%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL213-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 11:49:22 AM UTC 2026
% Result : Unsatisfiable 117.35s 15.23s
% Output : Proof 118.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL213-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 15:22:05 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 117.35/15.23 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
% 117.35/15.23
% 117.35/15.23 % SZS status Unsatisfiable
% 117.35/15.23
% 118.19/15.32 % SZS output start Proof
% 118.19/15.32 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 118.19/15.32 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 118.19/15.32 Axiom 3 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 118.19/15.32 Axiom 4 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 118.19/15.32 Axiom 5 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 118.19/15.32 Axiom 6 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 118.19/15.32 Axiom 7 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 118.19/15.33 Axiom 8 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 118.19/15.33
% 118.19/15.33 Goal 1 (prove_this): theorem(implies(implies(p, q), implies(implies(not(p), q), q))) = true.
% 118.19/15.33 Proof:
% 118.19/15.33 theorem(implies(implies(p, q), implies(implies(not(p), q), q)))
% 118.19/15.33 = { by axiom 2 (ifeq_axiom) R->L }
% 118.19/15.33 ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true)
% 118.19/15.33 = { by axiom 2 (ifeq_axiom) R->L }
% 118.19/15.33 ifeq(true, true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.33 = { by axiom 8 (rule_2) R->L }
% 118.19/15.33 ifeq(ifeq(theorem(implies(implies(implies(p, q), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q))))), true, ifeq(theorem(implies(implies(p, q), or(q, not(p)))), true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.33 = { by axiom 2 (ifeq_axiom) R->L }
% 118.19/15.33 ifeq(ifeq(theorem(implies(implies(implies(p, q), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q))))), true, ifeq(ifeq(true, true, theorem(implies(implies(p, q), or(q, not(p)))), true), true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.33 = { by axiom 5 (axiom_1_4) R->L }
% 118.19/15.33 ifeq(ifeq(theorem(implies(implies(implies(p, q), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q))))), true, ifeq(ifeq(axiom(implies(or(not(p), q), or(q, not(p)))), true, theorem(implies(implies(p, q), or(q, not(p)))), true), true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.33 = { by axiom 1 (implies_definition) R->L }
% 118.19/15.33 ifeq(ifeq(theorem(implies(implies(implies(p, q), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q))))), true, ifeq(ifeq(axiom(implies(implies(p, q), or(q, not(p)))), true, theorem(implies(implies(p, q), or(q, not(p)))), true), true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.33 = { by axiom 4 (rule_1) }
% 118.19/15.33 ifeq(ifeq(theorem(implies(implies(implies(p, q), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q))))), true, ifeq(true, true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.33 = { by axiom 2 (ifeq_axiom) }
% 118.19/15.33 ifeq(ifeq(theorem(implies(implies(implies(p, q), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q))))), true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.33 = { by axiom 1 (implies_definition) }
% 118.19/15.33 ifeq(ifeq(theorem(implies(implies(implies(p, q), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q))))), true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.33 = { by axiom 1 (implies_definition) }
% 118.19/15.34 ifeq(ifeq(theorem(implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q))))), true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.34 = { by axiom 2 (ifeq_axiom) R->L }
% 118.19/15.34 ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q))))), true), true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.34 = { by axiom 4 (rule_1) R->L }
% 118.19/15.34 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(or(not(implies(p, q)), or(q, not(p))), or(not(implies(p, q)), implies(implies(not(p), q), q)))), implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q)))))), true, theorem(implies(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(or(not(implies(p, q)), or(q, not(p))), or(not(implies(p, q)), implies(implies(not(p), q), q)))), implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q)))))), true), true, theorem(implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q))))), true), true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.34 = { by axiom 1 (implies_definition) }
% 118.19/15.34 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(or(not(implies(p, q)), or(q, not(p))), or(not(implies(p, q)), implies(implies(not(p), q), q)))), or(not(or(not(implies(p, q)), or(q, not(p)))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q)))))), true, theorem(implies(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(or(not(implies(p, q)), or(q, not(p))), or(not(implies(p, q)), implies(implies(not(p), q), q)))), implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q)))))), true), true, theorem(implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q))))), true), true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.34 = { by axiom 1 (implies_definition) }
% 118.19/15.34 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(or(not(implies(p, q)), or(q, not(p)))), or(not(implies(p, q)), implies(implies(not(p), q), q)))), or(not(or(not(implies(p, q)), or(q, not(p)))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q)))))), true, theorem(implies(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(or(not(implies(p, q)), or(q, not(p))), or(not(implies(p, q)), implies(implies(not(p), q), q)))), implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q)))))), true), true, theorem(implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q))))), true), true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.34 = { by axiom 1 (implies_definition) }
