%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL312-3 : 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 11:49:35 AM UTC 2026
% Result : Unsatisfiable 51.60s 11.93s
% Output : Proof 53.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL312-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n003.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Sun Sep 27 15:35:47 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 51.60/11.93 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
% 51.60/11.93
% 51.60/11.93 % SZS status Unsatisfiable
% 51.60/11.93
% 52.88/12.09 % SZS output start Proof
% 52.88/12.09 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 52.88/12.09 Axiom 2 (and_defn): and(X, Y) = not(or(not(X), not(Y))).
% 52.88/12.09 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 52.88/12.09 Axiom 4 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 52.88/12.09 Axiom 5 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 52.88/12.09 Axiom 6 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 52.88/12.09 Axiom 7 (equivalent_defn): equivalent(X, Y) = and(implies(X, Y), implies(Y, X)).
% 52.88/12.09 Axiom 8 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 52.88/12.09 Axiom 9 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 52.88/12.09 Axiom 10 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 52.88/12.10 Axiom 11 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 52.88/12.10
% 52.88/12.10 Goal 1 (prove_this): theorem(equivalent(implies(not(p), p), p)) = true.
% 52.88/12.10 Proof:
% 52.88/12.10 theorem(equivalent(implies(not(p), p), p))
% 52.88/12.10 = { by axiom 3 (ifeq_axiom) R->L }
% 52.88/12.10 ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true)
% 52.88/12.10 = { by axiom 3 (ifeq_axiom) R->L }
% 52.88/12.10 ifeq(true, true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.10 = { by axiom 11 (rule_2) R->L }
% 52.88/12.10 ifeq(ifeq(theorem(implies(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))), or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p)))), true, ifeq(theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.10 = { by axiom 3 (ifeq_axiom) R->L }
% 52.88/12.10 ifeq(ifeq(ifeq(true, true, theorem(implies(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))), or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p)))), true), true, ifeq(theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.10 = { by axiom 8 (axiom_1_4) R->L }
% 52.88/12.10 ifeq(ifeq(ifeq(axiom(implies(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))), or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p)))), true, theorem(implies(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))), or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p)))), true), true, ifeq(theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.10 = { by axiom 6 (rule_1) }
% 52.88/12.10 ifeq(ifeq(true, true, ifeq(theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.10 = { by axiom 3 (ifeq_axiom) }
% 52.88/12.10 ifeq(ifeq(theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.10 = { by axiom 3 (ifeq_axiom) R->L }
% 52.88/12.10 ifeq(ifeq(ifeq(true, true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.11 = { by axiom 11 (rule_2) R->L }
% 52.88/12.11 ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(implies(not(p), p), p), implies(implies(p, implies(not(p), p)), not(implies(implies(not(p), p), p)))), implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))))), true, ifeq(theorem(or(equivalent(implies(not(p), p), p), implies(implies(p, implies(not(p), p)), not(implies(implies(not(p), p), p))))), true, theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true), true), true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.11 = { by axiom 3 (ifeq_axiom) R->L }
% 52.88/12.11 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(equivalent(implies(not(p), p), p), implies(implies(p, implies(not(p), p)), not(implies(implies(not(p), p), p)))), implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))))), true), true, ifeq(theorem(or(equivalent(implies(not(p), p), p), implies(implies(p, implies(not(p), p)), not(implies(implies(not(p), p), p))))), true, theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true), true), true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.11 = { by axiom 10 (axiom_1_5) R->L }
% 52.88/12.11 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(equivalent(implies(not(p), p), p), or(not(implies(p, implies(not(p), p))), not(implies(implies(not(p), p), p)))), or(not(implies(p, implies(not(p), p))), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))))), true, theorem(implies(or(equivalent(implies(not(p), p), p), implies(implies(p, implies(not(p), p)), not(implies(implies(not(p), p), p)))), implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))))), true), true, ifeq(theorem(or(equivalent(implies(not(p), p), p), implies(implies(p, implies(not(p), p)), not(implies(implies(not(p), p), p))))), true, theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true), true), true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.11 = { by axiom 1 (implies_definition) R->L }
