%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL238-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:49:27 AM UTC 2026
% Result : Unsatisfiable 61.51s 8.33s
% Output : Proof 63.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL238-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.47 % Computer : n003.cluster.edu
% 0.21/0.47 % Model : x86_64 x86_64
% 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.47 % Memory : 8046.5625MB
% 0.21/0.47 % OS : Linux 6.8.0-71-generic
% 0.21/0.47 % CPULimit : 300
% 0.21/0.47 % WCLimit : 300
% 0.21/0.47 % DateTime : Sun Sep 27 15:30:25 UTC 2026
% 0.21/0.47 % CPUTime :
% 0.21/0.47 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 61.51/8.33 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
% 61.51/8.33
% 61.51/8.33 % SZS status Unsatisfiable
% 61.51/8.33
% 62.35/8.45 % SZS output start Proof
% 62.35/8.45 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 62.35/8.45 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 62.35/8.45 Axiom 3 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 62.35/8.45 Axiom 4 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 62.35/8.45 Axiom 5 (and_defn): and(X, Y) = not(or(not(X), not(Y))).
% 62.35/8.45 Axiom 6 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 62.35/8.45 Axiom 7 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 62.35/8.45 Axiom 8 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 62.35/8.45 Axiom 9 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 62.35/8.45 Axiom 10 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 62.35/8.45
% 62.35/8.45 Lemma 11: not(implies(X, not(Y))) = and(X, Y).
% 62.35/8.45 Proof:
% 62.35/8.45 not(implies(X, not(Y)))
% 62.35/8.45 = { by axiom 1 (implies_definition) }
% 62.35/8.45 not(or(not(X), not(Y)))
% 62.35/8.45 = { by axiom 5 (and_defn) R->L }
% 62.35/8.45 and(X, Y)
% 62.35/8.45
% 62.35/8.45 Lemma 12: implies(implies(X, not(Y)), Z) = or(and(X, Y), Z).
% 62.35/8.45 Proof:
% 62.35/8.45 implies(implies(X, not(Y)), Z)
% 62.35/8.45 = { by axiom 1 (implies_definition) }
% 62.35/8.45 or(not(implies(X, not(Y))), Z)
% 62.35/8.45 = { by lemma 11 }
% 62.35/8.45 or(and(X, Y), Z)
% 62.35/8.45
% 62.35/8.45 Lemma 13: not(implies(X, and(Y, Z))) = and(X, implies(Y, not(Z))).
% 62.35/8.45 Proof:
% 62.35/8.45 not(implies(X, and(Y, Z)))
% 62.35/8.45 = { by lemma 11 R->L }
% 62.35/8.45 not(implies(X, not(implies(Y, not(Z)))))
% 62.35/8.45 = { by lemma 11 }
% 62.35/8.46 and(X, implies(Y, not(Z)))
% 62.35/8.46
% 62.35/8.46 Goal 1 (prove_this): theorem(implies(and(p, q), and(q, p))) = true.
% 62.35/8.46 Proof:
% 62.35/8.46 theorem(implies(and(p, q), and(q, p)))
% 62.35/8.46 = { by axiom 2 (ifeq_axiom) R->L }
% 62.35/8.46 ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true)
% 62.35/8.46 = { by axiom 2 (ifeq_axiom) R->L }
% 62.35/8.46 ifeq(true, true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.46 = { by axiom 8 (rule_2) R->L }
% 62.35/8.46 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p))))), true, ifeq(theorem(implies(and(p, q), or(and(p, q), and(p, q)))), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.46 = { by axiom 2 (ifeq_axiom) R->L }
% 62.35/8.47 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p))))), true, ifeq(ifeq(true, true, theorem(implies(and(p, q), or(and(p, q), and(p, q)))), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.47 = { by axiom 8 (rule_2) R->L }
% 62.35/8.47 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), or(and(p, q), and(p, q))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q)))))), true, ifeq(theorem(implies(or(and(p, q), and(p, q)), or(and(p, q), and(p, q)))), true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q))))), true), true), true, theorem(implies(and(p, q), or(and(p, q), and(p, q)))), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.47 = { by axiom 2 (ifeq_axiom) R->L }
% 62.35/8.47 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), or(and(p, q), and(p, q))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q)))))), true, ifeq(ifeq(true, true, theorem(implies(or(and(p, q), and(p, q)), or(and(p, q), and(p, q)))), true), true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q))))), true), true), true, theorem(implies(and(p, q), or(and(p, q), and(p, q)))), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.47 = { by axiom 7 (axiom_1_4) R->L }
% 62.35/8.47 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), or(and(p, q), and(p, q))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q)))))), true, ifeq(ifeq(axiom(implies(or(and(p, q), and(p, q)), or(and(p, q), and(p, q)))), true, theorem(implies(or(and(p, q), and(p, q)), or(and(p, q), and(p, q)))), true), true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q))))), true), true), true, theorem(implies(and(p, q), or(and(p, q), and(p, q)))), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.47 = { by axiom 6 (rule_1) }
