%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL205-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 2.13s 0.77s
% Output : Proof 2.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL205-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 15:26:17 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.13/0.77 Command-line arguments: --no-flatten-goal
% 2.13/0.77
% 2.13/0.77 % SZS status Unsatisfiable
% 2.13/0.77
% 2.13/0.79 % SZS output start Proof
% 2.13/0.79 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 2.13/0.79 Axiom 2 (axiom_1_3): axiom(or(not(X), or(Y, X))) = true.
% 2.13/0.79 Axiom 3 (axiom_1_2): axiom(or(not(or(X, X)), X)) = true.
% 2.13/0.79 Axiom 4 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 2.13/0.79 Axiom 5 (axiom_1_4): axiom(or(not(or(X, Y)), or(Y, X))) = true.
% 2.13/0.79 Axiom 6 (axiom_1_5): axiom(or(not(or(X, or(Y, Z))), or(Y, or(X, Z)))) = true.
% 2.13/0.79 Axiom 7 (rule_2): ifeq(theorem(X), true, ifeq(axiom(or(not(X), Y)), true, theorem(Y), true), true) = true.
% 2.13/0.79 Axiom 8 (rule_3): ifeq(theorem(or(not(X), Y)), true, ifeq(axiom(or(not(Z), X)), true, theorem(or(not(Z), Y)), true), true) = true.
% 2.13/0.79
% 2.13/0.79 Goal 1 (prove_this): theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))) = true.
% 2.13/0.79 Proof:
% 2.13/0.79 theorem(or(not(not(or(not(p), q))), or(not(p), not(q))))
% 2.13/0.79 = { by axiom 1 (ifeq_axiom) R->L }
% 2.13/0.79 ifeq(true, true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.13/0.79 = { by axiom 7 (rule_2) R->L }
% 2.13/0.79 ifeq(ifeq(theorem(or(not(not(or(not(p), q))), not(q))), true, ifeq(axiom(or(not(or(not(not(or(not(p), q))), not(q))), or(not(p), or(not(not(or(not(p), q))), not(q))))), true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.13/0.79 = { by axiom 2 (axiom_1_3) }
% 2.13/0.79 ifeq(ifeq(theorem(or(not(not(or(not(p), q))), not(q))), true, ifeq(true, true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.13/0.79 = { by axiom 1 (ifeq_axiom) }
% 2.13/0.79 ifeq(ifeq(theorem(or(not(not(or(not(p), q))), not(q))), true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.13/0.79 = { by axiom 1 (ifeq_axiom) R->L }
% 2.13/0.79 ifeq(ifeq(ifeq(true, true, theorem(or(not(not(or(not(p), q))), not(q))), true), true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.13/0.79 = { by axiom 8 (rule_3) R->L }
% 2.13/0.79 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(p), q)), not(not(or(not(p), q))))), true, ifeq(axiom(or(not(q), or(not(p), q))), true, theorem(or(not(q), not(not(or(not(p), q))))), true), true), true, theorem(or(not(not(or(not(p), q))), not(q))), true), true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.13/0.79 = { by axiom 2 (axiom_1_3) }
% 2.13/0.79 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(p), q)), not(not(or(not(p), q))))), true, ifeq(true, true, theorem(or(not(q), not(not(or(not(p), q))))), true), true), true, theorem(or(not(not(or(not(p), q))), not(q))), true), true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.13/0.79 = { by axiom 1 (ifeq_axiom) }
% 2.13/0.79 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(p), q)), not(not(or(not(p), q))))), true, theorem(or(not(q), not(not(or(not(p), q))))), true), true, theorem(or(not(not(or(not(p), q))), not(q))), true), true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.13/0.80 = { by axiom 1 (ifeq_axiom) R->L }
% 2.13/0.80 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(p), q)), not(not(or(not(p), q))))), true), true, theorem(or(not(q), not(not(or(not(p), q))))), true), true, theorem(or(not(not(or(not(p), q))), not(q))), true), true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.13/0.80 = { by axiom 8 (rule_3) R->L }
% 2.13/0.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(or(not(p), q)), not(or(not(p), q)))), not(or(not(p), q)))), true, ifeq(axiom(or(not(not(or(not(p), q))), or(not(or(not(p), q)), not(or(not(p), q))))), true, theorem(or(not(not(or(not(p), q))), not(or(not(p), q)))), true), true), true, theorem(or(not(or(not(p), q)), not(not(or(not(p), q))))), true), true, theorem(or(not(q), not(not(or(not(p), q))))), true), true, theorem(or(not(not(or(not(p), q))), not(q))), true), true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.13/0.80 = { by axiom 1 (ifeq_axiom) R->L }
% 2.13/0.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(or(not(p), q)), not(or(not(p), q)))), not(or(not(p), q)))), true), true, ifeq(axiom(or(not(not(or(not(p), q))), or(not(or(not(p), q)), not(or(not(p), q))))), true, theorem(or(not(not(or(not(p), q))), not(or(not(p), q)))), true), true), true, theorem(or(not(or(not(p), q)), not(not(or(not(p), q))))), true), true, theorem(or(not(q), not(not(or(not(p), q))))), true), true, theorem(or(not(not(or(not(p), q))), not(q))), true), true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.13/0.80 = { by axiom 3 (axiom_1_2) R->L }