% 52.88/12.11 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(equivalent(implies(not(p), p), p), implies(implies(p, implies(not(p), p)), not(implies(implies(not(p), p), p)))), or(not(implies(p, implies(not(p), p))), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))))), true, theorem(implies(or(equivalent(implies(not(p), p), p), implies(implies(p, implies(not(p), p)), not(implies(implies(not(p), p), p)))), implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))))), true), true, ifeq(theorem(or(equivalent(implies(not(p), p), p), implies(implies(p, implies(not(p), p)), not(implies(implies(not(p), p), p))))), true, theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true), true), true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.12 = { by axiom 1 (implies_definition) R->L }
% 52.88/12.12 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(equivalent(implies(not(p), p), p), implies(implies(p, implies(not(p), p)), not(implies(implies(not(p), p), p)))), implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))))), true, theorem(implies(or(equivalent(implies(not(p), p), p), implies(implies(p, implies(not(p), p)), not(implies(implies(not(p), p), p)))), implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))))), true), true, ifeq(theorem(or(equivalent(implies(not(p), p), p), implies(implies(p, implies(not(p), p)), not(implies(implies(not(p), p), p))))), true, theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true), true), true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.12 = { by axiom 6 (rule_1) }
% 52.88/12.12 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(equivalent(implies(not(p), p), p), implies(implies(p, implies(not(p), p)), not(implies(implies(not(p), p), p))))), true, theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true), true), true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.12 = { by axiom 3 (ifeq_axiom) }
% 52.88/12.12 ifeq(ifeq(ifeq(ifeq(theorem(or(equivalent(implies(not(p), p), p), implies(implies(p, implies(not(p), p)), not(implies(implies(not(p), p), p))))), true, theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true), true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.12 = { by axiom 1 (implies_definition) }
% 52.88/12.12 ifeq(ifeq(ifeq(ifeq(theorem(or(equivalent(implies(not(p), p), p), or(not(implies(p, implies(not(p), p))), not(implies(implies(not(p), p), p))))), true, theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true), true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.12 = { by axiom 7 (equivalent_defn) }
% 52.88/12.12 ifeq(ifeq(ifeq(ifeq(theorem(or(and(implies(implies(not(p), p), p), implies(p, implies(not(p), p))), or(not(implies(p, implies(not(p), p))), not(implies(implies(not(p), p), p))))), true, theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true), true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.12 = { by axiom 2 (and_defn) }
% 52.88/12.12 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(implies(implies(not(p), p), p)), not(implies(p, implies(not(p), p))))), or(not(implies(p, implies(not(p), p))), not(implies(implies(not(p), p), p))))), true, theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true), true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.12 = { by axiom 1 (implies_definition) R->L }
% 52.88/12.12 ifeq(ifeq(ifeq(ifeq(theorem(or(not(implies(implies(implies(not(p), p), p), not(implies(p, implies(not(p), p))))), or(not(implies(p, implies(not(p), p))), not(implies(implies(not(p), p), p))))), true, theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true), true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.13 = { by axiom 1 (implies_definition) R->L }
% 52.88/12.13 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(not(p), p), p), not(implies(p, implies(not(p), p)))), or(not(implies(p, implies(not(p), p))), not(implies(implies(not(p), p), p))))), true, theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true), true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.13 = { by axiom 1 (implies_definition) }
% 52.88/12.13 ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(implies(implies(not(p), p), p)), not(implies(p, implies(not(p), p)))), or(not(implies(p, implies(not(p), p))), not(implies(implies(not(p), p), p))))), true, theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true), true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.13 = { by axiom 3 (ifeq_axiom) R->L }
% 52.88/12.13 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(implies(implies(not(p), p), p)), not(implies(p, implies(not(p), p)))), or(not(implies(p, implies(not(p), p))), not(implies(implies(not(p), p), p))))), true), true, theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true), true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.13 = { by axiom 8 (axiom_1_4) R->L }
% 52.88/12.13 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(implies(implies(not(p), p), p)), not(implies(p, implies(not(p), p)))), or(not(implies(p, implies(not(p), p))), not(implies(implies(not(p), p), p))))), true, theorem(implies(or(not(implies(implies(not(p), p), p)), not(implies(p, implies(not(p), p)))), or(not(implies(p, implies(not(p), p))), not(implies(implies(not(p), p), p))))), true), true, theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true), true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.13 = { by axiom 6 (rule_1) }
