%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL337-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 11:49:37 AM UTC 2026
% Result : Unsatisfiable 86.71s 11.50s
% Output : Proof 93.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL337-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 15:35:03 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 86.71/11.50 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 86.71/11.50
% 86.71/11.50 % SZS status Unsatisfiable
% 86.71/11.50
% 90.69/12.00 % SZS output start Proof
% 90.69/12.00 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 90.69/12.00 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 90.69/12.00 Axiom 3 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 90.69/12.00 Axiom 4 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 90.69/12.00 Axiom 5 (and_defn): and(X, Y) = not(or(not(X), not(Y))).
% 90.69/12.00 Axiom 6 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 90.69/12.00 Axiom 7 (equivalent_defn): equivalent(X, Y) = and(implies(X, Y), implies(Y, X)).
% 90.69/12.00 Axiom 8 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 91.50/12.00 Axiom 9 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 91.50/12.00 Axiom 10 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 91.50/12.02 Axiom 11 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 91.50/12.02
% 91.50/12.02 Goal 1 (prove_this): theorem(equivalent(implies(p, implies(p, q)), implies(p, q))) = true.
% 91.50/12.02 Proof:
% 91.50/12.02 theorem(equivalent(implies(p, implies(p, q)), implies(p, q)))
% 91.50/12.02 = { by axiom 2 (ifeq_axiom) R->L }
% 91.50/12.02 ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true)
% 91.50/12.02 = { by axiom 2 (ifeq_axiom) R->L }
% 91.50/12.02 ifeq(true, true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.02 = { by axiom 9 (rule_2) R->L }
% 91.50/12.02 ifeq(ifeq(theorem(implies(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q)))), or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))))))), true, ifeq(theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.03 = { by axiom 1 (implies_definition) }
% 91.50/12.03 ifeq(ifeq(theorem(implies(or(not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))), not(implies(implies(p, implies(p, q)), implies(p, q)))), or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))))))), true, ifeq(theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.03 = { by axiom 2 (ifeq_axiom) R->L }
% 91.50/12.03 ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))), not(implies(implies(p, implies(p, q)), implies(p, q)))), or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))))))), true), true, ifeq(theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.03 = { by axiom 8 (axiom_1_4) R->L }
% 91.50/12.03 ifeq(ifeq(ifeq(axiom(implies(or(not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))), not(implies(implies(p, implies(p, q)), implies(p, q)))), or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))))))), true, theorem(implies(or(not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))), not(implies(implies(p, implies(p, q)), implies(p, q)))), or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))))))), true), true, ifeq(theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.03 = { by axiom 6 (rule_1) }
% 91.50/12.03 ifeq(ifeq(true, true, ifeq(theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.04 = { by axiom 2 (ifeq_axiom) }
% 91.50/12.04 ifeq(ifeq(theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.04 = { by axiom 1 (implies_definition) R->L }
% 91.50/12.04 ifeq(ifeq(theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.04 = { by axiom 2 (ifeq_axiom) R->L }
% 91.50/12.04 ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.05 = { by axiom 9 (rule_2) R->L }
% 91.50/12.05 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), not(implies(implies(p, implies(p, q)), implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))))), true, ifeq(theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), not(implies(implies(p, implies(p, q)), implies(p, q)))))), true, theorem(or(not(implies(implies(p, q), implies(p, implies(p, q)))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q)))))), true), true), true, theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.05 = { by axiom 2 (ifeq_axiom) R->L }
% 91.50/12.06 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), not(implies(implies(p, implies(p, q)), implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))))), true, ifeq(ifeq(true, true, theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), not(implies(implies(p, implies(p, q)), implies(p, q)))))), true), true, theorem(or(not(implies(implies(p, q), implies(p, implies(p, q)))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q)))))), true), true), true, theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.06 = { by axiom 8 (axiom_1_4) R->L }
% 91.50/12.06 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), not(implies(implies(p, implies(p, q)), implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))))), true, ifeq(ifeq(axiom(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), not(implies(implies(p, implies(p, q)), implies(p, q)))))), true, theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), not(implies(implies(p, implies(p, q)), implies(p, q)))))), true), true, theorem(or(not(implies(implies(p, q), implies(p, implies(p, q)))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q)))))), true), true), true, theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.06 = { by axiom 6 (rule_1) }
% 91.50/12.07 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), not(implies(implies(p, implies(p, q)), implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))))), true, ifeq(true, true, theorem(or(not(implies(implies(p, q), implies(p, implies(p, q)))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q)))))), true), true), true, theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.07 = { by axiom 2 (ifeq_axiom) }
% 91.50/12.07 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), not(implies(implies(p, implies(p, q)), implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))))), true, theorem(or(not(implies(implies(p, q), implies(p, implies(p, q)))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q)))))), true), true, theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.08 = { by axiom 2 (ifeq_axiom) R->L }
