%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL211-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 11:49:21 AM UTC 2026
% Result : Unsatisfiable 115.69s 15.16s
% Output : Proof 117.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL211-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n009.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sun Sep 27 15:26:44 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 115.69/15.16 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
% 115.69/15.16
% 115.69/15.16 % SZS status Unsatisfiable
% 115.69/15.16
% 116.51/15.29 % SZS output start Proof
% 116.51/15.29 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 116.51/15.29 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 116.51/15.29 Axiom 3 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 116.51/15.29 Axiom 4 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 116.51/15.29 Axiom 5 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 116.51/15.29 Axiom 6 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 116.51/15.29 Axiom 7 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 116.51/15.29 Axiom 8 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 116.51/15.29 Axiom 9 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 116.51/15.29
% 116.51/15.29 Goal 1 (prove_this): theorem(implies(not(q), implies(or(p, q), p))) = true.
% 116.51/15.29 Proof:
% 116.51/15.30 theorem(implies(not(q), implies(or(p, q), p)))
% 116.51/15.30 = { by axiom 2 (ifeq_axiom) R->L }
% 116.51/15.30 ifeq(true, true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 116.51/15.30 = { by axiom 7 (rule_2) R->L }
% 116.51/15.30 ifeq(ifeq(theorem(implies(or(q, implies(not(q), implies(or(p, q), p))), or(implies(not(q), implies(or(p, q), p)), q))), true, ifeq(theorem(or(q, implies(not(q), implies(or(p, q), p)))), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 116.51/15.30 = { by axiom 2 (ifeq_axiom) R->L }
% 116.51/15.30 ifeq(ifeq(ifeq(true, true, theorem(implies(or(q, implies(not(q), implies(or(p, q), p))), or(implies(not(q), implies(or(p, q), p)), q))), true), true, ifeq(theorem(or(q, implies(not(q), implies(or(p, q), p)))), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 116.51/15.30 = { by axiom 6 (axiom_1_4) R->L }
% 116.51/15.30 ifeq(ifeq(ifeq(axiom(implies(or(q, implies(not(q), implies(or(p, q), p))), or(implies(not(q), implies(or(p, q), p)), q))), true, theorem(implies(or(q, implies(not(q), implies(or(p, q), p))), or(implies(not(q), implies(or(p, q), p)), q))), true), true, ifeq(theorem(or(q, implies(not(q), implies(or(p, q), p)))), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 116.51/15.30 = { by axiom 5 (rule_1) }
% 116.51/15.30 ifeq(ifeq(true, true, ifeq(theorem(or(q, implies(not(q), implies(or(p, q), p)))), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 116.51/15.30 = { by axiom 2 (ifeq_axiom) }
% 116.51/15.30 ifeq(ifeq(theorem(or(q, implies(not(q), implies(or(p, q), p)))), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 116.51/15.30 = { by axiom 2 (ifeq_axiom) R->L }
% 116.51/15.30 ifeq(ifeq(ifeq(true, true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.30 = { by axiom 7 (rule_2) R->L }
% 117.28/15.30 ifeq(ifeq(ifeq(ifeq(theorem(implies(or(q, implies(or(p, q), p)), implies(not(q), or(q, implies(or(p, q), p))))), true, ifeq(theorem(or(q, implies(or(p, q), p))), true, theorem(implies(not(q), or(q, implies(or(p, q), p)))), true), true), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.30 = { by axiom 2 (ifeq_axiom) R->L }
% 117.28/15.30 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(q, implies(or(p, q), p)), implies(not(q), or(q, implies(or(p, q), p))))), true), true, ifeq(theorem(or(q, implies(or(p, q), p))), true, theorem(implies(not(q), or(q, implies(or(p, q), p)))), true), true), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.30 = { by axiom 3 (axiom_1_3) R->L }
% 117.28/15.30 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(q, implies(or(p, q), p)), or(not(not(q)), or(q, implies(or(p, q), p))))), true, theorem(implies(or(q, implies(or(p, q), p)), implies(not(q), or(q, implies(or(p, q), p))))), true), true, ifeq(theorem(or(q, implies(or(p, q), p))), true, theorem(implies(not(q), or(q, implies(or(p, q), p)))), true), true), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.30 = { by axiom 1 (implies_definition) R->L }
% 117.28/15.30 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(q, implies(or(p, q), p)), implies(not(q), or(q, implies(or(p, q), p))))), true, theorem(implies(or(q, implies(or(p, q), p)), implies(not(q), or(q, implies(or(p, q), p))))), true), true, ifeq(theorem(or(q, implies(or(p, q), p))), true, theorem(implies(not(q), or(q, implies(or(p, q), p)))), true), true), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.30 = { by axiom 5 (rule_1) }
