%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL235-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 11:49:26 AM UTC 2026
% Result : Unsatisfiable 178.53s 23.06s
% Output : Proof 184.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL235-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n002.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 15:32:23 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 178.53/23.06 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
% 178.53/23.06
% 178.53/23.06 % SZS status Unsatisfiable
% 178.53/23.06
% 181.67/23.35 % SZS output start Proof
% 181.67/23.35 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 181.67/23.35 Axiom 2 (and_defn): and(X, Y) = not(or(not(X), not(Y))).
% 181.67/23.35 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 181.67/23.35 Axiom 4 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 181.67/23.35 Axiom 5 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 181.67/23.35 Axiom 6 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 181.67/23.35 Axiom 7 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 181.67/23.35 Axiom 8 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 181.67/23.35 Axiom 9 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 181.67/23.36 Axiom 10 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 181.67/23.36
% 181.67/23.36 Goal 1 (prove_this): theorem(implies(not(and(p, q)), or(not(p), not(q)))) = true.
% 181.67/23.36 Proof:
% 181.67/23.36 theorem(implies(not(and(p, q)), or(not(p), not(q))))
% 181.67/23.36 = { by axiom 3 (ifeq_axiom) R->L }
% 181.67/23.36 ifeq(true, true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 181.67/23.36 = { by axiom 10 (rule_2) R->L }
% 181.67/23.36 ifeq(ifeq(theorem(implies(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))), or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q)))))), true, ifeq(theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 181.67/23.36 = { by axiom 1 (implies_definition) }
% 181.67/23.36 ifeq(ifeq(theorem(or(not(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q)))))), true, ifeq(theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 181.67/23.36 = { by axiom 3 (ifeq_axiom) R->L }
% 181.67/23.36 ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, ifeq(theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 181.67/23.36 = { by axiom 9 (axiom_1_5) R->L }
% 181.67/23.37 ifeq(ifeq(ifeq(axiom(implies(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))), or(not(and(p, q)), or(not(not(and(p, q))), or(not(p), not(q)))))), true, theorem(or(not(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, ifeq(theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 181.67/23.37 = { by axiom 1 (implies_definition) }
% 181.67/23.37 ifeq(ifeq(ifeq(axiom(or(not(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), or(not(and(p, q)), or(not(not(and(p, q))), or(not(p), not(q)))))), true, theorem(or(not(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, ifeq(theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 181.67/23.37 = { by axiom 1 (implies_definition) R->L }
% 181.67/23.37 ifeq(ifeq(ifeq(axiom(or(not(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q)))))), true, theorem(or(not(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, ifeq(theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 181.67/23.37 = { by axiom 6 (rule_1) }
% 181.67/23.37 ifeq(ifeq(true, true, ifeq(theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 181.67/23.37 = { by axiom 3 (ifeq_axiom) }
% 181.67/23.37 ifeq(ifeq(theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 181.67/23.37 = { by axiom 3 (ifeq_axiom) R->L }
% 181.67/23.37 ifeq(ifeq(ifeq(true, true, theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 181.67/23.38 = { by axiom 10 (rule_2) R->L }
% 181.67/23.38 ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(or(or(not(p), not(q)), not(and(p, q)))), or(not(and(p, q)), or(not(p), not(q)))), or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(theorem(or(not(or(or(not(p), not(q)), not(and(p, q)))), or(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 181.67/23.38 = { by axiom 1 (implies_definition) }
% 181.67/23.38 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(or(or(not(p), not(q)), not(and(p, q)))), or(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(theorem(or(not(or(or(not(p), not(q)), not(and(p, q)))), or(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 181.67/23.38 = { by axiom 3 (ifeq_axiom) R->L }
% 181.67/23.40 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(or(or(not(p), not(q)), not(and(p, q)))), or(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(ifeq(true, true, theorem(or(not(or(or(not(p), not(q)), not(and(p, q)))), or(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 182.44/23.40 = { by axiom 7 (axiom_1_4) R->L }
% 182.44/23.40 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(or(or(not(p), not(q)), not(and(p, q)))), or(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(ifeq(axiom(implies(or(or(not(p), not(q)), not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(not(or(or(not(p), not(q)), not(and(p, q)))), or(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 182.44/23.40 = { by axiom 1 (implies_definition) }
% 182.44/23.40 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(or(or(not(p), not(q)), not(and(p, q)))), or(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(ifeq(axiom(or(not(or(or(not(p), not(q)), not(and(p, q)))), or(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(not(or(or(not(p), not(q)), not(and(p, q)))), or(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 182.44/23.40 = { by axiom 6 (rule_1) }
