not(not(p)), implies(p, not(q))))), true), true), true, theorem(implies(not(p), implies(p, not(q)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.78 = { by axiom 9 (axiom_1_6) R->L }
% 208.87/26.78 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(not(p)), or(not(q), not(p))), or(not(not(p)), implies(p, not(q)))))), true, theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(not(p)), or(not(q), not(p))), or(not(not(p)), implies(p, not(q)))))), true), true, ifeq(theorem(implies(or(not(q), not(p)), implies(p, not(q)))), true, theorem(implies(or(not(not(p)), or(not(q), not(p))), or(not(not(p)), implies(p, not(q))))), true), true), true, theorem(implies(not(p), implies(p, not(q)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.78 = { by axiom 4 (rule_1) }
% 208.87/26.78 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true, ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(or(not(q), not(p)), implies(p, not(q)))), true, theorem(implies(or(not(not(p)), or(not(q), not(p))), or(not(not(p)), implies(p, not(q))))), true), true), true, theorem(implies(not(p), implies(p, not(q)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.78 = { by axiom 2 (ifeq_axiom) }
% 208.87/26.78 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true, ifeq(ifeq(ifeq(theorem(implies(or(not(q), not(p)), implies(p, not(q)))), true, theorem(implies(or(not(not(p)), or(not(q), not(p))), or(not(not(p)), implies(p, not(q))))), true), true, theorem(implies(not(p), implies(p, not(q)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.78 = { by axiom 2 (ifeq_axiom) R->L }
% 208.87/26.78 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(q), not(p)), implies(p, not(q)))), true), true, theorem(implies(or(not(not(p)), or(not(q), not(p))), or(not(not(p)), implies(p, not(q))))), true), true, theorem(implies(not(p), implies(p, not(q)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.78 = { by axiom 7 (axiom_1_4) R->L }
% 208.87/26.78 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(q), not(p)), or(not(p), not(q)))), true, theorem(implies(or(not(q), not(p)), implies(p, not(q)))), true), true, theorem(implies(or(not(not(p)), or(not(q), not(p))), or(not(not(p)), implies(p, not(q))))), true), true, theorem(implies(not(p), implies(p, not(q)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.78 = { by axiom 1 (implies_definition) R->L }
% 208.87/26.78 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(q), not(p)), implies(p, not(q)))), true, theorem(implies(or(not(q), not(p)), implies(p, not(q)))), true), true, theorem(implies(or(not(not(p)), or(not(q), not(p))), or(not(not(p)), implies(p, not(q))))), true), true, theorem(implies(not(p), implies(p, not(q)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.78 = { by axiom 4 (rule_1) }
% 208.87/26.78 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(not(p)), or(not(q), not(p))), or(not(not(p)), implies(p, not(q))))), true), true, theorem(implies(not(p), implies(p, not(q)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.79 = { by axiom 2 (ifeq_axiom) }
% 208.87/26.79 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true, ifeq(ifeq(theorem(implies(or(not(not(p)), or(not(q), not(p))), or(not(not(p)), implies(p, not(q))))), true, theorem(implies(not(p), implies(p, not(q)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.79 = { by axiom 1 (implies_definition) R->L }
% 208.87/26.79 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true, ifeq(ifeq(theorem(implies(implies(not(p), or(not(q), not(p))), or(not(not(p)), implies(p, not(q))))), true, theorem(implies(not(p), implies(p, not(q)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.79 = { by axiom 1 (implies_definition) R->L }
% 208.87/26.79 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true, ifeq(ifeq(theorem(implies(implies(not(p), or(not(q), not(p))), implies(not(p), implies(p, not(q))))), true, theorem(implies(not(p), implies(p, not(q)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.79 = { by axiom 2 (ifeq_axiom) R->L }
% 208.87/26.79 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true, ifeq(ifeq(theorem(implies(implies(not(p), or(not(q), not(p))), implies(not(p), implies(p, not(q))))), true, ifeq(true, true, theorem(implies(not(p), implies(p, not(q)))), true), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.79 = { by axiom 4 (rule_1) R->L }
% 208.87/26.79 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true, ifeq(ifeq(theorem(implies(implies(not(p), or(not(q), not(p))), implies(not(p), implies(p, not(q))))), true, ifeq(ifeq(axiom(implies(not(p), or(not(q), not(p)))), true, theorem(implies(not(p), or(not(q), not(p)))), true), true, theorem(implies(not(p), implies(p, not(q)))), true), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.79 = { by axiom 5 (axiom_1_3) }