% 91.50/12.08 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), not(implies(implies(p, implies(p, q)), implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))))), true), true, theorem(or(not(implies(implies(p, q), implies(p, implies(p, q)))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q)))))), true), true, theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.08 = { by axiom 11 (axiom_1_5) R->L }
% 91.50/12.08 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), not(implies(implies(p, implies(p, q)), implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), or(not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))), not(implies(implies(p, implies(p, q)), implies(p, q))))))), true, theorem(implies(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), not(implies(implies(p, implies(p, q)), implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))))), true), true, theorem(or(not(implies(implies(p, q), implies(p, implies(p, q)))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q)))))), true), true, theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.08 = { by axiom 1 (implies_definition) R->L }
% 91.50/12.09 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), not(implies(implies(p, implies(p, q)), implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), or(not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))), not(implies(implies(p, implies(p, q)), implies(p, q))))))), true, theorem(implies(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), not(implies(implies(p, implies(p, q)), implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))))), true), true, theorem(or(not(implies(implies(p, q), implies(p, implies(p, q)))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q)))))), true), true, theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.09 = { by axiom 1 (implies_definition) R->L }
% 91.50/12.09 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), not(implies(implies(p, implies(p, q)), implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))))), true, theorem(implies(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), not(implies(implies(p, implies(p, q)), implies(p, q))))), or(not(implies(implies(p, q), implies(p, implies(p, q)))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))))), true), true, theorem(or(not(implies(implies(p, q), implies(p, implies(p, q)))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q)))))), true), true, theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.09 = { by axiom 6 (rule_1) }
% 91.50/12.09 ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(implies(implies(p, q), implies(p, implies(p, q)))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q)))))), true), true, theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.10 = { by axiom 2 (ifeq_axiom) }
% 91.50/12.10 ifeq(ifeq(ifeq(theorem(or(not(implies(implies(p, q), implies(p, implies(p, q)))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q)))))), true, theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.10 = { by axiom 1 (implies_definition) R->L }
% 91.50/12.10 ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, q), implies(p, implies(p, q))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q)))))), true, theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.10 = { by axiom 2 (ifeq_axiom) R->L }
% 91.50/12.10 ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, q), implies(p, implies(p, q))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q)))))), true, ifeq(true, true, theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.10 = { by axiom 6 (rule_1) R->L }
% 91.50/12.11 ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, q), implies(p, implies(p, q))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q)))))), true, ifeq(ifeq(axiom(implies(implies(p, q), implies(p, implies(p, q)))), true, theorem(implies(implies(p, q), implies(p, implies(p, q)))), true), true, theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.11 = { by axiom 1 (implies_definition) }
% 91.50/12.11 ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, q), implies(p, implies(p, q))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q)))))), true, ifeq(ifeq(axiom(implies(implies(p, q), or(not(p), implies(p, q)))), true, theorem(implies(implies(p, q), implies(p, implies(p, q)))), true), true, theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.11 = { by axiom 3 (axiom_1_3) }
% 91.50/12.11 ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, q), implies(p, implies(p, q))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q)))))), true, ifeq(ifeq(true, true, theorem(implies(implies(p, q), implies(p, implies(p, q)))), true), true, theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.11 = { by axiom 2 (ifeq_axiom) }
% 91.50/12.11 ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, q), implies(p, implies(p, q))), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q)))))), true, ifeq(theorem(implies(implies(p, q), implies(p, implies(p, q)))), true, theorem(implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q))))), not(implies(implies(p, implies(p, q)), implies(p, q))))), true), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.11 = { by axiom 9 (rule_2) }
% 91.50/12.11 ifeq(ifeq(true, true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.11 = { by axiom 2 (ifeq_axiom) }
% 91.50/12.11 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), not(or(not(implies(implies(p, implies(p, q)), implies(p, q))), not(implies(implies(p, q), implies(p, implies(p, q)))))))), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.11 = { by axiom 5 (and_defn) R->L }
% 91.50/12.11 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), and(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), implies(p, implies(p, q)))))), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.12 = { by axiom 7 (equivalent_defn) R->L }
% 91.50/12.12 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(true, true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.12 = { by axiom 9 (rule_2) R->L }
% 91.50/12.12 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.13 = { by axiom 2 (ifeq_axiom) R->L }
% 91.50/12.13 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.13 = { by axiom 9 (rule_2) R->L }