% 182.44/23.41 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(or(or(not(p), not(q)), not(and(p, q)))), or(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(true, true, theorem(or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 182.44/23.41 = { by axiom 3 (ifeq_axiom) }
% 182.44/23.41 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(or(or(not(p), not(q)), not(and(p, q)))), or(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 182.44/23.41 = { by axiom 3 (ifeq_axiom) R->L }
% 182.44/23.41 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(or(or(not(p), not(q)), not(and(p, q)))), or(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 182.44/23.41 = { by axiom 8 (axiom_1_6) R->L }
% 182.44/23.41 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(or(not(p), not(q)), not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))), implies(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q)))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(not(or(or(not(p), not(q)), not(and(p, q)))), or(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 182.44/23.42 = { by axiom 1 (implies_definition) }
% 182.44/23.42 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(implies(or(or(not(p), not(q)), not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), implies(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q)))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(not(or(or(not(p), not(q)), not(and(p, q)))), or(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 182.44/23.42 = { by axiom 1 (implies_definition) }
% 182.44/23.42 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(or(or(not(p), not(q)), not(and(p, q)))), or(not(and(p, q)), or(not(p), not(q))))), implies(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q)))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(not(or(or(not(p), not(q)), not(and(p, q)))), or(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 182.44/23.42 = { by axiom 1 (implies_definition) }
% 182.44/23.42 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(or(or(not(p), not(q)), not(and(p, q)))), or(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(not(or(or(not(p), not(q)), not(and(p, q)))), or(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 182.44/23.42 = { by axiom 6 (rule_1) }
% 182.44/23.42 ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 182.44/23.42 = { by axiom 3 (ifeq_axiom) }
% 182.44/23.42 ifeq(ifeq(ifeq(theorem(or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))))), true, theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 182.44/23.42 = { by axiom 3 (ifeq_axiom) R->L }
% 182.44/23.43 ifeq(ifeq(ifeq(theorem(or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))))), true, ifeq(true, true, theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true), true), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 182.44/23.43 = { by axiom 6 (rule_1) R->L }
% 182.44/23.43 ifeq(ifeq(ifeq(theorem(or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))))), true, ifeq(ifeq(axiom(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), true, theorem(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), true), true, theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true), true), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 182.44/23.43 = { by axiom 1 (implies_definition) R->L }
% 182.44/23.43 ifeq(ifeq(ifeq(theorem(or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))))), true, ifeq(ifeq(axiom(implies(not(and(p, q)), or(or(not(p), not(q)), not(and(p, q))))), true, theorem(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), true), true, theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true), true), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 182.44/23.43 = { by axiom 4 (axiom_1_3) }
% 182.44/23.43 ifeq(ifeq(ifeq(theorem(or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))))), true, ifeq(ifeq(true, true, theorem(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), true), true, theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true), true), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 182.44/23.43 = { by axiom 3 (ifeq_axiom) }
% 182.44/23.43 ifeq(ifeq(ifeq(theorem(or(not(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))))), true, ifeq(theorem(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), true, theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true), true), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 182.44/23.43 = { by axiom 1 (implies_definition) R->L }
% 182.44/23.43 ifeq(ifeq(ifeq(theorem(implies(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q)))), or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q)))))), true, ifeq(theorem(or(not(not(and(p, q))), or(or(not(p), not(q)), not(and(p, q))))), true, theorem(or(not(not(and(p, q))), or(not(and(p, q)), or(not(p), not(q))))), true), true), true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 182.44/23.43 = { by axiom 10 (rule_2) }
% 182.44/23.43 ifeq(ifeq(true, true, theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 182.44/23.43 = { by axiom 3 (ifeq_axiom) }
% 182.44/23.43 ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true)
% 182.44/23.43 = { by axiom 3 (ifeq_axiom) R->L }
% 182.44/23.43 ifeq(true, true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 182.44/23.44 = { by axiom 10 (rule_2) R->L }