% 62.35/8.47 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), or(and(p, q), and(p, q))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q)))))), true, ifeq(true, true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q))))), true), true), true, theorem(implies(and(p, q), or(and(p, q), and(p, q)))), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.47 = { by axiom 2 (ifeq_axiom) }
% 62.35/8.47 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), or(and(p, q), and(p, q))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q)))))), true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q))))), true), true, theorem(implies(and(p, q), or(and(p, q), and(p, q)))), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.48 = { by axiom 2 (ifeq_axiom) R->L }
% 62.35/8.48 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(and(p, q), and(p, q)), or(and(p, q), and(p, q))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q)))))), true), true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q))))), true), true, theorem(implies(and(p, q), or(and(p, q), and(p, q)))), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.48 = { by axiom 9 (axiom_1_6) R->L }
% 62.35/8.48 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(and(p, q), and(p, q)), or(and(p, q), and(p, q))), implies(or(not(and(p, q)), or(and(p, q), and(p, q))), or(not(and(p, q)), or(and(p, q), and(p, q)))))), true, theorem(implies(implies(or(and(p, q), and(p, q)), or(and(p, q), and(p, q))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q)))))), true), true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q))))), true), true, theorem(implies(and(p, q), or(and(p, q), and(p, q)))), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.48 = { by axiom 1 (implies_definition) R->L }
% 62.35/8.48 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(and(p, q), and(p, q)), or(and(p, q), and(p, q))), implies(implies(and(p, q), or(and(p, q), and(p, q))), or(not(and(p, q)), or(and(p, q), and(p, q)))))), true, theorem(implies(implies(or(and(p, q), and(p, q)), or(and(p, q), and(p, q))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q)))))), true), true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q))))), true), true, theorem(implies(and(p, q), or(and(p, q), and(p, q)))), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.48 = { by axiom 1 (implies_definition) R->L }
% 62.35/8.48 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(and(p, q), and(p, q)), or(and(p, q), and(p, q))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q)))))), true, theorem(implies(implies(or(and(p, q), and(p, q)), or(and(p, q), and(p, q))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q)))))), true), true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q))))), true), true, theorem(implies(and(p, q), or(and(p, q), and(p, q)))), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.48 = { by axiom 6 (rule_1) }
% 62.35/8.48 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q))))), true), true, theorem(implies(and(p, q), or(and(p, q), and(p, q)))), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.48 = { by axiom 2 (ifeq_axiom) }
% 62.35/8.48 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p))))), true, ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q))))), true, theorem(implies(and(p, q), or(and(p, q), and(p, q)))), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.48 = { by axiom 2 (ifeq_axiom) R->L }
% 62.35/8.48 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p))))), true, ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q))))), true, ifeq(true, true, theorem(implies(and(p, q), or(and(p, q), and(p, q)))), true), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.48 = { by axiom 6 (rule_1) R->L }
% 62.35/8.48 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p))))), true, ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q))))), true, ifeq(ifeq(axiom(implies(and(p, q), or(and(p, q), and(p, q)))), true, theorem(implies(and(p, q), or(and(p, q), and(p, q)))), true), true, theorem(implies(and(p, q), or(and(p, q), and(p, q)))), true), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.48 = { by axiom 3 (axiom_1_3) }
% 62.35/8.48 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p))))), true, ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q))))), true, ifeq(ifeq(true, true, theorem(implies(and(p, q), or(and(p, q), and(p, q)))), true), true, theorem(implies(and(p, q), or(and(p, q), and(p, q)))), true), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.48 = { by axiom 2 (ifeq_axiom) }
% 62.35/8.48 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p))))), true, ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), or(and(p, q), and(p, q))))), true, ifeq(theorem(implies(and(p, q), or(and(p, q), and(p, q)))), true, theorem(implies(and(p, q), or(and(p, q), and(p, q)))), true), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.49 = { by axiom 8 (rule_2) }
