%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU819^2 : 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 : n014.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 08:31:42 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU819^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n014.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:34:15 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.23 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
% 0.19/0.28 % (2750168)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.28 % (2750175)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=847546332:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.28 % (2750175)Instruction limit reached!
% 0.19/0.28 % (2750175)------------------------------
% 0.19/0.28 % (2750175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (2750175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (2750175)CaDiCaL version: 2.1.3
% 0.19/0.28 % (2750175)Termination reason: Instruction limit
% 0.19/0.28 % (2750175)Termination phase: Property scanning
% 0.19/0.28 % (2750175)Time elapsed: 0.001 s
% 0.19/0.28 % (2750175)Peak memory usage: 10 MB
% 0.19/0.28 % (2750175)Instructions burned: 3 (million)
% 0.19/0.28 % (2750173)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=108857023:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.28 % (2750174)lrs+10_16_si=on:nwc=1.5:random_seed=172062097:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.28 % (2750177)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3280171481:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.28 % (2750176)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=3930306879: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)
% 0.19/0.28 % (2750177) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2750168-2750177"...
% 0.19/0.28 % (2750181)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2918095622:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.19/0.28 % (2750181)Instruction limit reached!
% 0.19/0.28 % (2750181)------------------------------
% 0.19/0.28 % (2750181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (2750181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (2750181)CaDiCaL version: 2.1.3
% 0.19/0.28 % (2750181)Termination reason: Instruction limit
% 0.19/0.28 % (2750181)Termination phase: Saturation
% 0.19/0.28 % (2750181)Time elapsed: 0.001 s
% 0.19/0.28 % (2750181)Peak memory usage: 11 MB
% 0.19/0.28 % (2750181)Instructions burned: 4 (million)
% 0.19/0.28 % (2750177)...printing done.
% 0.19/0.28 % (2750176) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2750168-2750176"...
% 0.19/0.28 % (2750177)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% 0.19/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.28 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.19/0.28 thf(func_def_2, type, powerset: ($i > $i)).
% 0.19/0.28 thf(func_def_3, type, setunion: ($i > $i)).
% 0.19/0.28 thf(func_def_4, type, nonempty: ($i > $o)).
% 0.19/0.28 thf(func_def_5, type, subset: ($i > $i > $o)).
% 0.19/0.28 thf(func_def_6, type, transitiveset: ($i > $o)).
% 0.19/0.28 thf(func_def_8, type, setunionTransitive: $o).
% 0.19/0.28 thf(func_def_9, type, stricttotalorderedByIn: ($i > $o)).
% 0.19/0.28 thf(func_def_10, type, wellorderedByIn: ($i > $o)).
% 0.19/0.28 thf(func_def_11, type, ordinal: ($i > $o)).
% 0.19/0.28 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.28 thf(func_def_13, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.19/0.28 thf(func_def_14, type, vNOT: ($o > $o)).
% 0.19/0.28 thf(func_def_15, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.28 thf(func_def_16, type, vAND: ($o > $o > $o)).
% 0.19/0.28 thf(func_def_17, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.19/0.28 thf(func_def_18, type, vIMP: ($o > $o > $o)).
% 0.19/0.28 thf(func_def_19, type, db1: !>[X0: $tType]:(X0)).
% 0.19/0.28 thf(func_def_20, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.19/0.28 thf(func_def_21, type, db2: !>[X0: $tType]:(X0)).
% 0.19/0.28 thf(func_def_22, type, vOR: ($o > $o > $o)).
% 0.19/0.28 thf(func_def_23, type, db3: !>[X0: $tType]:(X0)).
% 0.19/0.28 thf(func_def_28, type, sK2: ($i > $i)).
% 0.19/0.28 thf(f3,axiom,(
% 0.19/0.28 (! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (transitiveset @ X1)) => (transitiveset @ (setunion @ X0))) = setunionTransitive)),
% 0.19/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionTransitive)).
