%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL206-3 : TPTP v9.3.1. Bugfixed v2.4.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:49:20 AM UTC 2026
% Result : Unsatisfiable 129.08s 16.86s
% Output : Proof 130.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL206-3 : TPTP v9.3.1. Bugfixed v2.4.1.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n010.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 27 15:27:16 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 129.08/16.86 Command-line arguments: --no-flatten-goal
% 129.08/16.86
% 129.08/16.86 % SZS status Unsatisfiable
% 129.08/16.86
% 130.54/17.02 % SZS output start Proof
% 130.54/17.02 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 130.54/17.02 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 130.54/17.02 Axiom 3 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 130.54/17.02 Axiom 4 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 130.54/17.02 Axiom 5 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 130.54/17.02 Axiom 6 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 130.54/17.02 Axiom 7 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 130.54/17.02 Axiom 8 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 130.54/17.03 Axiom 9 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 130.54/17.03
% 130.54/17.03 Goal 1 (prove_this): theorem(implies(not(implies(p, q)), implies(not(p), not(q)))) = true.
% 130.54/17.03 Proof:
% 130.54/17.03 theorem(implies(not(implies(p, q)), implies(not(p), not(q))))
% 130.54/17.03 = { by axiom 2 (ifeq_axiom) R->L }
% 130.54/17.03 ifeq(true, true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.03 = { by axiom 9 (rule_2) R->L }
% 130.54/17.03 ifeq(ifeq(theorem(implies(implies(q, not(not(implies(p, q)))), or(not(not(implies(p, q))), not(q)))), true, ifeq(theorem(implies(q, not(not(implies(p, q))))), true, theorem(or(not(not(implies(p, q))), not(q))), true), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.03 = { by axiom 1 (implies_definition) }
% 130.54/17.03 ifeq(ifeq(theorem(implies(or(not(q), not(not(implies(p, q)))), or(not(not(implies(p, q))), not(q)))), true, ifeq(theorem(implies(q, not(not(implies(p, q))))), true, theorem(or(not(not(implies(p, q))), not(q))), true), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.03 = { by axiom 2 (ifeq_axiom) R->L }
% 130.54/17.03 ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(q), not(not(implies(p, q)))), or(not(not(implies(p, q))), not(q)))), true), true, ifeq(theorem(implies(q, not(not(implies(p, q))))), true, theorem(or(not(not(implies(p, q))), not(q))), true), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.03 = { by axiom 6 (axiom_1_4) R->L }
% 130.54/17.03 ifeq(ifeq(ifeq(axiom(implies(or(not(q), not(not(implies(p, q)))), or(not(not(implies(p, q))), not(q)))), true, theorem(implies(or(not(q), not(not(implies(p, q)))), or(not(not(implies(p, q))), not(q)))), true), true, ifeq(theorem(implies(q, not(not(implies(p, q))))), true, theorem(or(not(not(implies(p, q))), not(q))), true), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.03 = { by axiom 5 (rule_1) }
% 130.54/17.03 ifeq(ifeq(true, true, ifeq(theorem(implies(q, not(not(implies(p, q))))), true, theorem(or(not(not(implies(p, q))), not(q))), true), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.03 = { by axiom 2 (ifeq_axiom) }
% 130.54/17.03 ifeq(ifeq(theorem(implies(q, not(not(implies(p, q))))), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.03 = { by axiom 2 (ifeq_axiom) R->L }
% 130.54/17.03 ifeq(ifeq(ifeq(true, true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.03 = { by axiom 9 (rule_2) R->L }
% 130.54/17.03 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(p, q), not(not(implies(p, q)))), implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q))))))), true, ifeq(theorem(implies(implies(p, q), not(not(implies(p, q))))), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.03 = { by axiom 2 (ifeq_axiom) R->L }
% 130.54/17.03 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(p, q), not(not(implies(p, q)))), implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q))))))), true), true, ifeq(theorem(implies(implies(p, q), not(not(implies(p, q))))), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.03 = { by axiom 7 (axiom_1_6) R->L }
% 130.54/17.03 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(p, q), not(not(implies(p, q)))), implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q))))))), true, theorem(implies(implies(implies(p, q), not(not(implies(p, q)))), implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q))))))), true), true, ifeq(theorem(implies(implies(p, q), not(not(implies(p, q))))), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.03 = { by axiom 5 (rule_1) }
