%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL321-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 11:49:36 AM UTC 2026
% Result : Unsatisfiable 0.63s 0.56s
% Output : Proof 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL321-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 15:34:29 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.63/0.56 Command-line arguments: --flatten --complete-subsets
% 0.63/0.56
% 0.63/0.56 % SZS status Unsatisfiable
% 0.63/0.56
% 0.63/0.57 % SZS output start Proof
% 0.63/0.57 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 0.63/0.57 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.63/0.57 Axiom 3 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 0.63/0.57 Axiom 4 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 0.63/0.57 Axiom 5 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 0.63/0.57 Axiom 6 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 0.63/0.57 Axiom 7 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 0.63/0.57
% 0.63/0.57 Goal 1 (prove_this): theorem(or(implies(p, q), implies(p, not(q)))) = true.
% 0.63/0.57 Proof:
% 0.63/0.57 theorem(or(implies(p, q), implies(p, not(q))))
% 0.63/0.57 = { by axiom 2 (ifeq_axiom) R->L }
% 0.63/0.57 ifeq(true, true, theorem(or(implies(p, q), implies(p, not(q)))), true)
% 0.63/0.58 = { by axiom 6 (rule_2) R->L }
% 0.63/0.58 ifeq(ifeq(theorem(implies(or(implies(p, q), not(q)), implies(p, or(implies(p, q), not(q))))), true, ifeq(theorem(or(implies(p, q), not(q))), true, theorem(implies(p, or(implies(p, q), not(q)))), true), true), true, theorem(or(implies(p, q), implies(p, not(q)))), true)
% 0.63/0.58 = { by axiom 2 (ifeq_axiom) R->L }
% 0.63/0.58 ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(p, q), not(q)), implies(p, or(implies(p, q), not(q))))), true), true, ifeq(theorem(or(implies(p, q), not(q))), true, theorem(implies(p, or(implies(p, q), not(q)))), true), true), true, theorem(or(implies(p, q), implies(p, not(q)))), true)
% 0.63/0.58 = { by axiom 4 (axiom_1_3) R->L }
% 0.63/0.58 ifeq(ifeq(ifeq(axiom(implies(or(implies(p, q), not(q)), or(not(p), or(implies(p, q), not(q))))), true, theorem(implies(or(implies(p, q), not(q)), implies(p, or(implies(p, q), not(q))))), true), true, ifeq(theorem(or(implies(p, q), not(q))), true, theorem(implies(p, or(implies(p, q), not(q)))), true), true), true, theorem(or(implies(p, q), implies(p, not(q)))), true)
% 0.63/0.58 = { by axiom 1 (implies_definition) R->L }
% 0.63/0.58 ifeq(ifeq(ifeq(axiom(implies(or(implies(p, q), not(q)), implies(p, or(implies(p, q), not(q))))), true, theorem(implies(or(implies(p, q), not(q)), implies(p, or(implies(p, q), not(q))))), true), true, ifeq(theorem(or(implies(p, q), not(q))), true, theorem(implies(p, or(implies(p, q), not(q)))), true), true), true, theorem(or(implies(p, q), implies(p, not(q)))), true)
% 0.63/0.58 = { by axiom 3 (rule_1) }
% 0.63/0.58 ifeq(ifeq(true, true, ifeq(theorem(or(implies(p, q), not(q))), true, theorem(implies(p, or(implies(p, q), not(q)))), true), true), true, theorem(or(implies(p, q), implies(p, not(q)))), true)
% 0.63/0.58 = { by axiom 2 (ifeq_axiom) }
% 0.63/0.58 ifeq(ifeq(theorem(or(implies(p, q), not(q))), true, theorem(implies(p, or(implies(p, q), not(q)))), true), true, theorem(or(implies(p, q), implies(p, not(q)))), true)
% 0.63/0.58 = { by axiom 2 (ifeq_axiom) R->L }
% 0.63/0.58 ifeq(ifeq(ifeq(true, true, theorem(or(implies(p, q), not(q))), true), true, theorem(implies(p, or(implies(p, q), not(q)))), true), true, theorem(or(implies(p, q), implies(p, not(q)))), true)
% 0.63/0.58 = { by axiom 3 (rule_1) R->L }
% 0.63/0.58 ifeq(ifeq(ifeq(ifeq(axiom(or(not(q), implies(p, q))), true, theorem(or(not(q), implies(p, q))), true), true, theorem(or(implies(p, q), not(q))), true), true, theorem(implies(p, or(implies(p, q), not(q)))), true), true, theorem(or(implies(p, q), implies(p, not(q)))), true)
% 0.63/0.58 = { by axiom 1 (implies_definition) R->L }
% 0.63/0.58 ifeq(ifeq(ifeq(ifeq(axiom(implies(q, implies(p, q))), true, theorem(or(not(q), implies(p, q))), true), true, theorem(or(implies(p, q), not(q))), true), true, theorem(implies(p, or(implies(p, q), not(q)))), true), true, theorem(or(implies(p, q), implies(p, not(q)))), true)
% 0.63/0.58 = { by axiom 1 (implies_definition) }
% 0.63/0.58 ifeq(ifeq(ifeq(ifeq(axiom(implies(q, or(not(p), q))), true, theorem(or(not(q), implies(p, q))), true), true, theorem(or(implies(p, q), not(q))), true), true, theorem(implies(p, or(implies(p, q), not(q)))), true), true, theorem(or(implies(p, q), implies(p, not(q)))), true)
% 0.63/0.58 = { by axiom 4 (axiom_1_3) }
