%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL273-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 11:49:32 AM UTC 2026
% Result : Unsatisfiable 165.30s 21.44s
% Output : Proof 175.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL273-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n009.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Sun Sep 27 15:32:30 UTC 2026
% 0.19/0.47 % CPUTime :
% 0.19/0.47 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 165.30/21.44 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 165.30/21.44
% 165.30/21.44 % SZS status Unsatisfiable
% 165.30/21.44
% 171.65/22.27 % SZS output start Proof
% 171.65/22.27 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 171.65/22.27 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 171.65/22.27 Axiom 3 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 171.65/22.27 Axiom 4 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 171.65/22.27 Axiom 5 (and_defn): and(X, Y) = not(or(not(X), not(Y))).
% 171.65/22.27 Axiom 6 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 171.65/22.27 Axiom 7 (equivalent_defn): equivalent(X, Y) = and(implies(X, Y), implies(Y, X)).
% 171.65/22.27 Axiom 8 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 171.65/22.27 Axiom 9 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 171.65/22.27 Axiom 10 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 171.65/22.27 Axiom 11 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 171.65/22.27
% 171.65/22.27 Lemma 12: not(implies(X, not(Y))) = and(X, Y).
% 171.65/22.27 Proof:
% 171.65/22.27 not(implies(X, not(Y)))
% 171.65/22.27 = { by axiom 1 (implies_definition) }
% 171.65/22.27 not(or(not(X), not(Y)))
% 171.65/22.27 = { by axiom 5 (and_defn) R->L }
% 171.65/22.27 and(X, Y)
% 171.65/22.27
% 171.65/22.27 Lemma 13: implies(implies(X, not(Y)), Z) = or(and(X, Y), Z).
% 171.65/22.27 Proof:
% 171.65/22.27 implies(implies(X, not(Y)), Z)
% 171.65/22.27 = { by axiom 1 (implies_definition) }
% 171.65/22.27 or(not(implies(X, not(Y))), Z)
% 171.65/22.27 = { by lemma 12 }
% 171.65/22.30 or(and(X, Y), Z)
% 171.65/22.30
% 171.65/22.30 Goal 1 (prove_this): theorem(equivalent(and(p, q), and(q, p))) = true.
% 171.65/22.30 Proof:
% 171.65/22.30 theorem(equivalent(and(p, q), and(q, p)))
% 171.65/22.30 = { by axiom 2 (ifeq_axiom) R->L }
% 171.65/22.30 ifeq(true, true, theorem(equivalent(and(p, q), and(q, p))), true)
% 171.65/22.30 = { by axiom 9 (rule_2) R->L }
% 171.65/22.30 ifeq(ifeq(theorem(implies(or(and(q, p), not(and(p, q))), or(not(and(p, q)), and(q, p)))), true, ifeq(theorem(or(and(q, p), not(and(p, q)))), true, theorem(or(not(and(p, q)), and(q, p))), true), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 171.65/22.30 = { by axiom 2 (ifeq_axiom) R->L }
% 171.65/22.30 ifeq(ifeq(ifeq(true, true, theorem(implies(or(and(q, p), not(and(p, q))), or(not(and(p, q)), and(q, p)))), true), true, ifeq(theorem(or(and(q, p), not(and(p, q)))), true, theorem(or(not(and(p, q)), and(q, p))), true), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 171.65/22.30 = { by axiom 8 (axiom_1_4) R->L }
% 171.65/22.30 ifeq(ifeq(ifeq(axiom(implies(or(and(q, p), not(and(p, q))), or(not(and(p, q)), and(q, p)))), true, theorem(implies(or(and(q, p), not(and(p, q))), or(not(and(p, q)), and(q, p)))), true), true, ifeq(theorem(or(and(q, p), not(and(p, q)))), true, theorem(or(not(and(p, q)), and(q, p))), true), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 171.65/22.30 = { by axiom 6 (rule_1) }
% 171.65/22.30 ifeq(ifeq(true, true, ifeq(theorem(or(and(q, p), not(and(p, q)))), true, theorem(or(not(and(p, q)), and(q, p))), true), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 171.65/22.30 = { by axiom 2 (ifeq_axiom) }
% 171.65/22.30 ifeq(ifeq(theorem(or(and(q, p), not(and(p, q)))), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.30 = { by lemma 12 R->L }
% 172.44/22.30 ifeq(ifeq(theorem(or(and(q, p), not(not(implies(p, not(q)))))), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.30 = { by axiom 2 (ifeq_axiom) R->L }
% 172.44/22.30 ifeq(ifeq(ifeq(true, true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.31 = { by axiom 9 (rule_2) R->L }
% 172.44/22.31 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, ifeq(theorem(implies(not(implies(p, not(q))), not(implies(p, not(q))))), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.31 = { by lemma 13 }
% 172.44/22.31 ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(p, not(q))), implies(p, not(q))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, ifeq(theorem(implies(not(implies(p, not(q))), not(implies(p, not(q))))), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.31 = { by axiom 2 (ifeq_axiom) R->L }
% 172.44/22.31 ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(p, not(q))), implies(p, not(q))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, ifeq(ifeq(true, true, theorem(implies(not(implies(p, not(q))), not(implies(p, not(q))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.32 = { by axiom 9 (rule_2) R->L }
% 172.44/22.32 ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(p, not(q))), implies(p, not(q))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(q))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), not(implies(p, not(q))))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q))))))), true, ifeq(theorem(implies(not(implies(p, not(q))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), not(implies(p, not(q)))))), true, theorem(or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q)))))), true), true), true, theorem(implies(not(implies(p, not(q))), not(implies(p, not(q))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.32 = { by axiom 2 (ifeq_axiom) R->L }
% 172.44/22.32 ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(p, not(q))), implies(p, not(q))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(q))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), not(implies(p, not(q))))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q))))))), true, ifeq(ifeq(true, true, theorem(implies(not(implies(p, not(q))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), not(implies(p, not(q)))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q)))))), true), true), true, theorem(implies(not(implies(p, not(q))), not(implies(p, not(q))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.33 = { by axiom 3 (axiom_1_3) R->L }
% 172.44/22.33 ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(p, not(q))), implies(p, not(q))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(q))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), not(implies(p, not(q))))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q))))))), true, ifeq(ifeq(axiom(implies(not(implies(p, not(q))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), not(implies(p, not(q)))))), true, theorem(implies(not(implies(p, not(q))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), not(implies(p, not(q)))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q)))))), true), true), true, theorem(implies(not(implies(p, not(q))), not(implies(p, not(q))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.33 = { by axiom 6 (rule_1) }