% 130.54/17.03 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(implies(p, q), not(not(implies(p, q))))), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.03 = { by axiom 2 (ifeq_axiom) }
% 130.54/17.04 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(p, q), not(not(implies(p, q))))), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.04 = { by axiom 1 (implies_definition) }
% 130.54/17.04 ifeq(ifeq(ifeq(ifeq(theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.04 = { by axiom 2 (ifeq_axiom) R->L }
% 130.54/17.04 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.04 = { by axiom 9 (rule_2) R->L }
% 130.54/17.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q)))), implies(not(implies(p, q)), not(implies(p, q))))), true, ifeq(theorem(or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q))))), true, theorem(implies(not(implies(p, q)), not(implies(p, q)))), true), true), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.04 = { by axiom 2 (ifeq_axiom) R->L }
% 130.54/17.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q)))), implies(not(implies(p, q)), not(implies(p, q))))), true), true, ifeq(theorem(or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q))))), true, theorem(implies(not(implies(p, q)), not(implies(p, q)))), true), true), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.04 = { by axiom 4 (axiom_1_2) R->L }
% 130.54/17.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q)))), implies(not(implies(p, q)), not(implies(p, q))))), true, theorem(implies(or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q)))), implies(not(implies(p, q)), not(implies(p, q))))), true), true, ifeq(theorem(or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q))))), true, theorem(implies(not(implies(p, q)), not(implies(p, q)))), true), true), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.04 = { by axiom 5 (rule_1) }
% 130.54/17.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q))))), true, theorem(implies(not(implies(p, q)), not(implies(p, q)))), true), true), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.04 = { by axiom 2 (ifeq_axiom) }
% 130.54/17.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q))))), true, theorem(implies(not(implies(p, q)), not(implies(p, q)))), true), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.04 = { by axiom 2 (ifeq_axiom) R->L }
% 130.54/17.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q))))), true), true, theorem(implies(not(implies(p, q)), not(implies(p, q)))), true), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.04 = { by axiom 5 (rule_1) R->L }
% 130.54/17.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(implies(p, q)), or(implies(not(implies(p, q)), not(implies(p, q))), not(implies(p, q)))), or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q)))))), true, theorem(implies(implies(not(implies(p, q)), or(implies(not(implies(p, q)), not(implies(p, q))), not(implies(p, q)))), or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q)))))), true), true, theorem(or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q))))), true), true, theorem(implies(not(implies(p, q)), not(implies(p, q)))), true), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.04 = { by axiom 1 (implies_definition) }
% 130.54/17.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(implies(p, q)), or(implies(not(implies(p, q)), not(implies(p, q))), not(implies(p, q)))), or(implies(not(implies(p, q)), not(implies(p, q))), or(not(not(implies(p, q))), not(implies(p, q)))))), true, theorem(implies(implies(not(implies(p, q)), or(implies(not(implies(p, q)), not(implies(p, q))), not(implies(p, q)))), or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q)))))), true), true, theorem(or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q))))), true), true, theorem(implies(not(implies(p, q)), not(implies(p, q)))), true), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.04 = { by axiom 1 (implies_definition) }
% 130.54/17.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(not(implies(p, q))), or(implies(not(implies(p, q)), not(implies(p, q))), not(implies(p, q)))), or(implies(not(implies(p, q)), not(implies(p, q))), or(not(not(implies(p, q))), not(implies(p, q)))))), true, theorem(implies(implies(not(implies(p, q)), or(implies(not(implies(p, q)), not(implies(p, q))), not(implies(p, q)))), or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q)))))), true), true, theorem(or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q))))), true), true, theorem(implies(not(implies(p, q)), not(implies(p, q)))), true), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.05 = { by axiom 8 (axiom_1_5) }