% 182.44/23.44 ifeq(ifeq(theorem(implies(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q)))))), true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 182.44/23.44 = { by axiom 1 (implies_definition) }
% 182.44/23.44 ifeq(ifeq(theorem(or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q)))))), true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 182.44/23.44 = { by axiom 3 (ifeq_axiom) R->L }
% 182.44/23.44 ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 182.44/23.45 = { by axiom 6 (rule_1) R->L }
% 182.44/23.45 ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 182.44/23.45 = { by axiom 1 (implies_definition) R->L }
% 182.44/23.46 ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), implies(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 182.44/23.46 = { by axiom 1 (implies_definition) R->L }
% 182.44/23.46 ifeq(ifeq(ifeq(ifeq(axiom(or(not(implies(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))), implies(not(and(p, q)), or(not(p), not(q))))), implies(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 182.44/23.47 = { by axiom 1 (implies_definition) R->L }
% 182.44/23.47 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))), implies(not(and(p, q)), or(not(p), not(q)))), implies(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 182.44/23.47 = { by axiom 8 (axiom_1_6) }
% 182.44/23.47 ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 182.44/23.48 = { by axiom 3 (ifeq_axiom) }
% 182.44/23.48 ifeq(ifeq(ifeq(theorem(or(not(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 182.44/23.48 = { by axiom 3 (ifeq_axiom) R->L }
% 182.44/23.49 ifeq(ifeq(ifeq(theorem(or(not(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(true, true, theorem(or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 182.44/23.49 = { by axiom 6 (rule_1) R->L }
% 182.44/23.49 ifeq(ifeq(ifeq(theorem(or(not(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(ifeq(axiom(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 182.44/23.49 = { by axiom 1 (implies_definition) R->L }
% 182.44/23.50 ifeq(ifeq(ifeq(theorem(or(not(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(ifeq(axiom(implies(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 182.44/23.50 = { by axiom 5 (axiom_1_2) }
% 182.44/23.50 ifeq(ifeq(ifeq(theorem(or(not(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(ifeq(true, true, theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 182.44/23.50 = { by axiom 3 (ifeq_axiom) }
% 183.24/23.51 ifeq(ifeq(ifeq(theorem(or(not(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.51 = { by axiom 1 (implies_definition) R->L }
% 183.24/23.51 ifeq(ifeq(ifeq(theorem(implies(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q)))), or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.51 = { by axiom 10 (rule_2) }
% 183.24/23.51 ifeq(ifeq(true, true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.52 = { by axiom 3 (ifeq_axiom) }
% 183.24/23.52 ifeq(ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.52 = { by axiom 3 (ifeq_axiom) R->L }
% 183.24/23.52 ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.52 = { by axiom 10 (rule_2) R->L }
% 183.24/23.53 ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))))), true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.53 = { by axiom 1 (implies_definition) }
% 183.24/23.53 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))))), true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.53 = { by axiom 3 (ifeq_axiom) R->L }
% 183.24/23.54 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))))), true), true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.54 = { by axiom 9 (axiom_1_5) R->L }
% 183.24/23.54 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))))), true, theorem(or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))))), true), true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.54 = { by axiom 1 (implies_definition) }
% 183.24/23.55 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))))), true, theorem(or(not(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))))), true), true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.55 = { by axiom 6 (rule_1) }
% 183.24/23.55 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.55 = { by axiom 3 (ifeq_axiom) }
% 183.24/23.55 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.56 = { by axiom 3 (ifeq_axiom) R->L }
% 183.24/23.56 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.56 = { by axiom 8 (axiom_1_6) R->L }
% 183.24/23.56 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(and(p, q), implies(not(and(p, q)), or(not(p), not(q)))), implies(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q)), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.56 = { by axiom 1 (implies_definition) }
% 183.24/23.57 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(implies(and(p, q), implies(not(and(p, q)), or(not(p), not(q))))), implies(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q)), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.57 = { by axiom 1 (implies_definition) }
% 183.24/23.57 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q)), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.57 = { by axiom 1 (implies_definition) }
% 183.24/23.57 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.57 = { by axiom 6 (rule_1) }
% 183.24/23.57 ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.58 = { by axiom 3 (ifeq_axiom) }
% 183.24/23.58 ifeq(ifeq(ifeq(theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.58 = { by axiom 3 (ifeq_axiom) R->L }