% 118.19/15.34 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(or(not(implies(p, q)), or(q, not(p)))), or(not(implies(p, q)), implies(implies(not(p), q), q)))), or(not(or(not(implies(p, q)), or(q, not(p)))), or(not(implies(or(q, not(p)), implies(implies(not(p), q), q))), or(not(implies(p, q)), implies(implies(not(p), q), q)))))), true, theorem(implies(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(or(not(implies(p, q)), or(q, not(p))), or(not(implies(p, q)), implies(implies(not(p), q), q)))), implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q)))))), true), true, theorem(implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q))))), true), true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.35 = { by axiom 1 (implies_definition) }
% 118.19/15.35 ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(implies(or(q, not(p)), implies(implies(not(p), q), q))), or(not(or(not(implies(p, q)), or(q, not(p)))), or(not(implies(p, q)), implies(implies(not(p), q), q)))), or(not(or(not(implies(p, q)), or(q, not(p)))), or(not(implies(or(q, not(p)), implies(implies(not(p), q), q))), or(not(implies(p, q)), implies(implies(not(p), q), q)))))), true, theorem(implies(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(or(not(implies(p, q)), or(q, not(p))), or(not(implies(p, q)), implies(implies(not(p), q), q)))), implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q)))))), true), true, theorem(implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q))))), true), true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.35 = { by axiom 7 (axiom_1_5) }
% 118.19/15.35 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(or(not(implies(p, q)), or(q, not(p))), or(not(implies(p, q)), implies(implies(not(p), q), q)))), implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q)))))), true), true, theorem(implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q))))), true), true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.35 = { by axiom 2 (ifeq_axiom) }
% 118.19/15.35 ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(or(not(implies(p, q)), or(q, not(p))), or(not(implies(p, q)), implies(implies(not(p), q), q)))), implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q)))))), true, theorem(implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q))))), true), true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.35 = { by axiom 2 (ifeq_axiom) R->L }
% 118.19/15.35 ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(or(not(implies(p, q)), or(q, not(p))), or(not(implies(p, q)), implies(implies(not(p), q), q)))), implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q)))))), true, ifeq(true, true, theorem(implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q))))), true), true), true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.35 = { by axiom 4 (rule_1) R->L }
% 118.19/15.35 ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(or(not(implies(p, q)), or(q, not(p))), or(not(implies(p, q)), implies(implies(not(p), q), q)))), implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q)))))), true, ifeq(ifeq(axiom(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(or(not(implies(p, q)), or(q, not(p))), or(not(implies(p, q)), implies(implies(not(p), q), q))))), true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(or(not(implies(p, q)), or(q, not(p))), or(not(implies(p, q)), implies(implies(not(p), q), q))))), true), true, theorem(implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q))))), true), true), true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.35 = { by axiom 6 (axiom_1_6) }
% 118.19/15.35 ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(or(not(implies(p, q)), or(q, not(p))), or(not(implies(p, q)), implies(implies(not(p), q), q)))), implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q)))))), true, ifeq(ifeq(true, true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(or(not(implies(p, q)), or(q, not(p))), or(not(implies(p, q)), implies(implies(not(p), q), q))))), true), true, theorem(implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q))))), true), true), true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.35 = { by axiom 2 (ifeq_axiom) }
% 118.19/15.36 ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(or(not(implies(p, q)), or(q, not(p))), or(not(implies(p, q)), implies(implies(not(p), q), q)))), implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q)))))), true, ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(or(not(implies(p, q)), or(q, not(p))), or(not(implies(p, q)), implies(implies(not(p), q), q))))), true, theorem(implies(or(not(implies(p, q)), or(q, not(p))), implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), or(not(implies(p, q)), implies(implies(not(p), q), q))))), true), true), true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.36 = { by axiom 8 (rule_2) }
% 118.19/15.36 ifeq(ifeq(true, true, theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.36 = { by axiom 2 (ifeq_axiom) }
% 118.19/15.36 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(true, true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.36 = { by axiom 8 (rule_2) R->L }
% 118.19/15.36 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), q)), implies(or(q, not(p)), implies(implies(not(p), q), q)))), true, ifeq(theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.36 = { by axiom 2 (ifeq_axiom) R->L }