% 208.87/26.79 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true, ifeq(ifeq(theorem(implies(implies(not(p), or(not(q), not(p))), implies(not(p), implies(p, not(q))))), true, ifeq(ifeq(true, true, theorem(implies(not(p), or(not(q), not(p)))), true), true, theorem(implies(not(p), implies(p, not(q)))), true), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.79 = { by axiom 2 (ifeq_axiom) }
% 208.87/26.79 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true, ifeq(ifeq(theorem(implies(implies(not(p), or(not(q), not(p))), implies(not(p), implies(p, not(q))))), true, ifeq(theorem(implies(not(p), or(not(q), not(p)))), true, theorem(implies(not(p), implies(p, not(q)))), true), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.79 = { by axiom 8 (rule_2) }
% 208.87/26.79 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true, ifeq(true, true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.79 = { by axiom 2 (ifeq_axiom) }
% 208.87/26.79 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.80 = { by axiom 2 (ifeq_axiom) R->L }
% 208.87/26.80 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.80 = { by axiom 8 (rule_2) R->L }
% 208.87/26.80 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p)), implies(implies(p, not(q)), implies(not(implies(p, not(q))), p)))), true, ifeq(theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.80 = { by axiom 2 (ifeq_axiom) R->L }
% 208.87/26.80 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p)), implies(implies(p, not(q)), implies(not(implies(p, not(q))), p)))), true), true, ifeq(theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.80 = { by axiom 10 (axiom_1_5) R->L }
% 208.87/26.80 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(not(implies(p, not(q)))), or(not(implies(p, not(q))), p)), or(not(implies(p, not(q))), or(not(not(implies(p, not(q)))), p)))), true, theorem(implies(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p)), implies(implies(p, not(q)), implies(not(implies(p, not(q))), p)))), true), true, ifeq(theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.80 = { by axiom 1 (implies_definition) R->L }
% 208.87/26.80 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(implies(p, not(q))), or(not(implies(p, not(q))), p)), or(not(implies(p, not(q))), or(not(not(implies(p, not(q)))), p)))), true, theorem(implies(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p)), implies(implies(p, not(q)), implies(not(implies(p, not(q))), p)))), true), true, ifeq(theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 208.87/26.80 = { by axiom 1 (implies_definition) R->L }
% 208.87/26.80 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(implies(p, not(q))), or(not(implies(p, not(q))), p)), or(not(implies(p, not(q))), implies(not(implies(p, not(q))), p)))), true, theorem(implies(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p)), implies(implies(p, not(q)), implies(not(implies(p, not(q))), p)))), true), true, ifeq(theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.80 = { by axiom 1 (implies_definition) R->L }
% 209.69/26.80 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p)), or(not(implies(p, not(q))), implies(not(implies(p, not(q))), p)))), true, theorem(implies(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p)), implies(implies(p, not(q)), implies(not(implies(p, not(q))), p)))), true), true, ifeq(theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.80 = { by axiom 1 (implies_definition) R->L }
% 209.69/26.81 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p)), implies(implies(p, not(q)), implies(not(implies(p, not(q))), p)))), true, theorem(implies(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p)), implies(implies(p, not(q)), implies(not(implies(p, not(q))), p)))), true), true, ifeq(theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.81 = { by axiom 4 (rule_1) }
% 209.69/26.81 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.81 = { by axiom 2 (ifeq_axiom) }
% 209.69/26.81 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.81 = { by axiom 2 (ifeq_axiom) R->L }
% 209.69/26.81 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.81 = { by axiom 8 (rule_2) R->L }
% 209.69/26.81 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, not(implies(p, not(q)))), implies(implies(p, not(q)), p)), implies(or(not(not(implies(p, not(q)))), or(p, not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), p))))), true, ifeq(theorem(implies(or(p, not(implies(p, not(q)))), implies(implies(p, not(q)), p))), true, theorem(implies(or(not(not(implies(p, not(q)))), or(p, not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), p)))), true), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.81 = { by axiom 2 (ifeq_axiom) R->L }
