%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU577^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:30:09 AM UTC 2026
% Result : Theorem 0.31s 0.39s
% Output : Refutation 0.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU577^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.26 % Computer : n026.cluster.edu
% 0.11/0.26 % Model : x86_64 x86_64
% 0.11/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.26 % Memory : 8046.5625MB
% 0.11/0.26 % OS : Linux 6.8.0-71-generic
% 0.11/0.26 % CPULimit : 300
% 0.11/0.26 % WCLimit : 300
% 0.11/0.26 % DateTime : Tue Sep 29 13:54:27 UTC 2026
% 0.11/0.27 % CPUTime :
% 0.11/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.32 Running higher-order theorem proving
% 0.25/0.33 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.31/0.39 % (631063)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.31/0.39 % (631070)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1839387588:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.31/0.39 % (631070)Refutation not found, incomplete strategy
% 0.31/0.39 % (631070)------------------------------
% 0.31/0.39 % (631070)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.39 % (631070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.39 % (631070)CaDiCaL version: 2.1.3
% 0.31/0.39 % (631070)Termination reason: Refutation not found, incomplete strategy
% 0.31/0.39 % (631070)Time elapsed: 0.001 s
% 0.31/0.39 % (631070)Peak memory usage: 12 MB
% 0.31/0.39 % (631070)Instructions burned: 1 (million)
% 0.31/0.39 % (631070)------------------------------
% 0.31/0.39 % (631070)------------------------------
% 0.31/0.39 % (631074)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.31/0.39 % (631074)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
% 0.31/0.39 % (631069)lrs+10_16_si=on:nwc=1.5:random_seed=417508406:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.31/0.39 % (631068)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=266470663:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.31/0.39 % (631072)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2208143540:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.31/0.39 % (631071)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3937205802:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.31/0.39 % (631074)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3481374605:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.31/0.39 % (631073)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1642343209:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.31/0.39 % (631068) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-631063-631068"...
% 0.31/0.39 % (631072) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-631063-631072"...
% 0.31/0.39 % (631073) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-631063-631073"...
% 0.31/0.39 % (631071) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-631063-631071"...
% 0.31/0.39 % (631069) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-631063-631069"...
% 0.31/0.39 % (631072)...printing done.
% 0.31/0.39 % (631068)...printing done.
% 0.31/0.39 % (631072)Refutation found. Thanks to Tanya!
% 0.31/0.39 % SZS status Theorem for theBenchmark
% 0.31/0.39 % SZS output start Proof for theBenchmark
% 0.31/0.39 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.31/0.39 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.31/0.39 thf(func_def_1, type, powerset: ($i > $i)).
% 0.31/0.39 thf(func_def_2, type, powersetE: $o).
% 0.31/0.39 thf(func_def_4, type, subset: ($i > $i > $o)).
% 0.31/0.39 thf(func_def_5, type, subsetI1: $o).
% 0.31/0.39 thf(func_def_10, type, sK2: ($i > $i > $i)).
% 0.31/0.39 thf(f1,axiom,(
% 0.31/0.39 (powersetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))))),
% 0.31/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE)).
% 0.31/0.39 thf(f2,axiom,(
% 0.31/0.39 (subsetI1 = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.31/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1)).
% 0.31/0.39 thf(f3,conjecture,(
% 0.31/0.39 powersetE => (subsetI1 => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0)))),
% 0.31/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1)).
% 0.31/0.39 thf(f4,negated_conjecture,(
% 0.31/0.39 ~(powersetE => (subsetI1 => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0))))),
% 0.31/0.39 inference(negated_conjecture,[status(cth)],[f3])).
% 0.31/0.39 thf(f5,plain,(
% 0.31/0.39 (powersetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))))),
% 0.31/0.39 inference(rectify,[],[f1])).
% 0.31/0.39 thf(f6,plain,(
% 0.31/0.39 ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true))) <=> (powersetE = $true)),
% 0.31/0.39 inference(fool_elimination,[],[f5])).
% 0.31/0.39 thf(f7,plain,(
% 0.31/0.39 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 0.31/0.39 inference(rectify,[],[f2])).
% 0.31/0.39 thf(f8,plain,(
% 0.31/0.39 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => (((subset @ X1 @ X0)) = $true))),
% 0.31/0.39 inference(fool_elimination,[],[f7])).
% 0.31/0.39 thf(f9,plain,(
% 0.31/0.39 ~(powersetE => (subsetI1 => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (subset @ X0 @ X1))))),
% 0.31/0.39 inference(rectify,[],[f4])).
% 0.31/0.39 thf(f10,plain,(
% 0.31/0.39 ~((powersetE = $true) => ((subsetI1 = $true) => ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) => (((subset @ X0 @ X1)) = $true))))),
% 0.31/0.39 inference(fool_elimination,[],[f9])).
