%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 11:42:47 AM UTC 2026
% Result : Unsatisfiable 52.63s 7.26s
% Output : Proof 53.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 % Computer : n018.cluster.edu
% 0.20/0.47 % Model : x86_64 x86_64
% 0.20/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.47 % Memory : 8046.5625MB
% 0.20/0.47 % OS : Linux 6.8.0-71-generic
% 0.20/0.47 % CPULimit : 300
% 0.20/0.47 % WCLimit : 300
% 0.20/0.47 % DateTime : Sun Sep 27 13:57:08 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.47 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 52.63/7.26 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 52.63/7.26
% 52.63/7.26 % SZS status Unsatisfiable
% 52.63/7.26
% 53.48/7.29 % SZS output start Proof
% 53.48/7.29 Axiom 1 (idempotence_of_meet): meet(X, X) = X.
% 53.48/7.29 Axiom 2 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 53.48/7.29 Axiom 3 (x_meet_0): meet(X, n0) = n0.
% 53.48/7.29 Axiom 4 (x_meet_1): meet(X, n1) = X.
% 53.48/7.29 Axiom 5 (commutativity_of_join): join(X, Y) = join(Y, X).
% 53.48/7.29 Axiom 6 (x_join_0): join(X, n0) = X.
% 53.48/7.29 Axiom 7 (absorption1): meet(X, join(X, Y)) = X.
% 53.48/7.29 Axiom 8 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 53.48/7.29 Axiom 9 (absorption2): join(X, meet(X, Y)) = X.
% 53.48/7.29 Axiom 10 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 53.48/7.29 Axiom 11 (complement_of_a_meet_b): complement(r2, meet(a, b)) = true.
% 53.48/7.29 Axiom 12 (complement_of_a_join_b): complement(r1, join(a, b)) = true.
% 53.48/7.29 Axiom 13 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 53.48/7.29 Axiom 14 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 53.48/7.29 Axiom 15 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 53.48/7.29 Axiom 16 (complement_meet): ifeq(complement(X, Y), true, meet(X, Y), n0) = n0.
% 53.48/7.29 Axiom 17 (complement_join): ifeq(complement(X, Y), true, join(X, Y), n1) = n1.
% 53.48/7.29 Axiom 18 (meet_join_complement): ifeq2(join(X, Y), n1, ifeq2(meet(X, Y), n0, complement(X, Y), true), true) = true.
% 53.48/7.29 Axiom 19 (modular): ifeq3(meet(X, Y), X, meet(Y, join(X, Z)), join(X, meet(Z, Y))) = join(X, meet(Z, Y)).
% 53.48/7.29
% 53.48/7.29 Lemma 20: meet(X, meet(X, Y)) = meet(X, Y).
% 53.48/7.29 Proof:
% 53.48/7.29 meet(X, meet(X, Y))
% 53.48/7.29 = { by axiom 8 (associativity_of_meet) R->L }
% 53.48/7.29 meet(meet(X, X), Y)
% 53.48/7.29 = { by axiom 1 (idempotence_of_meet) }
% 53.48/7.29 meet(X, Y)
% 53.48/7.29
% 53.48/7.29 Lemma 21: meet(X, meet(Y, Z)) = meet(Y, meet(X, Z)).
% 53.48/7.29 Proof:
% 53.48/7.29 meet(X, meet(Y, Z))
% 53.48/7.29 = { by axiom 2 (commutativity_of_meet) R->L }
% 53.48/7.29 meet(meet(Y, Z), X)
% 53.48/7.29 = { by axiom 8 (associativity_of_meet) }
% 53.48/7.29 meet(Y, meet(Z, X))
% 53.48/7.29 = { by axiom 2 (commutativity_of_meet) }
% 53.48/7.29 meet(Y, meet(X, Z))
% 53.48/7.29
% 53.48/7.29 Lemma 22: meet(X, join(Y, X)) = X.
% 53.48/7.29 Proof:
% 53.48/7.29 meet(X, join(Y, X))
% 53.48/7.29 = { by axiom 5 (commutativity_of_join) R->L }
% 53.48/7.29 meet(X, join(X, Y))
% 53.48/7.29 = { by axiom 7 (absorption1) }
% 53.48/7.29 X
% 53.48/7.29
% 53.48/7.29 Lemma 23: meet(r1, join(b, a)) = n0.
