%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL202-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 11:49:19 AM UTC 2026
% Result : Unsatisfiable 14.89s 2.40s
% Output : Proof 17.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL202-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 15:27:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.89/2.40 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
% 14.89/2.40
% 14.89/2.40 % SZS status Unsatisfiable
% 14.89/2.40
% 16.48/2.55 % SZS output start Proof
% 16.48/2.55 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 16.48/2.55 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 16.48/2.55 Axiom 3 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 16.48/2.55 Axiom 4 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 16.48/2.55 Axiom 5 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 16.48/2.55 Axiom 6 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 16.48/2.55 Axiom 7 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 16.48/2.55 Axiom 8 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 16.48/2.55 Axiom 9 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 16.48/2.55
% 16.48/2.55 Goal 1 (prove_this): theorem(implies(not(or(p, q)), or(p, not(q)))) = true.
% 16.48/2.55 Proof:
% 16.48/2.55 theorem(implies(not(or(p, q)), or(p, not(q))))
% 16.48/2.55 = { by axiom 2 (ifeq_axiom) R->L }
% 16.48/2.55 ifeq(true, true, theorem(implies(not(or(p, q)), or(p, not(q)))), true)
% 16.48/2.55 = { by axiom 2 (ifeq_axiom) R->L }
% 16.48/2.55 ifeq(true, true, ifeq(true, true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.55 = { by axiom 9 (rule_2) R->L }
% 16.48/2.56 ifeq(ifeq(theorem(implies(or(not(not(q)), or(p, not(q))), or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q)))))), true, ifeq(theorem(or(not(not(q)), or(p, not(q)))), true, theorem(or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q))))), true), true), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.56 = { by axiom 1 (implies_definition) }
% 16.48/2.56 ifeq(ifeq(theorem(or(not(or(not(not(q)), or(p, not(q)))), or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q)))))), true, ifeq(theorem(or(not(not(q)), or(p, not(q)))), true, theorem(or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q))))), true), true), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.56 = { by axiom 2 (ifeq_axiom) R->L }
% 16.48/2.56 ifeq(ifeq(theorem(or(not(or(not(not(q)), or(p, not(q)))), or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q)))))), true, ifeq(ifeq(true, true, theorem(or(not(not(q)), or(p, not(q)))), true), true, theorem(or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q))))), true), true), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.56 = { by axiom 3 (axiom_1_3) R->L }
% 16.48/2.56 ifeq(ifeq(theorem(or(not(or(not(not(q)), or(p, not(q)))), or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q)))))), true, ifeq(ifeq(axiom(implies(not(q), or(p, not(q)))), true, theorem(or(not(not(q)), or(p, not(q)))), true), true, theorem(or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q))))), true), true), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.56 = { by axiom 1 (implies_definition) }
% 16.48/2.56 ifeq(ifeq(theorem(or(not(or(not(not(q)), or(p, not(q)))), or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q)))))), true, ifeq(ifeq(axiom(or(not(not(q)), or(p, not(q)))), true, theorem(or(not(not(q)), or(p, not(q)))), true), true, theorem(or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q))))), true), true), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.56 = { by axiom 5 (rule_1) }
% 16.48/2.56 ifeq(ifeq(theorem(or(not(or(not(not(q)), or(p, not(q)))), or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q)))))), true, ifeq(true, true, theorem(or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q))))), true), true), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.56 = { by axiom 2 (ifeq_axiom) }
% 16.48/2.56 ifeq(ifeq(theorem(or(not(or(not(not(q)), or(p, not(q)))), or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q)))))), true, theorem(or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q))))), true), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.56 = { by axiom 2 (ifeq_axiom) R->L }
% 16.48/2.56 ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(not(q)), or(p, not(q)))), or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q)))))), true), true, theorem(or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q))))), true), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.56 = { by axiom 7 (axiom_1_6) R->L }
% 16.48/2.56 ifeq(ifeq(ifeq(axiom(implies(implies(not(q), or(p, not(q))), implies(or(not(not(or(p, q))), not(q)), or(not(not(or(p, q))), or(p, not(q)))))), true, theorem(or(not(or(not(not(q)), or(p, not(q)))), or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q)))))), true), true, theorem(or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q))))), true), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.57 = { by axiom 1 (implies_definition) }
% 16.48/2.57 ifeq(ifeq(ifeq(axiom(or(not(implies(not(q), or(p, not(q)))), implies(or(not(not(or(p, q))), not(q)), or(not(not(or(p, q))), or(p, not(q)))))), true, theorem(or(not(or(not(not(q)), or(p, not(q)))), or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q)))))), true), true, theorem(or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q))))), true), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.57 = { by axiom 1 (implies_definition) }