% 62.35/8.49 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p))))), true, ifeq(true, true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.49 = { by axiom 2 (ifeq_axiom) }
% 62.35/8.49 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p))))), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.49 = { by lemma 11 R->L }
% 62.35/8.49 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), not(implies(q, not(p))))))), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.49 = { by axiom 1 (implies_definition) }
% 62.35/8.49 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), or(not(implies(or(and(p, q), and(p, q)), and(q, p))), implies(and(p, q), not(implies(q, not(p))))))), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.49 = { by lemma 13 }
% 62.35/8.49 ifeq(ifeq(theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p))))))), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.49 = { by axiom 2 (ifeq_axiom) R->L }
% 62.35/8.49 ifeq(ifeq(ifeq(true, true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p))))))), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.49 = { by axiom 6 (rule_1) R->L }
% 62.35/8.49 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(and(p, q), and(p, q)), not(implies(q, not(p)))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), not(implies(q, not(p))))))), true, theorem(implies(implies(or(and(p, q), and(p, q)), not(implies(q, not(p)))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), not(implies(q, not(p))))))), true), true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p))))))), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.49 = { by axiom 1 (implies_definition) }
% 62.35/8.49 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(and(p, q), and(p, q)), not(implies(q, not(p)))), implies(implies(and(p, q), or(and(p, q), and(p, q))), or(not(and(p, q)), not(implies(q, not(p))))))), true, theorem(implies(implies(or(and(p, q), and(p, q)), not(implies(q, not(p)))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), not(implies(q, not(p))))))), true), true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p))))))), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.49 = { by axiom 1 (implies_definition) }
% 62.35/8.49 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(and(p, q), and(p, q)), not(implies(q, not(p)))), implies(or(not(and(p, q)), or(and(p, q), and(p, q))), or(not(and(p, q)), not(implies(q, not(p))))))), true, theorem(implies(implies(or(and(p, q), and(p, q)), not(implies(q, not(p)))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), not(implies(q, not(p))))))), true), true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p))))))), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.49 = { by axiom 9 (axiom_1_6) }
% 62.35/8.49 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(and(p, q), and(p, q)), not(implies(q, not(p)))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), not(implies(q, not(p))))))), true), true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p))))))), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.49 = { by axiom 2 (ifeq_axiom) }
% 62.35/8.49 ifeq(ifeq(ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), not(implies(q, not(p)))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), not(implies(q, not(p))))))), true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p))))))), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.49 = { by lemma 12 }
% 62.35/8.49 ifeq(ifeq(ifeq(theorem(or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), not(implies(q, not(p))))))), true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p))))))), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.50 = { by axiom 2 (ifeq_axiom) R->L }
% 62.35/8.50 ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), not(implies(q, not(p))))))), true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p))))))), true), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.50 = { by axiom 6 (rule_1) R->L }
% 62.35/8.50 ifeq(ifeq(ifeq(ifeq(axiom(implies(or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), not(implies(q, not(p)))))), implies(implies(and(p, q), or(and(p, q), and(p, q))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p)))))))), true, theorem(implies(or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), not(implies(q, not(p)))))), implies(implies(and(p, q), or(and(p, q), and(p, q))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p)))))))), true), true, ifeq(theorem(or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), not(implies(q, not(p))))))), true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p))))))), true), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.50 = { by axiom 1 (implies_definition) }
