%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL207-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 11:49:20 AM UTC 2026
% Result : Unsatisfiable 56.08s 7.52s
% Output : Proof 57.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL207-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 27 15:27:49 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 56.08/7.52 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
% 56.08/7.52
% 56.08/7.52 % SZS status Unsatisfiable
% 56.08/7.52
% 56.85/7.63 % SZS output start Proof
% 56.85/7.63 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 56.85/7.63 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 56.85/7.63 Axiom 3 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 56.85/7.63 Axiom 4 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 56.85/7.63 Axiom 5 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 56.85/7.63 Axiom 6 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 56.85/7.63 Axiom 7 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 56.85/7.63 Axiom 8 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 56.85/7.63
% 56.85/7.63 Goal 1 (prove_this): theorem(implies(not(implies(p, q)), implies(q, p))) = true.
% 56.85/7.63 Proof:
% 56.85/7.63 theorem(implies(not(implies(p, q)), implies(q, p)))
% 56.85/7.63 = { by axiom 2 (ifeq_axiom) R->L }
% 56.85/7.63 ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true)
% 56.85/7.63 = { by axiom 2 (ifeq_axiom) R->L }
% 56.85/7.63 ifeq(true, true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.63 = { by axiom 6 (rule_2) R->L }
% 56.85/7.63 ifeq(ifeq(theorem(implies(implies(not(implies(p, q)), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p))))), true, ifeq(theorem(implies(not(implies(p, q)), or(p, not(implies(p, q))))), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true), true), true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.63 = { by axiom 2 (ifeq_axiom) R->L }
% 56.85/7.63 ifeq(ifeq(theorem(implies(implies(not(implies(p, q)), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p))))), true, ifeq(ifeq(true, true, theorem(implies(not(implies(p, q)), or(p, not(implies(p, q))))), true), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true), true), true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.63 = { by axiom 3 (axiom_1_3) R->L }
% 56.85/7.63 ifeq(ifeq(theorem(implies(implies(not(implies(p, q)), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p))))), true, ifeq(ifeq(axiom(implies(not(implies(p, q)), or(p, not(implies(p, q))))), true, theorem(implies(not(implies(p, q)), or(p, not(implies(p, q))))), true), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true), true), true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.63 = { by axiom 4 (rule_1) }
% 56.85/7.63 ifeq(ifeq(theorem(implies(implies(not(implies(p, q)), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p))))), true, ifeq(true, true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true), true), true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.63 = { by axiom 2 (ifeq_axiom) }
% 56.85/7.64 ifeq(ifeq(theorem(implies(implies(not(implies(p, q)), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p))))), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true), true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.64 = { by axiom 1 (implies_definition) }
% 56.85/7.64 ifeq(ifeq(theorem(implies(implies(not(implies(p, q)), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p))))), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true), true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.64 = { by axiom 1 (implies_definition) }
% 56.85/7.64 ifeq(ifeq(theorem(implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p))))), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true), true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.64 = { by axiom 2 (ifeq_axiom) R->L }
% 56.85/7.64 ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p))))), true), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true), true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.64 = { by axiom 4 (rule_1) R->L }
% 56.85/7.64 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), or(not(not(implies(p, q))), implies(q, p)))), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p)))))), true, theorem(implies(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), or(not(not(implies(p, q))), implies(q, p)))), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p)))))), true), true, theorem(implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p))))), true), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true), true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.64 = { by axiom 1 (implies_definition) }
% 56.85/7.65 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), or(not(not(implies(p, q))), implies(q, p)))), or(not(or(not(not(implies(p, q))), or(p, not(implies(p, q))))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p)))))), true, theorem(implies(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), or(not(not(implies(p, q))), implies(q, p)))), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p)))))), true), true, theorem(implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p))))), true), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true), true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.65 = { by axiom 1 (implies_definition) }
% 56.85/7.65 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(or(not(not(implies(p, q))), or(p, not(implies(p, q))))), or(not(not(implies(p, q))), implies(q, p)))), or(not(or(not(not(implies(p, q))), or(p, not(implies(p, q))))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p)))))), true, theorem(implies(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), or(not(not(implies(p, q))), implies(q, p)))), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p)))))), true), true, theorem(implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p))))), true), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true), true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.65 = { by axiom 1 (implies_definition) }
