%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL027-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 11:48:51 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.61s
% Output : Proof 0.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL027-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n002.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sun Sep 27 15:20:36 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.61 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
% 0.23/0.61
% 0.23/0.61 % SZS status Unsatisfiable
% 0.23/0.61
% 0.31/0.62 % SZS output start Proof
% 0.31/0.62 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.31/0.62 Axiom 2 (c0_2): is_a_theorem(implies(X, implies(Y, X))) = true.
% 0.31/0.62 Axiom 3 (c0_5): is_a_theorem(implies(implies(implies(X, falsehood), falsehood), X)) = true.
% 0.31/0.62 Axiom 4 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 0.31/0.62 Axiom 5 (c0_6): is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))) = true.
% 0.31/0.62
% 0.31/0.62 Goal 1 (prove_c0_4): is_a_theorem(implies(falsehood, a)) = true.
% 0.31/0.63 Proof:
% 0.31/0.63 is_a_theorem(implies(falsehood, a))
% 0.31/0.63 = { by axiom 1 (ifeq_axiom) R->L }
% 0.31/0.63 ifeq(true, true, is_a_theorem(implies(falsehood, a)), true)
% 0.31/0.63 = { by axiom 4 (condensed_detachment) R->L }
% 0.31/0.63 ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)), implies(implies(falsehood, implies(implies(a, falsehood), falsehood)), implies(falsehood, a)))), true, ifeq(is_a_theorem(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a))), true, is_a_theorem(implies(implies(falsehood, implies(implies(a, falsehood), falsehood)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.31/0.63 = { by axiom 5 (c0_6) }
% 0.31/0.63 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a))), true, is_a_theorem(implies(implies(falsehood, implies(implies(a, falsehood), falsehood)), implies(falsehood, a))), true), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.31/0.63 = { by axiom 1 (ifeq_axiom) }
% 0.31/0.63 ifeq(ifeq(is_a_theorem(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a))), true, is_a_theorem(implies(implies(falsehood, implies(implies(a, falsehood), falsehood)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.31/0.63 = { by axiom 1 (ifeq_axiom) R->L }
% 0.31/0.63 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(implies(a, falsehood), falsehood)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.31/0.63 = { by axiom 3 (c0_5) R->L }
% 0.31/0.63 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true, is_a_theorem(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a))), true), true, is_a_theorem(implies(implies(falsehood, implies(implies(a, falsehood), falsehood)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.31/0.63 = { by axiom 1 (ifeq_axiom) R->L }
% 0.31/0.63 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true, is_a_theorem(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(implies(a, falsehood), falsehood)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.31/0.63 = { by axiom 2 (c0_2) R->L }
% 0.31/0.63 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, falsehood), falsehood), a), implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a)))), true, ifeq(is_a_theorem(implies(implies(implies(a, falsehood), falsehood), a)), true, is_a_theorem(implies(falsehood, implies(implies(implies(a, falsehood), falsehood), a))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(implies(a, falsehood), falsehood)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.31/0.63 = { by axiom 4 (condensed_detachment) }
% 0.31/0.63 ifeq(ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(implies(a, falsehood), falsehood)), implies(falsehood, a))), true), true, is_a_theorem(implies(falsehood, a)), true)
% 0.31/0.63 = { by axiom 1 (ifeq_axiom) }
% 0.31/0.63 ifeq(is_a_theorem(implies(implies(falsehood, implies(implies(a, falsehood), falsehood)), implies(falsehood, a))), true, is_a_theorem(implies(falsehood, a)), true)
% 0.31/0.63 = { by axiom 1 (ifeq_axiom) R->L }
% 0.31/0.63 ifeq(is_a_theorem(implies(implies(falsehood, implies(implies(a, falsehood), falsehood)), implies(falsehood, a))), true, ifeq(true, true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.31/0.63 = { by axiom 2 (c0_2) R->L }
% 0.31/0.63 ifeq(is_a_theorem(implies(implies(falsehood, implies(implies(a, falsehood), falsehood)), implies(falsehood, a))), true, ifeq(is_a_theorem(implies(falsehood, implies(implies(a, falsehood), falsehood))), true, is_a_theorem(implies(falsehood, a)), true), true)
% 0.31/0.63 = { by axiom 4 (condensed_detachment) }
% 0.31/0.63 true
% 0.31/0.63 % SZS output end Proof
% 0.31/0.63
% 0.31/0.63 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------