% 118.19/15.36 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), q)), implies(or(q, not(p)), implies(implies(not(p), q), q)))), true), true, ifeq(theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.36 = { by axiom 7 (axiom_1_5) R->L }
% 118.19/15.36 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(axiom(implies(or(not(implies(not(p), q)), or(not(or(q, not(p))), q)), or(not(or(q, not(p))), or(not(implies(not(p), q)), q)))), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), q)), implies(or(q, not(p)), implies(implies(not(p), q), q)))), true), true, ifeq(theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.36 = { by axiom 1 (implies_definition) R->L }
% 118.19/15.36 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(axiom(implies(implies(implies(not(p), q), or(not(or(q, not(p))), q)), or(not(or(q, not(p))), or(not(implies(not(p), q)), q)))), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), q)), implies(or(q, not(p)), implies(implies(not(p), q), q)))), true), true, ifeq(theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.36 = { by axiom 1 (implies_definition) R->L }
% 118.19/15.36 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(axiom(implies(implies(implies(not(p), q), or(not(or(q, not(p))), q)), or(not(or(q, not(p))), implies(implies(not(p), q), q)))), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), q)), implies(or(q, not(p)), implies(implies(not(p), q), q)))), true), true, ifeq(theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.36 = { by axiom 1 (implies_definition) R->L }
% 118.19/15.36 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(axiom(implies(implies(implies(not(p), q), implies(or(q, not(p)), q)), or(not(or(q, not(p))), implies(implies(not(p), q), q)))), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), q)), implies(or(q, not(p)), implies(implies(not(p), q), q)))), true), true, ifeq(theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.36 = { by axiom 1 (implies_definition) R->L }
% 118.19/15.36 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(axiom(implies(implies(implies(not(p), q), implies(or(q, not(p)), q)), implies(or(q, not(p)), implies(implies(not(p), q), q)))), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), q)), implies(or(q, not(p)), implies(implies(not(p), q), q)))), true), true, ifeq(theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.36 = { by axiom 4 (rule_1) }
% 118.19/15.36 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(true, true, ifeq(theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.36 = { by axiom 2 (ifeq_axiom) }
% 118.19/15.37 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.37 = { by axiom 2 (ifeq_axiom) R->L }
% 118.19/15.37 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.37 = { by axiom 8 (rule_2) R->L }
% 118.19/15.37 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q)), implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q))))), true, ifeq(theorem(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q))), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true), true), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.37 = { by axiom 2 (ifeq_axiom) R->L }
% 118.19/15.37 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q)), implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q))))), true), true, ifeq(theorem(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q))), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true), true), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.37 = { by axiom 6 (axiom_1_6) R->L }
% 118.19/15.37 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q)), implies(or(not(implies(not(p), q)), implies(or(q, not(p)), or(q, q))), or(not(implies(not(p), q)), implies(or(q, not(p)), q))))), true, theorem(implies(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q)), implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q))))), true), true, ifeq(theorem(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q))), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true), true), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.37 = { by axiom 1 (implies_definition) R->L }
% 118.19/15.37 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q)), implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), or(not(implies(not(p), q)), implies(or(q, not(p)), q))))), true, theorem(implies(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q)), implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q))))), true), true, ifeq(theorem(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q))), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true), true), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.37 = { by axiom 1 (implies_definition) R->L }
% 118.19/15.37 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q)), implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q))))), true, theorem(implies(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q)), implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q))))), true), true, ifeq(theorem(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q))), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true), true), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.38 = { by axiom 4 (rule_1) }
% 118.19/15.38 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q))), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true), true), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.38 = { by axiom 2 (ifeq_axiom) }
% 118.19/15.38 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q))), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.38 = { by axiom 2 (ifeq_axiom) R->L }