% 56.85/7.65 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(or(not(not(implies(p, q))), or(p, not(implies(p, q))))), or(not(not(implies(p, q))), implies(q, p)))), or(not(or(not(not(implies(p, q))), or(p, not(implies(p, q))))), or(not(implies(or(p, not(implies(p, q))), implies(q, p))), or(not(not(implies(p, q))), implies(q, p)))))), true, theorem(implies(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), or(not(not(implies(p, q))), implies(q, p)))), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p)))))), true), true, theorem(implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p))))), true), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true), true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.65 = { by axiom 1 (implies_definition) }
% 56.85/7.65 ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(implies(or(p, not(implies(p, q))), implies(q, p))), or(not(or(not(not(implies(p, q))), or(p, not(implies(p, q))))), or(not(not(implies(p, q))), implies(q, p)))), or(not(or(not(not(implies(p, q))), or(p, not(implies(p, q))))), or(not(implies(or(p, not(implies(p, q))), implies(q, p))), or(not(not(implies(p, q))), implies(q, p)))))), true, theorem(implies(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), or(not(not(implies(p, q))), implies(q, p)))), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p)))))), true), true, theorem(implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p))))), true), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true), true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.65 = { by axiom 8 (axiom_1_5) }
% 56.85/7.65 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), or(not(not(implies(p, q))), implies(q, p)))), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p)))))), true), true, theorem(implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p))))), true), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true), true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.65 = { by axiom 2 (ifeq_axiom) }
% 56.85/7.66 ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), or(not(not(implies(p, q))), implies(q, p)))), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p)))))), true, theorem(implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p))))), true), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true), true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.66 = { by axiom 2 (ifeq_axiom) R->L }
% 56.85/7.66 ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), or(not(not(implies(p, q))), implies(q, p)))), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p)))))), true, ifeq(true, true, theorem(implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p))))), true), true), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true), true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.66 = { by axiom 4 (rule_1) R->L }
% 56.85/7.67 ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), or(not(not(implies(p, q))), implies(q, p)))), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p)))))), true, ifeq(ifeq(axiom(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), or(not(not(implies(p, q))), implies(q, p))))), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), or(not(not(implies(p, q))), implies(q, p))))), true), true, theorem(implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p))))), true), true), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true), true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.67 = { by axiom 7 (axiom_1_6) }
% 56.85/7.67 ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), or(not(not(implies(p, q))), implies(q, p)))), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p)))))), true, ifeq(ifeq(true, true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), or(not(not(implies(p, q))), implies(q, p))))), true), true, theorem(implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p))))), true), true), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true), true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.67 = { by axiom 2 (ifeq_axiom) }
% 56.85/7.67 ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), or(not(not(implies(p, q))), implies(q, p)))), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p)))))), true, ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), or(not(not(implies(p, q))), implies(q, p))))), true, theorem(implies(or(not(not(implies(p, q))), or(p, not(implies(p, q)))), implies(implies(or(p, not(implies(p, q))), implies(q, p)), or(not(not(implies(p, q))), implies(q, p))))), true), true), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true), true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.67 = { by axiom 6 (rule_2) }
% 56.85/7.67 ifeq(ifeq(true, true, theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true), true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.67 = { by axiom 2 (ifeq_axiom) }
% 56.85/7.67 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(true, true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.67 = { by axiom 6 (rule_2) R->L }
% 56.85/7.67 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.67 = { by axiom 2 (ifeq_axiom) R->L }
% 56.85/7.67 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.67 = { by axiom 6 (rule_2) R->L }
% 56.85/7.67 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))))), true, ifeq(theorem(implies(or(p, not(implies(p, q))), implies(implies(p, q), p))), true, theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true), true), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.67 = { by axiom 1 (implies_definition) }
