%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT005-3 : TPTP v9.3.1. Released v1.0.0.
% 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 11:42:48 AM UTC 2026
% Result : Unsatisfiable 11.40s 1.93s
% Output : Proof 11.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT005-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.39 % Computer : n013.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 13:55:06 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.40/1.93 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 11.40/1.93
% 11.40/1.93 % SZS status Unsatisfiable
% 11.40/1.93
% 11.40/1.97 % SZS output start Proof
% 11.40/1.97 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 11.40/1.97 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 11.40/1.97 Axiom 3 (x_join_0): join(X, n0) = X.
% 11.40/1.97 Axiom 4 (absorption1): meet(X, join(X, Y)) = X.
% 11.40/1.97 Axiom 5 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 11.40/1.97 Axiom 6 (absorption2): join(X, meet(X, Y)) = X.
% 11.40/1.97 Axiom 7 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 11.40/1.97 Axiom 8 (complement_of_a_meet_b): complement(r2, meet(a, b)) = true.
% 11.40/1.97 Axiom 9 (complement_of_a_join_b): complement(r1, join(a, b)) = true.
% 11.40/1.97 Axiom 10 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 11.40/1.97 Axiom 11 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 11.40/1.97 Axiom 12 (complement_meet): ifeq(complement(X, Y), true, meet(X, Y), n0) = n0.
% 11.40/1.97 Axiom 13 (modular): ifeq3(meet(X, Y), X, meet(Y, join(X, Z)), join(X, meet(Z, Y))) = join(X, meet(Z, Y)).
% 11.40/1.97
% 11.40/1.97 Lemma 14: meet(Y, meet(Z, X)) = meet(X, meet(Y, Z)).
% 11.40/1.97 Proof:
% 11.40/1.97 meet(Y, meet(Z, X))
% 11.40/1.97 = { by axiom 1 (commutativity_of_meet) R->L }
% 11.40/1.97 meet(meet(Z, X), Y)
% 11.40/1.97 = { by axiom 1 (commutativity_of_meet) }
% 11.40/1.97 meet(meet(X, Z), Y)
% 11.40/1.97 = { by axiom 5 (associativity_of_meet) }
% 11.40/1.97 meet(X, meet(Z, Y))
% 11.40/1.97 = { by axiom 1 (commutativity_of_meet) }
% 11.40/1.97 meet(X, meet(Y, Z))
% 11.40/1.97
% 11.40/1.97 Lemma 15: join(X, meet(Y, X)) = X.
% 11.40/1.97 Proof:
% 11.40/1.97 join(X, meet(Y, X))
% 11.40/1.97 = { by axiom 1 (commutativity_of_meet) R->L }
% 11.40/1.97 join(X, meet(X, Y))
% 11.40/1.97 = { by axiom 6 (absorption2) }
% 11.40/1.97 X
% 11.40/1.97
% 11.40/1.97 Lemma 16: join(X, meet(Y, join(X, Z))) = meet(join(X, Y), join(X, Z)).
% 11.40/1.97 Proof:
% 11.40/1.97 join(X, meet(Y, join(X, Z)))
% 11.40/1.97 = { by axiom 13 (modular) R->L }
% 11.40/1.97 ifeq3(meet(X, join(X, Z)), X, meet(join(X, Z), join(X, Y)), join(X, meet(Y, join(X, Z))))
% 11.40/1.97 = { by axiom 4 (absorption1) }
% 11.40/1.97 ifeq3(X, X, meet(join(X, Z), join(X, Y)), join(X, meet(Y, join(X, Z))))
% 11.40/1.97 = { by axiom 11 (ifeq_axiom) }
% 11.40/1.97 meet(join(X, Z), join(X, Y))
% 11.40/1.97 = { by axiom 1 (commutativity_of_meet) }
% 11.40/1.98 meet(join(X, Y), join(X, Z))
% 11.40/1.98
% 11.40/1.98 Lemma 17: join(X, join(Y, meet(Z, X))) = join(Y, X).