% 16.48/2.57 ifeq(ifeq(ifeq(axiom(or(not(or(not(not(q)), or(p, not(q)))), implies(or(not(not(or(p, q))), not(q)), or(not(not(or(p, q))), or(p, not(q)))))), true, theorem(or(not(or(not(not(q)), or(p, not(q)))), or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q)))))), true), true, theorem(or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q))))), true), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.57 = { by axiom 1 (implies_definition) }
% 16.48/2.57 ifeq(ifeq(ifeq(axiom(or(not(or(not(not(q)), or(p, not(q)))), or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q)))))), true, theorem(or(not(or(not(not(q)), or(p, not(q)))), or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q)))))), true), true, theorem(or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q))))), true), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.57 = { by axiom 5 (rule_1) }
% 16.48/2.57 ifeq(ifeq(true, true, theorem(or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q))))), true), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.57 = { by axiom 2 (ifeq_axiom) }
% 16.48/2.57 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), or(not(not(or(p, q))), or(p, not(q))))), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.57 = { by axiom 1 (implies_definition) R->L }
% 16.48/2.57 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.57 = { by axiom 9 (rule_2) R->L }
% 16.48/2.57 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(theorem(implies(or(not(q), not(not(or(p, q)))), or(not(not(or(p, q))), not(q)))), true, ifeq(theorem(or(not(q), not(not(or(p, q))))), true, theorem(or(not(not(or(p, q))), not(q))), true), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.57 = { by axiom 1 (implies_definition) }
% 16.48/2.57 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(theorem(or(not(or(not(q), not(not(or(p, q))))), or(not(not(or(p, q))), not(q)))), true, ifeq(theorem(or(not(q), not(not(or(p, q))))), true, theorem(or(not(not(or(p, q))), not(q))), true), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.57 = { by axiom 2 (ifeq_axiom) R->L }
% 16.48/2.57 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(q), not(not(or(p, q))))), or(not(not(or(p, q))), not(q)))), true), true, ifeq(theorem(or(not(q), not(not(or(p, q))))), true, theorem(or(not(not(or(p, q))), not(q))), true), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.57 = { by axiom 6 (axiom_1_4) R->L }
% 16.48/2.57 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(axiom(implies(or(not(q), not(not(or(p, q)))), or(not(not(or(p, q))), not(q)))), true, theorem(or(not(or(not(q), not(not(or(p, q))))), or(not(not(or(p, q))), not(q)))), true), true, ifeq(theorem(or(not(q), not(not(or(p, q))))), true, theorem(or(not(not(or(p, q))), not(q))), true), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.58 = { by axiom 1 (implies_definition) }
% 16.48/2.58 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(axiom(or(not(or(not(q), not(not(or(p, q))))), or(not(not(or(p, q))), not(q)))), true, theorem(or(not(or(not(q), not(not(or(p, q))))), or(not(not(or(p, q))), not(q)))), true), true, ifeq(theorem(or(not(q), not(not(or(p, q))))), true, theorem(or(not(not(or(p, q))), not(q))), true), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.58 = { by axiom 5 (rule_1) }
% 16.48/2.58 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(true, true, ifeq(theorem(or(not(q), not(not(or(p, q))))), true, theorem(or(not(not(or(p, q))), not(q))), true), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.58 = { by axiom 2 (ifeq_axiom) }
% 16.48/2.58 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(theorem(or(not(q), not(not(or(p, q))))), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.58 = { by axiom 2 (ifeq_axiom) R->L }
% 16.48/2.58 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(true, true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.58 = { by axiom 9 (rule_2) R->L }
% 16.48/2.58 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(not(or(p, q))), not(or(p, q))), or(not(or(p, q)), not(not(or(p, q)))))), true, ifeq(theorem(or(not(not(or(p, q))), not(or(p, q)))), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.58 = { by axiom 1 (implies_definition) }
% 16.48/2.58 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(not(or(p, q))), not(or(p, q)))), or(not(or(p, q)), not(not(or(p, q)))))), true, ifeq(theorem(or(not(not(or(p, q))), not(or(p, q)))), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.58 = { by axiom 2 (ifeq_axiom) R->L }
% 16.48/2.58 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(not(or(p, q))), not(or(p, q)))), or(not(or(p, q)), not(not(or(p, q)))))), true), true, ifeq(theorem(or(not(not(or(p, q))), not(or(p, q)))), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.58 = { by axiom 6 (axiom_1_4) R->L }
% 16.48/2.58 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(not(or(p, q))), not(or(p, q))), or(not(or(p, q)), not(not(or(p, q)))))), true, theorem(or(not(or(not(not(or(p, q))), not(or(p, q)))), or(not(or(p, q)), not(not(or(p, q)))))), true), true, ifeq(theorem(or(not(not(or(p, q))), not(or(p, q)))), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.58 = { by axiom 1 (implies_definition) }
% 16.48/2.58 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(not(or(p, q))), not(or(p, q)))), or(not(or(p, q)), not(not(or(p, q)))))), true, theorem(or(not(or(not(not(or(p, q))), not(or(p, q)))), or(not(or(p, q)), not(not(or(p, q)))))), true), true, ifeq(theorem(or(not(not(or(p, q))), not(or(p, q)))), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.58 = { by axiom 5 (rule_1) }
