%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU621^2 : 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 : n020.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 08:30:22 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 : SEU621^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n020.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 13:59:34 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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
% 0.23/0.30 % (1097352)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.30 % (1097359)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2807393305:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.30 % (1097359)Refutation not found, incomplete strategy
% 0.23/0.30 % (1097359)------------------------------
% 0.23/0.30 % (1097359)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (1097359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (1097359)CaDiCaL version: 2.1.3
% 0.23/0.30 % (1097359)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.30 % (1097359)Time elapsed: 0.001 s
% 0.23/0.30 % (1097359)Peak memory usage: 12 MB
% 0.23/0.30 % (1097359)Instructions burned: 1 (million)
% 0.23/0.30 % (1097359)------------------------------
% 0.23/0.30 % (1097359)------------------------------
% 0.23/0.30 % (1097363)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 % (1097363)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 % (1097360)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=3826229279: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)
% 0.23/0.30 % (1097357)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3745897056:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.30 % (1097358)lrs+10_16_si=on:nwc=1.5:random_seed=3379765009:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.30 % (1097362)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1226276096:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.30 % (1097361)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1612223367:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.30 % (1097363)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=2035300038:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.30 % (1097357) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1097352-1097357"...
% 0.23/0.30 % (1097358) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1097352-1097358"...
% 0.23/0.30 % (1097361) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1097352-1097361"...
% 0.23/0.30 % (1097360) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1097352-1097360"...
% 0.23/0.30 % (1097362) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1097352-1097362"...
% 0.23/0.30 % (1097357)...printing done.
% 0.23/0.30 % (1097358)...printing done.
% 0.23/0.30 % (1097361)...printing done.
% 0.23/0.30 % (1097363) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1097352-1097363"...
% 0.23/0.30 % (1097365)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2640640564:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.30 % (1097360)...printing done.
% 0.23/0.30 % (1097362)...printing done.
% 0.23/0.30 % (1097357)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 > $o)).
% 0.23/0.30 thf(func_def_2, type, setadjoin: ($i > $i > $i)).
% 0.23/0.30 thf(func_def_3, type, uniqinunit: $o).
% 0.23/0.30 thf(func_def_5, type, subset: ($i > $i > $o)).
% 0.23/0.30 thf(func_def_6, type, subsetI2: $o).
% 0.23/0.30 thf(func_def_13, type, sK4: ($i > $i > $i)).
% 0.23/0.30 thf(func_def_16, type, vNOT: ($o > $o)).
% 0.23/0.30 thf(f1,axiom,(
% 0.23/0.30 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 0.23/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit)).
% 0.23/0.30 thf(f2,axiom,(
% 0.23/0.30 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 0.23/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2)).
% 0.23/0.30 thf(f3,conjecture,(
% 0.23/0.30 uniqinunit => (subsetI2 => ! [X1 : $i,X0 : $i] : ((in @ X1 @ X0) => (subset @ (setadjoin @ X1 @ emptyset) @ X0)))),
% 0.23/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset)).
% 0.23/0.30 thf(f4,negated_conjecture,(
% 0.23/0.30 ~(uniqinunit => (subsetI2 => ! [X1 : $i,X0 : $i] : ((in @ X1 @ X0) => (subset @ (setadjoin @ X1 @ emptyset) @ X0))))),
% 0.23/0.30 inference(negated_conjecture,[status(cth)],[f3])).
% 0.23/0.30 thf(f5,plain,(
% 0.23/0.30 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 0.23/0.30 inference(rectify,[],[f2])).
% 0.23/0.30 thf(f6,plain,(
% 0.23/0.30 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (((subset @ X0 @ X1)) = $true)) <=> (subsetI2 = $true)),
% 0.23/0.30 inference(fool_elimination,[],[f5])).
% 0.23/0.30 thf(f7,plain,(
% 0.23/0.30 ~(uniqinunit => (subsetI2 => ! [X0 : $i,X1 : $i] : ((in @ X0 @ X1) => (subset @ (setadjoin @ X0 @ emptyset) @ X1))))),
% 0.23/0.30 inference(rectify,[],[f4])).
% 0.23/0.30 thf(f8,plain,(
% 0.23/0.30 ~((uniqinunit = $true) => ((subsetI2 = $true) => ! [X1 : $i,X0 : $i] : ((((in @ X0 @ X1)) = $true) => (((subset @ (setadjoin @ X0 @ emptyset) @ X1)) = $true))))),
% 0.23/0.30 inference(fool_elimination,[],[f7])).
% 0.23/0.30 thf(f9,plain,(
% 0.23/0.30 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 0.23/0.30 inference(rectify,[],[f1])).
% 0.23/0.30 thf(f10,plain,(
% 0.23/0.30 (uniqinunit = $true) <=> ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (setadjoin @ X1 @ emptyset))) = $true) => (X0 = X1))),
% 0.23/0.30 inference(fool_elimination,[],[f9])).