% 209.69/26.81 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(p, not(implies(p, not(q)))), implies(implies(p, not(q)), p)), implies(or(not(not(implies(p, not(q)))), or(p, not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), p))))), true), true, ifeq(theorem(implies(or(p, not(implies(p, not(q)))), implies(implies(p, not(q)), p))), true, theorem(implies(or(not(not(implies(p, not(q)))), or(p, not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), p)))), true), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.81 = { by axiom 9 (axiom_1_6) R->L }
% 209.69/26.82 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, not(implies(p, not(q)))), implies(implies(p, not(q)), p)), implies(or(not(not(implies(p, not(q)))), or(p, not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), p))))), true, theorem(implies(implies(or(p, not(implies(p, not(q)))), implies(implies(p, not(q)), p)), implies(or(not(not(implies(p, not(q)))), or(p, not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), p))))), true), true, ifeq(theorem(implies(or(p, not(implies(p, not(q)))), implies(implies(p, not(q)), p))), true, theorem(implies(or(not(not(implies(p, not(q)))), or(p, not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), p)))), true), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.82 = { by axiom 4 (rule_1) }
% 209.69/26.82 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(or(p, not(implies(p, not(q)))), implies(implies(p, not(q)), p))), true, theorem(implies(or(not(not(implies(p, not(q)))), or(p, not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), p)))), true), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.82 = { by axiom 2 (ifeq_axiom) }
% 209.69/26.82 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(p, not(implies(p, not(q)))), implies(implies(p, not(q)), p))), true, theorem(implies(or(not(not(implies(p, not(q)))), or(p, not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), p)))), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.82 = { by axiom 2 (ifeq_axiom) R->L }
% 209.69/26.82 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(p, not(implies(p, not(q)))), implies(implies(p, not(q)), p))), true), true, theorem(implies(or(not(not(implies(p, not(q)))), or(p, not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), p)))), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.82 = { by axiom 7 (axiom_1_4) R->L }
% 209.69/26.82 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(p, not(implies(p, not(q)))), or(not(implies(p, not(q))), p))), true, theorem(implies(or(p, not(implies(p, not(q)))), implies(implies(p, not(q)), p))), true), true, theorem(implies(or(not(not(implies(p, not(q)))), or(p, not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), p)))), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.82 = { by axiom 1 (implies_definition) R->L }
% 209.69/26.82 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(p, not(implies(p, not(q)))), implies(implies(p, not(q)), p))), true, theorem(implies(or(p, not(implies(p, not(q)))), implies(implies(p, not(q)), p))), true), true, theorem(implies(or(not(not(implies(p, not(q)))), or(p, not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), p)))), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.82 = { by axiom 4 (rule_1) }
% 209.69/26.83 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(not(implies(p, not(q)))), or(p, not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), p)))), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.83 = { by axiom 2 (ifeq_axiom) }
% 209.69/26.83 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(not(implies(p, not(q)))), or(p, not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), p)))), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.83 = { by axiom 1 (implies_definition) R->L }
% 209.69/26.83 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(q))), or(p, not(implies(p, not(q))))), or(not(not(implies(p, not(q)))), implies(implies(p, not(q)), p)))), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.83 = { by axiom 1 (implies_definition) R->L }
% 209.69/26.83 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(q))), or(p, not(implies(p, not(q))))), implies(not(implies(p, not(q))), implies(implies(p, not(q)), p)))), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.83 = { by axiom 2 (ifeq_axiom) R->L }