% 117.28/15.30 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(q, implies(or(p, q), p))), true, theorem(implies(not(q), or(q, implies(or(p, q), p)))), true), true), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.30 = { by axiom 2 (ifeq_axiom) }
% 117.28/15.30 ifeq(ifeq(ifeq(ifeq(theorem(or(q, implies(or(p, q), p))), true, theorem(implies(not(q), or(q, implies(or(p, q), p)))), true), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.30 = { by axiom 2 (ifeq_axiom) R->L }
% 117.28/15.30 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(q, implies(or(p, q), p))), true), true, theorem(implies(not(q), or(q, implies(or(p, q), p)))), true), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.30 = { by axiom 5 (rule_1) R->L }
% 117.28/15.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, q), or(q, p)), or(q, implies(or(p, q), p)))), true, theorem(implies(implies(or(p, q), or(q, p)), or(q, implies(or(p, q), p)))), true), true, theorem(or(q, implies(or(p, q), p))), true), true, theorem(implies(not(q), or(q, implies(or(p, q), p)))), true), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.31 = { by axiom 1 (implies_definition) }
% 117.28/15.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, q), or(q, p)), or(q, or(not(or(p, q)), p)))), true, theorem(implies(implies(or(p, q), or(q, p)), or(q, implies(or(p, q), p)))), true), true, theorem(or(q, implies(or(p, q), p))), true), true, theorem(implies(not(q), or(q, implies(or(p, q), p)))), true), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.31 = { by axiom 1 (implies_definition) }
% 117.28/15.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(or(p, q)), or(q, p)), or(q, or(not(or(p, q)), p)))), true, theorem(implies(implies(or(p, q), or(q, p)), or(q, implies(or(p, q), p)))), true), true, theorem(or(q, implies(or(p, q), p))), true), true, theorem(implies(not(q), or(q, implies(or(p, q), p)))), true), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.31 = { by axiom 9 (axiom_1_5) }
% 117.28/15.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(p, q), or(q, p)), or(q, implies(or(p, q), p)))), true), true, theorem(or(q, implies(or(p, q), p))), true), true, theorem(implies(not(q), or(q, implies(or(p, q), p)))), true), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.31 = { by axiom 2 (ifeq_axiom) }
% 117.28/15.31 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, q), or(q, p)), or(q, implies(or(p, q), p)))), true, theorem(or(q, implies(or(p, q), p))), true), true, theorem(implies(not(q), or(q, implies(or(p, q), p)))), true), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.31 = { by axiom 2 (ifeq_axiom) R->L }
% 117.28/15.31 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, q), or(q, p)), or(q, implies(or(p, q), p)))), true, ifeq(true, true, theorem(or(q, implies(or(p, q), p))), true), true), true, theorem(implies(not(q), or(q, implies(or(p, q), p)))), true), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.31 = { by axiom 5 (rule_1) R->L }
% 117.28/15.31 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, q), or(q, p)), or(q, implies(or(p, q), p)))), true, ifeq(ifeq(axiom(implies(or(p, q), or(q, p))), true, theorem(implies(or(p, q), or(q, p))), true), true, theorem(or(q, implies(or(p, q), p))), true), true), true, theorem(implies(not(q), or(q, implies(or(p, q), p)))), true), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.31 = { by axiom 6 (axiom_1_4) }
% 117.28/15.31 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, q), or(q, p)), or(q, implies(or(p, q), p)))), true, ifeq(ifeq(true, true, theorem(implies(or(p, q), or(q, p))), true), true, theorem(or(q, implies(or(p, q), p))), true), true), true, theorem(implies(not(q), or(q, implies(or(p, q), p)))), true), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.31 = { by axiom 2 (ifeq_axiom) }
% 117.28/15.31 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, q), or(q, p)), or(q, implies(or(p, q), p)))), true, ifeq(theorem(implies(or(p, q), or(q, p))), true, theorem(or(q, implies(or(p, q), p))), true), true), true, theorem(implies(not(q), or(q, implies(or(p, q), p)))), true), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.31 = { by axiom 7 (rule_2) }
% 117.28/15.31 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(not(q), or(q, implies(or(p, q), p)))), true), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.31 = { by axiom 2 (ifeq_axiom) }
% 117.28/15.31 ifeq(ifeq(ifeq(theorem(implies(not(q), or(q, implies(or(p, q), p)))), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.31 = { by axiom 2 (ifeq_axiom) R->L }