% 16.48/2.58 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(not(not(or(p, q))), not(or(p, q)))), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.58 = { by axiom 2 (ifeq_axiom) }
% 16.48/2.58 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(or(not(not(or(p, q))), not(or(p, q)))), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.58 = { by axiom 2 (ifeq_axiom) R->L }
% 16.48/2.58 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(not(or(p, q))), not(or(p, q)))), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.58 = { by axiom 9 (rule_2) R->L }
% 16.48/2.58 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(not(or(p, q))), or(or(not(not(or(p, q))), not(or(p, q))), not(or(p, q)))), or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q)))))), true, ifeq(theorem(or(not(not(or(p, q))), or(or(not(not(or(p, q))), not(or(p, q))), not(or(p, q))))), true, theorem(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(or(p, q)))), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.58 = { by axiom 1 (implies_definition) }
% 16.48/2.59 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(not(or(p, q))), or(or(not(not(or(p, q))), not(or(p, q))), not(or(p, q))))), or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q)))))), true, ifeq(theorem(or(not(not(or(p, q))), or(or(not(not(or(p, q))), not(or(p, q))), not(or(p, q))))), true, theorem(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(or(p, q)))), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.59 = { by axiom 2 (ifeq_axiom) R->L }
% 16.48/2.59 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(not(or(p, q))), or(or(not(not(or(p, q))), not(or(p, q))), not(or(p, q))))), or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q)))))), true), true, ifeq(theorem(or(not(not(or(p, q))), or(or(not(not(or(p, q))), not(or(p, q))), not(or(p, q))))), true, theorem(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(or(p, q)))), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.59 = { by axiom 8 (axiom_1_5) R->L }
% 16.48/2.59 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(not(or(p, q))), or(or(not(not(or(p, q))), not(or(p, q))), not(or(p, q)))), or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q)))))), true, theorem(or(not(or(not(not(or(p, q))), or(or(not(not(or(p, q))), not(or(p, q))), not(or(p, q))))), or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q)))))), true), true, ifeq(theorem(or(not(not(or(p, q))), or(or(not(not(or(p, q))), not(or(p, q))), not(or(p, q))))), true, theorem(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(or(p, q)))), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.59 = { by axiom 1 (implies_definition) }
% 16.48/2.59 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(not(or(p, q))), or(or(not(not(or(p, q))), not(or(p, q))), not(or(p, q))))), or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q)))))), true, theorem(or(not(or(not(not(or(p, q))), or(or(not(not(or(p, q))), not(or(p, q))), not(or(p, q))))), or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q)))))), true), true, ifeq(theorem(or(not(not(or(p, q))), or(or(not(not(or(p, q))), not(or(p, q))), not(or(p, q))))), true, theorem(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(or(p, q)))), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.59 = { by axiom 5 (rule_1) }
% 16.48/2.59 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(not(not(or(p, q))), or(or(not(not(or(p, q))), not(or(p, q))), not(or(p, q))))), true, theorem(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(or(p, q)))), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.59 = { by axiom 2 (ifeq_axiom) }
% 16.48/2.59 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(not(or(p, q))), or(or(not(not(or(p, q))), not(or(p, q))), not(or(p, q))))), true, theorem(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(or(p, q)))), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.59 = { by axiom 2 (ifeq_axiom) R->L }
% 16.48/2.59 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(not(or(p, q))), or(or(not(not(or(p, q))), not(or(p, q))), not(or(p, q))))), true), true, theorem(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(or(p, q)))), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 16.48/2.60 = { by axiom 3 (axiom_1_3) R->L }
% 16.48/2.60 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(not(or(p, q)), or(or(not(not(or(p, q))), not(or(p, q))), not(or(p, q))))), true, theorem(or(not(not(or(p, q))), or(or(not(not(or(p, q))), not(or(p, q))), not(or(p, q))))), true), true, theorem(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(or(p, q)))), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.60 = { by axiom 1 (implies_definition) }
% 17.24/2.60 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(not(or(p, q))), or(or(not(not(or(p, q))), not(or(p, q))), not(or(p, q))))), true, theorem(or(not(not(or(p, q))), or(or(not(not(or(p, q))), not(or(p, q))), not(or(p, q))))), true), true, theorem(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(or(p, q)))), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.60 = { by axiom 5 (rule_1) }
% 17.24/2.60 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(or(p, q)))), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.60 = { by axiom 2 (ifeq_axiom) }
% 17.24/2.60 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), true, theorem(or(not(not(or(p, q))), not(or(p, q)))), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.61 = { by axiom 2 (ifeq_axiom) R->L }
% 17.24/2.61 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), true, theorem(or(not(not(or(p, q))), not(or(p, q)))), true), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.61 = { by axiom 5 (rule_1) R->L }