% 52.88/12.13 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true), true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.13 = { by axiom 3 (ifeq_axiom) }
% 52.88/12.13 ifeq(ifeq(ifeq(theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.13 = { by axiom 3 (ifeq_axiom) R->L }
% 52.88/12.13 ifeq(ifeq(ifeq(theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true, ifeq(true, true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.13 = { by axiom 6 (rule_1) R->L }
% 52.88/12.13 ifeq(ifeq(ifeq(theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true, ifeq(ifeq(axiom(implies(p, implies(not(p), p))), true, theorem(implies(p, implies(not(p), p))), true), true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.13 = { by axiom 1 (implies_definition) }
% 52.88/12.13 ifeq(ifeq(ifeq(theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true, ifeq(ifeq(axiom(implies(p, or(not(not(p)), p))), true, theorem(implies(p, implies(not(p), p))), true), true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.13 = { by axiom 4 (axiom_1_3) }
% 52.88/12.13 ifeq(ifeq(ifeq(theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true, ifeq(ifeq(true, true, theorem(implies(p, implies(not(p), p))), true), true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.13 = { by axiom 3 (ifeq_axiom) }
% 52.88/12.13 ifeq(ifeq(ifeq(theorem(implies(implies(p, implies(not(p), p)), or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p))))), true, ifeq(theorem(implies(p, implies(not(p), p))), true, theorem(or(equivalent(implies(not(p), p), p), not(implies(implies(not(p), p), p)))), true), true), true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.13 = { by axiom 11 (rule_2) }
% 52.88/12.13 ifeq(ifeq(true, true, theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.13 = { by axiom 3 (ifeq_axiom) }
% 52.88/12.13 ifeq(theorem(or(not(implies(implies(not(p), p), p)), equivalent(implies(not(p), p), p))), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.13 = { by axiom 1 (implies_definition) R->L }
% 52.88/12.13 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(true, true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.13 = { by axiom 11 (rule_2) R->L }
% 52.88/12.13 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.14 = { by axiom 3 (ifeq_axiom) R->L }
% 52.88/12.14 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.14 = { by axiom 11 (rule_2) R->L }
% 52.88/12.14 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true, ifeq(theorem(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p)))), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.14 = { by axiom 3 (ifeq_axiom) R->L }
% 52.88/12.14 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true, ifeq(ifeq(true, true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p)))), true), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.14 = { by axiom 9 (axiom_1_6) R->L }
% 52.88/12.14 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true, ifeq(ifeq(axiom(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p)))), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p)))), true), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.14 = { by axiom 6 (rule_1) }
% 52.88/12.14 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true, ifeq(true, true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.14 = { by axiom 3 (ifeq_axiom) }
% 52.88/12.14 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.14 = { by axiom 3 (ifeq_axiom) R->L }
% 52.88/12.14 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.14 = { by axiom 11 (rule_2) R->L }
% 52.88/12.14 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, p), p), implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p)))), true, ifeq(theorem(implies(or(p, p), p)), true, theorem(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p))), true), true), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.14 = { by axiom 3 (ifeq_axiom) R->L }
% 52.88/12.14 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, p), p), implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p)))), true, ifeq(ifeq(true, true, theorem(implies(or(p, p), p)), true), true, theorem(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p))), true), true), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.14 = { by axiom 5 (axiom_1_2) R->L }
% 52.88/12.15 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, p), p), implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p)))), true, ifeq(ifeq(axiom(implies(or(p, p), p)), true, theorem(implies(or(p, p), p)), true), true, theorem(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p))), true), true), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.15 = { by axiom 6 (rule_1) }
% 52.88/12.15 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, p), p), implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p)))), true, ifeq(true, true, theorem(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p))), true), true), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.15 = { by axiom 3 (ifeq_axiom) }