% 62.35/8.50 ifeq(ifeq(ifeq(ifeq(axiom(implies(or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), not(implies(q, not(p)))))), or(not(implies(and(p, q), or(and(p, q), and(p, q)))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p)))))))), true, theorem(implies(or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), not(implies(q, not(p)))))), implies(implies(and(p, q), or(and(p, q), and(p, q))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p)))))))), true), true, ifeq(theorem(or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), not(implies(q, not(p))))))), true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p))))))), true), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 62.35/8.50 = { by axiom 1 (implies_definition) }
% 62.35/8.50 ifeq(ifeq(ifeq(ifeq(axiom(implies(or(and(or(and(p, q), and(p, q)), implies(q, not(p))), or(not(implies(and(p, q), or(and(p, q), and(p, q)))), implies(and(p, q), not(implies(q, not(p)))))), or(not(implies(and(p, q), or(and(p, q), and(p, q)))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p)))))))), true, theorem(implies(or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), not(implies(q, not(p)))))), implies(implies(and(p, q), or(and(p, q), and(p, q))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p)))))))), true), true, ifeq(theorem(or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), not(implies(q, not(p))))))), true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p))))))), true), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.50 = { by axiom 10 (axiom_1_5) }
% 63.07/8.50 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), not(implies(q, not(p)))))), implies(implies(and(p, q), or(and(p, q), and(p, q))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p)))))))), true), true, ifeq(theorem(or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), not(implies(q, not(p))))))), true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p))))))), true), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.50 = { by axiom 2 (ifeq_axiom) }
% 63.07/8.50 ifeq(ifeq(ifeq(theorem(implies(or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), not(implies(q, not(p)))))), implies(implies(and(p, q), or(and(p, q), and(p, q))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p)))))))), true, ifeq(theorem(or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(implies(and(p, q), or(and(p, q), and(p, q))), implies(and(p, q), not(implies(q, not(p))))))), true, theorem(implies(implies(and(p, q), or(and(p, q), and(p, q))), or(and(or(and(p, q), and(p, q)), implies(q, not(p))), implies(and(p, q), not(implies(q, not(p))))))), true), true), true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.50 = { by axiom 8 (rule_2) }
% 63.07/8.50 ifeq(ifeq(true, true, theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.50 = { by axiom 2 (ifeq_axiom) }
% 63.07/8.50 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(true, true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.50 = { by axiom 8 (rule_2) R->L }
% 63.07/8.51 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(theorem(implies(or(and(q, p), not(or(and(p, q), and(p, q)))), or(not(or(and(p, q), and(p, q))), and(q, p)))), true, ifeq(theorem(or(and(q, p), not(or(and(p, q), and(p, q))))), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.51 = { by axiom 2 (ifeq_axiom) R->L }
% 63.07/8.51 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(or(and(q, p), not(or(and(p, q), and(p, q)))), or(not(or(and(p, q), and(p, q))), and(q, p)))), true), true, ifeq(theorem(or(and(q, p), not(or(and(p, q), and(p, q))))), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.51 = { by axiom 7 (axiom_1_4) R->L }
% 63.07/8.51 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(axiom(implies(or(and(q, p), not(or(and(p, q), and(p, q)))), or(not(or(and(p, q), and(p, q))), and(q, p)))), true, theorem(implies(or(and(q, p), not(or(and(p, q), and(p, q)))), or(not(or(and(p, q), and(p, q))), and(q, p)))), true), true, ifeq(theorem(or(and(q, p), not(or(and(p, q), and(p, q))))), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.51 = { by axiom 6 (rule_1) }
% 63.07/8.51 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(true, true, ifeq(theorem(or(and(q, p), not(or(and(p, q), and(p, q))))), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.51 = { by axiom 2 (ifeq_axiom) }
% 63.07/8.51 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(theorem(or(and(q, p), not(or(and(p, q), and(p, q))))), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.51 = { by lemma 12 R->L }
% 63.07/8.51 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(theorem(or(and(q, p), not(implies(implies(p, not(q)), and(p, q))))), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.51 = { by lemma 12 R->L }
% 63.07/8.51 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(theorem(implies(implies(q, not(p)), not(implies(implies(p, not(q)), and(p, q))))), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.51 = { by axiom 1 (implies_definition) }
% 63.07/8.51 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(theorem(implies(or(not(q), not(p)), not(implies(implies(p, not(q)), and(p, q))))), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.51 = { by lemma 13 }