% 118.19/15.38 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q))), true), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.38 = { by axiom 4 (rule_1) R->L }
% 118.19/15.38 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(q, q), q), implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q)))), true, theorem(implies(implies(or(q, q), q), implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q)))), true), true, theorem(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q))), true), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.38 = { by axiom 1 (implies_definition) }
% 118.19/15.38 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(q, q), q), implies(implies(or(q, not(p)), or(q, q)), or(not(or(q, not(p))), q)))), true, theorem(implies(implies(or(q, q), q), implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q)))), true), true, theorem(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q))), true), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.38 = { by axiom 1 (implies_definition) }
% 118.19/15.38 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(q, q), q), implies(or(not(or(q, not(p))), or(q, q)), or(not(or(q, not(p))), q)))), true, theorem(implies(implies(or(q, q), q), implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q)))), true), true, theorem(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q))), true), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.38 = { by axiom 6 (axiom_1_6) }
% 118.19/15.38 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(q, q), q), implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q)))), true), true, theorem(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q))), true), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.38 = { by axiom 2 (ifeq_axiom) }
% 118.19/15.39 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(q, q), q), implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q)))), true, theorem(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q))), true), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.39 = { by axiom 2 (ifeq_axiom) R->L }
% 118.19/15.39 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(q, q), q), implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q)))), true, ifeq(true, true, theorem(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q))), true), true), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.39 = { by axiom 4 (rule_1) R->L }
% 118.19/15.39 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(q, q), q), implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q)))), true, ifeq(ifeq(axiom(implies(or(q, q), q)), true, theorem(implies(or(q, q), q)), true), true, theorem(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q))), true), true), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.39 = { by axiom 3 (axiom_1_2) }
% 118.19/15.39 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(q, q), q), implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q)))), true, ifeq(ifeq(true, true, theorem(implies(or(q, q), q)), true), true, theorem(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q))), true), true), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.39 = { by axiom 2 (ifeq_axiom) }
% 118.19/15.39 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(q, q), q), implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q)))), true, ifeq(theorem(implies(or(q, q), q)), true, theorem(implies(implies(or(q, not(p)), or(q, q)), implies(or(q, not(p)), q))), true), true), true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.39 = { by axiom 8 (rule_2) }
% 118.19/15.39 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.39 = { by axiom 2 (ifeq_axiom) }
% 118.19/15.39 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.39 = { by axiom 2 (ifeq_axiom) R->L }
% 118.19/15.39 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true, ifeq(true, true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.39 = { by axiom 4 (rule_1) R->L }
% 118.19/15.39 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true, ifeq(ifeq(axiom(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q)))), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q)))), true), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.39 = { by axiom 6 (axiom_1_6) }
% 118.19/15.40 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true, ifeq(ifeq(true, true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q)))), true), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.40 = { by axiom 2 (ifeq_axiom) }
% 118.19/15.40 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(ifeq(theorem(implies(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q))), implies(implies(not(p), q), implies(or(q, not(p)), q)))), true, ifeq(theorem(implies(implies(not(p), q), implies(or(q, not(p)), or(q, q)))), true, theorem(implies(implies(not(p), q), implies(or(q, not(p)), q))), true), true), true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.40 = { by axiom 8 (rule_2) }
% 118.19/15.40 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(ifeq(true, true, theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.40 = { by axiom 2 (ifeq_axiom) }
% 118.19/15.40 ifeq(theorem(implies(implies(or(q, not(p)), implies(implies(not(p), q), q)), implies(implies(p, q), implies(implies(not(p), q), q)))), true, ifeq(theorem(implies(or(q, not(p)), implies(implies(not(p), q), q))), true, theorem(implies(implies(p, q), implies(implies(not(p), q), q))), true), true)
% 118.19/15.40 = { by axiom 8 (rule_2) }
% 118.19/15.40 true
% 118.19/15.40 % SZS output end Proof
% 118.19/15.40
% 118.19/15.40 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------