% 0.63/0.58 ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(q), implies(p, q))), true), true, theorem(or(implies(p, q), not(q))), true), true, theorem(implies(p, or(implies(p, q), not(q)))), true), true, theorem(or(implies(p, q), implies(p, not(q)))), true)
% 0.63/0.58 = { by axiom 2 (ifeq_axiom) }
% 0.63/0.58 ifeq(ifeq(ifeq(theorem(or(not(q), implies(p, q))), true, theorem(or(implies(p, q), not(q))), true), true, theorem(implies(p, or(implies(p, q), not(q)))), true), true, theorem(or(implies(p, q), implies(p, not(q)))), true)
% 0.63/0.58 = { by axiom 2 (ifeq_axiom) R->L }
% 0.63/0.58 ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(not(q), implies(p, q))), true, theorem(or(implies(p, q), not(q))), true), true), true, theorem(implies(p, or(implies(p, q), not(q)))), true), true, theorem(or(implies(p, q), implies(p, not(q)))), true)
% 0.63/0.58 = { by axiom 3 (rule_1) R->L }
% 0.63/0.58 ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(q), implies(p, q)), or(implies(p, q), not(q)))), true, theorem(implies(or(not(q), implies(p, q)), or(implies(p, q), not(q)))), true), true, ifeq(theorem(or(not(q), implies(p, q))), true, theorem(or(implies(p, q), not(q))), true), true), true, theorem(implies(p, or(implies(p, q), not(q)))), true), true, theorem(or(implies(p, q), implies(p, not(q)))), true)
% 0.63/0.58 = { by axiom 5 (axiom_1_4) }
% 0.63/0.58 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(q), implies(p, q)), or(implies(p, q), not(q)))), true), true, ifeq(theorem(or(not(q), implies(p, q))), true, theorem(or(implies(p, q), not(q))), true), true), true, theorem(implies(p, or(implies(p, q), not(q)))), true), true, theorem(or(implies(p, q), implies(p, not(q)))), true)
% 0.63/0.58 = { by axiom 2 (ifeq_axiom) }
% 0.63/0.58 ifeq(ifeq(ifeq(theorem(implies(or(not(q), implies(p, q)), or(implies(p, q), not(q)))), true, ifeq(theorem(or(not(q), implies(p, q))), true, theorem(or(implies(p, q), not(q))), true), true), true, theorem(implies(p, or(implies(p, q), not(q)))), true), true, theorem(or(implies(p, q), implies(p, not(q)))), true)
% 0.63/0.58 = { by axiom 6 (rule_2) }
% 0.63/0.58 ifeq(ifeq(true, true, theorem(implies(p, or(implies(p, q), not(q)))), true), true, theorem(or(implies(p, q), implies(p, not(q)))), true)
% 0.63/0.58 = { by axiom 2 (ifeq_axiom) }
% 0.63/0.58 ifeq(theorem(implies(p, or(implies(p, q), not(q)))), true, theorem(or(implies(p, q), implies(p, not(q)))), true)
% 0.63/0.58 = { by axiom 2 (ifeq_axiom) R->L }
% 0.63/0.58 ifeq(true, true, ifeq(theorem(implies(p, or(implies(p, q), not(q)))), true, theorem(or(implies(p, q), implies(p, not(q)))), true), true)
% 0.63/0.58 = { by axiom 3 (rule_1) R->L }
% 0.63/0.58 ifeq(ifeq(axiom(implies(implies(p, or(implies(p, q), not(q))), or(implies(p, q), implies(p, not(q))))), true, theorem(implies(implies(p, or(implies(p, q), not(q))), or(implies(p, q), implies(p, not(q))))), true), true, ifeq(theorem(implies(p, or(implies(p, q), not(q)))), true, theorem(or(implies(p, q), implies(p, not(q)))), true), true)
% 0.63/0.58 = { by axiom 1 (implies_definition) }
% 0.63/0.58 ifeq(ifeq(axiom(implies(implies(p, or(implies(p, q), not(q))), or(implies(p, q), or(not(p), not(q))))), true, theorem(implies(implies(p, or(implies(p, q), not(q))), or(implies(p, q), implies(p, not(q))))), true), true, ifeq(theorem(implies(p, or(implies(p, q), not(q)))), true, theorem(or(implies(p, q), implies(p, not(q)))), true), true)
% 0.63/0.58 = { by axiom 1 (implies_definition) }
% 0.63/0.58 ifeq(ifeq(axiom(implies(or(not(p), or(implies(p, q), not(q))), or(implies(p, q), or(not(p), not(q))))), true, theorem(implies(implies(p, or(implies(p, q), not(q))), or(implies(p, q), implies(p, not(q))))), true), true, ifeq(theorem(implies(p, or(implies(p, q), not(q)))), true, theorem(or(implies(p, q), implies(p, not(q)))), true), true)
% 0.63/0.58 = { by axiom 7 (axiom_1_5) }
% 0.63/0.58 ifeq(ifeq(true, true, theorem(implies(implies(p, or(implies(p, q), not(q))), or(implies(p, q), implies(p, not(q))))), true), true, ifeq(theorem(implies(p, or(implies(p, q), not(q)))), true, theorem(or(implies(p, q), implies(p, not(q)))), true), true)
% 0.63/0.58 = { by axiom 2 (ifeq_axiom) }
% 0.63/0.58 ifeq(theorem(implies(implies(p, or(implies(p, q), not(q))), or(implies(p, q), implies(p, not(q))))), true, ifeq(theorem(implies(p, or(implies(p, q), not(q)))), true, theorem(or(implies(p, q), implies(p, not(q)))), true), true)
% 0.63/0.58 = { by axiom 6 (rule_2) }
% 0.63/0.58 true
% 0.63/0.58 % SZS output end Proof
% 0.63/0.58
% 0.63/0.58 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------