% 117.28/15.31 ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(not(q), or(q, implies(or(p, q), p)))), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.31 = { by axiom 5 (rule_1) R->L }
% 117.28/15.31 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(q), or(q, implies(or(p, q), p))), or(q, implies(not(q), implies(or(p, q), p))))), true, theorem(implies(implies(not(q), or(q, implies(or(p, q), p))), or(q, implies(not(q), implies(or(p, q), p))))), true), true, ifeq(theorem(implies(not(q), or(q, implies(or(p, q), p)))), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.31 = { by axiom 1 (implies_definition) }
% 117.28/15.32 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(q), or(q, implies(or(p, q), p))), or(q, or(not(not(q)), implies(or(p, q), p))))), true, theorem(implies(implies(not(q), or(q, implies(or(p, q), p))), or(q, implies(not(q), implies(or(p, q), p))))), true), true, ifeq(theorem(implies(not(q), or(q, implies(or(p, q), p)))), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.32 = { by axiom 1 (implies_definition) }
% 117.28/15.32 ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(not(q)), or(q, implies(or(p, q), p))), or(q, or(not(not(q)), implies(or(p, q), p))))), true, theorem(implies(implies(not(q), or(q, implies(or(p, q), p))), or(q, implies(not(q), implies(or(p, q), p))))), true), true, ifeq(theorem(implies(not(q), or(q, implies(or(p, q), p)))), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.32 = { by axiom 9 (axiom_1_5) }
% 117.28/15.32 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(q), or(q, implies(or(p, q), p))), or(q, implies(not(q), implies(or(p, q), p))))), true), true, ifeq(theorem(implies(not(q), or(q, implies(or(p, q), p)))), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.32 = { by axiom 2 (ifeq_axiom) }
% 117.28/15.32 ifeq(ifeq(ifeq(theorem(implies(implies(not(q), or(q, implies(or(p, q), p))), or(q, implies(not(q), implies(or(p, q), p))))), true, ifeq(theorem(implies(not(q), or(q, implies(or(p, q), p)))), true, theorem(or(q, implies(not(q), implies(or(p, q), p)))), true), true), true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.32 = { by axiom 7 (rule_2) }
% 117.28/15.32 ifeq(ifeq(true, true, theorem(or(implies(not(q), implies(or(p, q), p)), q)), true), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.32 = { by axiom 2 (ifeq_axiom) }
% 117.28/15.32 ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true)
% 117.28/15.32 = { by axiom 2 (ifeq_axiom) R->L }
% 117.28/15.32 ifeq(true, true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.32 = { by axiom 7 (rule_2) R->L }
% 117.28/15.32 ifeq(ifeq(theorem(implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p))))), true, ifeq(theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.32 = { by axiom 2 (ifeq_axiom) R->L }
% 117.28/15.32 ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p))))), true), true, ifeq(theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.32 = { by axiom 5 (rule_1) R->L }
% 117.28/15.32 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))), implies(not(q), implies(or(p, q), p))), implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))))), true, theorem(implies(implies(or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))), implies(not(q), implies(or(p, q), p))), implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))))), true), true, theorem(implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p))))), true), true, ifeq(theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.33 = { by axiom 1 (implies_definition) }
% 117.28/15.33 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))), implies(not(q), implies(or(p, q), p))), implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), or(not(or(implies(not(q), implies(or(p, q), p)), q)), implies(not(q), implies(or(p, q), p)))))), true, theorem(implies(implies(or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))), implies(not(q), implies(or(p, q), p))), implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))))), true), true, theorem(implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p))))), true), true, ifeq(theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.33 = { by axiom 1 (implies_definition) }
% 117.28/15.33 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))), implies(not(q), implies(or(p, q), p))), implies(or(not(or(implies(not(q), implies(or(p, q), p)), q)), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), or(not(or(implies(not(q), implies(or(p, q), p)), q)), implies(not(q), implies(or(p, q), p)))))), true, theorem(implies(implies(or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))), implies(not(q), implies(or(p, q), p))), implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))))), true), true, theorem(implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p))))), true), true, ifeq(theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.33 = { by axiom 8 (axiom_1_6) }