% 52.88/12.15 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, p), p), implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p)))), true, theorem(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p))), true), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.15 = { by axiom 3 (ifeq_axiom) R->L }
% 52.88/12.15 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(p, p), p), implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p)))), true), true, theorem(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p))), true), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.15 = { by axiom 9 (axiom_1_6) R->L }
% 52.88/12.15 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, p), p), implies(or(not(or(p, not(p))), or(p, p)), or(not(or(p, not(p))), p)))), true, theorem(implies(implies(or(p, p), p), implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p)))), true), true, theorem(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p))), true), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.15 = { by axiom 1 (implies_definition) R->L }
% 52.88/12.15 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, p), p), implies(implies(or(p, not(p)), or(p, p)), or(not(or(p, not(p))), p)))), true, theorem(implies(implies(or(p, p), p), implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p)))), true), true, theorem(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p))), true), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.15 = { by axiom 1 (implies_definition) R->L }
% 52.88/12.15 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, p), p), implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p)))), true, theorem(implies(implies(or(p, p), p), implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p)))), true), true, theorem(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p))), true), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.15 = { by axiom 6 (rule_1) }
% 52.88/12.15 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p))), true), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.16 = { by axiom 3 (ifeq_axiom) }
% 52.88/12.16 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p))), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.16 = { by axiom 3 (ifeq_axiom) R->L }
% 52.88/12.16 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p))), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true), true), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.16 = { by axiom 6 (rule_1) R->L }
% 52.88/12.16 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p)), implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p))))), true, theorem(implies(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p)), implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p))))), true), true, ifeq(theorem(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p))), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true), true), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.16 = { by axiom 1 (implies_definition) }
% 52.88/12.16 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p)), implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), or(not(implies(not(p), p)), implies(or(p, not(p)), p))))), true, theorem(implies(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p)), implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p))))), true), true, ifeq(theorem(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p))), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true), true), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.16 = { by axiom 1 (implies_definition) }
% 52.88/12.16 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p)), implies(or(not(implies(not(p), p)), implies(or(p, not(p)), or(p, p))), or(not(implies(not(p), p)), implies(or(p, not(p)), p))))), true, theorem(implies(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p)), implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p))))), true), true, ifeq(theorem(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p))), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true), true), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.16 = { by axiom 9 (axiom_1_6) }
% 52.88/12.16 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p)), implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p))))), true), true, ifeq(theorem(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p))), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true), true), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.16 = { by axiom 3 (ifeq_axiom) }
% 52.88/12.17 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p)), implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p))))), true, ifeq(theorem(implies(implies(or(p, not(p)), or(p, p)), implies(or(p, not(p)), p))), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), or(p, p))), implies(implies(not(p), p), implies(or(p, not(p)), p)))), true), true), true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.17 = { by axiom 11 (rule_2) }
