%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL238-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 11:49:27 AM UTC 2026
% Result : Unsatisfiable 7.58s 1.50s
% Output : Proof 7.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL238-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n020.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Sun Sep 27 15:29:34 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.58/1.50 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
% 7.58/1.50
% 7.58/1.50 % SZS status Unsatisfiable
% 7.58/1.50
% 7.58/1.52 % SZS output start Proof
% 7.58/1.52 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 7.58/1.52 Axiom 2 (axiom_1_3): axiom(or(not(X), or(Y, X))) = true.
% 7.58/1.52 Axiom 3 (axiom_1_2): axiom(or(not(or(X, X)), X)) = true.
% 7.58/1.52 Axiom 4 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 7.58/1.52 Axiom 5 (axiom_1_4): axiom(or(not(or(X, Y)), or(Y, X))) = true.
% 7.58/1.52 Axiom 6 (axiom_1_5): axiom(or(not(or(X, or(Y, Z))), or(Y, or(X, Z)))) = true.
% 7.58/1.52 Axiom 7 (rule_2): ifeq(theorem(X), true, ifeq(axiom(or(not(X), Y)), true, theorem(Y), true), true) = true.
% 7.58/1.52 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.
% 7.58/1.52
% 7.58/1.52 Goal 1 (prove_this): theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))) = true.
% 7.58/1.52 Proof:
% 7.58/1.52 theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p)))))
% 7.58/1.52 = { by axiom 1 (ifeq_axiom) R->L }
% 7.58/1.52 ifeq(true, true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true)
% 7.58/1.52 = { by axiom 8 (rule_3) R->L }
% 7.58/1.52 ifeq(ifeq(theorem(or(not(or(not(p), not(q))), not(not(or(not(p), not(q)))))), true, ifeq(axiom(or(not(or(not(q), not(p))), or(not(p), not(q)))), true, theorem(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), true), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true)
% 7.58/1.52 = { by axiom 5 (axiom_1_4) }
% 7.58/1.52 ifeq(ifeq(theorem(or(not(or(not(p), not(q))), not(not(or(not(p), not(q)))))), true, ifeq(true, true, theorem(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), true), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true)
% 7.58/1.52 = { by axiom 1 (ifeq_axiom) }
% 7.58/1.52 ifeq(ifeq(theorem(or(not(or(not(p), not(q))), not(not(or(not(p), not(q)))))), true, theorem(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true)
% 7.58/1.53 = { by axiom 1 (ifeq_axiom) R->L }
% 7.58/1.53 ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(p), not(q))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true)
% 7.58/1.53 = { by axiom 7 (rule_2) R->L }
% 7.58/1.53 ifeq(ifeq(ifeq(ifeq(theorem(or(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))), or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))))), true, ifeq(axiom(or(not(or(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))), or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))))), or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))))), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q))))), true), true), true, theorem(or(not(or(not(p), not(q))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true)
% 7.58/1.53 = { by axiom 3 (axiom_1_2) }
% 7.58/1.53 ifeq(ifeq(ifeq(ifeq(theorem(or(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))), or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))))), true, ifeq(true, true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q))))), true), true), true, theorem(or(not(or(not(p), not(q))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true)
% 7.58/1.53 = { by axiom 1 (ifeq_axiom) }
% 7.58/1.53 ifeq(ifeq(ifeq(ifeq(theorem(or(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))), or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))))), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q))))), true), true, theorem(or(not(or(not(p), not(q))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true)
% 7.58/1.53 = { by axiom 1 (ifeq_axiom) R->L }
% 7.58/1.53 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))), or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))))), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q))))), true), true, theorem(or(not(or(not(p), not(q))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true)
% 7.58/1.53 = { by axiom 4 (rule_1) R->L }
% 7.58/1.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(not(or(not(p), not(q)))), or(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))), not(or(not(p), not(q)))))), true, theorem(or(not(not(or(not(p), not(q)))), or(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))), not(or(not(p), not(q)))))), true), true, theorem(or(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))), or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))))), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q))))), true), true, theorem(or(not(or(not(p), not(q))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true)