% 91.50/12.13 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, q), q), implies(implies(p, implies(p, q)), implies(p, q))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))))), true, ifeq(theorem(implies(implies(implies(p, q), q), implies(implies(p, implies(p, q)), implies(p, q)))), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true), true), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.13 = { by axiom 2 (ifeq_axiom) R->L }
% 91.50/12.13 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(implies(p, q), q), implies(implies(p, implies(p, q)), implies(p, q))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))))), true), true, ifeq(theorem(implies(implies(implies(p, q), q), implies(implies(p, implies(p, q)), implies(p, q)))), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true), true), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.13 = { by axiom 10 (axiom_1_6) R->L }
% 91.50/12.13 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(p, q), q), implies(implies(p, implies(p, q)), implies(p, q))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))))), true, theorem(implies(implies(implies(implies(p, q), q), implies(implies(p, implies(p, q)), implies(p, q))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))))), true), true, ifeq(theorem(implies(implies(implies(p, q), q), implies(implies(p, implies(p, q)), implies(p, q)))), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true), true), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.13 = { by axiom 6 (rule_1) }
% 91.50/12.14 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(implies(implies(p, q), q), implies(implies(p, implies(p, q)), implies(p, q)))), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true), true), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.14 = { by axiom 2 (ifeq_axiom) }
% 91.50/12.14 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, q), q), implies(implies(p, implies(p, q)), implies(p, q)))), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.14 = { by axiom 2 (ifeq_axiom) R->L }
% 91.50/12.14 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(p, q), q), implies(implies(p, implies(p, q)), implies(p, q)))), true), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.14 = { by axiom 10 (axiom_1_6) R->L }
% 91.50/12.14 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, q), q), implies(or(not(p), implies(p, q)), or(not(p), q)))), true, theorem(implies(implies(implies(p, q), q), implies(implies(p, implies(p, q)), implies(p, q)))), true), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.14 = { by axiom 1 (implies_definition) R->L }
% 91.50/12.14 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, q), q), implies(implies(p, implies(p, q)), or(not(p), q)))), true, theorem(implies(implies(implies(p, q), q), implies(implies(p, implies(p, q)), implies(p, q)))), true), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.15 = { by axiom 1 (implies_definition) R->L }
% 91.50/12.15 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, q), q), implies(implies(p, implies(p, q)), implies(p, q)))), true, theorem(implies(implies(implies(p, q), q), implies(implies(p, implies(p, q)), implies(p, q)))), true), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.15 = { by axiom 6 (rule_1) }
% 91.50/12.15 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.15 = { by axiom 2 (ifeq_axiom) }
% 91.50/12.15 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.16 = { by axiom 2 (ifeq_axiom) R->L }
% 91.50/12.16 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.16 = { by axiom 9 (rule_2) R->L }
% 91.50/12.16 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))))), true, ifeq(theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, implies(p, q)), implies(p, q)))), true, theorem(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q))))), true), true), true, ifeq(theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.17 = { by axiom 2 (ifeq_axiom) R->L }
% 91.50/12.17 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))))), true, ifeq(ifeq(true, true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, implies(p, q)), implies(p, q)))), true), true, theorem(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q))))), true), true), true, ifeq(theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.17 = { by axiom 4 (axiom_1_2) R->L }
% 91.50/12.17 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))))), true, ifeq(ifeq(axiom(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, implies(p, q)), implies(p, q)))), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, implies(p, q)), implies(p, q)))), true), true, theorem(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q))))), true), true), true, ifeq(theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.18 = { by axiom 6 (rule_1) }
% 91.50/12.18 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))))), true, ifeq(true, true, theorem(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q))))), true), true), true, ifeq(theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.18 = { by axiom 2 (ifeq_axiom) }
% 91.50/12.18 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))))), true, theorem(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q))))), true), true, ifeq(theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.19 = { by axiom 2 (ifeq_axiom) R->L }
% 91.50/12.19 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))))), true), true, theorem(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q))))), true), true, ifeq(theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.19 = { by axiom 10 (axiom_1_6) R->L }
% 91.50/12.20 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, implies(p, q)), implies(p, q))), implies(or(not(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), or(not(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), implies(implies(p, implies(p, q)), implies(p, q)))))), true, theorem(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))))), true), true, theorem(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q))))), true), true, ifeq(theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.20 = { by axiom 1 (implies_definition) R->L }
% 91.50/12.20 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), or(not(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), implies(implies(p, implies(p, q)), implies(p, q)))))), true, theorem(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))))), true), true, theorem(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q))))), true), true, ifeq(theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.20 = { by axiom 1 (implies_definition) R->L }