% 63.07/8.51 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.51 = { by axiom 2 (ifeq_axiom) R->L }
% 63.07/8.51 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.51 = { by axiom 8 (rule_2) R->L }
% 63.07/8.51 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, not(q)), and(implies(p, not(q)), implies(p, not(q)))), implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))))), true, ifeq(theorem(implies(implies(p, not(q)), and(implies(p, not(q)), implies(p, not(q))))), true, theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true), true), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.51 = { by axiom 2 (ifeq_axiom) R->L }
% 63.07/8.51 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(p, not(q)), and(implies(p, not(q)), implies(p, not(q)))), implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))))), true), true, ifeq(theorem(implies(implies(p, not(q)), and(implies(p, not(q)), implies(p, not(q))))), true, theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true), true), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.51 = { by axiom 9 (axiom_1_6) R->L }
% 63.07/8.51 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, not(q)), and(implies(p, not(q)), implies(p, not(q)))), implies(or(not(or(not(q), not(p))), implies(p, not(q))), or(not(or(not(q), not(p))), and(implies(p, not(q)), implies(p, not(q))))))), true, theorem(implies(implies(implies(p, not(q)), and(implies(p, not(q)), implies(p, not(q)))), implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))))), true), true, ifeq(theorem(implies(implies(p, not(q)), and(implies(p, not(q)), implies(p, not(q))))), true, theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true), true), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.51 = { by axiom 1 (implies_definition) R->L }
% 63.07/8.51 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, not(q)), and(implies(p, not(q)), implies(p, not(q)))), implies(implies(or(not(q), not(p)), implies(p, not(q))), or(not(or(not(q), not(p))), and(implies(p, not(q)), implies(p, not(q))))))), true, theorem(implies(implies(implies(p, not(q)), and(implies(p, not(q)), implies(p, not(q)))), implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))))), true), true, ifeq(theorem(implies(implies(p, not(q)), and(implies(p, not(q)), implies(p, not(q))))), true, theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true), true), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.51 = { by axiom 1 (implies_definition) R->L }
% 63.07/8.52 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, not(q)), and(implies(p, not(q)), implies(p, not(q)))), implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))))), true, theorem(implies(implies(implies(p, not(q)), and(implies(p, not(q)), implies(p, not(q)))), implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))))), true), true, ifeq(theorem(implies(implies(p, not(q)), and(implies(p, not(q)), implies(p, not(q))))), true, theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true), true), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.52 = { by axiom 6 (rule_1) }
% 63.07/8.52 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(implies(p, not(q)), and(implies(p, not(q)), implies(p, not(q))))), true, theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true), true), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.52 = { by axiom 2 (ifeq_axiom) }
% 63.07/8.52 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(p, not(q)), and(implies(p, not(q)), implies(p, not(q))))), true, theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.52 = { by axiom 1 (implies_definition) }
% 63.07/8.52 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(or(not(implies(p, not(q))), and(implies(p, not(q)), implies(p, not(q))))), true, theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.52 = { by axiom 2 (ifeq_axiom) R->L }
% 63.07/8.52 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(implies(p, not(q))), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.52 = { by axiom 6 (rule_1) R->L }
% 63.07/8.52 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(implies(p, not(q))), not(implies(p, not(q)))), not(implies(p, not(q))))), true, theorem(implies(or(not(implies(p, not(q))), not(implies(p, not(q)))), not(implies(p, not(q))))), true), true, theorem(or(not(implies(p, not(q))), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.52 = { by axiom 4 (axiom_1_2) }
% 63.07/8.52 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(implies(p, not(q))), not(implies(p, not(q)))), not(implies(p, not(q))))), true), true, theorem(or(not(implies(p, not(q))), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.52 = { by axiom 2 (ifeq_axiom) }
% 63.07/8.52 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(implies(p, not(q))), not(implies(p, not(q)))), not(implies(p, not(q))))), true, theorem(or(not(implies(p, not(q))), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.52 = { by axiom 1 (implies_definition) R->L }