% 53.48/7.29 Proof:
% 53.48/7.29 meet(r1, join(b, a))
% 53.48/7.29 = { by axiom 13 (ifeq_axiom) R->L }
% 53.48/7.29 ifeq(true, true, meet(r1, join(b, a)), n0)
% 53.48/7.29 = { by axiom 12 (complement_of_a_join_b) R->L }
% 53.48/7.29 ifeq(complement(r1, join(a, b)), true, meet(r1, join(b, a)), n0)
% 53.48/7.29 = { by axiom 5 (commutativity_of_join) }
% 53.48/7.29 ifeq(complement(r1, join(b, a)), true, meet(r1, join(b, a)), n0)
% 53.48/7.29 = { by axiom 16 (complement_meet) }
% 53.48/7.29 n0
% 53.48/7.29
% 53.48/7.29 Lemma 24: join(X, meet(Y, X)) = X.
% 53.48/7.29 Proof:
% 53.48/7.29 join(X, meet(Y, X))
% 53.48/7.29 = { by axiom 2 (commutativity_of_meet) }
% 53.48/7.29 join(X, meet(X, Y))
% 53.48/7.29 = { by axiom 9 (absorption2) }
% 53.48/7.29 X
% 53.48/7.29
% 53.48/7.29 Lemma 25: join(Y, join(X, Z)) = join(X, join(Y, Z)).
% 53.48/7.29 Proof:
% 53.48/7.29 join(Y, join(X, Z))
% 53.48/7.29 = { by axiom 5 (commutativity_of_join) R->L }
% 53.48/7.29 join(join(X, Z), Y)
% 53.48/7.29 = { by axiom 10 (associativity_of_join) }
% 53.48/7.29 join(X, join(Z, Y))
% 53.48/7.29 = { by axiom 5 (commutativity_of_join) }
% 53.48/7.29 join(X, join(Y, Z))
% 53.48/7.29
% 53.48/7.29 Lemma 26: meet(X, meet(Y, join(Z, X))) = meet(X, Y).
% 53.48/7.29 Proof:
% 53.48/7.29 meet(X, meet(Y, join(Z, X)))
% 53.48/7.29 = { by lemma 21 R->L }
% 53.48/7.29 meet(Y, meet(X, join(Z, X)))
% 53.48/7.29 = { by lemma 22 }
% 53.48/7.29 meet(Y, X)
% 53.48/7.29 = { by axiom 2 (commutativity_of_meet) }
% 53.48/7.29 meet(X, Y)
% 53.48/7.29
% 53.48/7.29 Lemma 27: join(X, meet(Y, join(X, Z))) = meet(join(X, Y), join(X, Z)).
% 53.48/7.29 Proof:
% 53.48/7.29 join(X, meet(Y, join(X, Z)))
% 53.48/7.29 = { by axiom 19 (modular) R->L }
% 53.48/7.29 ifeq3(meet(X, join(X, Z)), X, meet(join(X, Z), join(X, Y)), join(X, meet(Y, join(X, Z))))
% 53.48/7.29 = { by axiom 7 (absorption1) }
% 53.48/7.29 ifeq3(X, X, meet(join(X, Z), join(X, Y)), join(X, meet(Y, join(X, Z))))
% 53.48/7.29 = { by axiom 15 (ifeq_axiom) }
% 53.48/7.29 meet(join(X, Z), join(X, Y))
% 53.48/7.29 = { by axiom 2 (commutativity_of_meet) }
% 53.48/7.29 meet(join(X, Y), join(X, Z))
% 53.48/7.29
% 53.48/7.29 Lemma 28: join(X, meet(Y, join(Z, X))) = meet(join(X, Y), join(X, Z)).
% 53.48/7.29 Proof:
% 53.48/7.29 join(X, meet(Y, join(Z, X)))
% 53.48/7.29 = { by axiom 5 (commutativity_of_join) R->L }
% 53.48/7.29 join(X, meet(Y, join(X, Z)))
% 53.48/7.29 = { by lemma 27 }
% 53.48/7.29 meet(join(X, Y), join(X, Z))
% 53.48/7.29
% 53.48/7.29 Lemma 29: join(X, join(Y, meet(Z, X))) = join(X, Y).