% 117.28/15.33 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))), implies(not(q), implies(or(p, q), p))), implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))))), true), true, theorem(implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p))))), true), true, ifeq(theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.33 = { by axiom 2 (ifeq_axiom) }
% 117.28/15.34 ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))), implies(not(q), implies(or(p, q), p))), implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))))), true, theorem(implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p))))), true), true, ifeq(theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.34 = { by axiom 2 (ifeq_axiom) R->L }
% 117.28/15.34 ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))), implies(not(q), implies(or(p, q), p))), implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))))), true, ifeq(true, true, theorem(implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p))))), true), true), true, ifeq(theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.34 = { by axiom 5 (rule_1) R->L }
% 117.28/15.34 ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))), implies(not(q), implies(or(p, q), p))), implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))))), true, ifeq(ifeq(axiom(implies(or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))), implies(not(q), implies(or(p, q), p)))), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))), implies(not(q), implies(or(p, q), p)))), true), true, theorem(implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p))))), true), true), true, ifeq(theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.34 = { by axiom 4 (axiom_1_2) }
% 117.28/15.34 ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))), implies(not(q), implies(or(p, q), p))), implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))))), true, ifeq(ifeq(true, true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))), implies(not(q), implies(or(p, q), p)))), true), true, theorem(implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p))))), true), true), true, ifeq(theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.35 = { by axiom 2 (ifeq_axiom) }
% 117.28/15.35 ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))), implies(not(q), implies(or(p, q), p))), implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))))), true, ifeq(theorem(implies(or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))), implies(not(q), implies(or(p, q), p)))), true, theorem(implies(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))), implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p))))), true), true), true, ifeq(theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.35 = { by axiom 7 (rule_2) }
% 117.28/15.35 ifeq(ifeq(true, true, ifeq(theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.35 = { by axiom 2 (ifeq_axiom) }
% 117.28/15.35 ifeq(ifeq(theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.35 = { by axiom 2 (ifeq_axiom) R->L }
% 117.28/15.35 ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.35 = { by axiom 7 (rule_2) R->L }
% 117.28/15.35 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(q), or(not(q), implies(or(p, q), p))), or(not(q), implies(not(q), implies(or(p, q), p))))), true, ifeq(theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.35 = { by axiom 2 (ifeq_axiom) R->L }
% 117.28/15.35 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(q), or(not(q), implies(or(p, q), p))), or(not(q), implies(not(q), implies(or(p, q), p))))), true), true, ifeq(theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.35 = { by axiom 9 (axiom_1_5) R->L }
% 117.28/15.35 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(not(q)), or(not(q), implies(or(p, q), p))), or(not(q), or(not(not(q)), implies(or(p, q), p))))), true, theorem(implies(implies(not(q), or(not(q), implies(or(p, q), p))), or(not(q), implies(not(q), implies(or(p, q), p))))), true), true, ifeq(theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.35 = { by axiom 1 (implies_definition) R->L }
% 117.28/15.35 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(q), or(not(q), implies(or(p, q), p))), or(not(q), or(not(not(q)), implies(or(p, q), p))))), true, theorem(implies(implies(not(q), or(not(q), implies(or(p, q), p))), or(not(q), implies(not(q), implies(or(p, q), p))))), true), true, ifeq(theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.35 = { by axiom 1 (implies_definition) R->L }
