%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL111-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 11:49:04 AM UTC 2026
% Result : Unsatisfiable 4.56s 1.08s
% Output : Proof 4.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL111-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 15:27:17 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.56/1.08 Command-line arguments: --no-flatten-goal
% 4.56/1.08
% 4.56/1.08 % SZS status Unsatisfiable
% 4.56/1.08
% 4.56/1.09 % SZS output start Proof
% 4.56/1.09 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 4.56/1.09 Axiom 2 (mv_1): is_a_theorem(implies(X, implies(Y, X))) = true.
% 4.56/1.09 Axiom 3 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 4.56/1.09 Axiom 4 (mv_2): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 4.56/1.09 Axiom 5 (mv_3): is_a_theorem(implies(implies(implies(X, Y), Y), implies(implies(Y, X), X))) = true.
% 4.56/1.09
% 4.56/1.09 Goal 1 (prove_mv_25): is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b)))) = true.
% 4.56/1.09 Proof:
% 4.56/1.09 is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b))))
% 4.56/1.09 = { by axiom 1 (ifeq_axiom) R->L }
% 4.56/1.09 ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b)))), true)
% 4.56/1.09 = { by axiom 3 (condensed_detachment) R->L }
% 4.56/1.09 ifeq(ifeq(is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), implies(c, b))), implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b))))), true, ifeq(is_a_theorem(implies(implies(c, a), implies(implies(a, b), implies(c, b)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b)))), true)
% 4.56/1.09 = { by axiom 4 (mv_2) }
% 4.56/1.09 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(c, a), implies(implies(a, b), implies(c, b)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b)))), true)
% 4.56/1.09 = { by axiom 1 (ifeq_axiom) }
% 4.56/1.09 ifeq(ifeq(is_a_theorem(implies(implies(c, a), implies(implies(a, b), implies(c, b)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b)))), true)
% 4.56/1.09 = { by axiom 4 (mv_2) }
% 4.56/1.09 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b)))), true)
% 4.56/1.09 = { by axiom 1 (ifeq_axiom) }
% 4.56/1.09 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b)))), true)
% 4.56/1.09 = { by axiom 1 (ifeq_axiom) R->L }
% 4.56/1.09 ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b)))), true), true)
% 4.56/1.09 = { by axiom 3 (condensed_detachment) R->L }
% 4.56/1.09 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), implies(c, b)), implies(c, b))), implies(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b))), implies(implies(a, b), implies(implies(c, a), implies(c, b)))))), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), implies(c, b)), implies(c, b)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b))), implies(implies(a, b), implies(implies(c, a), implies(c, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b)))), true), true)
% 4.56/1.09 = { by axiom 4 (mv_2) }
% 4.56/1.09 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), implies(c, b)), implies(c, b)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b))), implies(implies(a, b), implies(implies(c, a), implies(c, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b)))), true), true)
% 4.56/1.09 = { by axiom 1 (ifeq_axiom) }
% 4.56/1.09 ifeq(ifeq(is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), implies(c, b)), implies(c, b)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b))), implies(implies(a, b), implies(implies(c, a), implies(c, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b)))), true), true)
% 4.56/1.09 = { by axiom 1 (ifeq_axiom) R->L }
% 4.56/1.09 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), implies(c, b)), implies(c, b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b))), implies(implies(a, b), implies(implies(c, a), implies(c, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b)))), true), true)
% 4.56/1.09 = { by axiom 5 (mv_3) R->L }
% 4.56/1.09 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(c, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(c, b)), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), implies(c, b)), implies(c, b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b))), implies(implies(a, b), implies(implies(c, a), implies(c, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b)))), true), true)
% 4.56/1.09 = { by axiom 1 (ifeq_axiom) R->L }
% 4.56/1.09 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(c, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(c, b)), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), implies(c, b)), implies(c, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b))), implies(implies(a, b), implies(implies(c, a), implies(c, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b)))), true), true)
% 4.56/1.09 = { by axiom 3 (condensed_detachment) R->L }
% 4.56/1.09 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(c, b), implies(a, b)), implies(a, b))), implies(implies(implies(implies(implies(c, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(c, b)), implies(c, b))), implies(implies(a, b), implies(implies(implies(a, b), implies(c, b)), implies(c, b)))))), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(implies(c, b), implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(implies(c, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(c, b)), implies(c, b))), implies(implies(a, b), implies(implies(implies(a, b), implies(c, b)), implies(c, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(c, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(c, b)), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), implies(c, b)), implies(c, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b))), implies(implies(a, b), implies(implies(c, a), implies(c, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b)))), true), true)
% 4.56/1.09 = { by axiom 2 (mv_1) }
% 4.56/1.09 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(c, b), implies(a, b)), implies(a, b))), implies(implies(implies(implies(implies(c, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(c, b)), implies(c, b))), implies(implies(a, b), implies(implies(implies(a, b), implies(c, b)), implies(c, b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(c, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(c, b)), implies(c, b))), implies(implies(a, b), implies(implies(implies(a, b), implies(c, b)), implies(c, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(c, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(c, b)), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), implies(c, b)), implies(c, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b))), implies(implies(a, b), implies(implies(c, a), implies(c, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b)))), true), true)
% 4.56/1.09 = { by axiom 1 (ifeq_axiom) }
% 4.56/1.09 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(c, b), implies(a, b)), implies(a, b))), implies(implies(implies(implies(implies(c, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(c, b)), implies(c, b))), implies(implies(a, b), implies(implies(implies(a, b), implies(c, b)), implies(c, b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(c, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(c, b)), implies(c, b))), implies(implies(a, b), implies(implies(implies(a, b), implies(c, b)), implies(c, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(c, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(c, b)), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), implies(c, b)), implies(c, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b))), implies(implies(a, b), implies(implies(c, a), implies(c, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b)))), true), true)
% 4.56/1.09 = { by axiom 4 (mv_2) }
% 4.56/1.09 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(c, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(c, b)), implies(c, b))), implies(implies(a, b), implies(implies(implies(a, b), implies(c, b)), implies(c, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(c, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(c, b)), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), implies(c, b)), implies(c, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b))), implies(implies(a, b), implies(implies(c, a), implies(c, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b)))), true), true)
% 4.56/1.09 = { by axiom 1 (ifeq_axiom) }
% 4.56/1.09 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(c, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(c, b)), implies(c, b))), implies(implies(a, b), implies(implies(implies(a, b), implies(c, b)), implies(c, b))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(c, b), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), implies(c, b)), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), implies(c, b)), implies(c, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b))), implies(implies(a, b), implies(implies(c, a), implies(c, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b)))), true), true)
% 4.56/1.09 = { by axiom 3 (condensed_detachment) }
% 4.56/1.09 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b))), implies(implies(a, b), implies(implies(c, a), implies(c, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b)))), true), true)
% 4.56/1.09 = { by axiom 1 (ifeq_axiom) }
% 4.56/1.09 ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b))), implies(implies(a, b), implies(implies(c, a), implies(c, b))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(c, b)), implies(c, b)), implies(implies(c, a), implies(c, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(c, a), implies(c, b)))), true), true)
% 4.56/1.09 = { by axiom 3 (condensed_detachment) }
% 4.56/1.09 true
% 4.56/1.09 % SZS output end Proof
% 4.56/1.09
% 4.56/1.09 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------