%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU596^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 : Wed Sep 30 08:30:14 AM UTC 2026
% Result : Theorem 0.23s 0.30s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU596^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n015.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:59:33 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.30 % (3564072)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.30 % (3564081)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2271294206:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.30 % (3564081) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3564072-3564081"...
% 0.23/0.30 % (3564081)...printing done.
% 0.23/0.30 % (3564083)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.30 % (3564083)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.23/0.30 % (3564081)Refutation found. Thanks to Tanya!
% 0.23/0.30 % SZS status Theorem for theBenchmark
% 0.23/0.30 % SZS output start Proof for theBenchmark
% 0.23/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.30 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.23/0.30 thf(func_def_2, type, emptyI: $o).
% 0.23/0.30 thf(func_def_4, type, binintersect: ($i > $i > $i)).
% 0.23/0.30 thf(func_def_5, type, binintersectEL: $o).
% 0.23/0.30 thf(func_def_6, type, binintersectER: $o).
% 0.23/0.30 thf(func_def_18, type, sK9: ($i > $i)).
% 0.23/0.30 thf(f1,axiom,(
% 0.23/0.30 (emptyI = ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)))),
% 0.23/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI)).
% 0.23/0.30 thf(f2,axiom,(
% 0.23/0.30 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)) = binintersectEL)),
% 0.23/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL)).
% 0.23/0.30 thf(f3,axiom,(
% 0.23/0.30 (! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)) = binintersectER)),
% 0.23/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER)).
% 0.23/0.30 thf(f4,conjecture,(
% 0.23/0.30 emptyI => (binintersectEL => (binintersectER => ! [X1 : $i,X0 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X1) & (in @ X2 @ X0)) => (((binintersect @ X0 @ X1)) = emptyset))))),
% 0.23/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjointsetsI1)).
% 0.23/0.30 thf(f5,negated_conjecture,(
% 0.23/0.30 ~(emptyI => (binintersectEL => (binintersectER => ! [X1 : $i,X0 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X1) & (in @ X2 @ X0)) => (((binintersect @ X0 @ X1)) = emptyset)))))),
% 0.23/0.30 inference(negated_conjecture,[status(cth)],[f4])).
% 0.23/0.30 thf(f6,plain,(
% 0.23/0.30 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X1 @ X0)) => (in @ X2 @ X0)) = binintersectER)),
% 0.23/0.30 inference(rectify,[],[f3])).
% 0.23/0.30 thf(f7,plain,(
% 0.23/0.30 ! [X0 : $i,X2 : $i,X1 : $i] : (($true = ((in @ X2 @ (binintersect @ X1 @ X0)))) => (((in @ X2 @ X0)) = $true)) <=> (binintersectER = $true)),
% 0.23/0.30 inference(fool_elimination,[],[f6])).
% 0.23/0.30 thf(f8,plain,(
% 0.23/0.30 (emptyI = ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (X0 = emptyset)))),
% 0.23/0.30 inference(rectify,[],[f1])).
% 0.23/0.30 thf(f9,plain,(
% 0.23/0.30 (emptyI = $true) <=> ! [X0 : $i] : (! [X1 : $i] : ~ (((in @ X1 @ X0)) = $true) => (emptyset = X0))),
% 0.23/0.30 inference(fool_elimination,[],[f8])).
% 0.23/0.30 thf(f10,plain,(
% 0.23/0.30 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (binintersect @ X2 @ X0)) => (in @ X1 @ X2)) = binintersectEL)),
% 0.23/0.30 inference(rectify,[],[f2])).
% 0.23/0.30 thf(f11,plain,(
% 0.23/0.30 (binintersectEL = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X1 @ (binintersect @ X2 @ X0))) = $true) => ($true = ((in @ X1 @ X2))))),
% 0.23/0.30 inference(fool_elimination,[],[f10])).
% 0.23/0.30 thf(f12,plain,(
% 0.23/0.30 ~(emptyI => (binintersectEL => (binintersectER => ! [X0 : $i,X1 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X0) & (in @ X2 @ X1)) => (emptyset = ((binintersect @ X1 @ X0)))))))),
% 0.23/0.30 inference(rectify,[],[f5])).
% 0.23/0.30 thf(f13,plain,(
% 0.23/0.30 ~((emptyI = $true) => ((binintersectEL = $true) => ((binintersectER = $true) => ! [X1 : $i,X0 : $i] : (~ ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) = $true)) => (emptyset = ((binintersect @ X1 @ X0)))))))),
% 0.23/0.30 inference(fool_elimination,[],[f12])).