% 56.85/7.67 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))))), true, ifeq(theorem(implies(or(p, not(implies(p, q))), or(not(implies(p, q)), p))), true, theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true), true), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.67 = { by axiom 2 (ifeq_axiom) R->L }
% 56.85/7.68 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))))), true, ifeq(ifeq(true, true, theorem(implies(or(p, not(implies(p, q))), or(not(implies(p, q)), p))), true), true, theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true), true), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.68 = { by axiom 5 (axiom_1_4) R->L }
% 56.85/7.68 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))))), true, ifeq(ifeq(axiom(implies(or(p, not(implies(p, q))), or(not(implies(p, q)), p))), true, theorem(implies(or(p, not(implies(p, q))), or(not(implies(p, q)), p))), true), true, theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true), true), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.68 = { by axiom 4 (rule_1) }
% 56.85/7.68 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))))), true, ifeq(true, true, theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true), true), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.68 = { by axiom 2 (ifeq_axiom) }
% 56.85/7.68 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))))), true, theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.68 = { by axiom 2 (ifeq_axiom) R->L }
% 56.85/7.68 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))))), true), true, theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.68 = { by axiom 4 (rule_1) R->L }
% 56.85/7.68 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, q), p), implies(implies(q, implies(p, q)), implies(q, p)))), true, theorem(implies(implies(implies(p, q), p), implies(implies(q, implies(p, q)), implies(q, p)))), true), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))))), true), true, theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.68 = { by axiom 1 (implies_definition) }
% 56.85/7.68 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, q), p), implies(implies(q, implies(p, q)), or(not(q), p)))), true, theorem(implies(implies(implies(p, q), p), implies(implies(q, implies(p, q)), implies(q, p)))), true), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))))), true), true, theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.68 = { by axiom 1 (implies_definition) }
% 56.85/7.68 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, q), p), implies(or(not(q), implies(p, q)), or(not(q), p)))), true, theorem(implies(implies(implies(p, q), p), implies(implies(q, implies(p, q)), implies(q, p)))), true), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))))), true), true, theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.68 = { by axiom 7 (axiom_1_6) }
% 56.85/7.68 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(p, q), p), implies(implies(q, implies(p, q)), implies(q, p)))), true), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))))), true), true, theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.69 = { by axiom 2 (ifeq_axiom) }
% 56.85/7.69 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, q), p), implies(implies(q, implies(p, q)), implies(q, p)))), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))))), true), true, theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.69 = { by axiom 2 (ifeq_axiom) R->L }
% 56.85/7.69 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(implies(implies(p, q), p), implies(implies(q, implies(p, q)), implies(q, p)))), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))))), true), true), true, theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.69 = { by axiom 4 (rule_1) R->L }
% 56.85/7.69 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(p, q), p), implies(implies(q, implies(p, q)), implies(q, p))), implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))))), true, theorem(implies(implies(implies(implies(p, q), p), implies(implies(q, implies(p, q)), implies(q, p))), implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))))), true), true, ifeq(theorem(implies(implies(implies(p, q), p), implies(implies(q, implies(p, q)), implies(q, p)))), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))))), true), true), true, theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.69 = { by axiom 1 (implies_definition) }
% 56.85/7.69 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(p, q), p), implies(implies(q, implies(p, q)), implies(q, p))), implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), or(not(or(p, not(implies(p, q)))), implies(implies(q, implies(p, q)), implies(q, p)))))), true, theorem(implies(implies(implies(implies(p, q), p), implies(implies(q, implies(p, q)), implies(q, p))), implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))))), true), true, ifeq(theorem(implies(implies(implies(p, q), p), implies(implies(q, implies(p, q)), implies(q, p)))), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))))), true), true), true, theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.69 = { by axiom 1 (implies_definition) }
% 56.85/7.69 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(p, q), p), implies(implies(q, implies(p, q)), implies(q, p))), implies(or(not(or(p, not(implies(p, q)))), implies(implies(p, q), p)), or(not(or(p, not(implies(p, q)))), implies(implies(q, implies(p, q)), implies(q, p)))))), true, theorem(implies(implies(implies(implies(p, q), p), implies(implies(q, implies(p, q)), implies(q, p))), implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))))), true), true, ifeq(theorem(implies(implies(implies(p, q), p), implies(implies(q, implies(p, q)), implies(q, p)))), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))))), true), true), true, theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.69 = { by axiom 7 (axiom_1_6) }