% 52.88/12.17 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.17 = { by axiom 3 (ifeq_axiom) }
% 52.88/12.17 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.17 = { by axiom 3 (ifeq_axiom) R->L }
% 52.88/12.17 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.17 = { by axiom 6 (rule_1) R->L }
% 52.88/12.17 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(not(p), p), implies(or(p, not(p)), p)), implies(or(p, not(p)), implies(implies(not(p), p), p)))), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), p)), implies(or(p, not(p)), implies(implies(not(p), p), p)))), true), true, ifeq(theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.17 = { by axiom 1 (implies_definition) }
% 52.88/12.17 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(not(p), p), implies(or(p, not(p)), p)), or(not(or(p, not(p))), implies(implies(not(p), p), p)))), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), p)), implies(or(p, not(p)), implies(implies(not(p), p), p)))), true), true, ifeq(theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.17 = { by axiom 1 (implies_definition) }
% 52.88/12.17 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(not(p), p), or(not(or(p, not(p))), p)), or(not(or(p, not(p))), implies(implies(not(p), p), p)))), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), p)), implies(or(p, not(p)), implies(implies(not(p), p), p)))), true), true, ifeq(theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.17 = { by axiom 1 (implies_definition) }
% 52.88/12.17 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(not(p), p), or(not(or(p, not(p))), p)), or(not(or(p, not(p))), or(not(implies(not(p), p)), p)))), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), p)), implies(or(p, not(p)), implies(implies(not(p), p), p)))), true), true, ifeq(theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.17 = { by axiom 1 (implies_definition) }
% 52.88/12.17 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(implies(not(p), p)), or(not(or(p, not(p))), p)), or(not(or(p, not(p))), or(not(implies(not(p), p)), p)))), true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), p)), implies(or(p, not(p)), implies(implies(not(p), p), p)))), true), true, ifeq(theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.17 = { by axiom 10 (axiom_1_5) }
% 52.88/12.17 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), p)), implies(or(p, not(p)), implies(implies(not(p), p), p)))), true), true, ifeq(theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.17 = { by axiom 3 (ifeq_axiom) }
% 52.88/12.17 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(theorem(implies(implies(implies(not(p), p), implies(or(p, not(p)), p)), implies(or(p, not(p)), implies(implies(not(p), p), p)))), true, ifeq(theorem(implies(implies(not(p), p), implies(or(p, not(p)), p))), true, theorem(implies(or(p, not(p)), implies(implies(not(p), p), p))), true), true), true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 52.88/12.17 = { by axiom 11 (rule_2) }
% 53.71/12.17 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(true, true, ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.17 = { by axiom 3 (ifeq_axiom) }
% 53.71/12.17 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(theorem(or(p, not(p))), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.17 = { by axiom 3 (ifeq_axiom) R->L }
% 53.71/12.17 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(true, true, theorem(or(p, not(p))), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.17 = { by axiom 11 (rule_2) R->L }
% 53.71/12.17 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(or(implies(p, p), implies(p, p)), implies(p, p))), true, ifeq(theorem(or(implies(p, p), implies(p, p))), true, theorem(implies(p, p)), true), true), true, theorem(or(p, not(p))), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.17 = { by axiom 3 (ifeq_axiom) R->L }
% 53.71/12.18 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(p, p), implies(p, p)), implies(p, p))), true), true, ifeq(theorem(or(implies(p, p), implies(p, p))), true, theorem(implies(p, p)), true), true), true, theorem(or(p, not(p))), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.18 = { by axiom 5 (axiom_1_2) R->L }
% 53.71/12.18 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(implies(p, p), implies(p, p)), implies(p, p))), true, theorem(implies(or(implies(p, p), implies(p, p)), implies(p, p))), true), true, ifeq(theorem(or(implies(p, p), implies(p, p))), true, theorem(implies(p, p)), true), true), true, theorem(or(p, not(p))), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.18 = { by axiom 6 (rule_1) }
% 53.71/12.18 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(implies(p, p), implies(p, p))), true, theorem(implies(p, p)), true), true), true, theorem(or(p, not(p))), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.18 = { by axiom 3 (ifeq_axiom) }
% 53.71/12.18 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(theorem(or(implies(p, p), implies(p, p))), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.18 = { by axiom 3 (ifeq_axiom) R->L }