% 11.40/1.98 Proof:
% 11.40/1.98 join(X, join(Y, meet(Z, X)))
% 11.40/1.98 = { by axiom 2 (commutativity_of_join) R->L }
% 11.40/1.98 join(X, join(meet(Z, X), Y))
% 11.40/1.98 = { by axiom 7 (associativity_of_join) R->L }
% 11.40/1.98 join(join(X, meet(Z, X)), Y)
% 11.40/1.98 = { by lemma 15 }
% 11.40/1.98 join(X, Y)
% 11.40/1.98 = { by axiom 2 (commutativity_of_join) }
% 11.40/1.98 join(Y, X)
% 11.40/1.98
% 11.40/1.98 Lemma 18: meet(join(r1, meet(r2, b)), join(r1, a)) = r1.
% 11.40/1.98 Proof:
% 11.40/1.98 meet(join(r1, meet(r2, b)), join(r1, a))
% 11.40/1.98 = { by lemma 16 R->L }
% 11.40/1.98 join(r1, meet(meet(r2, b), join(r1, a)))
% 11.40/1.98 = { by axiom 1 (commutativity_of_meet) R->L }
% 11.40/1.98 join(r1, meet(join(r1, a), meet(r2, b)))
% 11.40/1.98 = { by lemma 14 R->L }
% 11.40/1.98 join(r1, meet(r2, meet(b, join(r1, a))))
% 11.40/1.98 = { by axiom 1 (commutativity_of_meet) R->L }
% 11.40/1.98 join(r1, meet(r2, meet(join(r1, a), b)))
% 11.40/1.98 = { by axiom 4 (absorption1) R->L }
% 11.40/1.98 join(r1, meet(r2, meet(join(r1, a), meet(b, join(b, a)))))
% 11.40/1.98 = { by axiom 2 (commutativity_of_join) }
% 11.40/1.98 join(r1, meet(r2, meet(join(r1, a), meet(b, join(a, b)))))
% 11.40/1.98 = { by axiom 1 (commutativity_of_meet) R->L }
% 11.40/1.98 join(r1, meet(r2, meet(join(r1, a), meet(join(a, b), b))))
% 11.40/1.98 = { by axiom 5 (associativity_of_meet) R->L }
% 11.40/1.98 join(r1, meet(r2, meet(meet(join(r1, a), join(a, b)), b)))
% 11.40/1.98 = { by axiom 1 (commutativity_of_meet) }
% 11.40/1.98 join(r1, meet(r2, meet(b, meet(join(r1, a), join(a, b)))))
% 11.40/1.98 = { by axiom 2 (commutativity_of_join) R->L }
% 11.40/1.98 join(r1, meet(r2, meet(b, meet(join(a, r1), join(a, b)))))
% 11.40/1.98 = { by lemma 16 R->L }
% 11.40/1.98 join(r1, meet(r2, meet(b, join(a, meet(r1, join(a, b))))))
% 11.40/1.98 = { by axiom 10 (ifeq_axiom) R->L }
% 11.40/1.98 join(r1, meet(r2, meet(b, join(a, ifeq(true, true, meet(r1, join(a, b)), n0)))))
% 11.40/1.98 = { by axiom 9 (complement_of_a_join_b) R->L }
% 11.40/1.98 join(r1, meet(r2, meet(b, join(a, ifeq(complement(r1, join(a, b)), true, meet(r1, join(a, b)), n0)))))
% 11.40/1.98 = { by axiom 12 (complement_meet) }
% 11.40/1.98 join(r1, meet(r2, meet(b, join(a, n0))))
% 11.40/1.98 = { by axiom 3 (x_join_0) }
% 11.40/1.98 join(r1, meet(r2, meet(b, a)))
% 11.40/1.98 = { by axiom 1 (commutativity_of_meet) }
% 11.40/1.98 join(r1, meet(r2, meet(a, b)))
% 11.40/1.98 = { by axiom 10 (ifeq_axiom) R->L }
% 11.40/1.98 join(r1, ifeq(true, true, meet(r2, meet(a, b)), n0))
% 11.40/1.98 = { by axiom 8 (complement_of_a_meet_b) R->L }
% 11.40/1.98 join(r1, ifeq(complement(r2, meet(a, b)), true, meet(r2, meet(a, b)), n0))
% 11.40/1.98 = { by axiom 12 (complement_meet) }
% 11.40/1.98 join(r1, n0)
% 11.40/1.98 = { by axiom 3 (x_join_0) }
% 11.40/1.98 r1
% 11.40/1.98
% 11.40/1.98 Lemma 19: join(X, meet(join(X, Y), join(X, Z))) = meet(join(X, Y), join(X, Z)).