% 130.54/17.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(implies(p, q)), or(implies(not(implies(p, q)), not(implies(p, q))), not(implies(p, q)))), or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q)))))), true), true, theorem(or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q))))), true), true, theorem(implies(not(implies(p, q)), not(implies(p, q)))), true), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.05 = { by axiom 2 (ifeq_axiom) }
% 130.54/17.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, q)), or(implies(not(implies(p, q)), not(implies(p, q))), not(implies(p, q)))), or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q)))))), true, theorem(or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q))))), true), true, theorem(implies(not(implies(p, q)), not(implies(p, q)))), true), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.05 = { by axiom 2 (ifeq_axiom) R->L }
% 130.54/17.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, q)), or(implies(not(implies(p, q)), not(implies(p, q))), not(implies(p, q)))), or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q)))))), true, ifeq(true, true, theorem(or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q))))), true), true), true, theorem(implies(not(implies(p, q)), not(implies(p, q)))), true), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.05 = { by axiom 5 (rule_1) R->L }
% 130.54/17.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, q)), or(implies(not(implies(p, q)), not(implies(p, q))), not(implies(p, q)))), or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q)))))), true, ifeq(ifeq(axiom(implies(not(implies(p, q)), or(implies(not(implies(p, q)), not(implies(p, q))), not(implies(p, q))))), true, theorem(implies(not(implies(p, q)), or(implies(not(implies(p, q)), not(implies(p, q))), not(implies(p, q))))), true), true, theorem(or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q))))), true), true), true, theorem(implies(not(implies(p, q)), not(implies(p, q)))), true), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.05 = { by axiom 3 (axiom_1_3) }
% 130.54/17.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, q)), or(implies(not(implies(p, q)), not(implies(p, q))), not(implies(p, q)))), or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q)))))), true, ifeq(ifeq(true, true, theorem(implies(not(implies(p, q)), or(implies(not(implies(p, q)), not(implies(p, q))), not(implies(p, q))))), true), true, theorem(or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q))))), true), true), true, theorem(implies(not(implies(p, q)), not(implies(p, q)))), true), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.05 = { by axiom 2 (ifeq_axiom) }
% 130.54/17.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, q)), or(implies(not(implies(p, q)), not(implies(p, q))), not(implies(p, q)))), or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q)))))), true, ifeq(theorem(implies(not(implies(p, q)), or(implies(not(implies(p, q)), not(implies(p, q))), not(implies(p, q))))), true, theorem(or(implies(not(implies(p, q)), not(implies(p, q))), implies(not(implies(p, q)), not(implies(p, q))))), true), true), true, theorem(implies(not(implies(p, q)), not(implies(p, q)))), true), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.05 = { by axiom 9 (rule_2) }
% 130.54/17.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(not(implies(p, q)), not(implies(p, q)))), true), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.06 = { by axiom 2 (ifeq_axiom) }
% 130.54/17.06 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(not(implies(p, q)), not(implies(p, q)))), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.06 = { by axiom 2 (ifeq_axiom) R->L }
% 130.54/17.06 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(not(implies(p, q)), not(implies(p, q)))), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.06 = { by axiom 5 (rule_1) R->L }
% 130.54/17.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(not(implies(p, q))), not(implies(p, q))), or(not(implies(p, q)), not(not(implies(p, q)))))), true, theorem(implies(or(not(not(implies(p, q))), not(implies(p, q))), or(not(implies(p, q)), not(not(implies(p, q)))))), true), true, ifeq(theorem(implies(not(implies(p, q)), not(implies(p, q)))), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.06 = { by axiom 6 (axiom_1_4) }
% 130.54/17.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(not(implies(p, q))), not(implies(p, q))), or(not(implies(p, q)), not(not(implies(p, q)))))), true), true, ifeq(theorem(implies(not(implies(p, q)), not(implies(p, q)))), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.06 = { by axiom 2 (ifeq_axiom) }
% 130.54/17.06 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(not(implies(p, q))), not(implies(p, q))), or(not(implies(p, q)), not(not(implies(p, q)))))), true, ifeq(theorem(implies(not(implies(p, q)), not(implies(p, q)))), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.06 = { by axiom 1 (implies_definition) R->L }