% 53.71/12.18 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(implies(p, p), implies(p, p))), true), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.18 = { by axiom 6 (rule_1) R->L }
% 53.71/12.18 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), implies(p, p)))), true, theorem(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), implies(p, p)))), true), true, theorem(or(implies(p, p), implies(p, p))), true), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.18 = { by axiom 1 (implies_definition) }
% 53.71/12.18 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), or(not(p), p)))), true, theorem(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), implies(p, p)))), true), true, theorem(or(implies(p, p), implies(p, p))), true), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.18 = { by axiom 1 (implies_definition) }
% 53.71/12.18 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(p), or(implies(p, p), p)), or(implies(p, p), or(not(p), p)))), true, theorem(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), implies(p, p)))), true), true, theorem(or(implies(p, p), implies(p, p))), true), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.18 = { by axiom 10 (axiom_1_5) }
% 53.71/12.18 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), implies(p, p)))), true), true, theorem(or(implies(p, p), implies(p, p))), true), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.18 = { by axiom 3 (ifeq_axiom) }
% 53.71/12.18 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), implies(p, p)))), true, theorem(or(implies(p, p), implies(p, p))), true), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.18 = { by axiom 3 (ifeq_axiom) R->L }
% 53.71/12.18 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), implies(p, p)))), true, ifeq(true, true, theorem(or(implies(p, p), implies(p, p))), true), true), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.18 = { by axiom 6 (rule_1) R->L }
% 53.71/12.18 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), implies(p, p)))), true, ifeq(ifeq(axiom(implies(p, or(implies(p, p), p))), true, theorem(implies(p, or(implies(p, p), p))), true), true, theorem(or(implies(p, p), implies(p, p))), true), true), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.18 = { by axiom 4 (axiom_1_3) }
% 53.71/12.18 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), implies(p, p)))), true, ifeq(ifeq(true, true, theorem(implies(p, or(implies(p, p), p))), true), true, theorem(or(implies(p, p), implies(p, p))), true), true), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.18 = { by axiom 3 (ifeq_axiom) }
% 53.71/12.18 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), implies(p, p)))), true, ifeq(theorem(implies(p, or(implies(p, p), p))), true, theorem(or(implies(p, p), implies(p, p))), true), true), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.18 = { by axiom 11 (rule_2) }
% 53.71/12.18 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.18 = { by axiom 3 (ifeq_axiom) }
% 53.71/12.18 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(theorem(implies(p, p)), true, theorem(or(p, not(p))), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.19 = { by axiom 3 (ifeq_axiom) R->L }
% 53.71/12.19 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(p, p)), true, theorem(or(p, not(p))), true), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.19 = { by axiom 6 (rule_1) R->L }
% 53.71/12.19 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(p), p), or(p, not(p)))), true, theorem(implies(or(not(p), p), or(p, not(p)))), true), true, ifeq(theorem(implies(p, p)), true, theorem(or(p, not(p))), true), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.19 = { by axiom 8 (axiom_1_4) }
% 53.71/12.19 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(p), p), or(p, not(p)))), true), true, ifeq(theorem(implies(p, p)), true, theorem(or(p, not(p))), true), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.19 = { by axiom 3 (ifeq_axiom) }
% 53.71/12.19 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(theorem(implies(or(not(p), p), or(p, not(p)))), true, ifeq(theorem(implies(p, p)), true, theorem(or(p, not(p))), true), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.19 = { by axiom 1 (implies_definition) R->L }
% 53.71/12.19 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(ifeq(theorem(implies(implies(p, p), or(p, not(p)))), true, ifeq(theorem(implies(p, p)), true, theorem(or(p, not(p))), true), true), true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.19 = { by axiom 11 (rule_2) }
% 53.71/12.19 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(ifeq(true, true, theorem(implies(implies(not(p), p), p)), true), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.19 = { by axiom 3 (ifeq_axiom) }
% 53.71/12.19 ifeq(theorem(implies(implies(implies(not(p), p), p), equivalent(implies(not(p), p), p))), true, ifeq(theorem(implies(implies(not(p), p), p)), true, theorem(equivalent(implies(not(p), p), p)), true), true)
% 53.71/12.19 = { by axiom 11 (rule_2) }
% 53.71/12.19 true
% 53.71/12.19 % SZS output end Proof
% 53.71/12.19
% 53.71/12.19 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------