% 63.07/8.52 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, not(q)), not(implies(p, not(q)))), not(implies(p, not(q))))), true, theorem(or(not(implies(p, not(q))), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.52 = { by lemma 12 }
% 63.07/8.52 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(and(implies(p, not(q)), implies(p, not(q))), not(implies(p, not(q))))), true, theorem(or(not(implies(p, not(q))), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.52 = { by axiom 2 (ifeq_axiom) R->L }
% 63.07/8.53 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(and(implies(p, not(q)), implies(p, not(q))), not(implies(p, not(q))))), true, theorem(or(not(implies(p, not(q))), and(implies(p, not(q)), implies(p, not(q))))), true), true), true, theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.53 = { by axiom 6 (rule_1) R->L }
% 63.07/8.53 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(and(implies(p, not(q)), implies(p, not(q))), not(implies(p, not(q)))), or(not(implies(p, not(q))), and(implies(p, not(q)), implies(p, not(q)))))), true, theorem(implies(or(and(implies(p, not(q)), implies(p, not(q))), not(implies(p, not(q)))), or(not(implies(p, not(q))), and(implies(p, not(q)), implies(p, not(q)))))), true), true, ifeq(theorem(or(and(implies(p, not(q)), implies(p, not(q))), not(implies(p, not(q))))), true, theorem(or(not(implies(p, not(q))), and(implies(p, not(q)), implies(p, not(q))))), true), true), true, theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.53 = { by axiom 7 (axiom_1_4) }
% 63.07/8.53 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(and(implies(p, not(q)), implies(p, not(q))), not(implies(p, not(q)))), or(not(implies(p, not(q))), and(implies(p, not(q)), implies(p, not(q)))))), true), true, ifeq(theorem(or(and(implies(p, not(q)), implies(p, not(q))), not(implies(p, not(q))))), true, theorem(or(not(implies(p, not(q))), and(implies(p, not(q)), implies(p, not(q))))), true), true), true, theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.53 = { by axiom 2 (ifeq_axiom) }
% 63.07/8.53 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(implies(p, not(q)), implies(p, not(q))), not(implies(p, not(q)))), or(not(implies(p, not(q))), and(implies(p, not(q)), implies(p, not(q)))))), true, ifeq(theorem(or(and(implies(p, not(q)), implies(p, not(q))), not(implies(p, not(q))))), true, theorem(or(not(implies(p, not(q))), and(implies(p, not(q)), implies(p, not(q))))), true), true), true, theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.53 = { by axiom 8 (rule_2) }
% 63.07/8.53 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.53 = { by axiom 2 (ifeq_axiom) }
% 63.07/8.53 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.53 = { by axiom 2 (ifeq_axiom) R->L }
% 63.07/8.53 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true, ifeq(true, true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.53 = { by axiom 6 (rule_1) R->L }
% 63.07/8.53 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true, ifeq(ifeq(axiom(implies(or(not(q), not(p)), or(not(p), not(q)))), true, theorem(implies(or(not(q), not(p)), or(not(p), not(q)))), true), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.53 = { by axiom 7 (axiom_1_4) }
% 63.07/8.53 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true, ifeq(ifeq(true, true, theorem(implies(or(not(q), not(p)), or(not(p), not(q)))), true), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.53 = { by axiom 2 (ifeq_axiom) }
% 63.07/8.53 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true, ifeq(theorem(implies(or(not(q), not(p)), or(not(p), not(q)))), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.53 = { by axiom 1 (implies_definition) R->L }
% 63.07/8.53 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(ifeq(theorem(implies(implies(or(not(q), not(p)), implies(p, not(q))), implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q)))))), true, ifeq(theorem(implies(or(not(q), not(p)), implies(p, not(q)))), true, theorem(implies(or(not(q), not(p)), and(implies(p, not(q)), implies(p, not(q))))), true), true), true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.53 = { by axiom 8 (rule_2) }
% 63.07/8.53 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(ifeq(true, true, theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.53 = { by axiom 2 (ifeq_axiom) }
% 63.07/8.53 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(theorem(or(not(or(and(p, q), and(p, q))), and(q, p))), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.53 = { by axiom 1 (implies_definition) R->L }
% 63.07/8.53 ifeq(theorem(implies(implies(or(and(p, q), and(p, q)), and(q, p)), implies(and(p, q), and(q, p)))), true, ifeq(theorem(implies(or(and(p, q), and(p, q)), and(q, p))), true, theorem(implies(and(p, q), and(q, p))), true), true)
% 63.07/8.53 = { by axiom 8 (rule_2) }
% 63.07/8.53 true
% 63.07/8.53 % SZS output end Proof
% 63.07/8.53
% 63.07/8.54 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------