% 172.44/22.33 ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(p, not(q))), implies(p, not(q))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(q))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), not(implies(p, not(q))))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q))))))), true, ifeq(true, true, theorem(or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q)))))), true), true), true, theorem(implies(not(implies(p, not(q))), not(implies(p, not(q))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.34 = { by axiom 2 (ifeq_axiom) }
% 172.44/22.34 ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(p, not(q))), implies(p, not(q))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(q))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), not(implies(p, not(q))))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q))))))), true, theorem(or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q)))))), true), true, theorem(implies(not(implies(p, not(q))), not(implies(p, not(q))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.34 = { by axiom 2 (ifeq_axiom) R->L }
% 172.44/22.34 ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(p, not(q))), implies(p, not(q))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(implies(p, not(q))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), not(implies(p, not(q))))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q))))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q)))))), true), true, theorem(implies(not(implies(p, not(q))), not(implies(p, not(q))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.35 = { by axiom 11 (axiom_1_5) R->L }
% 172.44/22.35 ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(p, not(q))), implies(p, not(q))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(not(implies(p, not(q)))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), not(implies(p, not(q))))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), or(not(not(implies(p, not(q)))), not(implies(p, not(q))))))), true, theorem(implies(implies(not(implies(p, not(q))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), not(implies(p, not(q))))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q))))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q)))))), true), true, theorem(implies(not(implies(p, not(q))), not(implies(p, not(q))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.35 = { by axiom 1 (implies_definition) R->L }
% 172.44/22.35 ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(p, not(q))), implies(p, not(q))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(implies(p, not(q))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), not(implies(p, not(q))))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), or(not(not(implies(p, not(q)))), not(implies(p, not(q))))))), true, theorem(implies(implies(not(implies(p, not(q))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), not(implies(p, not(q))))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q))))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q)))))), true), true, theorem(implies(not(implies(p, not(q))), not(implies(p, not(q))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.35 = { by axiom 1 (implies_definition) R->L }
% 172.44/22.36 ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(p, not(q))), implies(p, not(q))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(implies(p, not(q))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), not(implies(p, not(q))))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q))))))), true, theorem(implies(implies(not(implies(p, not(q))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), not(implies(p, not(q))))), or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q))))))), true), true, theorem(or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q)))))), true), true, theorem(implies(not(implies(p, not(q))), not(implies(p, not(q))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.36 = { by axiom 6 (rule_1) }
% 172.44/22.36 ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(p, not(q))), implies(p, not(q))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, ifeq(ifeq(ifeq(true, true, theorem(or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q)))))), true), true, theorem(implies(not(implies(p, not(q))), not(implies(p, not(q))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.37 = { by axiom 2 (ifeq_axiom) }
% 172.44/22.37 ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(p, not(q))), implies(p, not(q))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, ifeq(ifeq(theorem(or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q)))))), true, theorem(implies(not(implies(p, not(q))), not(implies(p, not(q))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.37 = { by axiom 2 (ifeq_axiom) R->L }
% 172.44/22.37 ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(p, not(q))), implies(p, not(q))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, ifeq(ifeq(true, true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q)))))), true, theorem(implies(not(implies(p, not(q))), not(implies(p, not(q))))), true), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.37 = { by axiom 6 (rule_1) R->L }
% 172.44/22.37 ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(p, not(q))), implies(p, not(q))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, ifeq(ifeq(ifeq(axiom(implies(or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q))))), implies(not(implies(p, not(q))), not(implies(p, not(q)))))), true, theorem(implies(or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q))))), implies(not(implies(p, not(q))), not(implies(p, not(q)))))), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q)))))), true, theorem(implies(not(implies(p, not(q))), not(implies(p, not(q))))), true), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.37 = { by axiom 4 (axiom_1_2) }
% 172.44/22.37 ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(p, not(q))), implies(p, not(q))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q))))), implies(not(implies(p, not(q))), not(implies(p, not(q)))))), true), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q)))))), true, theorem(implies(not(implies(p, not(q))), not(implies(p, not(q))))), true), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.38 = { by axiom 2 (ifeq_axiom) }
% 172.44/22.38 ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(p, not(q))), implies(p, not(q))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, ifeq(ifeq(theorem(implies(or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q))))), implies(not(implies(p, not(q))), not(implies(p, not(q)))))), true, ifeq(theorem(or(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(not(implies(p, not(q))), not(implies(p, not(q)))))), true, theorem(implies(not(implies(p, not(q))), not(implies(p, not(q))))), true), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.38 = { by axiom 9 (rule_2) }
% 172.44/22.38 ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(p, not(q))), implies(p, not(q))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, ifeq(true, true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.38 = { by axiom 2 (ifeq_axiom) }