% 183.24/23.58 ifeq(ifeq(ifeq(theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(true, true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.58 = { by axiom 10 (rule_2) R->L }
% 183.24/23.58 ifeq(ifeq(ifeq(theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(ifeq(theorem(implies(or(and(p, q), implies(not(and(p, q)), or(not(p), not(q)))), or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q)))), true, ifeq(theorem(or(and(p, q), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.59 = { by axiom 1 (implies_definition) }
% 183.24/23.59 ifeq(ifeq(ifeq(theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(ifeq(theorem(or(not(or(and(p, q), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q)))), true, ifeq(theorem(or(and(p, q), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.59 = { by axiom 3 (ifeq_axiom) R->L }
% 183.24/23.59 ifeq(ifeq(ifeq(theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(ifeq(ifeq(true, true, theorem(or(not(or(and(p, q), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q)))), true), true, ifeq(theorem(or(and(p, q), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.59 = { by axiom 7 (axiom_1_4) R->L }
% 183.24/23.59 ifeq(ifeq(ifeq(theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(ifeq(ifeq(axiom(implies(or(and(p, q), implies(not(and(p, q)), or(not(p), not(q)))), or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q)))), true, theorem(or(not(or(and(p, q), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q)))), true), true, ifeq(theorem(or(and(p, q), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.59 = { by axiom 1 (implies_definition) }
% 183.24/23.60 ifeq(ifeq(ifeq(theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(ifeq(ifeq(axiom(or(not(or(and(p, q), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q)))), true, theorem(or(not(or(and(p, q), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q)))), true), true, ifeq(theorem(or(and(p, q), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.60 = { by axiom 6 (rule_1) }
% 183.24/23.60 ifeq(ifeq(ifeq(theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(ifeq(true, true, ifeq(theorem(or(and(p, q), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 183.24/23.60 = { by axiom 3 (ifeq_axiom) }
% 183.24/23.60 ifeq(ifeq(ifeq(theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(ifeq(theorem(or(and(p, q), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 184.03/23.60 = { by axiom 2 (and_defn) }
% 184.03/23.60 ifeq(ifeq(ifeq(theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(ifeq(theorem(or(not(or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 184.03/23.60 = { by axiom 3 (ifeq_axiom) R->L }
% 184.03/23.60 ifeq(ifeq(ifeq(theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 184.03/23.60 = { by axiom 4 (axiom_1_3) R->L }
% 184.03/23.61 ifeq(ifeq(ifeq(theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(ifeq(ifeq(axiom(implies(or(not(p), not(q)), or(not(not(and(p, q))), or(not(p), not(q))))), true, theorem(or(not(or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 184.03/23.61 = { by axiom 1 (implies_definition) }
% 184.03/23.61 ifeq(ifeq(ifeq(theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(ifeq(ifeq(axiom(or(not(or(not(p), not(q))), or(not(not(and(p, q))), or(not(p), not(q))))), true, theorem(or(not(or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 184.03/23.61 = { by axiom 1 (implies_definition) R->L }
% 184.03/23.61 ifeq(ifeq(ifeq(theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(ifeq(ifeq(axiom(or(not(or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(or(not(or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, theorem(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 184.03/23.61 = { by axiom 6 (rule_1) }
% 184.03/23.61 ifeq(ifeq(ifeq(theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(ifeq(true, true, theorem(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 184.03/23.61 = { by axiom 3 (ifeq_axiom) }
% 184.03/23.61 ifeq(ifeq(ifeq(theorem(or(not(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(theorem(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 184.03/23.61 = { by axiom 1 (implies_definition) R->L }
% 184.03/23.61 ifeq(ifeq(ifeq(theorem(implies(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q)), or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q))))))), true, ifeq(theorem(or(implies(not(and(p, q)), or(not(p), not(q))), and(p, q))), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), or(implies(not(and(p, q)), or(not(p), not(q))), implies(not(and(p, q)), or(not(p), not(q)))))), true), true), true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 184.03/23.61 = { by axiom 10 (rule_2) }
% 184.03/23.61 ifeq(ifeq(true, true, theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 184.03/23.61 = { by axiom 3 (ifeq_axiom) }
% 184.03/23.61 ifeq(theorem(or(not(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), implies(not(and(p, q)), or(not(p), not(q))))), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 184.03/23.61 = { by axiom 1 (implies_definition) R->L }
% 184.03/23.61 ifeq(theorem(implies(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q)))), implies(not(and(p, q)), or(not(p), not(q))))), true, ifeq(theorem(or(not(and(p, q)), implies(not(and(p, q)), or(not(p), not(q))))), true, theorem(implies(not(and(p, q)), or(not(p), not(q)))), true), true)
% 184.03/23.61 = { by axiom 10 (rule_2) }
% 184.03/23.61 true
% 184.03/23.61 % SZS output end Proof
% 184.03/23.61
% 184.03/23.61 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------