% 0.23/0.30 thf(f14,plain,(
% 0.23/0.30 (emptyI = $true) <=> ! [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0)) != $true) => (emptyset = X0))),
% 0.23/0.30 inference(flattening,[],[f9])).
% 0.23/0.30 thf(f15,plain,(
% 0.23/0.30 ((? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ X1)) != $true)) & (emptyset != ((binintersect @ X1 @ X0)))) & (binintersectER = $true)) & (binintersectEL = $true)) & (emptyI = $true)),
% 0.23/0.30 inference(ennf_transformation,[],[f13])).
% 0.23/0.30 thf(f16,plain,(
% 0.23/0.30 ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ X1)) != $true)) & (emptyset != ((binintersect @ X1 @ X0)))) & (binintersectEL = $true) & (binintersectER = $true) & (emptyI = $true)),
% 0.23/0.30 inference(flattening,[],[f15])).
% 0.23/0.30 thf(f17,plain,(
% 0.23/0.30 ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) = $true) | ($true != ((in @ X2 @ (binintersect @ X1 @ X0))))) <=> (binintersectER = $true)),
% 0.23/0.30 inference(ennf_transformation,[],[f7])).
% 0.23/0.30 thf(f18,plain,(
% 0.23/0.30 (emptyI = $true) <=> ! [X0 : $i] : ((emptyset = X0) | ? [X1 : $i] : (((in @ X1 @ X0)) = $true))),
% 0.23/0.30 inference(ennf_transformation,[],[f14])).
% 0.23/0.30 thf(f19,plain,(
% 0.23/0.30 ! [X1 : $i,X2 : $i,X0 : $i] : (($true = ((in @ X1 @ X2))) | (((in @ X1 @ (binintersect @ X2 @ X0))) != $true)) <=> (binintersectEL = $true)),
% 0.23/0.30 inference(ennf_transformation,[],[f11])).
% 0.23/0.30 thf(f20,plain,(
% 0.23/0.30 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) = $true) | ($true != ((in @ X2 @ (binintersect @ X1 @ X0))))) | (binintersectER != $true)) & ((binintersectER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) != $true) & ($true = ((in @ X2 @ (binintersect @ X1 @ X0))))))),
% 0.23/0.30 inference(nnf_transformation,[],[f17])).
% 0.23/0.30 thf(f21,plain,(
% 0.23/0.30 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) = $true) | ($true != ((in @ X2 @ (binintersect @ X1 @ X0))))) | (binintersectER != $true)) & ((binintersectER = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X5 @ X3))) & ($true = ((in @ X5 @ (binintersect @ X4 @ X3))))))),
% 0.23/0.30 inference(rectify,[],[f20])).
% 0.23/0.30 thf(f22,plain,(
% 0.23/0.30 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) = $true) | ($true != ((in @ X2 @ (binintersect @ X1 @ X0))))) | (binintersectER != $true)) & ((binintersectER = $true) | (($true != ((in @ sK2 @ sK0))) & ($true = ((in @ sK2 @ (binintersect @ sK1 @ sK0))))))),
% 0.23/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0),skolemize(X4,sK1),skolemize(X5,sK2)],[f21])).
% 0.23/0.30 thf(f23,plain,(
% 0.23/0.30 (! [X2 : $i] : (($true != ((in @ X2 @ sK3))) | ($true != ((in @ X2 @ sK4)))) & (emptyset != ((binintersect @ sK4 @ sK3)))) & (binintersectEL = $true) & (binintersectER = $true) & (emptyI = $true)),
% 0.23/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f16])).
% 0.23/0.30 thf(f24,plain,(
% 0.23/0.30 (! [X1 : $i,X2 : $i,X0 : $i] : (($true = ((in @ X1 @ X2))) | (((in @ X1 @ (binintersect @ X2 @ X0))) != $true)) | (binintersectEL != $true)) & ((binintersectEL = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (($true != ((in @ X1 @ X2))) & (((in @ X1 @ (binintersect @ X2 @ X0))) = $true)))),
% 0.23/0.30 inference(nnf_transformation,[],[f19])).
