%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SEU140+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 12:45:18 PM UTC 2026
% Result : Theorem 0.12s 0.44s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU140+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n011.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 28 03:43:00 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.44 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
% 0.12/0.44
% 0.12/0.44 % SZS status Theorem
% 0.12/0.44
% 0.12/0.44 % SZS output start Proof
% 0.12/0.44 Axiom 1 (commutativity_k3_xboole_0): set_intersection2(X, Y) = set_intersection2(Y, X).
% 0.12/0.44 Axiom 2 (t63_xboole_1): disjoint(b, c) = true.
% 0.12/0.44 Axiom 3 (t63_xboole_1_1): subset(a, b) = true.
% 0.12/0.44 Axiom 4 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.12/0.44 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.12/0.44 Axiom 6 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 0.12/0.44 Axiom 7 (t3_xboole_1): ifeq2(subset(X, empty_set), true, X, empty_set) = empty_set.
% 0.12/0.44 Axiom 8 (d7_xboole_0_1): ifeq2(disjoint(X, Y), true, set_intersection2(X, Y), empty_set) = empty_set.
% 0.12/0.44 Axiom 9 (d7_xboole_0): ifeq3(set_intersection2(X, Y), empty_set, disjoint(X, Y), true) = true.
% 0.12/0.44 Axiom 10 (t26_xboole_1): ifeq(subset(X, Y), true, subset(set_intersection2(X, Z), set_intersection2(Y, Z)), true) = true.
% 0.12/0.44
% 0.12/0.44 Goal 1 (t63_xboole_1_2): disjoint(a, c) = true.
% 0.12/0.44 Proof:
% 0.12/0.44 disjoint(a, c)
% 0.12/0.44 = { by axiom 6 (ifeq_axiom) R->L }
% 0.12/0.44 ifeq3(empty_set, empty_set, disjoint(a, c), true)
% 0.12/0.44 = { by axiom 7 (t3_xboole_1) R->L }
% 0.12/0.44 ifeq3(ifeq2(subset(set_intersection2(c, a), empty_set), true, set_intersection2(c, a), empty_set), empty_set, disjoint(a, c), true)
% 0.12/0.44 = { by axiom 8 (d7_xboole_0_1) R->L }
% 0.12/0.44 ifeq3(ifeq2(subset(set_intersection2(c, a), ifeq2(disjoint(b, c), true, set_intersection2(b, c), empty_set)), true, set_intersection2(c, a), empty_set), empty_set, disjoint(a, c), true)
% 0.12/0.44 = { by axiom 2 (t63_xboole_1) }
% 0.12/0.44 ifeq3(ifeq2(subset(set_intersection2(c, a), ifeq2(true, true, set_intersection2(b, c), empty_set)), true, set_intersection2(c, a), empty_set), empty_set, disjoint(a, c), true)
% 0.12/0.44 = { by axiom 4 (ifeq_axiom) }
% 0.12/0.44 ifeq3(ifeq2(subset(set_intersection2(c, a), set_intersection2(b, c)), true, set_intersection2(c, a), empty_set), empty_set, disjoint(a, c), true)
% 0.12/0.44 = { by axiom 1 (commutativity_k3_xboole_0) R->L }
% 0.12/0.44 ifeq3(ifeq2(subset(set_intersection2(a, c), set_intersection2(b, c)), true, set_intersection2(c, a), empty_set), empty_set, disjoint(a, c), true)
% 0.12/0.44 = { by axiom 5 (ifeq_axiom) R->L }
% 0.12/0.44 ifeq3(ifeq2(ifeq(true, true, subset(set_intersection2(a, c), set_intersection2(b, c)), true), true, set_intersection2(c, a), empty_set), empty_set, disjoint(a, c), true)
% 0.12/0.44 = { by axiom 3 (t63_xboole_1_1) R->L }
% 0.12/0.44 ifeq3(ifeq2(ifeq(subset(a, b), true, subset(set_intersection2(a, c), set_intersection2(b, c)), true), true, set_intersection2(c, a), empty_set), empty_set, disjoint(a, c), true)
% 0.12/0.44 = { by axiom 10 (t26_xboole_1) }
% 0.12/0.44 ifeq3(ifeq2(true, true, set_intersection2(c, a), empty_set), empty_set, disjoint(a, c), true)
% 0.12/0.44 = { by axiom 4 (ifeq_axiom) }
% 0.12/0.44 ifeq3(set_intersection2(c, a), empty_set, disjoint(a, c), true)
% 0.12/0.44 = { by axiom 1 (commutativity_k3_xboole_0) R->L }
% 0.12/0.44 ifeq3(set_intersection2(a, c), empty_set, disjoint(a, c), true)
% 0.12/0.44 = { by axiom 9 (d7_xboole_0) }
% 0.12/0.44 true
% 0.12/0.44 % SZS output end Proof
% 0.12/0.44
% 0.12/0.44 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------