% 172.44/22.38 ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(p, not(q))), implies(p, not(q))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.38 = { by lemma 13 R->L }
% 172.44/22.38 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(q))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.39 = { by axiom 1 (implies_definition) }
% 172.44/22.39 ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.39 = { by axiom 2 (ifeq_axiom) R->L }
% 172.44/22.39 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 172.44/22.40 = { by axiom 9 (rule_2) R->L }
% 172.44/22.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, not(q)), not(not(implies(p, not(q))))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))))), true, ifeq(theorem(implies(implies(implies(p, not(q)), not(not(implies(p, not(q))))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, theorem(implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))))), true), true), true, theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.41 = { by axiom 2 (ifeq_axiom) R->L }
% 173.25/22.41 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, not(q)), not(not(implies(p, not(q))))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))))), true, ifeq(ifeq(true, true, theorem(implies(implies(implies(p, not(q)), not(not(implies(p, not(q))))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true), true, theorem(implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))))), true), true), true, theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.42 = { by axiom 10 (axiom_1_6) R->L }
% 173.25/22.42 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, not(q)), not(not(implies(p, not(q))))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))))), true, ifeq(ifeq(axiom(implies(implies(implies(p, not(q)), not(not(implies(p, not(q))))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true, theorem(implies(implies(implies(p, not(q)), not(not(implies(p, not(q))))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true), true, theorem(implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))))), true), true), true, theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.42 = { by axiom 6 (rule_1) }
% 173.25/22.43 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, not(q)), not(not(implies(p, not(q))))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))))), true, ifeq(true, true, theorem(implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))))), true), true), true, theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.43 = { by axiom 2 (ifeq_axiom) }
% 173.25/22.43 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, not(q)), not(not(implies(p, not(q))))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))))), true, theorem(implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))))), true), true, theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.44 = { by axiom 2 (ifeq_axiom) R->L }
% 173.25/22.44 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(implies(p, not(q)), not(not(implies(p, not(q))))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))))), true), true, theorem(implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))))), true), true, theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.44 = { by axiom 10 (axiom_1_6) R->L }
% 173.25/22.45 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(p, not(q)), not(not(implies(p, not(q))))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), implies(or(not(or(not(not(implies(p, not(q)))), not(implies(p, not(q))))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), or(not(or(not(not(implies(p, not(q)))), not(implies(p, not(q))))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))))), true, theorem(implies(implies(implies(implies(p, not(q)), not(not(implies(p, not(q))))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))))), true), true, theorem(implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))))), true), true, theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.45 = { by axiom 1 (implies_definition) R->L }
% 173.25/22.45 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(p, not(q)), not(not(implies(p, not(q))))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), or(not(or(not(not(implies(p, not(q)))), not(implies(p, not(q))))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))))), true, theorem(implies(implies(implies(implies(p, not(q)), not(not(implies(p, not(q))))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))))), true), true, theorem(implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))))), true), true, theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.45 = { by axiom 1 (implies_definition) R->L }
% 173.25/22.46 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(p, not(q)), not(not(implies(p, not(q))))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))))), true, theorem(implies(implies(implies(implies(p, not(q)), not(not(implies(p, not(q))))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))))), true), true, theorem(implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))))), true), true, theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.46 = { by axiom 6 (rule_1) }
% 173.25/22.46 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))))), true), true, theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.46 = { by axiom 2 (ifeq_axiom) }
% 173.25/22.46 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))))), true, theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.47 = { by axiom 2 (ifeq_axiom) R->L }
% 173.25/22.47 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))))), true, ifeq(true, true, theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.47 = { by axiom 6 (rule_1) R->L }
% 173.25/22.47 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))))), true, ifeq(ifeq(axiom(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), or(not(implies(p, not(q))), not(not(implies(p, not(q))))))), true, theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), or(not(implies(p, not(q))), not(not(implies(p, not(q))))))), true), true, theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.47 = { by axiom 8 (axiom_1_4) }
% 173.25/22.48 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))))), true, ifeq(ifeq(true, true, theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), or(not(implies(p, not(q))), not(not(implies(p, not(q))))))), true), true, theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.48 = { by axiom 2 (ifeq_axiom) }
% 173.25/22.48 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))))), true, ifeq(theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), or(not(implies(p, not(q))), not(not(implies(p, not(q))))))), true, theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.48 = { by axiom 1 (implies_definition) R->L }
% 173.25/22.48 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q)))))), implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))))), true, ifeq(theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(implies(p, not(q)), not(not(implies(p, not(q))))))), true, theorem(implies(or(not(not(implies(p, not(q)))), not(implies(p, not(q)))), implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q)))))))), true), true), true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.48 = { by axiom 9 (rule_2) }