% 11.40/1.98 Proof:
% 11.40/1.98 join(X, meet(join(X, Y), join(X, Z)))
% 11.40/1.98 = { by axiom 2 (commutativity_of_join) R->L }
% 11.40/1.98 join(meet(join(X, Y), join(X, Z)), X)
% 11.40/1.98 = { by axiom 4 (absorption1) R->L }
% 11.40/1.98 join(meet(join(X, Y), join(X, Z)), meet(X, join(X, Z)))
% 11.40/1.98 = { by axiom 1 (commutativity_of_meet) R->L }
% 11.40/1.98 join(meet(join(X, Y), join(X, Z)), meet(join(X, Z), X))
% 11.40/1.98 = { by axiom 4 (absorption1) R->L }
% 11.40/1.98 join(meet(join(X, Y), join(X, Z)), meet(join(X, Z), meet(X, join(X, Y))))
% 11.40/1.98 = { by lemma 14 R->L }
% 11.40/1.98 join(meet(join(X, Y), join(X, Z)), meet(X, meet(join(X, Y), join(X, Z))))
% 11.40/1.98 = { by lemma 15 }
% 11.40/1.98 meet(join(X, Y), join(X, Z))
% 11.40/1.98
% 11.40/1.98 Lemma 20: join(X, join(Y, meet(join(X, Z), join(X, W)))) = join(Y, meet(join(X, Z), join(X, W))).
% 11.40/1.98 Proof:
% 11.40/1.98 join(X, join(Y, meet(join(X, Z), join(X, W))))
% 11.40/1.98 = { by axiom 2 (commutativity_of_join) R->L }
% 11.40/1.98 join(X, join(meet(join(X, Z), join(X, W)), Y))
% 11.40/1.98 = { by axiom 7 (associativity_of_join) R->L }
% 11.40/1.98 join(join(X, meet(join(X, Z), join(X, W))), Y)
% 11.40/1.98 = { by lemma 19 }
% 11.40/1.98 join(meet(join(X, Z), join(X, W)), Y)
% 11.40/1.98 = { by axiom 2 (commutativity_of_join) }
% 11.40/1.98 join(Y, meet(join(X, Z), join(X, W)))
% 11.40/1.98
% 11.40/1.98 Goal 1 (prove_lemma): r1 = meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))).