% 0.19/0.28 thf(f6,axiom,(
% 0.19/0.28 ((^[X0 : $i] : ((transitiveset @ X0) & (wellorderedByIn @ X0))) = ordinal)),
% 0.19/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinal)).
% 0.19/0.28 thf(f7,conjecture,(
% 0.19/0.28 setunionTransitive => ! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (ordinal @ X1)) => (transitiveset @ (setunion @ X0)))),
% 0.19/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionOrdinalLem1)).
% 0.19/0.28 thf(f8,negated_conjecture,(
% 0.19/0.28 ~(setunionTransitive => ! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (ordinal @ X1)) => (transitiveset @ (setunion @ X0))))),
% 0.19/0.28 inference(negated_conjecture,[status(cth)],[f7])).
% 0.19/0.28 thf(f16,plain,(
% 0.19/0.28 (! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (transitiveset @ X1)) => (transitiveset @ (setunion @ X0))) = setunionTransitive)),
% 0.19/0.28 inference(rectify,[],[f3])).
% 0.19/0.28 thf(f17,plain,(
% 0.19/0.28 (setunionTransitive = $true) <=> ! [X0 : $i] : (! [X1 : $i] : ((((in @ X1 @ X0)) = $true) => (((transitiveset @ X1)) = $true)) => (((transitiveset @ (setunion @ X0))) = $true))),
% 0.19/0.28 inference(fool_elimination,[],[f16])).
% 0.19/0.28 thf(f18,plain,(
% 0.19/0.28 ~(setunionTransitive => ! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (ordinal @ X1)) => (transitiveset @ (setunion @ X0))))),
% 0.19/0.28 inference(rectify,[],[f8])).
% 0.19/0.28 thf(f19,plain,(
% 0.19/0.28 ~((setunionTransitive = $true) => ! [X0 : $i] : (! [X1 : $i] : ((((in @ X1 @ X0)) = $true) => (((ordinal @ X1)) = $true)) => (((transitiveset @ (setunion @ X0))) = $true)))),
% 0.19/0.28 inference(fool_elimination,[],[f18])).
% 0.19/0.28 thf(f20,plain,(
% 0.19/0.28 ((^[X0 : $i] : ((transitiveset @ X0) & (wellorderedByIn @ X0))) = ordinal)),
% 0.19/0.28 inference(rectify,[],[f6])).
% 0.19/0.28 thf(f21,plain,(
% 0.19/0.28 (ordinal = (^[Y0 : $i]: ((wellorderedByIn @ Y0) & (transitiveset @ Y0))))),
% 0.19/0.28 inference(fool_elimination,[],[f20])).
% 0.19/0.28 thf(f22,plain,(
% 0.19/0.28 (setunionTransitive = $true) <=> ! [X0 : $i] : (? [X1 : $i] : ((((transitiveset @ X1)) != $true) & (((in @ X1 @ X0)) = $true)) | (((transitiveset @ (setunion @ X0))) = $true))),
% 0.19/0.28 inference(ennf_transformation,[],[f17])).
% 0.19/0.28 thf(f23,plain,(
% 0.19/0.28 ? [X0 : $i] : (! [X1 : $i] : ((((ordinal @ X1)) = $true) | (((in @ X1 @ X0)) != $true)) & (((transitiveset @ (setunion @ X0))) != $true)) & (setunionTransitive = $true)),
% 0.19/0.28 inference(ennf_transformation,[],[f19])).
% 0.19/0.28 thf(f24,plain,(
% 0.19/0.28 (! [X1 : $i] : ((((ordinal @ X1)) = $true) | ($true != ((in @ X1 @ sK0)))) & ($true != ((transitiveset @ (setunion @ sK0))))) & (setunionTransitive = $true)),
% 0.19/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f23])).