% 0.31/0.39 thf(f11,plain,(
% 0.31/0.39 (? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) & (((in @ X0 @ (powerset @ X1))) = $true)) & (subsetI1 = $true)) & (powersetE = $true)),
% 0.31/0.39 inference(ennf_transformation,[],[f10])).
% 0.31/0.39 thf(f12,plain,(
% 0.31/0.39 ? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) & (((in @ X0 @ (powerset @ X1))) = $true)) & (powersetE = $true) & (subsetI1 = $true)),
% 0.31/0.39 inference(flattening,[],[f11])).
% 0.31/0.39 thf(f13,plain,(
% 0.31/0.39 (subsetI1 = $true) <=> ! [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)))),
% 0.31/0.39 inference(ennf_transformation,[],[f8])).
% 0.31/0.39 thf(f14,plain,(
% 0.31/0.39 ! [X2 : $i,X0 : $i,X1 : $i] : (((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) | (((in @ X1 @ (powerset @ X0))) != $true)) <=> (powersetE = $true)),
% 0.31/0.39 inference(ennf_transformation,[],[f6])).
% 0.31/0.39 thf(f15,plain,(
% 0.31/0.39 ! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true) | (((in @ X1 @ (powerset @ X0))) != $true)) <=> (powersetE = $true)),
% 0.31/0.39 inference(flattening,[],[f14])).
% 0.31/0.39 thf(f16,plain,(
% 0.31/0.39 ((subsetI1 = $true) | ? [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)))) & (! [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true))) | (subsetI1 != $true))),
% 0.31/0.39 inference(nnf_transformation,[],[f13])).
% 0.31/0.39 thf(f17,plain,(
% 0.31/0.39 ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)))) & (! [X3 : $i,X4 : $i] : ((((subset @ X3 @ X4)) = $true) | ? [X5 : $i] : ((((in @ X5 @ X4)) != $true) & (((in @ X5 @ X3)) = $true))) | (subsetI1 != $true))),
% 0.31/0.39 inference(rectify,[],[f16])).
% 0.31/0.39 thf(f18,plain,(
% 0.31/0.39 ((subsetI1 = $true) | ((((subset @ sK0 @ sK1)) != $true) & ! [X2 : $i] : ((((in @ X2 @ sK1)) = $true) | ($true != ((in @ X2 @ sK0)))))) & (! [X3 : $i,X4 : $i] : ((((subset @ X3 @ X4)) = $true) | ((((in @ (sK2 @ X4 @ X3) @ X4)) != $true) & (((in @ (sK2 @ X4 @ X3) @ X3)) = $true))) | (subsetI1 != $true))),
% 0.31/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X5,sK2 @ X4 @ X3)],[f17])).
% 0.31/0.39 thf(f19,plain,(
% 0.31/0.39 (($true != ((subset @ sK3 @ sK4))) & (((in @ sK3 @ (powerset @ sK4))) = $true)) & (powersetE = $true) & (subsetI1 = $true)),
% 0.31/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f12])).
% 0.31/0.39 thf(f20,plain,(
% 0.31/0.39 (! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true) | (((in @ X1 @ (powerset @ X0))) != $true)) | (powersetE != $true)) & ((powersetE = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true) & (((in @ X1 @ (powerset @ X0))) = $true)))),
% 0.31/0.39 inference(nnf_transformation,[],[f15])).
% 0.31/0.39 thf(f21,plain,(
% 0.31/0.39 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ X1)) = $true) | (((in @ X0 @ (powerset @ X1))) != $true)) | (powersetE != $true)) & ((powersetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ X3)) = $true) & (((in @ X5 @ X4)) != $true) & (((in @ X3 @ (powerset @ X4))) = $true)))),
% 0.31/0.39 inference(rectify,[],[f20])).
% 0.31/0.39 thf(f22,plain,(
% 0.31/0.39 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ X1)) = $true) | (((in @ X0 @ (powerset @ X1))) != $true)) | (powersetE != $true)) & ((powersetE = $true) | (($true = ((in @ sK7 @ sK5))) & (((in @ sK7 @ sK6)) != $true) & (((in @ sK5 @ (powerset @ sK6))) = $true)))),
% 0.31/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X3,sK5),skolemize(X4,sK6),skolemize(X5,sK7)],[f21])).
% 0.31/0.39 thf(f23,plain,(
% 0.31/0.39 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK2 @ X4 @ X3) @ X3)) = $true) | (subsetI1 != $true) | (((subset @ X3 @ X4)) = $true)) )),
% 0.31/0.39 inference(cnf_transformation,[],[f18])).
% 0.31/0.39 thf(f24,plain,(
% 0.31/0.39 ( ! [X3 : $i,X4 : $i] : ((subsetI1 != $true) | (((in @ (sK2 @ X4 @ X3) @ X4)) != $true) | (((subset @ X3 @ X4)) = $true)) )),
% 0.31/0.39 inference(cnf_transformation,[],[f18])).