% 209.69/26.83 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(q))), or(p, not(implies(p, not(q))))), implies(not(implies(p, not(q))), implies(implies(p, not(q)), p)))), true, ifeq(true, true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.83 = { by axiom 4 (rule_1) R->L }
% 209.69/26.83 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(q))), or(p, not(implies(p, not(q))))), implies(not(implies(p, not(q))), implies(implies(p, not(q)), p)))), true, ifeq(ifeq(axiom(implies(not(implies(p, not(q))), or(p, not(implies(p, not(q)))))), true, theorem(implies(not(implies(p, not(q))), or(p, not(implies(p, not(q)))))), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.83 = { by axiom 5 (axiom_1_3) }
% 209.69/26.83 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(q))), or(p, not(implies(p, not(q))))), implies(not(implies(p, not(q))), implies(implies(p, not(q)), p)))), true, ifeq(ifeq(true, true, theorem(implies(not(implies(p, not(q))), or(p, not(implies(p, not(q)))))), true), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.84 = { by axiom 2 (ifeq_axiom) }
% 209.69/26.84 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(q))), or(p, not(implies(p, not(q))))), implies(not(implies(p, not(q))), implies(implies(p, not(q)), p)))), true, ifeq(theorem(implies(not(implies(p, not(q))), or(p, not(implies(p, not(q)))))), true, theorem(implies(not(implies(p, not(q))), implies(implies(p, not(q)), p))), true), true), true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.84 = { by axiom 8 (rule_2) }
% 209.69/26.84 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.84 = { by axiom 2 (ifeq_axiom) }
% 209.69/26.84 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.84 = { by axiom 2 (ifeq_axiom) R->L }
% 209.69/26.84 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.84 = { by axiom 4 (rule_1) R->L }
% 209.69/26.84 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p)), implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p))))), true, theorem(implies(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p)), implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p))))), true), true, ifeq(theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.84 = { by axiom 1 (implies_definition) }
% 209.69/26.84 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p)), implies(implies(not(p), implies(p, not(q))), or(not(not(p)), implies(not(implies(p, not(q))), p))))), true, theorem(implies(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p)), implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p))))), true), true, ifeq(theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.84 = { by axiom 1 (implies_definition) }
% 209.69/26.84 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p)), implies(or(not(not(p)), implies(p, not(q))), or(not(not(p)), implies(not(implies(p, not(q))), p))))), true, theorem(implies(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p)), implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p))))), true), true, ifeq(theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.85 = { by axiom 9 (axiom_1_6) }
% 209.69/26.85 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p)), implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p))))), true), true, ifeq(theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.85 = { by axiom 2 (ifeq_axiom) }
% 209.69/26.85 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p)), implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p))))), true, ifeq(theorem(implies(implies(p, not(q)), implies(not(implies(p, not(q))), p))), true, theorem(implies(implies(not(p), implies(p, not(q))), implies(not(p), implies(not(implies(p, not(q))), p)))), true), true), true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.85 = { by axiom 8 (rule_2) }
% 209.69/26.85 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(ifeq(true, true, theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.85 = { by axiom 2 (ifeq_axiom) }
% 209.69/26.85 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(theorem(implies(not(p), implies(not(implies(p, not(q))), p))), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.85 = { by axiom 1 (implies_definition) }
% 209.69/26.85 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(theorem(implies(not(p), implies(not(or(not(p), not(q))), p))), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.85 = { by axiom 3 (and_defn) R->L }
% 209.69/26.85 ifeq(theorem(implies(implies(not(p), implies(and(p, q), p)), implies(and(p, q), p))), true, ifeq(theorem(implies(not(p), implies(and(p, q), p))), true, theorem(implies(and(p, q), p)), true), true)
% 209.69/26.85 = { by axiom 8 (rule_2) }
% 209.69/26.85 true
% 209.69/26.85 % SZS output end Proof
% 209.69/26.85
% 209.69/26.85 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------