%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL079-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/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 11:48:59 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.49s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL079-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 15:20:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.49 Command-line arguments: --flatten --complete-subsets
% 0.19/0.49
% 0.19/0.49 % SZS status Unsatisfiable
% 0.19/0.49
% 0.19/0.49 % SZS output start Proof
% 0.19/0.49 Axiom 1 (a_implies_b): is_a_theorem(implies(a, b)) = true.
% 0.19/0.49 Axiom 2 (b_implies_c): is_a_theorem(implies(b, c)) = true.
% 0.19/0.49 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.19/0.49 Axiom 4 (cn_18): is_a_theorem(implies(X, implies(Y, X))) = true.
% 0.19/0.49 Axiom 5 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 0.19/0.49 Axiom 6 (cn_35): is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))) = true.
% 0.19/0.49
% 0.19/0.49 Lemma 7: ifeq(is_a_theorem(implies(X, Y)), is_a_theorem(implies(a, b)), ifeq(is_a_theorem(X), is_a_theorem(implies(a, b)), is_a_theorem(Y), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b))) = is_a_theorem(implies(a, b)).
% 0.19/0.49 Proof:
% 0.19/0.49 ifeq(is_a_theorem(implies(X, Y)), is_a_theorem(implies(a, b)), ifeq(is_a_theorem(X), is_a_theorem(implies(a, b)), is_a_theorem(Y), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)))
% 0.19/0.49 = { by axiom 1 (a_implies_b) }
% 0.19/0.49 ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), is_a_theorem(implies(a, b)), is_a_theorem(Y), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)))
% 0.19/0.49 = { by axiom 1 (a_implies_b) }
% 0.19/0.49 ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)))
% 0.19/0.49 = { by axiom 1 (a_implies_b) }
% 0.19/0.49 ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), is_a_theorem(implies(a, b)))
% 0.19/0.49 = { by axiom 1 (a_implies_b) }
% 0.19/0.49 ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true)
% 0.19/0.49 = { by axiom 5 (condensed_detachment) }
% 0.19/0.49 true
% 0.19/0.49 = { by axiom 1 (a_implies_b) R->L }
% 0.19/0.49 is_a_theorem(implies(a, b))
% 0.19/0.49
% 0.19/0.49 Goal 1 (prove_transitivity): is_a_theorem(implies(a, c)) = true.
% 0.19/0.49 Proof:
% 0.19/0.49 is_a_theorem(implies(a, c))
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.49 ifeq(is_a_theorem(implies(a, b)), is_a_theorem(implies(a, b)), is_a_theorem(implies(a, c)), is_a_theorem(implies(a, b)))
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.49 ifeq(is_a_theorem(implies(a, b)), is_a_theorem(implies(a, b)), ifeq(is_a_theorem(implies(a, b)), is_a_theorem(implies(a, b)), is_a_theorem(implies(a, c)), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)))
% 0.19/0.49 = { by lemma 7 R->L }
% 0.19/0.49 ifeq(ifeq(is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), is_a_theorem(implies(a, b)), ifeq(is_a_theorem(implies(a, implies(b, c))), is_a_theorem(implies(a, b)), is_a_theorem(implies(implies(a, b), implies(a, c))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)), ifeq(is_a_theorem(implies(a, b)), is_a_theorem(implies(a, b)), is_a_theorem(implies(a, c)), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)))
% 0.19/0.49 = { by axiom 6 (cn_35) }
% 0.19/0.49 ifeq(ifeq(true, is_a_theorem(implies(a, b)), ifeq(is_a_theorem(implies(a, implies(b, c))), is_a_theorem(implies(a, b)), is_a_theorem(implies(implies(a, b), implies(a, c))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)), ifeq(is_a_theorem(implies(a, b)), is_a_theorem(implies(a, b)), is_a_theorem(implies(a, c)), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)))
% 0.19/0.49 = { by axiom 1 (a_implies_b) R->L }
% 0.19/0.49 ifeq(ifeq(is_a_theorem(implies(a, b)), is_a_theorem(implies(a, b)), ifeq(is_a_theorem(implies(a, implies(b, c))), is_a_theorem(implies(a, b)), is_a_theorem(implies(implies(a, b), implies(a, c))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)), ifeq(is_a_theorem(implies(a, b)), is_a_theorem(implies(a, b)), is_a_theorem(implies(a, c)), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)))
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) }