% 91.50/12.20 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))))), true, theorem(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))))), true), true, theorem(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q))))), true), true, ifeq(theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.21 = { by axiom 6 (rule_1) }
% 91.50/12.21 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q))))), true), true, ifeq(theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.21 = { by axiom 2 (ifeq_axiom) }
% 91.50/12.21 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q)))), implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q))))), true, ifeq(theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(implies(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)), implies(implies(p, implies(p, q)), implies(p, q)))), true), true), true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.21 = { by axiom 9 (rule_2) }
% 91.50/12.21 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(true, true, ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.21 = { by axiom 2 (ifeq_axiom) }
% 91.50/12.21 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 91.50/12.21 = { by axiom 2 (ifeq_axiom) R->L }
% 91.50/12.21 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(true, true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.22 = { by axiom 9 (rule_2) R->L }
% 93.12/12.22 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true, ifeq(theorem(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q)))), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.22 = { by axiom 2 (ifeq_axiom) R->L }
% 93.12/12.22 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true, ifeq(ifeq(true, true, theorem(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q)))), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.22 = { by axiom 3 (axiom_1_3) R->L }
% 93.12/12.22 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true, ifeq(ifeq(axiom(implies(implies(p, q), or(not(implies(p, implies(p, q))), implies(p, q)))), true, theorem(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q)))), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.22 = { by axiom 1 (implies_definition) R->L }
% 93.12/12.22 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true, ifeq(ifeq(axiom(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q)))), true, theorem(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q)))), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.22 = { by axiom 6 (rule_1) }
% 93.12/12.22 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true, ifeq(true, true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.23 = { by axiom 2 (ifeq_axiom) }
% 93.12/12.23 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.23 = { by axiom 2 (ifeq_axiom) R->L }
% 93.12/12.23 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.23 = { by axiom 9 (rule_2) R->L }
% 93.12/12.24 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true, ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.24 = { by axiom 2 (ifeq_axiom) R->L }
% 93.12/12.24 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true, ifeq(ifeq(true, true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q))))), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.24 = { by axiom 3 (axiom_1_3) R->L }
% 93.12/12.24 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true, ifeq(ifeq(axiom(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q))))), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q))))), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.24 = { by axiom 6 (rule_1) }
% 93.12/12.24 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true, ifeq(true, true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.24 = { by axiom 2 (ifeq_axiom) }
% 93.12/12.25 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.25 = { by axiom 2 (ifeq_axiom) R->L }
% 93.12/12.25 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.25 = { by axiom 6 (rule_1) R->L }
% 93.12/12.26 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(q, implies(implies(p, implies(p, q)), implies(p, q))), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))))), true, theorem(implies(implies(or(q, implies(implies(p, implies(p, q)), implies(p, q))), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))))), true), true, theorem(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.26 = { by axiom 1 (implies_definition) }
% 93.12/12.26 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(q, implies(implies(p, implies(p, q)), implies(p, q))), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), or(not(implies(implies(p, implies(p, q)), implies(p, q))), or(implies(implies(p, implies(p, q)), implies(p, q)), q))))), true, theorem(implies(implies(or(q, implies(implies(p, implies(p, q)), implies(p, q))), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))))), true), true, theorem(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.26 = { by axiom 1 (implies_definition) }
% 93.12/12.27 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(q, implies(implies(p, implies(p, q)), implies(p, q))), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), implies(or(not(implies(implies(p, implies(p, q)), implies(p, q))), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), or(not(implies(implies(p, implies(p, q)), implies(p, q))), or(implies(implies(p, implies(p, q)), implies(p, q)), q))))), true, theorem(implies(implies(or(q, implies(implies(p, implies(p, q)), implies(p, q))), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))))), true), true, theorem(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.27 = { by axiom 10 (axiom_1_6) }
% 93.12/12.27 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(q, implies(implies(p, implies(p, q)), implies(p, q))), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))))), true), true, theorem(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.28 = { by axiom 2 (ifeq_axiom) }
% 93.12/12.28 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(q, implies(implies(p, implies(p, q)), implies(p, q))), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))))), true, theorem(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.28 = { by axiom 2 (ifeq_axiom) R->L }