% 56.85/7.69 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(implies(p, q), p), implies(implies(q, implies(p, q)), implies(q, p))), implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))))), true), true, ifeq(theorem(implies(implies(implies(p, q), p), implies(implies(q, implies(p, q)), implies(q, p)))), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))))), true), true), true, theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.70 = { by axiom 2 (ifeq_axiom) }
% 56.85/7.70 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, q), p), implies(implies(q, implies(p, q)), implies(q, p))), implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))))), true, ifeq(theorem(implies(implies(implies(p, q), p), implies(implies(q, implies(p, q)), implies(q, p)))), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(p, q), p)), implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))))), true), true), true, theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.70 = { by axiom 6 (rule_2) }
% 56.85/7.70 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.70 = { by axiom 2 (ifeq_axiom) }
% 56.85/7.70 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.70 = { by axiom 2 (ifeq_axiom) R->L }
% 56.85/7.70 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 56.85/7.70 = { by axiom 4 (rule_1) R->L }
% 57.66/7.70 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))), implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p))))), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))), implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p))))), true), true, ifeq(theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 57.66/7.70 = { by axiom 1 (implies_definition) }
% 57.66/7.70 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))), or(not(implies(q, implies(p, q))), implies(or(p, not(implies(p, q))), implies(q, p))))), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))), implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p))))), true), true, ifeq(theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 57.66/7.70 = { by axiom 1 (implies_definition) }
% 57.66/7.70 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, not(implies(p, q))), or(not(implies(q, implies(p, q))), implies(q, p))), or(not(implies(q, implies(p, q))), implies(or(p, not(implies(p, q))), implies(q, p))))), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))), implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p))))), true), true, ifeq(theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 57.66/7.70 = { by axiom 1 (implies_definition) }
% 57.66/7.71 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, not(implies(p, q))), or(not(implies(q, implies(p, q))), implies(q, p))), or(not(implies(q, implies(p, q))), or(not(or(p, not(implies(p, q)))), implies(q, p))))), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))), implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p))))), true), true, ifeq(theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 57.66/7.71 = { by axiom 1 (implies_definition) }
% 57.66/7.71 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(or(p, not(implies(p, q)))), or(not(implies(q, implies(p, q))), implies(q, p))), or(not(implies(q, implies(p, q))), or(not(or(p, not(implies(p, q)))), implies(q, p))))), true, theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))), implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p))))), true), true, ifeq(theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 57.66/7.71 = { by axiom 8 (axiom_1_5) }
% 57.66/7.71 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))), implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p))))), true), true, ifeq(theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 57.66/7.71 = { by axiom 2 (ifeq_axiom) }
% 57.66/7.71 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p))), implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p))))), true, ifeq(theorem(implies(or(p, not(implies(p, q))), implies(implies(q, implies(p, q)), implies(q, p)))), true, theorem(implies(implies(q, implies(p, q)), implies(or(p, not(implies(p, q))), implies(q, p)))), true), true), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 57.66/7.71 = { by axiom 6 (rule_2) }
% 57.66/7.71 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(true, true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 57.66/7.71 = { by axiom 2 (ifeq_axiom) }
% 57.66/7.71 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 57.66/7.71 = { by axiom 2 (ifeq_axiom) R->L }
% 57.66/7.71 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(q, implies(p, q))), true), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 57.66/7.71 = { by axiom 3 (axiom_1_3) R->L }
% 57.66/7.71 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(axiom(implies(q, or(not(p), q))), true, theorem(implies(q, implies(p, q))), true), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 57.66/7.71 = { by axiom 1 (implies_definition) R->L }
% 57.66/7.71 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(ifeq(axiom(implies(q, implies(p, q))), true, theorem(implies(q, implies(p, q))), true), true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 57.66/7.71 = { by axiom 4 (rule_1) }
% 57.66/7.71 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(ifeq(true, true, theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 57.66/7.71 = { by axiom 2 (ifeq_axiom) }
% 57.66/7.71 ifeq(theorem(implies(implies(or(p, not(implies(p, q))), implies(q, p)), implies(not(implies(p, q)), implies(q, p)))), true, ifeq(theorem(implies(or(p, not(implies(p, q))), implies(q, p))), true, theorem(implies(not(implies(p, q)), implies(q, p))), true), true)
% 57.66/7.71 = { by axiom 6 (rule_2) }
% 57.66/7.71 true
% 57.66/7.71 % SZS output end Proof
% 57.66/7.71
% 57.66/7.71 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------