% 53.48/7.30 Proof:
% 53.48/7.30 join(X, join(Y, meet(Z, X)))
% 53.48/7.30 = { by lemma 25 }
% 53.48/7.30 join(Y, join(X, meet(Z, X)))
% 53.48/7.30 = { by lemma 24 }
% 53.48/7.30 join(Y, X)
% 53.48/7.30 = { by axiom 5 (commutativity_of_join) }
% 53.48/7.30 join(X, Y)
% 53.48/7.30
% 53.48/7.30 Lemma 30: join(meet(X, Y), meet(X, Z)) = meet(X, join(Z, meet(X, Y))).
% 53.48/7.30 Proof:
% 53.48/7.30 join(meet(X, Y), meet(X, Z))
% 53.48/7.30 = { by axiom 2 (commutativity_of_meet) R->L }
% 53.48/7.30 join(meet(X, Y), meet(Z, X))
% 53.48/7.30 = { by axiom 9 (absorption2) R->L }
% 53.48/7.30 join(meet(X, Y), meet(Z, join(X, meet(X, Y))))
% 53.48/7.30 = { by lemma 28 }
% 53.48/7.30 meet(join(meet(X, Y), Z), join(meet(X, Y), X))
% 53.48/7.30 = { by axiom 5 (commutativity_of_join) }
% 53.48/7.30 meet(join(meet(X, Y), Z), join(X, meet(X, Y)))
% 53.48/7.30 = { by axiom 9 (absorption2) }
% 53.48/7.30 meet(join(meet(X, Y), Z), X)
% 53.48/7.30 = { by axiom 2 (commutativity_of_meet) }
% 53.48/7.30 meet(X, join(meet(X, Y), Z))
% 53.48/7.30 = { by axiom 5 (commutativity_of_join) }
% 53.48/7.30 meet(X, join(Z, meet(X, Y)))
% 53.70/7.30
% 53.70/7.30 Lemma 31: join(meet(X, Y), meet(X, Z)) = meet(X, join(Y, meet(X, Z))).
% 53.70/7.30 Proof:
% 53.70/7.30 join(meet(X, Y), meet(X, Z))
% 53.70/7.30 = { by axiom 5 (commutativity_of_join) R->L }
% 53.70/7.30 join(meet(X, Z), meet(X, Y))
% 53.70/7.30 = { by lemma 30 }
% 53.70/7.30 meet(X, join(Y, meet(X, Z)))
% 53.70/7.30
% 53.70/7.30 Goal 1 (prove_complememt): complement(a, join(r1, meet(r2, b))) = true.
% 53.70/7.30 Proof:
% 53.70/7.30 complement(a, join(r1, meet(r2, b)))
% 53.70/7.30 = { by axiom 14 (ifeq_axiom) R->L }
% 53.70/7.30 ifeq2(n0, n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by axiom 16 (complement_meet) R->L }
% 53.70/7.30 ifeq2(ifeq(complement(r2, meet(b, a)), true, meet(r2, meet(b, a)), n0), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by axiom 2 (commutativity_of_meet) R->L }
% 53.70/7.30 ifeq2(ifeq(complement(r2, meet(a, b)), true, meet(r2, meet(b, a)), n0), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by axiom 11 (complement_of_a_meet_b) }
% 53.70/7.30 ifeq2(ifeq(true, true, meet(r2, meet(b, a)), n0), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by axiom 13 (ifeq_axiom) }
% 53.70/7.30 ifeq2(meet(r2, meet(b, a)), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by lemma 21 }
% 53.70/7.30 ifeq2(meet(b, meet(r2, a)), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by axiom 8 (associativity_of_meet) R->L }
% 53.70/7.30 ifeq2(meet(meet(b, r2), a), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by axiom 2 (commutativity_of_meet) R->L }
% 53.70/7.30 ifeq2(meet(meet(r2, b), a), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by axiom 6 (x_join_0) R->L }
% 53.70/7.30 ifeq2(meet(join(meet(r2, b), n0), a), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by axiom 3 (x_meet_0) R->L }
% 53.70/7.30 ifeq2(meet(join(meet(r2, b), meet(b, n0)), a), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by lemma 23 R->L }
% 53.70/7.30 ifeq2(meet(join(meet(r2, b), meet(b, meet(r1, join(b, a)))), a), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by axiom 2 (commutativity_of_meet) R->L }
% 53.70/7.30 ifeq2(meet(join(meet(r2, b), meet(b, meet(join(b, a), r1))), a), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by axiom 8 (associativity_of_meet) R->L }
% 53.70/7.30 ifeq2(meet(join(meet(r2, b), meet(meet(b, join(b, a)), r1)), a), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by axiom 7 (absorption1) }
% 53.70/7.30 ifeq2(meet(join(meet(r2, b), meet(b, r1)), a), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by axiom 2 (commutativity_of_meet) R->L }