% 0.31/0.39 thf(f27,plain,(
% 0.31/0.39 (subsetI1 = $true)),
% 0.31/0.39 inference(cnf_transformation,[],[f19])).
% 0.31/0.39 thf(f28,plain,(
% 0.31/0.39 (powersetE = $true)),
% 0.31/0.39 inference(cnf_transformation,[],[f19])).
% 0.31/0.39 thf(f29,plain,(
% 0.31/0.39 (((in @ sK3 @ (powerset @ sK4))) = $true)),
% 0.31/0.39 inference(cnf_transformation,[],[f19])).
% 0.31/0.39 thf(f30,plain,(
% 0.31/0.39 ($true != ((subset @ sK3 @ sK4)))),
% 0.31/0.39 inference(cnf_transformation,[],[f19])).
% 0.31/0.39 thf(f34,plain,(
% 0.31/0.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((powersetE != $true) | (((in @ X2 @ X0)) != $true) | (((in @ X0 @ (powerset @ X1))) != $true) | (((in @ X2 @ X1)) = $true)) )),
% 0.31/0.39 inference(cnf_transformation,[],[f22])).
% 0.31/0.39 thf(f38,plain,(
% 0.31/0.39 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK2 @ X4 @ X3) @ X3)) = $true) | (((subset @ X3 @ X4)) = $true)) )),
% 0.31/0.39 inference(forward_subsumption_resolution,[],[f23,f27])).
% 0.31/0.39 thf(f39,plain,(
% 0.31/0.39 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK2 @ X4 @ X3) @ X4)) != $true) | (((subset @ X3 @ X4)) = $true)) )),
% 0.31/0.39 inference(forward_subsumption_resolution,[],[f24,f27])).
% 0.31/0.39 thf(f43,plain,(
% 0.31/0.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) != $true) | (((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)) )),
% 0.31/0.39 inference(forward_subsumption_resolution,[],[f34,f28])).
% 0.31/0.39 thf(f44,plain,(
% 0.31/0.39 ( ! [X0 : $i] : (($true != $true) | (((in @ X0 @ sK4)) = $true) | (((in @ X0 @ sK3)) != $true)) )),
% 0.31/0.39 inference(superposition,[],[f43,f29])).
% 0.31/0.39 thf(f46,plain,(
% 0.31/0.39 ( ! [X0 : $i] : ((((in @ X0 @ sK4)) = $true) | (((in @ X0 @ sK3)) != $true)) )),
% 0.31/0.39 inference(trivial_inequality_removal,[],[f44])).
% 0.31/0.39 thf(f48,plain,(
% 0.31/0.39 ( ! [X0 : $i] : (($true != $true) | (((in @ (sK2 @ sK4 @ X0) @ sK3)) != $true) | (((subset @ X0 @ sK4)) = $true)) )),
% 0.31/0.39 inference(superposition,[],[f39,f46])).
% 0.31/0.39 thf(f49,plain,(
% 0.31/0.39 ( ! [X0 : $i] : ((((in @ (sK2 @ sK4 @ X0) @ sK3)) != $true) | (((subset @ X0 @ sK4)) = $true)) )),
% 0.31/0.39 inference(trivial_inequality_removal,[],[f48])).
% 0.31/0.39 thf(f50,plain,(
% 0.31/0.39 ($true != $true) | ($true = ((subset @ sK3 @ sK4))) | ($true = ((subset @ sK3 @ sK4)))),
% 0.31/0.39 inference(superposition,[],[f49,f38])).
% 0.31/0.39 thf(f51,plain,(
% 0.31/0.39 ($true = ((subset @ sK3 @ sK4))) | ($true != $true)),
% 0.31/0.39 inference(duplicate_literal_removal,[],[f50])).
% 0.31/0.39 thf(f52,plain,(
% 0.31/0.39 ($true = ((subset @ sK3 @ sK4)))),
% 0.31/0.39 inference(trivial_inequality_removal,[],[f51])).
% 0.31/0.39 thf(f53,plain,(
% 0.31/0.39 $false),
% 0.31/0.39 inference(forward_subsumption_resolution,[],[f52,f30])).
% 0.31/0.39 % SZS output end Proof for theBenchmark
% 0.31/0.39 % (631072)------------------------------
% 0.31/0.39 % (631072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.39 % (631072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.39 % (631072)CaDiCaL version: 2.1.3
% 0.31/0.39 % (631072)Termination reason: Refutation
% 0.31/0.39 % (631072)Time elapsed: 0.006 s
% 0.31/0.39 % (631072)Peak memory usage: 12 MB
% 0.31/0.39 % (631072)Instructions burned: 5 (million)
% 0.31/0.39 % (631063)Success in time 0.045 s
% 0.31/0.39 % Vampire exiting
%------------------------------------------------------------------------------