% 2.13/0.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(or(not(p), q)), not(or(not(p), q)))), not(or(not(p), q)))), true, theorem(or(not(or(not(or(not(p), q)), not(or(not(p), q)))), not(or(not(p), q)))), true), true, ifeq(axiom(or(not(not(or(not(p), q))), or(not(or(not(p), q)), not(or(not(p), q))))), true, theorem(or(not(not(or(not(p), q))), not(or(not(p), q)))), true), true), true, theorem(or(not(or(not(p), q)), not(not(or(not(p), q))))), true), true, theorem(or(not(q), not(not(or(not(p), q))))), true), true, theorem(or(not(not(or(not(p), q))), not(q))), true), true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.13/0.80 = { by axiom 4 (rule_1) }
% 2.13/0.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(axiom(or(not(not(or(not(p), q))), or(not(or(not(p), q)), not(or(not(p), q))))), true, theorem(or(not(not(or(not(p), q))), not(or(not(p), q)))), true), true), true, theorem(or(not(or(not(p), q)), not(not(or(not(p), q))))), true), true, theorem(or(not(q), not(not(or(not(p), q))))), true), true, theorem(or(not(not(or(not(p), q))), not(q))), true), true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.13/0.80 = { by axiom 1 (ifeq_axiom) }
% 2.95/0.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(not(or(not(p), q))), or(not(or(not(p), q)), not(or(not(p), q))))), true, theorem(or(not(not(or(not(p), q))), not(or(not(p), q)))), true), true, theorem(or(not(or(not(p), q)), not(not(or(not(p), q))))), true), true, theorem(or(not(q), not(not(or(not(p), q))))), true), true, theorem(or(not(not(or(not(p), q))), not(q))), true), true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.95/0.80 = { by axiom 2 (axiom_1_3) }
% 2.95/0.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(not(or(not(p), q))), not(or(not(p), q)))), true), true, theorem(or(not(or(not(p), q)), not(not(or(not(p), q))))), true), true, theorem(or(not(q), not(not(or(not(p), q))))), true), true, theorem(or(not(not(or(not(p), q))), not(q))), true), true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.95/0.80 = { by axiom 1 (ifeq_axiom) }
% 2.95/0.80 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(not(or(not(p), q))), not(or(not(p), q)))), true, theorem(or(not(or(not(p), q)), not(not(or(not(p), q))))), true), true, theorem(or(not(q), not(not(or(not(p), q))))), true), true, theorem(or(not(not(or(not(p), q))), not(q))), true), true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.95/0.80 = { by axiom 1 (ifeq_axiom) R->L }
% 2.95/0.80 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(not(or(not(p), q))), not(or(not(p), q)))), true, ifeq(true, true, theorem(or(not(or(not(p), q)), not(not(or(not(p), q))))), true), true), true, theorem(or(not(q), not(not(or(not(p), q))))), true), true, theorem(or(not(not(or(not(p), q))), not(q))), true), true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.95/0.80 = { by axiom 5 (axiom_1_4) R->L }
% 2.95/0.80 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(not(or(not(p), q))), not(or(not(p), q)))), true, ifeq(axiom(or(not(or(not(not(or(not(p), q))), not(or(not(p), q)))), or(not(or(not(p), q)), not(not(or(not(p), q)))))), true, theorem(or(not(or(not(p), q)), not(not(or(not(p), q))))), true), true), true, theorem(or(not(q), not(not(or(not(p), q))))), true), true, theorem(or(not(not(or(not(p), q))), not(q))), true), true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.95/0.80 = { by axiom 7 (rule_2) }
% 2.95/0.80 ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(q), not(not(or(not(p), q))))), true), true, theorem(or(not(not(or(not(p), q))), not(q))), true), true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.95/0.80 = { by axiom 1 (ifeq_axiom) }
% 2.95/0.80 ifeq(ifeq(ifeq(theorem(or(not(q), not(not(or(not(p), q))))), true, theorem(or(not(not(or(not(p), q))), not(q))), true), true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.95/0.80 = { by axiom 1 (ifeq_axiom) R->L }
% 2.95/0.80 ifeq(ifeq(ifeq(theorem(or(not(q), not(not(or(not(p), q))))), true, ifeq(true, true, theorem(or(not(not(or(not(p), q))), not(q))), true), true), true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.95/0.80 = { by axiom 5 (axiom_1_4) R->L }
% 2.95/0.80 ifeq(ifeq(ifeq(theorem(or(not(q), not(not(or(not(p), q))))), true, ifeq(axiom(or(not(or(not(q), not(not(or(not(p), q))))), or(not(not(or(not(p), q))), not(q)))), true, theorem(or(not(not(or(not(p), q))), not(q))), true), true), true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.95/0.80 = { by axiom 7 (rule_2) }
% 2.95/0.80 ifeq(ifeq(true, true, theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.95/0.81 = { by axiom 1 (ifeq_axiom) }
% 2.95/0.81 ifeq(theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true)
% 2.95/0.81 = { by axiom 1 (ifeq_axiom) R->L }
% 2.95/0.81 ifeq(theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true, ifeq(true, true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true), true)
% 2.95/0.81 = { by axiom 6 (axiom_1_5) R->L }
% 2.95/0.81 ifeq(theorem(or(not(p), or(not(not(or(not(p), q))), not(q)))), true, ifeq(axiom(or(not(or(not(p), or(not(not(or(not(p), q))), not(q)))), or(not(not(or(not(p), q))), or(not(p), not(q))))), true, theorem(or(not(not(or(not(p), q))), or(not(p), not(q)))), true), true)
% 2.95/0.81 = { by axiom 7 (rule_2) }
% 2.95/0.81 true
% 2.95/0.81 % SZS output end Proof
% 2.95/0.81
% 2.95/0.81 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------