% 7.58/1.53 = { by axiom 2 (axiom_1_3) }
% 7.58/1.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(not(or(not(p), not(q)))), or(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))), not(or(not(p), not(q)))))), true), true, theorem(or(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))), or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))))), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q))))), true), true, theorem(or(not(or(not(p), not(q))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true)
% 7.58/1.53 = { by axiom 1 (ifeq_axiom) }
% 7.58/1.53 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(not(or(not(p), not(q)))), or(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))), not(or(not(p), not(q)))))), true, theorem(or(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))), or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))))), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q))))), true), true, theorem(or(not(or(not(p), not(q))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true)
% 7.58/1.53 = { by axiom 1 (ifeq_axiom) R->L }
% 7.58/1.53 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(not(or(not(p), not(q)))), or(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))), not(or(not(p), not(q)))))), true, ifeq(true, true, theorem(or(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))), or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))))), true), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q))))), true), true, theorem(or(not(or(not(p), not(q))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true)
% 7.58/1.53 = { by axiom 6 (axiom_1_5) R->L }
% 7.58/1.53 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(not(or(not(p), not(q)))), or(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))), not(or(not(p), not(q)))))), true, ifeq(axiom(or(not(or(not(not(or(not(p), not(q)))), or(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))), not(or(not(p), not(q)))))), or(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))), or(not(not(or(not(p), not(q)))), not(or(not(p), not(q))))))), true, theorem(or(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))), or(not(not(or(not(p), not(q)))), not(or(not(p), not(q)))))), true), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q))))), true), true, theorem(or(not(or(not(p), not(q))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true)
% 7.58/1.54 = { by axiom 7 (rule_2) }
% 7.58/1.54 ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q))))), true), true, theorem(or(not(or(not(p), not(q))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true)
% 7.58/1.54 = { by axiom 1 (ifeq_axiom) }
% 7.58/1.54 ifeq(ifeq(ifeq(theorem(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q))))), true, theorem(or(not(or(not(p), not(q))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true)
% 7.58/1.54 = { by axiom 1 (ifeq_axiom) R->L }
% 7.58/1.54 ifeq(ifeq(ifeq(theorem(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q))))), true, ifeq(true, true, theorem(or(not(or(not(p), not(q))), not(not(or(not(p), not(q)))))), true), true), true, theorem(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true)
% 7.58/1.54 = { by axiom 5 (axiom_1_4) R->L }
% 7.58/1.54 ifeq(ifeq(ifeq(theorem(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q))))), true, ifeq(axiom(or(not(or(not(not(or(not(p), not(q)))), not(or(not(p), not(q))))), or(not(or(not(p), not(q))), not(not(or(not(p), not(q))))))), true, theorem(or(not(or(not(p), not(q))), not(not(or(not(p), not(q)))))), true), true), true, theorem(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true)
% 7.58/1.54 = { by axiom 7 (rule_2) }
% 7.58/1.54 ifeq(ifeq(true, true, theorem(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), true), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true)
% 7.58/1.54 = { by axiom 1 (ifeq_axiom) }
% 7.58/1.54 ifeq(theorem(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true)
% 7.58/1.54 = { by axiom 1 (ifeq_axiom) R->L }
% 7.58/1.54 ifeq(theorem(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), true, ifeq(true, true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true), true)
% 7.58/1.54 = { by axiom 5 (axiom_1_4) R->L }
% 7.58/1.54 ifeq(theorem(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), true, ifeq(axiom(or(not(or(not(or(not(q), not(p))), not(not(or(not(p), not(q)))))), or(not(not(or(not(p), not(q)))), not(or(not(q), not(p)))))), true, theorem(or(not(not(or(not(p), not(q)))), not(or(not(q), not(p))))), true), true)
% 7.58/1.54 = { by axiom 7 (rule_2) }
% 7.58/1.54 true
% 7.58/1.54 % SZS output end Proof
% 7.58/1.54
% 7.58/1.54 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------