% 173.25/22.48 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.48 = { by axiom 2 (ifeq_axiom) }
% 173.25/22.48 ifeq(ifeq(ifeq(theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.48 = { by axiom 2 (ifeq_axiom) R->L }
% 173.25/22.48 ifeq(ifeq(ifeq(theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true, ifeq(true, true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.48 = { by axiom 6 (rule_1) R->L }
% 173.25/22.48 ifeq(ifeq(ifeq(theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true, ifeq(ifeq(axiom(implies(or(not(q), not(p)), or(not(p), not(q)))), true, theorem(implies(or(not(q), not(p)), or(not(p), not(q)))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.48 = { by axiom 8 (axiom_1_4) }
% 173.25/22.49 ifeq(ifeq(ifeq(theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true, ifeq(ifeq(true, true, theorem(implies(or(not(q), not(p)), or(not(p), not(q)))), true), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.49 = { by axiom 2 (ifeq_axiom) }
% 173.25/22.49 ifeq(ifeq(ifeq(theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true, ifeq(theorem(implies(or(not(q), not(p)), or(not(p), not(q)))), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.49 = { by axiom 1 (implies_definition) R->L }
% 173.25/22.49 ifeq(ifeq(ifeq(theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true, ifeq(theorem(implies(implies(q, not(p)), or(not(p), not(q)))), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.49 = { by axiom 1 (implies_definition) R->L }
% 173.25/22.49 ifeq(ifeq(ifeq(theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true, ifeq(theorem(implies(implies(q, not(p)), implies(p, not(q)))), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.49 = { by lemma 13 }
% 173.25/22.49 ifeq(ifeq(ifeq(theorem(implies(or(and(q, p), implies(p, not(q))), or(and(q, p), not(not(implies(p, not(q))))))), true, ifeq(theorem(or(and(q, p), implies(p, not(q)))), true, theorem(or(and(q, p), not(not(implies(p, not(q)))))), true), true), true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.49 = { by axiom 9 (rule_2) }
% 173.25/22.49 ifeq(ifeq(true, true, theorem(or(not(and(p, q)), and(q, p))), true), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.49 = { by axiom 2 (ifeq_axiom) }
% 173.25/22.49 ifeq(theorem(or(not(and(p, q)), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.49 = { by axiom 1 (implies_definition) R->L }
% 173.25/22.49 ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true)
% 173.25/22.49 = { by axiom 2 (ifeq_axiom) R->L }
% 173.25/22.49 ifeq(true, true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 173.25/22.49 = { by axiom 9 (rule_2) R->L }
% 173.25/22.49 ifeq(ifeq(theorem(implies(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p)))), or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p))))), true, ifeq(theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 173.25/22.49 = { by axiom 2 (ifeq_axiom) R->L }
% 173.25/22.49 ifeq(ifeq(ifeq(true, true, theorem(implies(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p)))), or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p))))), true), true, ifeq(theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 173.25/22.49 = { by axiom 8 (axiom_1_4) R->L }
% 173.25/22.49 ifeq(ifeq(ifeq(axiom(implies(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p)))), or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p))))), true, theorem(implies(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p)))), or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p))))), true), true, ifeq(theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 173.25/22.50 = { by axiom 6 (rule_1) }
% 173.25/22.50 ifeq(ifeq(true, true, ifeq(theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 173.25/22.50 = { by axiom 2 (ifeq_axiom) }
% 173.25/22.50 ifeq(ifeq(theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 173.25/22.50 = { by axiom 2 (ifeq_axiom) R->L }
% 173.25/22.50 ifeq(ifeq(ifeq(true, true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 173.25/22.50 = { by axiom 9 (rule_2) R->L }
% 173.25/22.50 ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(p, q), not(and(q, p))), or(not(and(q, p)), and(p, q)))), true, ifeq(theorem(or(and(p, q), not(and(q, p)))), true, theorem(or(not(and(q, p)), and(p, q))), true), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 173.25/22.50 = { by axiom 2 (ifeq_axiom) R->L }
% 173.25/22.50 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(and(p, q), not(and(q, p))), or(not(and(q, p)), and(p, q)))), true), true, ifeq(theorem(or(and(p, q), not(and(q, p)))), true, theorem(or(not(and(q, p)), and(p, q))), true), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.50 = { by axiom 8 (axiom_1_4) R->L }
% 174.04/22.50 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(and(p, q), not(and(q, p))), or(not(and(q, p)), and(p, q)))), true, theorem(implies(or(and(p, q), not(and(q, p))), or(not(and(q, p)), and(p, q)))), true), true, ifeq(theorem(or(and(p, q), not(and(q, p)))), true, theorem(or(not(and(q, p)), and(p, q))), true), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.50 = { by axiom 6 (rule_1) }
% 174.04/22.50 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(and(p, q), not(and(q, p)))), true, theorem(or(not(and(q, p)), and(p, q))), true), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.50 = { by axiom 2 (ifeq_axiom) }
% 174.04/22.50 ifeq(ifeq(ifeq(ifeq(theorem(or(and(p, q), not(and(q, p)))), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.51 = { by lemma 12 R->L }
% 174.04/22.51 ifeq(ifeq(ifeq(ifeq(theorem(or(and(p, q), not(not(implies(q, not(p)))))), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.51 = { by axiom 2 (ifeq_axiom) R->L }
% 174.04/22.51 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.51 = { by axiom 9 (rule_2) R->L }
% 174.04/22.51 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, ifeq(theorem(implies(not(implies(q, not(p))), not(implies(q, not(p))))), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.51 = { by lemma 13 }
% 174.04/22.52 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(q, not(p))), implies(q, not(p))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, ifeq(theorem(implies(not(implies(q, not(p))), not(implies(q, not(p))))), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.52 = { by axiom 2 (ifeq_axiom) R->L }
% 174.04/22.52 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(q, not(p))), implies(q, not(p))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, ifeq(ifeq(true, true, theorem(implies(not(implies(q, not(p))), not(implies(q, not(p))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.52 = { by axiom 9 (rule_2) R->L }
% 174.04/22.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(q, not(p))), implies(q, not(p))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(q, not(p))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), not(implies(q, not(p))))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p))))))), true, ifeq(theorem(implies(not(implies(q, not(p))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), not(implies(q, not(p)))))), true, theorem(or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p)))))), true), true), true, theorem(implies(not(implies(q, not(p))), not(implies(q, not(p))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.53 = { by axiom 2 (ifeq_axiom) R->L }