% 53.70/7.30 ifeq2(meet(join(meet(r2, b), meet(r1, b)), a), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by lemma 24 R->L }
% 53.70/7.30 ifeq2(meet(join(meet(r2, b), meet(r1, join(b, meet(r2, b)))), a), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by lemma 28 }
% 53.70/7.30 ifeq2(meet(meet(join(meet(r2, b), r1), join(meet(r2, b), b)), a), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by axiom 5 (commutativity_of_join) }
% 53.70/7.30 ifeq2(meet(meet(join(meet(r2, b), r1), join(b, meet(r2, b))), a), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by axiom 2 (commutativity_of_meet) }
% 53.70/7.30 ifeq2(meet(meet(join(b, meet(r2, b)), join(meet(r2, b), r1)), a), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by lemma 24 }
% 53.70/7.30 ifeq2(meet(meet(b, join(meet(r2, b), r1)), a), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by axiom 5 (commutativity_of_join) }
% 53.70/7.30 ifeq2(meet(meet(b, join(r1, meet(r2, b))), a), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by axiom 8 (associativity_of_meet) }
% 53.70/7.30 ifeq2(meet(b, meet(join(r1, meet(r2, b)), a)), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by lemma 21 R->L }
% 53.70/7.30 ifeq2(meet(join(r1, meet(r2, b)), meet(b, a)), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by axiom 2 (commutativity_of_meet) R->L }
% 53.70/7.30 ifeq2(meet(join(r1, meet(r2, b)), meet(a, b)), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by axiom 6 (x_join_0) R->L }
% 53.70/7.30 ifeq2(meet(join(r1, meet(r2, b)), meet(a, join(b, n0))), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by lemma 23 R->L }
% 53.70/7.30 ifeq2(meet(join(r1, meet(r2, b)), meet(a, join(b, meet(r1, join(b, a))))), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by lemma 27 }
% 53.70/7.30 ifeq2(meet(join(r1, meet(r2, b)), meet(a, meet(join(b, r1), join(b, a)))), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by lemma 26 }
% 53.70/7.30 ifeq2(meet(join(r1, meet(r2, b)), meet(a, join(b, r1))), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by lemma 29 R->L }
% 53.70/7.30 ifeq2(meet(join(r1, meet(r2, b)), meet(a, join(b, join(r1, meet(r2, b))))), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by lemma 26 }
% 53.70/7.30 ifeq2(meet(join(r1, meet(r2, b)), a), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by axiom 2 (commutativity_of_meet) }
% 53.70/7.30 ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true)
% 53.70/7.30 = { by axiom 14 (ifeq_axiom) R->L }
% 53.70/7.30 ifeq2(n1, n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.30 = { by axiom 17 (complement_join) R->L }
% 53.70/7.30 ifeq2(ifeq(complement(r1, join(b, a)), true, join(r1, join(b, a)), n1), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.30 = { by axiom 5 (commutativity_of_join) R->L }
% 53.70/7.30 ifeq2(ifeq(complement(r1, join(a, b)), true, join(r1, join(b, a)), n1), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.30 = { by axiom 12 (complement_of_a_join_b) }
% 53.70/7.30 ifeq2(ifeq(true, true, join(r1, join(b, a)), n1), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by axiom 13 (ifeq_axiom) }
% 53.70/7.31 ifeq2(join(r1, join(b, a)), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by lemma 25 R->L }
% 53.70/7.31 ifeq2(join(b, join(r1, a)), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by axiom 10 (associativity_of_join) R->L }
% 53.70/7.31 ifeq2(join(join(b, r1), a), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by lemma 29 R->L }
% 53.70/7.31 ifeq2(join(join(b, join(r1, meet(r2, b))), a), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by axiom 10 (associativity_of_join) }