% 0.23/0.30 thf(f11,plain,(
% 0.23/0.30 (? [X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) = $true) & (((subset @ (setadjoin @ X0 @ emptyset) @ X1)) != $true)) & (subsetI2 = $true)) & (uniqinunit = $true)),
% 0.23/0.30 inference(ennf_transformation,[],[f8])).
% 0.23/0.30 thf(f12,plain,(
% 0.23/0.30 (uniqinunit = $true) & ? [X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) = $true) & (((subset @ (setadjoin @ X0 @ emptyset) @ X1)) != $true)) & (subsetI2 = $true)),
% 0.23/0.30 inference(flattening,[],[f11])).
% 0.23/0.30 thf(f13,plain,(
% 0.23/0.30 (uniqinunit = $true) <=> ! [X1 : $i,X0 : $i] : ((((in @ X0 @ (setadjoin @ X1 @ emptyset))) != $true) | (X0 = X1))),
% 0.23/0.30 inference(ennf_transformation,[],[f10])).
% 0.23/0.30 thf(f14,plain,(
% 0.23/0.30 (subsetI2 = $true) <=> ! [X1 : $i,X0 : $i] : ((((subset @ X0 @ X1)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true)))),
% 0.23/0.30 inference(ennf_transformation,[],[f6])).
% 0.23/0.30 thf(f15,plain,(
% 0.23/0.30 ((uniqinunit = $true) | ? [X1 : $i,X0 : $i] : ((((in @ X0 @ (setadjoin @ X1 @ emptyset))) = $true) & (X0 != X1))) & (! [X1 : $i,X0 : $i] : ((((in @ X0 @ (setadjoin @ X1 @ emptyset))) != $true) | (X0 = X1)) | (uniqinunit != $true))),
% 0.23/0.30 inference(nnf_transformation,[],[f13])).
% 0.23/0.30 thf(f16,plain,(
% 0.23/0.30 ((uniqinunit = $true) | ? [X0 : $i,X1 : $i] : ((((in @ X1 @ (setadjoin @ X0 @ emptyset))) = $true) & (X0 != X1))) & (! [X2 : $i,X3 : $i] : ((((in @ X3 @ (setadjoin @ X2 @ emptyset))) != $true) | (X2 = X3)) | (uniqinunit != $true))),
% 0.23/0.30 inference(rectify,[],[f15])).
% 0.23/0.30 thf(f17,plain,(
% 0.23/0.30 ((uniqinunit = $true) | ((((in @ sK1 @ (setadjoin @ sK0 @ emptyset))) = $true) & (sK1 != sK0))) & (! [X2 : $i,X3 : $i] : ((((in @ X3 @ (setadjoin @ X2 @ emptyset))) != $true) | (X2 = X3)) | (uniqinunit != $true))),
% 0.23/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16])).
% 0.23/0.30 thf(f18,plain,(
% 0.23/0.30 ((subsetI2 = $true) | ? [X1 : $i,X0 : $i] : ((((subset @ X0 @ X1)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ X1)) = $true)))) & (! [X1 : $i,X0 : $i] : ((((subset @ X0 @ X1)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true))) | (subsetI2 != $true))),
% 0.23/0.30 inference(nnf_transformation,[],[f14])).
% 0.23/0.30 thf(f19,plain,(
% 0.23/0.30 ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)))) & (! [X3 : $i,X4 : $i] : ((((subset @ X4 @ X3)) = $true) | ? [X5 : $i] : ((((in @ X5 @ X4)) = $true) & (((in @ X5 @ X3)) != $true))) | (subsetI2 != $true))),
% 0.23/0.30 inference(rectify,[],[f18])).
% 0.23/0.30 thf(f20,plain,(
% 0.23/0.30 ((subsetI2 = $true) | ((((subset @ sK3 @ sK2)) != $true) & ! [X2 : $i] : ((((in @ X2 @ sK3)) != $true) | (((in @ X2 @ sK2)) = $true)))) & (! [X3 : $i,X4 : $i] : ((((subset @ X4 @ X3)) = $true) | ((((in @ (sK4 @ X4 @ X3) @ X4)) = $true) & (((in @ (sK4 @ X4 @ X3) @ X3)) != $true))) | (subsetI2 != $true))),
% 0.23/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,vAPP]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X5,sK4 @ X4 @ X3)],[f19])).
% 0.23/0.30 thf(f21,plain,(
% 0.23/0.30 (uniqinunit = $true) & ((((in @ sK5 @ sK6)) = $true) & (((subset @ (setadjoin @ sK5 @ emptyset) @ sK6)) != $true)) & (subsetI2 = $true)),
% 0.23/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X1,sK6)],[f12])).