% 174.04/22.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(q, not(p))), implies(q, not(p))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(q, not(p))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), not(implies(q, not(p))))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p))))))), true, ifeq(ifeq(true, true, theorem(implies(not(implies(q, not(p))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), not(implies(q, not(p)))))), true), true, theorem(or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p)))))), true), true), true, theorem(implies(not(implies(q, not(p))), not(implies(q, not(p))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.53 = { by axiom 3 (axiom_1_3) R->L }
% 174.04/22.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(q, not(p))), implies(q, not(p))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(q, not(p))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), not(implies(q, not(p))))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p))))))), true, ifeq(ifeq(axiom(implies(not(implies(q, not(p))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), not(implies(q, not(p)))))), true, theorem(implies(not(implies(q, not(p))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), not(implies(q, not(p)))))), true), true, theorem(or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p)))))), true), true), true, theorem(implies(not(implies(q, not(p))), not(implies(q, not(p))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.54 = { by axiom 6 (rule_1) }
% 174.04/22.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(q, not(p))), implies(q, not(p))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(q, not(p))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), not(implies(q, not(p))))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p))))))), true, ifeq(true, true, theorem(or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p)))))), true), true), true, theorem(implies(not(implies(q, not(p))), not(implies(q, not(p))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.55 = { by axiom 2 (ifeq_axiom) }
% 174.04/22.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(q, not(p))), implies(q, not(p))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(q, not(p))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), not(implies(q, not(p))))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p))))))), true, theorem(or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p)))))), true), true, theorem(implies(not(implies(q, not(p))), not(implies(q, not(p))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.55 = { by axiom 2 (ifeq_axiom) R->L }
% 174.04/22.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(q, not(p))), implies(q, not(p))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(implies(q, not(p))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), not(implies(q, not(p))))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p))))))), true), true, theorem(or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p)))))), true), true, theorem(implies(not(implies(q, not(p))), not(implies(q, not(p))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.56 = { by axiom 11 (axiom_1_5) R->L }
% 174.04/22.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(q, not(p))), implies(q, not(p))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(not(implies(q, not(p)))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), not(implies(q, not(p))))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), or(not(not(implies(q, not(p)))), not(implies(q, not(p))))))), true, theorem(implies(implies(not(implies(q, not(p))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), not(implies(q, not(p))))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p))))))), true), true, theorem(or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p)))))), true), true, theorem(implies(not(implies(q, not(p))), not(implies(q, not(p))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.56 = { by axiom 1 (implies_definition) R->L }
% 174.04/22.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(q, not(p))), implies(q, not(p))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(implies(q, not(p))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), not(implies(q, not(p))))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), or(not(not(implies(q, not(p)))), not(implies(q, not(p))))))), true, theorem(implies(implies(not(implies(q, not(p))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), not(implies(q, not(p))))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p))))))), true), true, theorem(or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p)))))), true), true, theorem(implies(not(implies(q, not(p))), not(implies(q, not(p))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.57 = { by axiom 1 (implies_definition) R->L }
% 174.04/22.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(q, not(p))), implies(q, not(p))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(implies(q, not(p))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), not(implies(q, not(p))))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p))))))), true, theorem(implies(implies(not(implies(q, not(p))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), not(implies(q, not(p))))), or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p))))))), true), true, theorem(or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p)))))), true), true, theorem(implies(not(implies(q, not(p))), not(implies(q, not(p))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.57 = { by axiom 6 (rule_1) }
% 174.04/22.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(q, not(p))), implies(q, not(p))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, ifeq(ifeq(ifeq(true, true, theorem(or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p)))))), true), true, theorem(implies(not(implies(q, not(p))), not(implies(q, not(p))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.58 = { by axiom 2 (ifeq_axiom) }
% 174.04/22.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(q, not(p))), implies(q, not(p))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, ifeq(ifeq(theorem(or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p)))))), true, theorem(implies(not(implies(q, not(p))), not(implies(q, not(p))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.58 = { by axiom 2 (ifeq_axiom) R->L }
% 174.04/22.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(q, not(p))), implies(q, not(p))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, ifeq(ifeq(true, true, ifeq(theorem(or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p)))))), true, theorem(implies(not(implies(q, not(p))), not(implies(q, not(p))))), true), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.59 = { by axiom 6 (rule_1) R->L }