% 53.70/7.31 ifeq2(join(b, join(join(r1, meet(r2, b)), a)), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by axiom 5 (commutativity_of_join) }
% 53.70/7.31 ifeq2(join(b, join(a, join(r1, meet(r2, b)))), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by lemma 25 }
% 53.70/7.31 ifeq2(join(a, join(b, join(r1, meet(r2, b)))), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by axiom 5 (commutativity_of_join) R->L }
% 53.70/7.31 ifeq2(join(a, join(join(r1, meet(r2, b)), b)), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by axiom 4 (x_meet_1) R->L }
% 53.70/7.31 ifeq2(join(a, join(join(r1, meet(r2, b)), meet(b, n1))), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by axiom 17 (complement_join) R->L }
% 53.70/7.31 ifeq2(join(a, join(join(r1, meet(r2, b)), meet(b, ifeq(complement(r2, meet(b, a)), true, join(r2, meet(b, a)), n1)))), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by axiom 2 (commutativity_of_meet) R->L }
% 53.70/7.31 ifeq2(join(a, join(join(r1, meet(r2, b)), meet(b, ifeq(complement(r2, meet(a, b)), true, join(r2, meet(b, a)), n1)))), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by axiom 11 (complement_of_a_meet_b) }
% 53.70/7.31 ifeq2(join(a, join(join(r1, meet(r2, b)), meet(b, ifeq(true, true, join(r2, meet(b, a)), n1)))), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by axiom 13 (ifeq_axiom) }
% 53.70/7.31 ifeq2(join(a, join(join(r1, meet(r2, b)), meet(b, join(r2, meet(b, a))))), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by lemma 20 R->L }
% 53.70/7.31 ifeq2(join(a, join(join(r1, meet(r2, b)), meet(b, meet(b, join(r2, meet(b, a)))))), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by lemma 31 R->L }
% 53.70/7.31 ifeq2(join(a, join(join(r1, meet(r2, b)), meet(b, join(meet(b, r2), meet(b, a))))), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by lemma 30 R->L }
% 53.70/7.31 ifeq2(join(a, join(join(r1, meet(r2, b)), join(meet(b, a), meet(b, meet(b, r2))))), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by lemma 20 }
% 53.70/7.31 ifeq2(join(a, join(join(r1, meet(r2, b)), join(meet(b, a), meet(b, r2)))), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by lemma 31 }
% 53.70/7.31 ifeq2(join(a, join(join(r1, meet(r2, b)), meet(b, join(a, meet(b, r2))))), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by axiom 2 (commutativity_of_meet) R->L }
% 53.70/7.31 ifeq2(join(a, join(join(r1, meet(r2, b)), meet(b, join(a, meet(r2, b))))), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by axiom 10 (associativity_of_join) R->L }
% 53.70/7.31 ifeq2(join(join(a, join(r1, meet(r2, b))), meet(b, join(a, meet(r2, b)))), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by lemma 22 R->L }
% 53.70/7.31 ifeq2(join(join(a, join(r1, meet(r2, b))), meet(b, meet(join(a, meet(r2, b)), join(r1, join(a, meet(r2, b)))))), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by lemma 25 R->L }
% 53.70/7.31 ifeq2(join(join(a, join(r1, meet(r2, b))), meet(b, meet(join(a, meet(r2, b)), join(a, join(r1, meet(r2, b)))))), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by axiom 8 (associativity_of_meet) R->L }
% 53.70/7.31 ifeq2(join(join(a, join(r1, meet(r2, b))), meet(meet(b, join(a, meet(r2, b))), join(a, join(r1, meet(r2, b))))), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by lemma 24 }
% 53.70/7.31 ifeq2(join(a, join(r1, meet(r2, b))), n1, ifeq2(meet(a, join(r1, meet(r2, b))), n0, complement(a, join(r1, meet(r2, b))), true), true)
% 53.70/7.31 = { by axiom 18 (meet_join_complement) }
% 53.70/7.31 true
% 53.70/7.31 % SZS output end Proof
% 53.70/7.31
% 53.70/7.31 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------