% 0.19/0.28 thf(f25,plain,(
% 0.19/0.28 ((setunionTransitive = $true) | ? [X0 : $i] : (! [X1 : $i] : ((((transitiveset @ X1)) = $true) | (((in @ X1 @ X0)) != $true)) & (((transitiveset @ (setunion @ X0))) != $true))) & (! [X0 : $i] : (? [X1 : $i] : ((((transitiveset @ X1)) != $true) & (((in @ X1 @ X0)) = $true)) | (((transitiveset @ (setunion @ X0))) = $true)) | (setunionTransitive != $true))),
% 0.19/0.28 inference(nnf_transformation,[],[f22])).
% 0.19/0.28 thf(f26,plain,(
% 0.19/0.28 ((setunionTransitive = $true) | ? [X0 : $i] : (! [X1 : $i] : ((((transitiveset @ X1)) = $true) | (((in @ X1 @ X0)) != $true)) & (((transitiveset @ (setunion @ X0))) != $true))) & (! [X2 : $i] : (? [X3 : $i] : (($true != ((transitiveset @ X3))) & (((in @ X3 @ X2)) = $true)) | ($true = ((transitiveset @ (setunion @ X2))))) | (setunionTransitive != $true))),
% 0.19/0.28 inference(rectify,[],[f25])).
% 0.19/0.28 thf(f27,plain,(
% 0.19/0.28 ((setunionTransitive = $true) | (! [X1 : $i] : ((((transitiveset @ X1)) = $true) | ($true != ((in @ X1 @ sK1)))) & ($true != ((transitiveset @ (setunion @ sK1)))))) & (! [X2 : $i] : ((($true != ((transitiveset @ (sK2 @ X2)))) & ($true = ((in @ (sK2 @ X2) @ X2)))) | ($true = ((transitiveset @ (setunion @ X2))))) | (setunionTransitive != $true))),
% 0.19/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,vAPP]),skolemize(X0,sK1),skolemize(X3,sK2 @ X2)],[f26])).
% 0.19/0.28 thf(f30,plain,(
% 0.19/0.28 (setunionTransitive = $true)),
% 0.19/0.28 inference(cnf_transformation,[],[f24])).
% 0.19/0.28 thf(f31,plain,(
% 0.19/0.28 ($true != ((transitiveset @ (setunion @ sK0))))),
% 0.19/0.28 inference(cnf_transformation,[],[f24])).
% 0.19/0.28 thf(f32,plain,(
% 0.19/0.28 ( ! [X1 : $i] : (($true != ((in @ X1 @ sK0))) | (((ordinal @ X1)) = $true)) )),
% 0.19/0.28 inference(cnf_transformation,[],[f24])).
% 0.19/0.28 thf(f33,plain,(
% 0.19/0.28 (ordinal = (^[Y0 : $i]: ((wellorderedByIn @ Y0) & (transitiveset @ Y0))))),
% 0.19/0.28 inference(cnf_transformation,[],[f21])).
% 0.19/0.28 thf(f35,plain,(
% 0.19/0.28 ( ! [X2 : $i] : ((setunionTransitive != $true) | ($true = ((transitiveset @ (setunion @ X2)))) | ($true = ((in @ (sK2 @ X2) @ X2)))) )),
% 0.19/0.28 inference(cnf_transformation,[],[f27])).
% 0.19/0.28 thf(f36,plain,(
% 0.19/0.28 ( ! [X2 : $i] : (($true = ((transitiveset @ (setunion @ X2)))) | ($true != ((transitiveset @ (sK2 @ X2)))) | (setunionTransitive != $true)) )),
% 0.19/0.28 inference(cnf_transformation,[],[f27])).
% 0.19/0.28 thf(f53,plain,(
% 0.19/0.28 ( ! [X2 : $i] : (($true != ((transitiveset @ (sK2 @ X2)))) | ($true = ((transitiveset @ (setunion @ X2))))) )),
% 0.19/0.28 inference(forward_subsumption_resolution,[],[f36,f30])).