% 0.23/0.30 thf(f25,plain,(
% 0.23/0.30 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X0 @ X1))) | ($true != ((in @ X0 @ (binintersect @ X1 @ X2))))) | (binintersectEL != $true)) & ((binintersectEL = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X3 @ X4))) & ($true = ((in @ X3 @ (binintersect @ X4 @ X5))))))),
% 0.23/0.30 inference(rectify,[],[f24])).
% 0.23/0.30 thf(f26,plain,(
% 0.23/0.30 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X0 @ X1))) | ($true != ((in @ X0 @ (binintersect @ X1 @ X2))))) | (binintersectEL != $true)) & ((binintersectEL = $true) | (($true != ((in @ sK5 @ sK6))) & ($true = ((in @ sK5 @ (binintersect @ sK6 @ sK7))))))),
% 0.23/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X3,sK5),skolemize(X4,sK6),skolemize(X5,sK7)],[f25])).
% 0.23/0.30 thf(f27,plain,(
% 0.23/0.30 ((emptyI = $true) | ? [X0 : $i] : ((emptyset != X0) & ! [X1 : $i] : (((in @ X1 @ X0)) != $true))) & (! [X0 : $i] : ((emptyset = X0) | ? [X1 : $i] : (((in @ X1 @ X0)) = $true)) | (emptyI != $true))),
% 0.23/0.30 inference(nnf_transformation,[],[f18])).
% 0.23/0.30 thf(f28,plain,(
% 0.23/0.30 ((emptyI = $true) | ? [X0 : $i] : ((emptyset != X0) & ! [X1 : $i] : (((in @ X1 @ X0)) != $true))) & (! [X2 : $i] : ((emptyset = X2) | ? [X3 : $i] : ($true = ((in @ X3 @ X2)))) | (emptyI != $true))),
% 0.23/0.30 inference(rectify,[],[f27])).
% 0.23/0.30 thf(f29,plain,(
% 0.23/0.30 ((emptyI = $true) | ((emptyset != sK8) & ! [X1 : $i] : ($true != ((in @ X1 @ sK8))))) & (! [X2 : $i] : ((emptyset = X2) | ($true = ((in @ (sK9 @ X2) @ X2)))) | (emptyI != $true))),
% 0.23/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK8,vAPP]),skolemize(X0,sK8),skolemize(X3,sK9 @ X2)],[f28])).
% 0.23/0.30 thf(f32,plain,(
% 0.23/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((binintersectER != $true) | ($true != ((in @ X2 @ (binintersect @ X1 @ X0)))) | (((in @ X2 @ X0)) = $true)) )),
% 0.23/0.30 inference(cnf_transformation,[],[f22])).
% 0.23/0.30 thf(f33,plain,(
% 0.23/0.30 (emptyI = $true)),
% 0.23/0.30 inference(cnf_transformation,[],[f23])).
% 0.23/0.30 thf(f34,plain,(
% 0.23/0.30 (binintersectER = $true)),
% 0.23/0.30 inference(cnf_transformation,[],[f23])).
% 0.23/0.30 thf(f35,plain,(
% 0.23/0.30 (binintersectEL = $true)),
% 0.23/0.30 inference(cnf_transformation,[],[f23])).
% 0.23/0.30 thf(f36,plain,(
% 0.23/0.30 (emptyset != ((binintersect @ sK4 @ sK3)))),
% 0.23/0.30 inference(cnf_transformation,[],[f23])).
% 0.23/0.30 thf(f37,plain,(
% 0.23/0.30 ( ! [X2 : $i] : (($true != ((in @ X2 @ sK3))) | ($true != ((in @ X2 @ sK4)))) )),
% 0.23/0.30 inference(cnf_transformation,[],[f23])).
% 0.23/0.30 thf(f40,plain,(
% 0.23/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((binintersectEL != $true) | ($true != ((in @ X0 @ (binintersect @ X1 @ X2)))) | ($true = ((in @ X0 @ X1)))) )),
% 0.23/0.30 inference(cnf_transformation,[],[f26])).
% 0.23/0.30 thf(f41,plain,(
% 0.23/0.30 ( ! [X2 : $i] : ((emptyset = X2) | (emptyI != $true) | ($true = ((in @ (sK9 @ X2) @ X2)))) )),
% 0.23/0.30 inference(cnf_transformation,[],[f29])).