% 0.19/0.49 ifeq(ifeq(is_a_theorem(implies(a, implies(b, c))), is_a_theorem(implies(a, b)), is_a_theorem(implies(implies(a, b), implies(a, c))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)), ifeq(is_a_theorem(implies(a, b)), is_a_theorem(implies(a, b)), is_a_theorem(implies(a, c)), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)))
% 0.19/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.49 ifeq(ifeq(ifeq(is_a_theorem(implies(a, b)), is_a_theorem(implies(a, b)), is_a_theorem(implies(a, implies(b, c))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)), is_a_theorem(implies(implies(a, b), implies(a, c))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)), ifeq(is_a_theorem(implies(a, b)), is_a_theorem(implies(a, b)), is_a_theorem(implies(a, c)), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)))
% 0.19/0.50 = { by axiom 1 (a_implies_b) }
% 0.19/0.50 ifeq(ifeq(ifeq(true, is_a_theorem(implies(a, b)), is_a_theorem(implies(a, implies(b, c))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)), is_a_theorem(implies(implies(a, b), implies(a, c))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)), ifeq(is_a_theorem(implies(a, b)), is_a_theorem(implies(a, b)), is_a_theorem(implies(a, c)), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)))
% 0.19/0.50 = { by axiom 2 (b_implies_c) R->L }
% 0.19/0.50 ifeq(ifeq(ifeq(is_a_theorem(implies(b, c)), is_a_theorem(implies(a, b)), is_a_theorem(implies(a, implies(b, c))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)), is_a_theorem(implies(implies(a, b), implies(a, c))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)), ifeq(is_a_theorem(implies(a, b)), is_a_theorem(implies(a, b)), is_a_theorem(implies(a, c)), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)))
% 0.19/0.50 = { by axiom 3 (ifeq_axiom) R->L }
% 0.19/0.50 ifeq(ifeq(ifeq(is_a_theorem(implies(a, b)), is_a_theorem(implies(a, b)), ifeq(is_a_theorem(implies(b, c)), is_a_theorem(implies(a, b)), is_a_theorem(implies(a, implies(b, c))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)), is_a_theorem(implies(implies(a, b), implies(a, c))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)), ifeq(is_a_theorem(implies(a, b)), is_a_theorem(implies(a, b)), is_a_theorem(implies(a, c)), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)))
% 0.19/0.50 = { by axiom 1 (a_implies_b) }
% 0.19/0.50 ifeq(ifeq(ifeq(true, is_a_theorem(implies(a, b)), ifeq(is_a_theorem(implies(b, c)), is_a_theorem(implies(a, b)), is_a_theorem(implies(a, implies(b, c))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)), is_a_theorem(implies(implies(a, b), implies(a, c))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)), ifeq(is_a_theorem(implies(a, b)), is_a_theorem(implies(a, b)), is_a_theorem(implies(a, c)), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)))
% 0.19/0.50 = { by axiom 4 (cn_18) R->L }
% 0.19/0.50 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, c), implies(a, implies(b, c)))), is_a_theorem(implies(a, b)), ifeq(is_a_theorem(implies(b, c)), is_a_theorem(implies(a, b)), is_a_theorem(implies(a, implies(b, c))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)), is_a_theorem(implies(implies(a, b), implies(a, c))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)), ifeq(is_a_theorem(implies(a, b)), is_a_theorem(implies(a, b)), is_a_theorem(implies(a, c)), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)))
% 0.19/0.50 = { by lemma 7 }
% 0.19/0.50 ifeq(ifeq(is_a_theorem(implies(a, b)), is_a_theorem(implies(a, b)), is_a_theorem(implies(implies(a, b), implies(a, c))), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)), ifeq(is_a_theorem(implies(a, b)), is_a_theorem(implies(a, b)), is_a_theorem(implies(a, c)), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)))
% 0.19/0.50 = { by axiom 3 (ifeq_axiom) }
% 0.19/0.50 ifeq(is_a_theorem(implies(implies(a, b), implies(a, c))), is_a_theorem(implies(a, b)), ifeq(is_a_theorem(implies(a, b)), is_a_theorem(implies(a, b)), is_a_theorem(implies(a, c)), is_a_theorem(implies(a, b))), is_a_theorem(implies(a, b)))
% 0.19/0.50 = { by lemma 7 }
% 0.19/0.50 is_a_theorem(implies(a, b))
% 0.19/0.50 = { by axiom 1 (a_implies_b) }
% 0.19/0.50 true
% 0.19/0.50 % SZS output end Proof
% 0.19/0.50
% 0.19/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------