% 130.54/17.06 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, q)), not(implies(p, q))), or(not(implies(p, q)), not(not(implies(p, q)))))), true, ifeq(theorem(implies(not(implies(p, q)), not(implies(p, q)))), true, theorem(or(not(implies(p, q)), not(not(implies(p, q))))), true), true), true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.06 = { by axiom 9 (rule_2) }
% 130.54/17.06 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.06 = { by axiom 2 (ifeq_axiom) }
% 130.54/17.06 ifeq(ifeq(ifeq(theorem(implies(or(not(q), implies(p, q)), or(not(q), not(not(implies(p, q)))))), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.06 = { by axiom 1 (implies_definition) R->L }
% 130.54/17.06 ifeq(ifeq(ifeq(theorem(implies(implies(q, implies(p, q)), or(not(q), not(not(implies(p, q)))))), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.06 = { by axiom 1 (implies_definition) R->L }
% 130.54/17.06 ifeq(ifeq(ifeq(theorem(implies(implies(q, implies(p, q)), implies(q, not(not(implies(p, q)))))), true, theorem(implies(q, not(not(implies(p, q))))), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.06 = { by axiom 2 (ifeq_axiom) R->L }
% 130.54/17.06 ifeq(ifeq(ifeq(theorem(implies(implies(q, implies(p, q)), implies(q, not(not(implies(p, q)))))), true, ifeq(true, true, theorem(implies(q, not(not(implies(p, q))))), true), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.06 = { by axiom 5 (rule_1) R->L }
% 130.54/17.06 ifeq(ifeq(ifeq(theorem(implies(implies(q, implies(p, q)), implies(q, not(not(implies(p, q)))))), true, ifeq(ifeq(axiom(implies(q, implies(p, q))), true, theorem(implies(q, implies(p, q))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.06 = { by axiom 1 (implies_definition) }
% 130.54/17.06 ifeq(ifeq(ifeq(theorem(implies(implies(q, implies(p, q)), implies(q, not(not(implies(p, q)))))), true, ifeq(ifeq(axiom(implies(q, or(not(p), q))), true, theorem(implies(q, implies(p, q))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.06 = { by axiom 3 (axiom_1_3) }
% 130.54/17.06 ifeq(ifeq(ifeq(theorem(implies(implies(q, implies(p, q)), implies(q, not(not(implies(p, q)))))), true, ifeq(ifeq(true, true, theorem(implies(q, implies(p, q))), true), true, theorem(implies(q, not(not(implies(p, q))))), true), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.06 = { by axiom 2 (ifeq_axiom) }
% 130.54/17.06 ifeq(ifeq(ifeq(theorem(implies(implies(q, implies(p, q)), implies(q, not(not(implies(p, q)))))), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(q, not(not(implies(p, q))))), true), true), true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.06 = { by axiom 9 (rule_2) }
% 130.54/17.06 ifeq(ifeq(true, true, theorem(or(not(not(implies(p, q))), not(q))), true), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.06 = { by axiom 2 (ifeq_axiom) }
% 130.54/17.06 ifeq(theorem(or(not(not(implies(p, q))), not(q))), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.06 = { by axiom 1 (implies_definition) R->L }
% 130.54/17.06 ifeq(theorem(implies(not(implies(p, q)), not(q))), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true)
% 130.54/17.06 = { by axiom 2 (ifeq_axiom) R->L }
% 130.54/17.06 ifeq(true, true, ifeq(theorem(implies(not(implies(p, q)), not(q))), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true), true)
% 130.54/17.06 = { by axiom 9 (rule_2) R->L }
% 130.54/17.06 ifeq(ifeq(theorem(implies(implies(not(q), or(not(not(p)), not(q))), implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), or(not(not(p)), not(q)))))), true, ifeq(theorem(implies(not(q), or(not(not(p)), not(q)))), true, theorem(implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), or(not(not(p)), not(q))))), true), true), true, ifeq(theorem(implies(not(implies(p, q)), not(q))), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true), true)
% 130.54/17.06 = { by axiom 2 (ifeq_axiom) R->L }
% 130.54/17.07 ifeq(ifeq(theorem(implies(implies(not(q), or(not(not(p)), not(q))), implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), or(not(not(p)), not(q)))))), true, ifeq(ifeq(true, true, theorem(implies(not(q), or(not(not(p)), not(q)))), true), true, theorem(implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), or(not(not(p)), not(q))))), true), true), true, ifeq(theorem(implies(not(implies(p, q)), not(q))), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true), true)
% 130.54/17.07 = { by axiom 3 (axiom_1_3) R->L }