% 0.19/0.28 thf(f54,plain,(
% 0.19/0.28 ( ! [X1 : $i] : ((((ordinal @ X1)) = (((^[Y0 : $i]: ((wellorderedByIn @ Y0) & (transitiveset @ Y0))) @ X1)))) )),
% 0.19/0.28 inference(argument_congruence,[],[f33])).
% 0.19/0.28 thf(f56,plain,(
% 0.19/0.28 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((wellorderedByIn @ Y0) & (transitiveset @ Y0))) @ X1))) | (((ordinal @ X1)) = $false)) )),
% 0.19/0.28 inference(iff_proxy_clausification,[],[f54])).
% 0.19/0.28 thf(f57,plain,(
% 0.19/0.28 ( ! [X1 : $i] : (($true = (((wellorderedByIn @ X1) & (transitiveset @ X1)))) | (((ordinal @ X1)) = $false)) )),
% 0.19/0.28 inference(beta-eta_normalization,[],[f56])).
% 0.19/0.28 thf(f58,plain,(
% 0.19/0.28 ( ! [X1 : $i] : ((((ordinal @ X1)) = $false) | (((transitiveset @ X1)) = $true)) )),
% 0.19/0.28 inference(and_proxy_clausification,[],[f57])).
% 0.19/0.28 thf(f69,plain,(
% 0.19/0.28 ( ! [X2 : $i] : (($true = ((in @ (sK2 @ X2) @ X2))) | ($true = ((transitiveset @ (setunion @ X2))))) )),
% 0.19/0.28 inference(forward_subsumption_resolution,[],[f35,f30])).
% 0.19/0.28 thf(f70,plain,(
% 0.19/0.28 ($true != $true) | ($true = ((transitiveset @ (setunion @ sK0)))) | ($true = ((ordinal @ (sK2 @ sK0))))),
% 0.19/0.28 inference(superposition,[],[f32,f69])).
% 0.19/0.28 thf(f71,plain,(
% 0.19/0.28 ($true = ((transitiveset @ (setunion @ sK0)))) | ($true = ((ordinal @ (sK2 @ sK0))))),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f70])).
% 0.19/0.28 thf(f72,plain,(
% 0.19/0.28 ($true = ((ordinal @ (sK2 @ sK0))))),
% 0.19/0.28 inference(forward_subsumption_resolution,[],[f71,f31])).
% 0.19/0.28 thf(f74,plain,(
% 0.19/0.28 ($true = ((transitiveset @ (sK2 @ sK0)))) | ($true = $false)),
% 0.19/0.28 inference(superposition,[],[f58,f72])).
% 0.19/0.28 thf(f75,plain,(
% 0.19/0.28 ($true = ((transitiveset @ (sK2 @ sK0))))),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f74])).
% 0.19/0.28 thf(f77,plain,(
% 0.19/0.28 ($true = ((transitiveset @ (setunion @ sK0)))) | ($true != $true)),
% 0.19/0.28 inference(superposition,[],[f53,f75])).
% 0.19/0.28 thf(f78,plain,(
% 0.19/0.28 ($true = ((transitiveset @ (setunion @ sK0))))),
% 0.19/0.28 inference(trivial_inequality_removal,[],[f77])).
% 0.19/0.28 thf(f79,plain,(
% 0.19/0.28 $false),
% 0.19/0.28 inference(forward_subsumption_resolution,[],[f78,f31])).
% 0.19/0.28 % SZS output end Proof for theBenchmark
% 0.19/0.28 % (2750177)------------------------------
% 0.19/0.28 % (2750177)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (2750177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (2750177)CaDiCaL version: 2.1.3
% 0.19/0.28 % (2750177)Termination reason: Refutation
% 0.19/0.28 % (2750177)Time elapsed: 0.005 s
% 0.19/0.28 % (2750177)Peak memory usage: 12 MB
% 0.19/0.28 % (2750177)Instructions burned: 7 (million)
% 0.19/0.28 % (2750168)Success in time 0.044 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------