% 0.23/0.30 thf(f48,plain,(
% 0.23/0.30 ( ! [X2 : $i] : (($true = ((in @ (sK9 @ X2) @ X2))) | (emptyset = X2)) )),
% 0.23/0.30 inference(forward_subsumption_resolution,[],[f41,f33])).
% 0.23/0.30 thf(f51,plain,(
% 0.23/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X2 @ (binintersect @ X1 @ X0)))) | (((in @ X2 @ X0)) = $true)) )),
% 0.23/0.30 inference(forward_subsumption_resolution,[],[f32,f34])).
% 0.23/0.30 thf(f52,plain,(
% 0.23/0.30 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK9 @ (binintersect @ X0 @ X1)) @ X1))) | (emptyset = ((binintersect @ X0 @ X1))) | ($true != $true)) )),
% 0.23/0.30 inference(superposition,[],[f51,f48])).
% 0.23/0.30 thf(f53,plain,(
% 0.23/0.30 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK9 @ (binintersect @ X0 @ X1)) @ X1))) | (emptyset = ((binintersect @ X0 @ X1)))) )),
% 0.23/0.30 inference(trivial_inequality_removal,[],[f52])).
% 0.23/0.30 thf(f54,plain,(
% 0.23/0.30 ( ! [X0 : $i] : (($true != ((in @ (sK9 @ (binintersect @ X0 @ sK3)) @ sK4))) | ($true != $true) | (emptyset = ((binintersect @ X0 @ sK3)))) )),
% 0.23/0.30 inference(superposition,[],[f37,f53])).
% 0.23/0.30 thf(f56,plain,(
% 0.23/0.30 ( ! [X0 : $i] : (($true != ((in @ (sK9 @ (binintersect @ X0 @ sK3)) @ sK4))) | (emptyset = ((binintersect @ X0 @ sK3)))) )),
% 0.23/0.30 inference(trivial_inequality_removal,[],[f54])).
% 0.23/0.30 thf(f62,plain,(
% 0.23/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (binintersect @ X1 @ X2)))) | ($true = ((in @ X0 @ X1)))) )),
% 0.23/0.30 inference(forward_subsumption_resolution,[],[f40,f35])).
% 0.23/0.30 thf(f63,plain,(
% 0.23/0.30 ( ! [X0 : $i,X1 : $i] : ((emptyset = ((binintersect @ X0 @ X1))) | ($true != $true) | ($true = ((in @ (sK9 @ (binintersect @ X0 @ X1)) @ X0)))) )),
% 0.23/0.30 inference(superposition,[],[f62,f48])).
% 0.23/0.30 thf(f68,plain,(
% 0.23/0.30 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK9 @ (binintersect @ X0 @ X1)) @ X0))) | (emptyset = ((binintersect @ X0 @ X1)))) )),
% 0.23/0.30 inference(trivial_inequality_removal,[],[f63])).
% 0.23/0.30 thf(f69,plain,(
% 0.23/0.30 (emptyset = ((binintersect @ sK4 @ sK3))) | ($true != $true) | (emptyset = ((binintersect @ sK4 @ sK3)))),
% 0.23/0.30 inference(superposition,[],[f56,f68])).
% 0.23/0.30 thf(f78,plain,(
% 0.23/0.30 (emptyset = ((binintersect @ sK4 @ sK3))) | ($true != $true)),
% 0.23/0.30 inference(duplicate_literal_removal,[],[f69])).
% 0.23/0.30 thf(f79,plain,(
% 0.23/0.30 (emptyset = ((binintersect @ sK4 @ sK3)))),
% 0.23/0.30 inference(trivial_inequality_removal,[],[f78])).
% 0.23/0.30 thf(f81,plain,(
% 0.23/0.30 $false),
% 0.23/0.30 inference(forward_subsumption_resolution,[],[f79,f36])).
% 0.23/0.30 % SZS output end Proof for theBenchmark
% 0.23/0.30 % (3564081)------------------------------
% 0.23/0.30 % (3564081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (3564081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (3564081)CaDiCaL version: 2.1.3
% 0.23/0.30 % (3564081)Termination reason: Refutation
% 0.23/0.30 % (3564081)Time elapsed: 0.003 s
% 0.23/0.30 % (3564081)Peak memory usage: 12 MB
% 0.23/0.30 % (3564081)Instructions burned: 7 (million)
% 0.23/0.30 % (3564072)Success in time 0.033 s
% 0.23/0.30 % Vampire exiting
%------------------------------------------------------------------------------