%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL356-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 0.46s 0.50s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL356-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n013.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 27 15:36:06 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.50 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
% 0.46/0.50
% 0.46/0.50 % SZS status Unsatisfiable
% 0.46/0.50
% 0.46/0.50 % SZS output start Proof
% 0.46/0.50 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.46/0.51 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.
% 0.46/0.51 Axiom 3 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 0.46/0.51
% 0.46/0.51 Goal 1 (prove_cn_05): is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(u, y), implies(x, implies(u, z))))) = true.
% 0.46/0.51 Proof:
% 0.46/0.51 is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(u, y), implies(x, implies(u, z)))))
% 0.46/0.51 = { by axiom 1 (ifeq_axiom) R->L }
% 0.46/0.51 ifeq(true, true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(u, y), implies(x, implies(u, z))))), true)
% 0.46/0.51 = { by axiom 2 (condensed_detachment) R->L }
% 0.46/0.51 ifeq(ifeq(is_a_theorem(implies(implies(implies(u, y), implies(implies(y, z), implies(u, z))), implies(implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z))), implies(implies(u, y), implies(x, implies(u, z)))))), true, ifeq(is_a_theorem(implies(implies(u, y), implies(implies(y, z), implies(u, z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z))), implies(implies(u, y), implies(x, implies(u, z))))), true), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(u, y), implies(x, implies(u, z))))), true)
% 0.46/0.51 = { by axiom 3 (cn_1) }
% 0.46/0.51 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(u, y), implies(implies(y, z), implies(u, z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z))), implies(implies(u, y), implies(x, implies(u, z))))), true), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(u, y), implies(x, implies(u, z))))), true)
% 0.46/0.51 = { by axiom 1 (ifeq_axiom) }
% 0.46/0.51 ifeq(ifeq(is_a_theorem(implies(implies(u, y), implies(implies(y, z), implies(u, z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z))), implies(implies(u, y), implies(x, implies(u, z))))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(u, y), implies(x, implies(u, z))))), true)
% 0.46/0.51 = { by axiom 3 (cn_1) }
% 0.46/0.51 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z))), implies(implies(u, y), implies(x, implies(u, z))))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(u, y), implies(x, implies(u, z))))), true)
% 0.46/0.51 = { by axiom 1 (ifeq_axiom) }
% 0.46/0.51 ifeq(is_a_theorem(implies(implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z))), implies(implies(u, y), implies(x, implies(u, z))))), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(u, y), implies(x, implies(u, z))))), true)
% 0.46/0.51 = { by axiom 1 (ifeq_axiom) R->L }
% 0.46/0.51 ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z))), implies(implies(u, y), implies(x, implies(u, z))))), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(u, y), implies(x, implies(u, z))))), true), true)
% 0.46/0.51 = { by axiom 2 (condensed_detachment) R->L }
% 0.46/0.51 ifeq(ifeq(is_a_theorem(implies(implies(implies(x, implies(y, z)), implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z)))), implies(implies(implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z))), implies(implies(u, y), implies(x, implies(u, z)))), implies(implies(x, implies(y, z)), implies(implies(u, y), implies(x, implies(u, z))))))), true, ifeq(is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z))))), true, is_a_theorem(implies(implies(implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z))), implies(implies(u, y), implies(x, implies(u, z)))), implies(implies(x, implies(y, z)), implies(implies(u, y), implies(x, implies(u, z)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z))), implies(implies(u, y), implies(x, implies(u, z))))), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(u, y), implies(x, implies(u, z))))), true), true)
% 0.46/0.51 = { by axiom 3 (cn_1) }
% 0.46/0.51 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z))))), true, is_a_theorem(implies(implies(implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z))), implies(implies(u, y), implies(x, implies(u, z)))), implies(implies(x, implies(y, z)), implies(implies(u, y), implies(x, implies(u, z)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z))), implies(implies(u, y), implies(x, implies(u, z))))), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(u, y), implies(x, implies(u, z))))), true), true)
% 0.46/0.51 = { by axiom 1 (ifeq_axiom) }
% 0.46/0.51 ifeq(ifeq(is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z))))), true, is_a_theorem(implies(implies(implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z))), implies(implies(u, y), implies(x, implies(u, z)))), implies(implies(x, implies(y, z)), implies(implies(u, y), implies(x, implies(u, z)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z))), implies(implies(u, y), implies(x, implies(u, z))))), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(u, y), implies(x, implies(u, z))))), true), true)
% 0.46/0.51 = { by axiom 3 (cn_1) }
% 0.46/0.51 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z))), implies(implies(u, y), implies(x, implies(u, z)))), implies(implies(x, implies(y, z)), implies(implies(u, y), implies(x, implies(u, z)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z))), implies(implies(u, y), implies(x, implies(u, z))))), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(u, y), implies(x, implies(u, z))))), true), true)
% 0.46/0.51 = { by axiom 1 (ifeq_axiom) }
% 0.46/0.51 ifeq(is_a_theorem(implies(implies(implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z))), implies(implies(u, y), implies(x, implies(u, z)))), implies(implies(x, implies(y, z)), implies(implies(u, y), implies(x, implies(u, z)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(y, z), implies(u, z)), implies(x, implies(u, z))), implies(implies(u, y), implies(x, implies(u, z))))), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(u, y), implies(x, implies(u, z))))), true), true)
% 0.46/0.51 = { by axiom 2 (condensed_detachment) }
% 0.46/0.51 true
% 0.46/0.51 % SZS output end Proof
% 0.46/0.51
% 0.46/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------