% 11.40/1.98 Proof:
% 11.40/1.98 r1
% 11.40/1.98 = { by lemma 18 R->L }
% 11.40/1.98 meet(join(r1, meet(r2, b)), join(r1, a))
% 11.40/1.98 = { by lemma 17 R->L }
% 11.40/1.98 meet(join(r1, meet(r2, b)), join(a, join(r1, meet(r2, a))))
% 11.40/1.98 = { by axiom 6 (absorption2) R->L }
% 11.40/1.99 meet(join(r1, meet(r2, b)), join(a, join(join(r1, meet(r2, a)), meet(join(r1, meet(r2, a)), join(r1, meet(r2, b))))))
% 11.40/1.99 = { by axiom 1 (commutativity_of_meet) R->L }
% 11.40/1.99 meet(join(r1, meet(r2, b)), join(a, join(join(r1, meet(r2, a)), meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))))))
% 11.40/1.99 = { by axiom 7 (associativity_of_join) }
% 11.40/1.99 meet(join(r1, meet(r2, b)), join(a, join(r1, join(meet(r2, a), meet(join(r1, meet(r2, b)), join(r1, meet(r2, a)))))))
% 11.40/1.99 = { by lemma 20 }
% 11.40/1.99 meet(join(r1, meet(r2, b)), join(a, join(meet(r2, a), meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))))))
% 11.40/1.99 = { by axiom 2 (commutativity_of_join) }
% 11.40/1.99 meet(join(r1, meet(r2, b)), join(a, join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(r2, a))))
% 11.40/1.99 = { by lemma 17 }
% 11.40/1.99 meet(join(r1, meet(r2, b)), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), a))
% 11.40/1.99 = { by axiom 2 (commutativity_of_join) }
% 11.40/1.99 meet(join(r1, meet(r2, b)), join(a, meet(join(r1, meet(r2, b)), join(r1, meet(r2, a)))))
% 11.40/1.99 = { by lemma 20 R->L }
% 11.40/1.99 meet(join(r1, meet(r2, b)), join(r1, join(a, meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))))))
% 11.40/1.99 = { by axiom 7 (associativity_of_join) R->L }
% 11.40/1.99 meet(join(r1, meet(r2, b)), join(join(r1, a), meet(join(r1, meet(r2, b)), join(r1, meet(r2, a)))))
% 11.40/1.99 = { by axiom 2 (commutativity_of_join) R->L }
% 11.40/1.99 meet(join(r1, meet(r2, b)), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(r1, a)))
% 11.40/1.99 = { by axiom 11 (ifeq_axiom) R->L }
% 11.40/1.99 ifeq3(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, meet(r2, b)), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(r1, a))), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, a), join(r1, meet(r2, b)))))
% 11.40/1.99 = { by axiom 4 (absorption1) R->L }
% 11.40/1.99 ifeq3(meet(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(r1, meet(r2, b)))), meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, meet(r2, b)), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(r1, a))), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, a), join(r1, meet(r2, b)))))
% 11.40/1.99 = { by axiom 2 (commutativity_of_join) R->L }
% 11.40/1.99 ifeq3(meet(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(join(r1, meet(r2, b)), meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))))), meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, meet(r2, b)), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(r1, a))), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, a), join(r1, meet(r2, b)))))
% 11.40/1.99 = { by axiom 1 (commutativity_of_meet) }
% 11.40/1.99 ifeq3(meet(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(join(r1, meet(r2, b)), meet(join(r1, meet(r2, a)), join(r1, meet(r2, b))))), meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, meet(r2, b)), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(r1, a))), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, a), join(r1, meet(r2, b)))))
% 11.40/1.99 = { by lemma 15 }
% 11.40/1.99 ifeq3(meet(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(r1, meet(r2, b))), meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, meet(r2, b)), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), join(r1, a))), join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, a), join(r1, meet(r2, b)))))
% 11.40/1.99 = { by axiom 13 (modular) }
% 11.40/1.99 join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, a), join(r1, meet(r2, b))))
% 11.40/1.99 = { by axiom 1 (commutativity_of_meet) }
% 11.40/1.99 join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), meet(join(r1, meet(r2, b)), join(r1, a)))
% 11.40/1.99 = { by lemma 18 }
% 11.40/1.99 join(meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))), r1)
% 11.40/1.99 = { by axiom 2 (commutativity_of_join) }
% 11.40/1.99 join(r1, meet(join(r1, meet(r2, b)), join(r1, meet(r2, a))))
% 11.40/1.99 = { by lemma 19 }
% 11.40/1.99 meet(join(r1, meet(r2, b)), join(r1, meet(r2, a)))
% 11.40/1.99 % SZS output end Proof
% 11.40/1.99
% 11.40/1.99 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------