%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL359-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/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 11:49:39 AM UTC 2026
% Result : Unsatisfiable 12.65s 2.31s
% Output : Proof 14.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL359-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n003.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sun Sep 27 15:38:10 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.65/2.31 Command-line arguments: --flatten-regeneralise
% 12.65/2.31
% 12.65/2.31 % SZS status Unsatisfiable
% 12.65/2.31
% 14.27/2.32 % SZS output start Proof
% 14.27/2.32 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 14.27/2.32 Axiom 2 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 14.27/2.32 Axiom 3 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 14.27/2.32
% 14.27/2.32 Goal 1 (prove_cn_08): is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))) = true.
% 14.27/2.32 Proof:
% 14.27/2.32 is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))
% 14.27/2.32 = { by axiom 1 (ifeq_axiom) R->L }
% 14.27/2.32 ifeq(true, true, is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true)
% 14.27/2.32 = { by axiom 1 (ifeq_axiom) R->L }
% 14.27/2.32 ifeq(true, true, ifeq(true, true, is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true)
% 14.27/2.32 = { by axiom 2 (condensed_detachment) R->L }
% 14.27/2.32 ifeq(ifeq(is_a_theorem(implies(implies(implies(x, y), implies(implies(y, u), implies(x, u))), implies(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))))), true, ifeq(is_a_theorem(implies(implies(x, y), implies(implies(y, u), implies(x, u)))), true, is_a_theorem(implies(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true), true), true, ifeq(true, true, is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true)
% 14.27/2.32 = { by axiom 3 (cn_1) }
% 14.27/2.32 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(x, y), implies(implies(y, u), implies(x, u)))), true, is_a_theorem(implies(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true), true), true, ifeq(true, true, is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true)
% 14.27/2.32 = { by axiom 1 (ifeq_axiom) }
% 14.27/2.32 ifeq(ifeq(is_a_theorem(implies(implies(x, y), implies(implies(y, u), implies(x, u)))), true, is_a_theorem(implies(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true)
% 14.27/2.33 = { by axiom 3 (cn_1) }
% 14.27/2.33 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true)
% 14.27/2.33 = { by axiom 1 (ifeq_axiom) }
% 14.27/2.33 ifeq(is_a_theorem(implies(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true, ifeq(true, true, is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true)
% 14.27/2.33 = { by axiom 2 (condensed_detachment) R->L }
% 14.27/2.33 ifeq(is_a_theorem(implies(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u))), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u))), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true, is_a_theorem(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true), true, is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true)
% 14.27/2.33 = { by axiom 1 (ifeq_axiom) R->L }
% 14.27/2.33 ifeq(is_a_theorem(implies(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u))), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u))), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true, is_a_theorem(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true), true, is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true)
% 14.27/2.33 = { by axiom 3 (cn_1) R->L }
% 14.27/2.33 ifeq(is_a_theorem(implies(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(y, u), implies(x, u)), implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u))), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u))), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true, is_a_theorem(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true), true, is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true)
% 14.27/2.33 = { by axiom 1 (ifeq_axiom) R->L }
% 14.27/2.33 ifeq(is_a_theorem(implies(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(y, u), implies(x, u)), implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u))), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u))), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true, is_a_theorem(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true), true, is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true)
% 14.27/2.33 = { by axiom 3 (cn_1) R->L }
% 14.27/2.34 ifeq(is_a_theorem(implies(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(y, u), implies(x, u)), implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u)))), implies(implies(implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u))), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u))))))), true, ifeq(is_a_theorem(implies(implies(implies(y, u), implies(x, u)), implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u))), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u))), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true, is_a_theorem(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true), true, is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true)
% 14.27/2.34 = { by axiom 2 (condensed_detachment) }
% 14.27/2.34 ifeq(is_a_theorem(implies(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u))), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true, is_a_theorem(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true), true, is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true)
% 14.27/2.34 = { by axiom 1 (ifeq_axiom) }
% 14.27/2.34 ifeq(is_a_theorem(implies(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u))), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true, is_a_theorem(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true, is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true)
% 14.27/2.34 = { by axiom 1 (ifeq_axiom) R->L }
% 14.27/2.34 ifeq(is_a_theorem(implies(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u))), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true, is_a_theorem(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true, is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true)
% 14.27/2.34 = { by axiom 3 (cn_1) R->L }
% 14.27/2.34 ifeq(is_a_theorem(implies(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, x), implies(implies(x, u), implies(z, u)))), true, is_a_theorem(implies(implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u))), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true, is_a_theorem(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true, is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true)
% 14.27/2.34 = { by axiom 1 (ifeq_axiom) R->L }
% 14.27/2.34 ifeq(is_a_theorem(implies(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(z, x), implies(implies(x, u), implies(z, u)))), true, is_a_theorem(implies(implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u))), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true), true, is_a_theorem(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true, is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true)
% 14.27/2.34 = { by axiom 3 (cn_1) R->L }
% 14.27/2.34 ifeq(is_a_theorem(implies(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(z, x), implies(implies(x, u), implies(z, u))), implies(implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u))), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true, ifeq(is_a_theorem(implies(implies(z, x), implies(implies(x, u), implies(z, u)))), true, is_a_theorem(implies(implies(implies(implies(x, u), implies(z, u)), implies(implies(y, u), implies(z, u))), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true), true, is_a_theorem(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true, is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true)
% 14.27/2.34 = { by axiom 2 (condensed_detachment) }
% 14.27/2.34 ifeq(is_a_theorem(implies(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true, is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true)
% 14.27/2.34 = { by axiom 1 (ifeq_axiom) }
% 14.27/2.34 ifeq(is_a_theorem(implies(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u)))), implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u)))))), true, ifeq(is_a_theorem(implies(implies(implies(y, u), implies(x, u)), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true, is_a_theorem(implies(implies(x, y), implies(implies(z, x), implies(implies(y, u), implies(z, u))))), true), true)
% 14.27/2.34 = { by axiom 2 (condensed_detachment) }
% 14.27/2.34 true
% 14.27/2.34 % SZS output end Proof
% 14.27/2.34
% 14.27/2.34 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------