% 17.24/2.61 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), or(not(not(or(p, q))), not(or(p, q))))), true, theorem(or(not(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), or(not(not(or(p, q))), not(or(p, q))))), true), true, ifeq(theorem(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), true, theorem(or(not(not(or(p, q))), not(or(p, q)))), true), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.61 = { by axiom 1 (implies_definition) R->L }
% 17.24/2.61 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q)))), or(not(not(or(p, q))), not(or(p, q))))), true, theorem(or(not(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), or(not(not(or(p, q))), not(or(p, q))))), true), true, ifeq(theorem(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), true, theorem(or(not(not(or(p, q))), not(or(p, q)))), true), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.61 = { by axiom 4 (axiom_1_2) }
% 17.24/2.61 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), or(not(not(or(p, q))), not(or(p, q))))), true), true, ifeq(theorem(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), true, theorem(or(not(not(or(p, q))), not(or(p, q)))), true), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.61 = { by axiom 2 (ifeq_axiom) }
% 17.24/2.61 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), or(not(not(or(p, q))), not(or(p, q))))), true, ifeq(theorem(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), true, theorem(or(not(not(or(p, q))), not(or(p, q)))), true), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.61 = { by axiom 1 (implies_definition) R->L }
% 17.24/2.61 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q)))), or(not(not(or(p, q))), not(or(p, q))))), true, ifeq(theorem(or(or(not(not(or(p, q))), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q))))), true, theorem(or(not(not(or(p, q))), not(or(p, q)))), true), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.61 = { by axiom 9 (rule_2) }
% 17.24/2.61 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.61 = { by axiom 2 (ifeq_axiom) }
% 17.24/2.61 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.61 = { by axiom 2 (ifeq_axiom) R->L }
% 17.24/2.61 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.61 = { by axiom 9 (rule_2) R->L }
% 17.24/2.61 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(q), or(p, q)), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q))))))), true, ifeq(theorem(or(not(q), or(p, q))), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.61 = { by axiom 1 (implies_definition) }
% 17.24/2.61 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q))))))), true, ifeq(theorem(or(not(q), or(p, q))), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.61 = { by axiom 2 (ifeq_axiom) R->L }
% 17.24/2.62 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q))))))), true, ifeq(ifeq(true, true, theorem(or(not(q), or(p, q))), true), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.62 = { by axiom 3 (axiom_1_3) R->L }
% 17.24/2.62 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q))))))), true, ifeq(ifeq(axiom(implies(q, or(p, q))), true, theorem(or(not(q), or(p, q))), true), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.62 = { by axiom 1 (implies_definition) }
% 17.24/2.62 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q))))))), true, ifeq(ifeq(axiom(or(not(q), or(p, q))), true, theorem(or(not(q), or(p, q))), true), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.62 = { by axiom 5 (rule_1) }
% 17.24/2.62 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q))))))), true, ifeq(true, true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.62 = { by axiom 2 (ifeq_axiom) }
% 17.24/2.62 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q))))))), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.62 = { by axiom 2 (ifeq_axiom) R->L }
% 17.24/2.62 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q))))))), true), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.62 = { by axiom 5 (rule_1) R->L }
% 17.24/2.62 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(or(not(q), or(p, q))), or(not(q), not(not(or(p, q))))))), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(or(not(q), or(p, q))), or(not(q), not(not(or(p, q))))))), true), true, theorem(or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q))))))), true), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.62 = { by axiom 1 (implies_definition) R->L }
% 17.24/2.62 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(or(p, q)), not(not(or(p, q))))), implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q))))))), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(or(not(q), or(p, q))), or(not(q), not(not(or(p, q))))))), true), true, theorem(or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q))))))), true), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.63 = { by axiom 1 (implies_definition) R->L }
% 17.24/2.63 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(implies(or(p, q), not(not(or(p, q))))), implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q))))))), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(or(not(q), or(p, q))), or(not(q), not(not(or(p, q))))))), true), true, theorem(or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q))))))), true), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.63 = { by axiom 1 (implies_definition) R->L }