% 174.04/22.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(q, not(p))), implies(q, not(p))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, ifeq(ifeq(ifeq(axiom(implies(or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p))))), implies(not(implies(q, not(p))), not(implies(q, not(p)))))), true, theorem(implies(or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p))))), implies(not(implies(q, not(p))), not(implies(q, not(p)))))), true), true, ifeq(theorem(or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p)))))), true, theorem(implies(not(implies(q, not(p))), not(implies(q, not(p))))), true), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.59 = { by axiom 4 (axiom_1_2) }
% 174.04/22.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(q, not(p))), implies(q, not(p))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p))))), implies(not(implies(q, not(p))), not(implies(q, not(p)))))), true), true, ifeq(theorem(or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p)))))), true, theorem(implies(not(implies(q, not(p))), not(implies(q, not(p))))), true), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.59 = { by axiom 2 (ifeq_axiom) }
% 174.04/22.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(q, not(p))), implies(q, not(p))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, ifeq(ifeq(theorem(implies(or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p))))), implies(not(implies(q, not(p))), not(implies(q, not(p)))))), true, ifeq(theorem(or(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(not(implies(q, not(p))), not(implies(q, not(p)))))), true, theorem(implies(not(implies(q, not(p))), not(implies(q, not(p))))), true), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.60 = { by axiom 9 (rule_2) }
% 174.04/22.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(q, not(p))), implies(q, not(p))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, ifeq(true, true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.04/22.60 = { by axiom 2 (ifeq_axiom) }
% 174.04/22.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(and(not(implies(q, not(p))), implies(q, not(p))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.82/22.60 = { by lemma 13 R->L }
% 174.82/22.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(q, not(p))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.82/22.61 = { by axiom 1 (implies_definition) }
% 174.82/22.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.82/22.61 = { by axiom 2 (ifeq_axiom) R->L }
% 174.82/22.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.82/22.62 = { by axiom 9 (rule_2) R->L }
% 174.82/22.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(q, not(p)), not(not(implies(q, not(p))))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))))), true, ifeq(theorem(implies(implies(implies(q, not(p)), not(not(implies(q, not(p))))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, theorem(implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))))), true), true), true, theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.82/22.63 = { by axiom 2 (ifeq_axiom) R->L }
% 174.82/22.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(q, not(p)), not(not(implies(q, not(p))))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))))), true, ifeq(ifeq(true, true, theorem(implies(implies(implies(q, not(p)), not(not(implies(q, not(p))))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true), true, theorem(implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))))), true), true), true, theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.82/22.63 = { by axiom 10 (axiom_1_6) R->L }
% 174.82/22.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(q, not(p)), not(not(implies(q, not(p))))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))))), true, ifeq(ifeq(axiom(implies(implies(implies(q, not(p)), not(not(implies(q, not(p))))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true, theorem(implies(implies(implies(q, not(p)), not(not(implies(q, not(p))))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true), true, theorem(implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))))), true), true), true, theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.82/22.64 = { by axiom 6 (rule_1) }
% 174.82/22.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(q, not(p)), not(not(implies(q, not(p))))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))))), true, ifeq(true, true, theorem(implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))))), true), true), true, theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.82/22.65 = { by axiom 2 (ifeq_axiom) }
% 174.82/22.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(q, not(p)), not(not(implies(q, not(p))))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))))), true, theorem(implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))))), true), true, theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.82/22.66 = { by axiom 2 (ifeq_axiom) R->L }
% 174.82/22.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(implies(q, not(p)), not(not(implies(q, not(p))))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))))), true), true, theorem(implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))))), true), true, theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.82/22.66 = { by axiom 10 (axiom_1_6) R->L }
% 174.82/22.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(q, not(p)), not(not(implies(q, not(p))))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), implies(or(not(or(not(not(implies(q, not(p)))), not(implies(q, not(p))))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), or(not(or(not(not(implies(q, not(p)))), not(implies(q, not(p))))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))))), true, theorem(implies(implies(implies(implies(q, not(p)), not(not(implies(q, not(p))))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))))), true), true, theorem(implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))))), true), true, theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.82/22.67 = { by axiom 1 (implies_definition) R->L }
% 174.82/22.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(q, not(p)), not(not(implies(q, not(p))))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), or(not(or(not(not(implies(q, not(p)))), not(implies(q, not(p))))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))))), true, theorem(implies(implies(implies(implies(q, not(p)), not(not(implies(q, not(p))))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))))), true), true, theorem(implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))))), true), true, theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.82/22.67 = { by axiom 1 (implies_definition) R->L }
% 174.82/22.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(q, not(p)), not(not(implies(q, not(p))))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))))), true, theorem(implies(implies(implies(implies(q, not(p)), not(not(implies(q, not(p))))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))))), true), true, theorem(implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))))), true), true, theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.82/22.68 = { by axiom 6 (rule_1) }