% 130.54/17.07 ifeq(ifeq(theorem(implies(implies(not(q), or(not(not(p)), not(q))), implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), or(not(not(p)), not(q)))))), true, ifeq(ifeq(axiom(implies(not(q), or(not(not(p)), not(q)))), true, theorem(implies(not(q), or(not(not(p)), not(q)))), true), true, theorem(implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), or(not(not(p)), not(q))))), true), true), true, ifeq(theorem(implies(not(implies(p, q)), not(q))), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true), true)
% 130.54/17.07 = { by axiom 5 (rule_1) }
% 130.54/17.07 ifeq(ifeq(theorem(implies(implies(not(q), or(not(not(p)), not(q))), implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), or(not(not(p)), not(q)))))), true, ifeq(true, true, theorem(implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), or(not(not(p)), not(q))))), true), true), true, ifeq(theorem(implies(not(implies(p, q)), not(q))), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true), true)
% 130.54/17.07 = { by axiom 2 (ifeq_axiom) }
% 130.54/17.07 ifeq(ifeq(theorem(implies(implies(not(q), or(not(not(p)), not(q))), implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), or(not(not(p)), not(q)))))), true, theorem(implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), or(not(not(p)), not(q))))), true), true, ifeq(theorem(implies(not(implies(p, q)), not(q))), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true), true)
% 130.54/17.07 = { by axiom 2 (ifeq_axiom) R->L }
% 130.54/17.07 ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(q), or(not(not(p)), not(q))), implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), or(not(not(p)), not(q)))))), true), true, theorem(implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), or(not(not(p)), not(q))))), true), true, ifeq(theorem(implies(not(implies(p, q)), not(q))), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true), true)
% 130.54/17.07 = { by axiom 7 (axiom_1_6) R->L }
% 130.54/17.07 ifeq(ifeq(ifeq(axiom(implies(implies(not(q), or(not(not(p)), not(q))), implies(or(not(not(implies(p, q))), not(q)), or(not(not(implies(p, q))), or(not(not(p)), not(q)))))), true, theorem(implies(implies(not(q), or(not(not(p)), not(q))), implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), or(not(not(p)), not(q)))))), true), true, theorem(implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), or(not(not(p)), not(q))))), true), true, ifeq(theorem(implies(not(implies(p, q)), not(q))), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true), true)
% 130.54/17.07 = { by axiom 1 (implies_definition) R->L }
% 130.54/17.07 ifeq(ifeq(ifeq(axiom(implies(implies(not(q), or(not(not(p)), not(q))), implies(implies(not(implies(p, q)), not(q)), or(not(not(implies(p, q))), or(not(not(p)), not(q)))))), true, theorem(implies(implies(not(q), or(not(not(p)), not(q))), implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), or(not(not(p)), not(q)))))), true), true, theorem(implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), or(not(not(p)), not(q))))), true), true, ifeq(theorem(implies(not(implies(p, q)), not(q))), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true), true)
% 130.54/17.07 = { by axiom 1 (implies_definition) R->L }
% 130.54/17.07 ifeq(ifeq(ifeq(axiom(implies(implies(not(q), or(not(not(p)), not(q))), implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), or(not(not(p)), not(q)))))), true, theorem(implies(implies(not(q), or(not(not(p)), not(q))), implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), or(not(not(p)), not(q)))))), true), true, theorem(implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), or(not(not(p)), not(q))))), true), true, ifeq(theorem(implies(not(implies(p, q)), not(q))), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true), true)
% 130.54/17.07 = { by axiom 5 (rule_1) }
% 130.54/17.07 ifeq(ifeq(true, true, theorem(implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), or(not(not(p)), not(q))))), true), true, ifeq(theorem(implies(not(implies(p, q)), not(q))), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true), true)
% 130.54/17.07 = { by axiom 2 (ifeq_axiom) }
% 130.54/17.07 ifeq(theorem(implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), or(not(not(p)), not(q))))), true, ifeq(theorem(implies(not(implies(p, q)), not(q))), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true), true)
% 130.54/17.07 = { by axiom 1 (implies_definition) R->L }
% 130.54/17.07 ifeq(theorem(implies(implies(not(implies(p, q)), not(q)), implies(not(implies(p, q)), implies(not(p), not(q))))), true, ifeq(theorem(implies(not(implies(p, q)), not(q))), true, theorem(implies(not(implies(p, q)), implies(not(p), not(q)))), true), true)
% 130.54/17.07 = { by axiom 9 (rule_2) }
% 130.54/17.07 true
% 130.54/17.07 % SZS output end Proof
% 130.54/17.07
% 130.54/17.07 RESULT: Unsatisfiable (the axioms are contradictory).
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