% 117.28/15.35 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(q), or(not(q), implies(or(p, q), p))), or(not(q), implies(not(q), implies(or(p, q), p))))), true, theorem(implies(implies(not(q), or(not(q), implies(or(p, q), p))), or(not(q), implies(not(q), implies(or(p, q), p))))), true), true, ifeq(theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.35 = { by axiom 5 (rule_1) }
% 117.28/15.35 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.36 = { by axiom 2 (ifeq_axiom) }
% 117.28/15.36 ifeq(ifeq(ifeq(ifeq(theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.36 = { by axiom 2 (ifeq_axiom) R->L }
% 117.28/15.36 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.36 = { by axiom 7 (rule_2) R->L }
% 117.28/15.36 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(or(p, q), p), not(q)), or(not(q), implies(or(p, q), p))), implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p)))))), true, ifeq(theorem(implies(or(implies(or(p, q), p), not(q)), or(not(q), implies(or(p, q), p)))), true, theorem(implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p))))), true), true), true, theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.36 = { by axiom 2 (ifeq_axiom) R->L }
% 117.28/15.36 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(or(p, q), p), not(q)), or(not(q), implies(or(p, q), p))), implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p)))))), true, ifeq(ifeq(true, true, theorem(implies(or(implies(or(p, q), p), not(q)), or(not(q), implies(or(p, q), p)))), true), true, theorem(implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p))))), true), true), true, theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.36 = { by axiom 6 (axiom_1_4) R->L }
% 117.28/15.36 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(or(p, q), p), not(q)), or(not(q), implies(or(p, q), p))), implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p)))))), true, ifeq(ifeq(axiom(implies(or(implies(or(p, q), p), not(q)), or(not(q), implies(or(p, q), p)))), true, theorem(implies(or(implies(or(p, q), p), not(q)), or(not(q), implies(or(p, q), p)))), true), true, theorem(implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p))))), true), true), true, theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.36 = { by axiom 5 (rule_1) }
% 117.28/15.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(or(p, q), p), not(q)), or(not(q), implies(or(p, q), p))), implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p)))))), true, ifeq(true, true, theorem(implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p))))), true), true), true, theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.37 = { by axiom 2 (ifeq_axiom) }
% 117.28/15.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(implies(or(p, q), p), not(q)), or(not(q), implies(or(p, q), p))), implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p)))))), true, theorem(implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p))))), true), true, theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.37 = { by axiom 2 (ifeq_axiom) R->L }
% 117.28/15.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(implies(or(p, q), p), not(q)), or(not(q), implies(or(p, q), p))), implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p)))))), true), true, theorem(implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p))))), true), true, theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.37 = { by axiom 8 (axiom_1_6) R->L }
% 117.28/15.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(or(p, q), p), not(q)), or(not(q), implies(or(p, q), p))), implies(or(not(not(q)), or(implies(or(p, q), p), not(q))), or(not(not(q)), or(not(q), implies(or(p, q), p)))))), true, theorem(implies(implies(or(implies(or(p, q), p), not(q)), or(not(q), implies(or(p, q), p))), implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p)))))), true), true, theorem(implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p))))), true), true, theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.37 = { by axiom 1 (implies_definition) R->L }
% 117.28/15.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(or(p, q), p), not(q)), or(not(q), implies(or(p, q), p))), implies(implies(not(q), or(implies(or(p, q), p), not(q))), or(not(not(q)), or(not(q), implies(or(p, q), p)))))), true, theorem(implies(implies(or(implies(or(p, q), p), not(q)), or(not(q), implies(or(p, q), p))), implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p)))))), true), true, theorem(implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p))))), true), true, theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.37 = { by axiom 1 (implies_definition) R->L }