% 174.82/22.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))))), true), true, theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.82/22.68 = { by axiom 2 (ifeq_axiom) }
% 174.82/22.69 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))))), true, theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.82/22.69 = { by axiom 2 (ifeq_axiom) R->L }
% 174.82/22.69 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))))), true, ifeq(true, true, theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.82/22.69 = { by axiom 6 (rule_1) R->L }
% 174.82/22.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))))), true, ifeq(ifeq(axiom(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), or(not(implies(q, not(p))), not(not(implies(q, not(p))))))), true, theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), or(not(implies(q, not(p))), not(not(implies(q, not(p))))))), true), true, theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 174.82/22.70 = { by axiom 8 (axiom_1_4) }
% 174.82/22.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))))), true, ifeq(ifeq(true, true, theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), or(not(implies(q, not(p))), not(not(implies(q, not(p))))))), true), true, theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.70 = { by axiom 2 (ifeq_axiom) }
% 175.65/22.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))))), true, ifeq(theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), or(not(implies(q, not(p))), not(not(implies(q, not(p))))))), true, theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.70 = { by axiom 1 (implies_definition) R->L }
% 175.65/22.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p)))))), implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))))), true, ifeq(theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(implies(q, not(p)), not(not(implies(q, not(p))))))), true, theorem(implies(or(not(not(implies(q, not(p)))), not(implies(q, not(p)))), implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p)))))))), true), true), true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.71 = { by axiom 9 (rule_2) }
% 175.65/22.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.71 = { by axiom 2 (ifeq_axiom) }
% 175.65/22.71 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.71 = { by axiom 2 (ifeq_axiom) R->L }
% 175.65/22.72 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true, ifeq(true, true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.72 = { by axiom 6 (rule_1) R->L }
% 175.65/22.72 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true, ifeq(ifeq(axiom(implies(or(not(p), not(q)), or(not(q), not(p)))), true, theorem(implies(or(not(p), not(q)), or(not(q), not(p)))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.72 = { by axiom 8 (axiom_1_4) }
% 175.65/22.72 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true, ifeq(ifeq(true, true, theorem(implies(or(not(p), not(q)), or(not(q), not(p)))), true), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.72 = { by axiom 2 (ifeq_axiom) }
% 175.65/22.72 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true, ifeq(theorem(implies(or(not(p), not(q)), or(not(q), not(p)))), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.72 = { by axiom 1 (implies_definition) R->L }
% 175.65/22.72 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true, ifeq(theorem(implies(implies(p, not(q)), or(not(q), not(p)))), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.72 = { by axiom 1 (implies_definition) R->L }
% 175.65/22.72 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true, ifeq(theorem(implies(implies(p, not(q)), implies(q, not(p)))), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.73 = { by lemma 13 }
% 175.65/22.73 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(p, q), implies(q, not(p))), or(and(p, q), not(not(implies(q, not(p))))))), true, ifeq(theorem(or(and(p, q), implies(q, not(p)))), true, theorem(or(and(p, q), not(not(implies(q, not(p)))))), true), true), true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.73 = { by axiom 9 (rule_2) }
% 175.65/22.73 ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(and(q, p)), and(p, q))), true), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.73 = { by axiom 2 (ifeq_axiom) }
% 175.65/22.73 ifeq(ifeq(ifeq(theorem(or(not(and(q, p)), and(p, q))), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.73 = { by axiom 1 (implies_definition) R->L }
% 175.65/22.73 ifeq(ifeq(ifeq(theorem(implies(and(q, p), and(p, q))), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.73 = { by axiom 2 (ifeq_axiom) R->L }
% 175.65/22.73 ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(and(q, p), and(p, q))), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.73 = { by axiom 9 (rule_2) R->L }
% 175.65/22.73 ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(and(p, q), and(q, p)), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p))))), implies(implies(and(q, p), and(p, q)), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))))), true, ifeq(theorem(or(equivalent(and(p, q), and(q, p)), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p)))))), true, theorem(implies(implies(and(q, p), and(p, q)), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p)))))), true), true), true, ifeq(theorem(implies(and(q, p), and(p, q))), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.74 = { by axiom 2 (ifeq_axiom) R->L }
% 175.65/22.74 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(equivalent(and(p, q), and(q, p)), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p))))), implies(implies(and(q, p), and(p, q)), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))))), true), true, ifeq(theorem(or(equivalent(and(p, q), and(q, p)), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p)))))), true, theorem(implies(implies(and(q, p), and(p, q)), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p)))))), true), true), true, ifeq(theorem(implies(and(q, p), and(p, q))), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.74 = { by axiom 11 (axiom_1_5) R->L }
% 175.65/22.74 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(equivalent(and(p, q), and(q, p)), or(not(implies(and(q, p), and(p, q))), not(implies(and(p, q), and(q, p))))), or(not(implies(and(q, p), and(p, q))), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))))), true, theorem(implies(or(equivalent(and(p, q), and(q, p)), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p))))), implies(implies(and(q, p), and(p, q)), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))))), true), true, ifeq(theorem(or(equivalent(and(p, q), and(q, p)), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p)))))), true, theorem(implies(implies(and(q, p), and(p, q)), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p)))))), true), true), true, ifeq(theorem(implies(and(q, p), and(p, q))), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.74 = { by axiom 1 (implies_definition) R->L }
