%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL218-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 11:49:23 AM UTC 2026
% Result : Unsatisfiable 13.44s 2.28s
% Output : Proof 14.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL218-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.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 15:29:10 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.44/2.28 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
% 13.44/2.28
% 13.44/2.28 % SZS status Unsatisfiable
% 13.44/2.28
% 14.22/2.32 % SZS output start Proof
% 14.22/2.32 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 14.22/2.32 Axiom 2 (axiom_1_3): axiom(or(not(X), or(Y, X))) = true.
% 14.22/2.32 Axiom 3 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 14.22/2.32 Axiom 4 (axiom_1_4): axiom(or(not(or(X, Y)), or(Y, X))) = true.
% 14.22/2.32 Axiom 5 (axiom_1_5): axiom(or(not(or(X, or(Y, Z))), or(Y, or(X, Z)))) = true.
% 14.22/2.32 Axiom 6 (rule_2): ifeq(theorem(X), true, ifeq(axiom(or(not(X), Y)), true, theorem(Y), true), true) = true.
% 14.22/2.32 Axiom 7 (rule_3): ifeq(theorem(or(not(X), Y)), true, ifeq(axiom(or(not(Z), X)), true, theorem(or(not(Z), Y)), true), true) = true.
% 14.22/2.32
% 14.22/2.32 Goal 1 (prove_this): theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))) = true.
% 14.22/2.32 Proof:
% 14.22/2.32 theorem(or(not(or(not(or(p, q)), q)), or(not(p), q)))
% 14.22/2.32 = { by axiom 1 (ifeq_axiom) R->L }
% 14.22/2.32 ifeq(true, true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 14.22/2.32 = { by axiom 6 (rule_2) R->L }
% 14.22/2.32 ifeq(ifeq(theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true, ifeq(axiom(or(not(or(not(p), or(not(or(q, not(or(p, q)))), q))), or(not(or(q, not(or(p, q)))), or(not(p), q)))), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 14.22/2.32 = { by axiom 5 (axiom_1_5) }
% 14.22/2.32 ifeq(ifeq(theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true, ifeq(true, true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 14.22/2.32 = { by axiom 1 (ifeq_axiom) }
% 14.22/2.32 ifeq(ifeq(theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 14.22/2.32 = { by axiom 1 (ifeq_axiom) R->L }
% 14.22/2.32 ifeq(ifeq(ifeq(true, true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 14.22/2.32 = { by axiom 7 (rule_3) R->L }
% 14.22/2.32 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(p, q)), or(not(or(q, not(or(p, q)))), q))), true, ifeq(axiom(or(not(or(q, p)), or(p, q))), true, theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true), true), true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 14.22/2.33 = { by axiom 4 (axiom_1_4) }
% 14.22/2.33 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(p, q)), or(not(or(q, not(or(p, q)))), q))), true, ifeq(true, true, theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true), true), true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 14.22/2.33 = { by axiom 1 (ifeq_axiom) }
% 14.22/2.33 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(p, q)), or(not(or(q, not(or(p, q)))), q))), true, theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 14.22/2.33 = { by axiom 1 (ifeq_axiom) R->L }
% 14.22/2.33 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(p, q)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 14.22/2.33 = { by axiom 3 (rule_1) R->L }
% 14.22/2.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(q, not(or(p, q)))), or(not(or(p, q)), q))), true, theorem(or(not(or(q, not(or(p, q)))), or(not(or(p, q)), q))), true), true, theorem(or(not(or(p, q)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 14.22/2.33 = { by axiom 4 (axiom_1_4) }
% 14.22/2.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(q, not(or(p, q)))), or(not(or(p, q)), q))), true), true, theorem(or(not(or(p, q)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 14.22/2.33 = { by axiom 1 (ifeq_axiom) }
% 14.22/2.33 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(q, not(or(p, q)))), or(not(or(p, q)), q))), true, theorem(or(not(or(p, q)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 14.22/2.33 = { by axiom 1 (ifeq_axiom) R->L }
% 14.22/2.33 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(q, not(or(p, q)))), or(not(or(p, q)), q))), true, ifeq(true, true, theorem(or(not(or(p, q)), or(not(or(q, not(or(p, q)))), q))), true), true), true, theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 14.22/2.34 = { by axiom 5 (axiom_1_5) R->L }
% 14.22/2.34 ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(q, not(or(p, q)))), or(not(or(p, q)), q))), true, ifeq(axiom(or(not(or(not(or(q, not(or(p, q)))), or(not(or(p, q)), q))), or(not(or(p, q)), or(not(or(q, not(or(p, q)))), q)))), true, theorem(or(not(or(p, q)), or(not(or(q, not(or(p, q)))), q))), true), true), true, theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 14.22/2.34 = { by axiom 6 (rule_2) }
% 14.22/2.34 ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 14.22/2.34 = { by axiom 1 (ifeq_axiom) }
% 14.22/2.34 ifeq(ifeq(ifeq(theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 14.22/2.34 = { by axiom 1 (ifeq_axiom) R->L }
% 14.22/2.34 ifeq(ifeq(ifeq(theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true, ifeq(true, true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 14.22/2.34 = { by axiom 2 (axiom_1_3) R->L }
% 14.22/2.34 ifeq(ifeq(ifeq(theorem(or(not(or(q, p)), or(not(or(q, not(or(p, q)))), q))), true, ifeq(axiom(or(not(p), or(q, p))), true, theorem(or(not(p), or(not(or(q, not(or(p, q)))), q))), true), true), true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 14.22/2.34 = { by axiom 7 (rule_3) }
% 14.22/2.34 ifeq(ifeq(true, true, theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 14.22/2.34 = { by axiom 1 (ifeq_axiom) }
% 14.22/2.34 ifeq(theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true)
% 14.22/2.34 = { by axiom 1 (ifeq_axiom) R->L }
% 14.22/2.34 ifeq(theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true, ifeq(true, true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true), true)
% 14.22/2.34 = { by axiom 4 (axiom_1_4) R->L }
% 14.22/2.34 ifeq(theorem(or(not(or(q, not(or(p, q)))), or(not(p), q))), true, ifeq(axiom(or(not(or(not(or(p, q)), q)), or(q, not(or(p, q))))), true, theorem(or(not(or(not(or(p, q)), q)), or(not(p), q))), true), true)
% 14.22/2.34 = { by axiom 7 (rule_3) }
% 14.22/2.34 true
% 14.22/2.34 % SZS output end Proof
% 14.22/2.34
% 14.22/2.34 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------