% 93.12/12.28 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(q, implies(implies(p, implies(p, q)), implies(p, q))), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))))), true, ifeq(true, true, theorem(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.29 = { by axiom 6 (rule_1) R->L }
% 93.12/12.29 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(q, implies(implies(p, implies(p, q)), implies(p, q))), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))))), true, ifeq(ifeq(axiom(implies(or(q, implies(implies(p, implies(p, q)), implies(p, q))), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true, theorem(implies(or(q, implies(implies(p, implies(p, q)), implies(p, q))), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.29 = { by axiom 8 (axiom_1_4) }
% 93.12/12.29 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(q, implies(implies(p, implies(p, q)), implies(p, q))), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))))), true, ifeq(ifeq(true, true, theorem(implies(or(q, implies(implies(p, implies(p, q)), implies(p, q))), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.29 = { by axiom 2 (ifeq_axiom) }
% 93.12/12.30 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(q, implies(implies(p, implies(p, q)), implies(p, q))), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))))), true, ifeq(theorem(implies(or(q, implies(implies(p, implies(p, q)), implies(p, q))), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true, theorem(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(q, implies(implies(p, implies(p, q)), implies(p, q)))), implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true), true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.30 = { by axiom 9 (rule_2) }
% 93.12/12.30 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.30 = { by axiom 2 (ifeq_axiom) }
% 93.12/12.30 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.30 = { by axiom 2 (ifeq_axiom) R->L }
% 93.12/12.30 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.31 = { by axiom 6 (rule_1) R->L }
% 93.12/12.31 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))))), true, theorem(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))))), true), true, ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.31 = { by axiom 1 (implies_definition) }
% 93.12/12.31 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), or(not(implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))))), true, theorem(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))))), true), true, ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.12/12.31 = { by axiom 1 (implies_definition) }
% 93.12/12.31 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), implies(or(not(implies(p, q)), implies(implies(p, implies(p, q)), implies(p, q))), or(not(implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))))), true, theorem(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))))), true), true, ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.90/12.32 = { by axiom 10 (axiom_1_6) }
% 93.90/12.32 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))))), true), true, ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.90/12.32 = { by axiom 2 (ifeq_axiom) }
% 93.90/12.32 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))))), true, ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true, theorem(implies(implies(implies(p, q), implies(implies(p, implies(p, q)), implies(p, q))), implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)))), true), true), true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.90/12.32 = { by axiom 9 (rule_2) }
% 93.90/12.32 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.90/12.32 = { by axiom 2 (ifeq_axiom) }
% 93.90/12.32 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.90/12.32 = { by axiom 2 (ifeq_axiom) R->L }
% 93.90/12.32 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.90/12.33 = { by axiom 6 (rule_1) R->L }
% 93.90/12.33 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)))), true, theorem(implies(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)))), true), true, ifeq(theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.90/12.33 = { by axiom 1 (implies_definition) }
% 93.90/12.33 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), or(not(implies(p, q)), q)))), true, theorem(implies(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)))), true), true, ifeq(theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.90/12.33 = { by axiom 1 (implies_definition) }
% 93.90/12.33 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(implies(p, q)), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), or(not(implies(p, q)), q)))), true, theorem(implies(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)))), true), true, ifeq(theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.90/12.33 = { by axiom 11 (axiom_1_5) }
% 93.90/12.33 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)))), true), true, ifeq(theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.90/12.33 = { by axiom 2 (ifeq_axiom) }
% 93.90/12.33 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q)), or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q)))), true, ifeq(theorem(implies(implies(p, q), or(implies(implies(p, implies(p, q)), implies(p, q)), q))), true, theorem(or(implies(implies(p, implies(p, q)), implies(p, q)), implies(implies(p, q), q))), true), true), true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.90/12.33 = { by axiom 9 (rule_2) }
% 93.90/12.33 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(ifeq(true, true, theorem(implies(implies(p, implies(p, q)), implies(p, q))), true), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.90/12.33 = { by axiom 2 (ifeq_axiom) }
% 93.90/12.33 ifeq(theorem(implies(implies(implies(p, implies(p, q)), implies(p, q)), equivalent(implies(p, implies(p, q)), implies(p, q)))), true, ifeq(theorem(implies(implies(p, implies(p, q)), implies(p, q))), true, theorem(equivalent(implies(p, implies(p, q)), implies(p, q))), true), true)
% 93.90/12.33 = { by axiom 9 (rule_2) }
% 93.90/12.33 true
% 93.90/12.33 % SZS output end Proof
% 93.90/12.33
% 93.90/12.33 RESULT: Unsatisfiable (the axioms are contradictory).
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