% 175.65/22.74 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(equivalent(and(p, q), and(q, p)), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p))))), or(not(implies(and(q, p), and(p, q))), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))))), true, theorem(implies(or(equivalent(and(p, q), and(q, p)), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p))))), implies(implies(and(q, p), and(p, q)), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))))), true), true, ifeq(theorem(or(equivalent(and(p, q), and(q, p)), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p)))))), true, theorem(implies(implies(and(q, p), and(p, q)), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p)))))), true), true), true, ifeq(theorem(implies(and(q, p), and(p, q))), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.74 = { by axiom 1 (implies_definition) R->L }
% 175.65/22.74 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(equivalent(and(p, q), and(q, p)), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p))))), implies(implies(and(q, p), and(p, q)), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))))), true, theorem(implies(or(equivalent(and(p, q), and(q, p)), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p))))), implies(implies(and(q, p), and(p, q)), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))))), true), true, ifeq(theorem(or(equivalent(and(p, q), and(q, p)), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p)))))), true, theorem(implies(implies(and(q, p), and(p, q)), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p)))))), true), true), true, ifeq(theorem(implies(and(q, p), and(p, q))), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.74 = { by axiom 6 (rule_1) }
% 175.65/22.75 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(equivalent(and(p, q), and(q, p)), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p)))))), true, theorem(implies(implies(and(q, p), and(p, q)), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p)))))), true), true), true, ifeq(theorem(implies(and(q, p), and(p, q))), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.75 = { by axiom 2 (ifeq_axiom) }
% 175.65/22.75 ifeq(ifeq(ifeq(ifeq(theorem(or(equivalent(and(p, q), and(q, p)), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p)))))), true, theorem(implies(implies(and(q, p), and(p, q)), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p)))))), true), true, ifeq(theorem(implies(and(q, p), and(p, q))), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.75 = { by axiom 2 (ifeq_axiom) R->L }
% 175.65/22.75 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(equivalent(and(p, q), and(q, p)), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p)))))), true), true, theorem(implies(implies(and(q, p), and(p, q)), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p)))))), true), true, ifeq(theorem(implies(and(q, p), and(p, q))), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.75 = { by axiom 8 (axiom_1_4) R->L }
% 175.65/22.75 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(implies(and(p, q), and(q, p))), not(implies(and(q, p), and(p, q)))), or(not(implies(and(q, p), and(p, q))), not(implies(and(p, q), and(q, p)))))), true, theorem(or(equivalent(and(p, q), and(q, p)), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p)))))), true), true, theorem(implies(implies(and(q, p), and(p, q)), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p)))))), true), true, ifeq(theorem(implies(and(q, p), and(p, q))), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.75 = { by axiom 1 (implies_definition) R->L }
% 175.65/22.75 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(and(p, q), and(q, p)), not(implies(and(q, p), and(p, q)))), or(not(implies(and(q, p), and(p, q))), not(implies(and(p, q), and(q, p)))))), true, theorem(or(equivalent(and(p, q), and(q, p)), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p)))))), true), true, theorem(implies(implies(and(q, p), and(p, q)), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p)))))), true), true, ifeq(theorem(implies(and(q, p), and(p, q))), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.75 = { by lemma 13 }
% 175.65/22.76 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(and(implies(and(p, q), and(q, p)), implies(and(q, p), and(p, q))), or(not(implies(and(q, p), and(p, q))), not(implies(and(p, q), and(q, p)))))), true, theorem(or(equivalent(and(p, q), and(q, p)), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p)))))), true), true, theorem(implies(implies(and(q, p), and(p, q)), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p)))))), true), true, ifeq(theorem(implies(and(q, p), and(p, q))), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.76 = { by axiom 1 (implies_definition) R->L }
% 175.65/22.76 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(and(implies(and(p, q), and(q, p)), implies(and(q, p), and(p, q))), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p)))))), true, theorem(or(equivalent(and(p, q), and(q, p)), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p)))))), true), true, theorem(implies(implies(and(q, p), and(p, q)), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p)))))), true), true, ifeq(theorem(implies(and(q, p), and(p, q))), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.76 = { by axiom 7 (equivalent_defn) R->L }
% 175.65/22.76 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(equivalent(and(p, q), and(q, p)), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p)))))), true, theorem(or(equivalent(and(p, q), and(q, p)), implies(implies(and(q, p), and(p, q)), not(implies(and(p, q), and(q, p)))))), true), true, theorem(implies(implies(and(q, p), and(p, q)), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p)))))), true), true, ifeq(theorem(implies(and(q, p), and(p, q))), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.76 = { by axiom 6 (rule_1) }
% 175.65/22.76 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(and(q, p), and(p, q)), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p)))))), true), true, ifeq(theorem(implies(and(q, p), and(p, q))), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.76 = { by axiom 2 (ifeq_axiom) }
% 175.65/22.76 ifeq(ifeq(ifeq(theorem(implies(implies(and(q, p), and(p, q)), or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p)))))), true, ifeq(theorem(implies(and(q, p), and(p, q))), true, theorem(or(equivalent(and(p, q), and(q, p)), not(implies(and(p, q), and(q, p))))), true), true), true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.76 = { by axiom 9 (rule_2) }
% 175.65/22.76 ifeq(ifeq(true, true, theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.76 = { by axiom 2 (ifeq_axiom) }
% 175.65/22.76 ifeq(theorem(or(not(implies(and(p, q), and(q, p))), equivalent(and(p, q), and(q, p)))), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.76 = { by axiom 1 (implies_definition) R->L }
% 175.65/22.76 ifeq(theorem(implies(implies(and(p, q), and(q, p)), equivalent(and(p, q), and(q, p)))), true, ifeq(theorem(implies(and(p, q), and(q, p))), true, theorem(equivalent(and(p, q), and(q, p))), true), true)
% 175.65/22.76 = { by axiom 9 (rule_2) }
% 175.65/22.76 true
% 175.65/22.76 % SZS output end Proof
% 175.65/22.76
% 175.65/22.76 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------