% 17.24/2.63 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, q), not(not(or(p, q)))), implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q))))))), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(or(not(q), or(p, q))), or(not(q), not(not(or(p, q))))))), true), true, theorem(or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q))))))), true), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.63 = { by axiom 7 (axiom_1_6) }
% 17.24/2.63 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(or(not(q), or(p, q))), or(not(q), not(not(or(p, q))))))), true), true, theorem(or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q))))))), true), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.63 = { by axiom 2 (ifeq_axiom) }
% 17.24/2.63 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(or(not(q), or(p, q))), or(not(q), not(not(or(p, q))))))), true, theorem(or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q))))))), true), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.63 = { by axiom 2 (ifeq_axiom) R->L }
% 17.24/2.63 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(or(not(q), or(p, q))), or(not(q), not(not(or(p, q))))))), true, theorem(or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q))))))), true), true), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.63 = { by axiom 5 (rule_1) R->L }
% 17.24/2.64 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(or(not(q), or(p, q))), or(not(q), not(not(or(p, q))))))), or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))))), true, theorem(or(not(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(or(not(q), or(p, q))), or(not(q), not(not(or(p, q))))))), or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))))), true), true, ifeq(theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(or(not(q), or(p, q))), or(not(q), not(not(or(p, q))))))), true, theorem(or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q))))))), true), true), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.64 = { by axiom 1 (implies_definition) R->L }
% 17.24/2.64 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(or(not(q), or(p, q))), or(not(q), not(not(or(p, q)))))), or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))))), true, theorem(or(not(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(or(not(q), or(p, q))), or(not(q), not(not(or(p, q))))))), or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))))), true), true, ifeq(theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(or(not(q), or(p, q))), or(not(q), not(not(or(p, q))))))), true, theorem(or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q))))))), true), true), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.64 = { by axiom 8 (axiom_1_5) }
% 17.24/2.64 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(or(not(q), or(p, q))), or(not(q), not(not(or(p, q))))))), or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))))), true), true, ifeq(theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(or(not(q), or(p, q))), or(not(q), not(not(or(p, q))))))), true, theorem(or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q))))))), true), true), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.64 = { by axiom 2 (ifeq_axiom) }
% 17.24/2.64 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(or(not(q), or(p, q))), or(not(q), not(not(or(p, q))))))), or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))))), true, ifeq(theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(or(not(q), or(p, q))), or(not(q), not(not(or(p, q))))))), true, theorem(or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q))))))), true), true), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.64 = { by axiom 1 (implies_definition) R->L }
% 17.24/2.64 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(or(not(q), or(p, q))), or(not(q), not(not(or(p, q)))))), or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))))), true, ifeq(theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(or(not(q), or(p, q))), or(not(q), not(not(or(p, q))))))), true, theorem(or(not(or(not(q), or(p, q))), or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q))))))), true), true), true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.64 = { by axiom 9 (rule_2) }
% 17.24/2.64 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.64 = { by axiom 2 (ifeq_axiom) }
% 17.24/2.64 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(theorem(or(not(or(not(or(p, q)), not(not(or(p, q))))), or(not(q), not(not(or(p, q)))))), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.64 = { by axiom 1 (implies_definition) R->L }
% 17.24/2.65 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(ifeq(theorem(implies(or(not(or(p, q)), not(not(or(p, q)))), or(not(q), not(not(or(p, q)))))), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.65 = { by axiom 9 (rule_2) }
% 17.24/2.65 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(ifeq(true, true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.65 = { by axiom 2 (ifeq_axiom) }
% 17.24/2.65 ifeq(theorem(or(not(or(not(not(or(p, q))), not(q))), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(theorem(or(not(not(or(p, q))), not(q))), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.65 = { by axiom 1 (implies_definition) R->L }
% 17.24/2.65 ifeq(theorem(implies(or(not(not(or(p, q))), not(q)), implies(not(or(p, q)), or(p, not(q))))), true, ifeq(theorem(or(not(not(or(p, q))), not(q))), true, theorem(implies(not(or(p, q)), or(p, not(q)))), true), true)
% 17.24/2.65 = { by axiom 9 (rule_2) }
% 17.24/2.65 true
% 17.24/2.65 % SZS output end Proof
% 17.24/2.65
% 17.24/2.65 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------