% 117.28/15.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(implies(or(p, q), p), not(q)), or(not(q), implies(or(p, q), p))), implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p)))))), true, theorem(implies(implies(or(implies(or(p, q), p), not(q)), or(not(q), implies(or(p, q), p))), implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p)))))), true), true, theorem(implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p))))), true), true, theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.38 = { by axiom 5 (rule_1) }
% 117.28/15.38 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p))))), true), true, theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.38 = { by axiom 2 (ifeq_axiom) }
% 117.28/15.38 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p))))), true, theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.38 = { by axiom 2 (ifeq_axiom) R->L }
% 117.28/15.38 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p))))), true, ifeq(true, true, theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true), true), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.38 = { by axiom 5 (rule_1) R->L }
% 117.28/15.38 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p))))), true, ifeq(ifeq(axiom(implies(not(q), or(implies(or(p, q), p), not(q)))), true, theorem(implies(not(q), or(implies(or(p, q), p), not(q)))), true), true, theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true), true), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.38 = { by axiom 3 (axiom_1_3) }
% 117.28/15.38 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p))))), true, ifeq(ifeq(true, true, theorem(implies(not(q), or(implies(or(p, q), p), not(q)))), true), true, theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true), true), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.38 = { by axiom 2 (ifeq_axiom) }
% 117.28/15.39 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(q), or(implies(or(p, q), p), not(q))), implies(not(q), or(not(q), implies(or(p, q), p))))), true, ifeq(theorem(implies(not(q), or(implies(or(p, q), p), not(q)))), true, theorem(implies(not(q), or(not(q), implies(or(p, q), p)))), true), true), true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.39 = { by axiom 7 (rule_2) }
% 117.28/15.39 ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.39 = { by axiom 2 (ifeq_axiom) }
% 117.28/15.39 ifeq(ifeq(ifeq(theorem(or(not(q), implies(not(q), implies(or(p, q), p)))), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.39 = { by axiom 1 (implies_definition) R->L }
% 117.28/15.39 ifeq(ifeq(ifeq(theorem(implies(q, implies(not(q), implies(or(p, q), p)))), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.39 = { by axiom 2 (ifeq_axiom) R->L }
% 117.28/15.39 ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(q, implies(not(q), implies(or(p, q), p)))), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.39 = { by axiom 5 (rule_1) R->L }
% 117.28/15.39 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(q, implies(not(q), implies(or(p, q), p))), implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))))), true, theorem(implies(implies(q, implies(not(q), implies(or(p, q), p))), implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))))), true), true, ifeq(theorem(implies(q, implies(not(q), implies(or(p, q), p)))), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.39 = { by axiom 8 (axiom_1_6) }
% 117.28/15.39 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(q, implies(not(q), implies(or(p, q), p))), implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))))), true), true, ifeq(theorem(implies(q, implies(not(q), implies(or(p, q), p)))), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.39 = { by axiom 2 (ifeq_axiom) }
% 117.28/15.39 ifeq(ifeq(ifeq(theorem(implies(implies(q, implies(not(q), implies(or(p, q), p))), implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p)))))), true, ifeq(theorem(implies(q, implies(not(q), implies(or(p, q), p)))), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), or(implies(not(q), implies(or(p, q), p)), implies(not(q), implies(or(p, q), p))))), true), true), true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.39 = { by axiom 7 (rule_2) }
% 117.28/15.39 ifeq(ifeq(true, true, theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.39 = { by axiom 2 (ifeq_axiom) }
% 117.28/15.39 ifeq(theorem(implies(or(implies(not(q), implies(or(p, q), p)), q), implies(not(q), implies(or(p, q), p)))), true, ifeq(theorem(or(implies(not(q), implies(or(p, q), p)), q)), true, theorem(implies(not(q), implies(or(p, q), p))), true), true)
% 117.28/15.39 = { by axiom 7 (rule_2) }
% 117.28/15.39 true
% 117.28/15.39 % SZS output end Proof
% 117.28/15.39
% 117.28/15.39 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------