% 0.23/0.30 thf(f22,plain,(
% 0.23/0.30 ( ! [X2 : $i,X3 : $i] : ((((in @ X3 @ (setadjoin @ X2 @ emptyset))) != $true) | (X2 = X3) | (uniqinunit != $true)) )),
% 0.23/0.30 inference(cnf_transformation,[],[f17])).
% 0.23/0.30 thf(f25,plain,(
% 0.23/0.30 ( ! [X3 : $i,X4 : $i] : ((((subset @ X4 @ X3)) = $true) | (((in @ (sK4 @ X4 @ X3) @ X3)) != $true) | (subsetI2 != $true)) )),
% 0.23/0.30 inference(cnf_transformation,[],[f20])).
% 0.23/0.30 thf(f26,plain,(
% 0.23/0.30 ( ! [X3 : $i,X4 : $i] : ((((subset @ X4 @ X3)) = $true) | (((in @ (sK4 @ X4 @ X3) @ X4)) = $true) | (subsetI2 != $true)) )),
% 0.23/0.30 inference(cnf_transformation,[],[f20])).
% 0.23/0.30 thf(f29,plain,(
% 0.23/0.30 (subsetI2 = $true)),
% 0.23/0.30 inference(cnf_transformation,[],[f21])).
% 0.23/0.30 thf(f30,plain,(
% 0.23/0.30 (((subset @ (setadjoin @ sK5 @ emptyset) @ sK6)) != $true)),
% 0.23/0.30 inference(cnf_transformation,[],[f21])).
% 0.23/0.30 thf(f31,plain,(
% 0.23/0.30 (((in @ sK5 @ sK6)) = $true)),
% 0.23/0.30 inference(cnf_transformation,[],[f21])).
% 0.23/0.30 thf(f32,plain,(
% 0.23/0.30 (uniqinunit = $true)),
% 0.23/0.30 inference(cnf_transformation,[],[f21])).
% 0.23/0.30 thf(f37,plain,(
% 0.23/0.30 ( ! [X2 : $i,X3 : $i] : ((X2 = X3) | ($true != $true) | (((in @ X3 @ (setadjoin @ X2 @ emptyset))) != $true)) )),
% 0.23/0.30 inference(definition_unfolding,[],[f22,f32])).
% 0.23/0.30 thf(f40,plain,(
% 0.23/0.30 ( ! [X3 : $i,X4 : $i] : (($true != $true) | (((in @ (sK4 @ X4 @ X3) @ X4)) = $true) | (((subset @ X4 @ X3)) = $true)) )),
% 0.23/0.30 inference(definition_unfolding,[],[f26,f29])).
% 0.23/0.30 thf(f41,plain,(
% 0.23/0.30 ( ! [X3 : $i,X4 : $i] : ((((subset @ X4 @ X3)) = $true) | ($true != $true) | (((in @ (sK4 @ X4 @ X3) @ X3)) != $true)) )),
% 0.23/0.30 inference(definition_unfolding,[],[f25,f29])).
% 0.23/0.30 thf(f42,plain,(
% 0.23/0.30 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK4 @ X4 @ X3) @ X3)) != $true) | (((subset @ X4 @ X3)) = $true)) )),
% 0.23/0.30 inference(trivial_inequality_removal,[],[f41])).
% 0.23/0.30 thf(f43,plain,(
% 0.23/0.30 ( ! [X2 : $i,X3 : $i] : ((((in @ X3 @ (setadjoin @ X2 @ emptyset))) != $true) | (X2 = X3)) )),
% 0.23/0.30 inference(trivial_inequality_removal,[],[f37])).
% 0.23/0.30 thf(f44,plain,(
% 0.23/0.30 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK4 @ X4 @ X3) @ X4)) = $true) | (((subset @ X4 @ X3)) = $true)) )),
% 0.23/0.30 inference(trivial_inequality_removal,[],[f40])).
% 0.23/0.30 thf(f46,plain,(
% 0.23/0.30 ( ! [X0 : $i,X1 : $i] : ((((subset @ (setadjoin @ X0 @ emptyset) @ X1)) = $true) | (((sK4 @ (setadjoin @ X0 @ emptyset) @ X1)) = X0) | ($true != $true)) )),
% 0.23/0.30 inference(constrained_superposition,[],[f43,f44])).
% 0.23/0.30 thf(f47,plain,(
% 0.23/0.30 ( ! [X0 : $i,X1 : $i] : ((((subset @ (setadjoin @ X0 @ emptyset) @ X1)) = $true) | (((sK4 @ (setadjoin @ X0 @ emptyset) @ X1)) = X0)) )),
% 0.23/0.30 inference(trivial_inequality_removal,[],[f46])).
% 0.23/0.30 thf(f50,plain,(
% 0.23/0.30 (sK5 = ((sK4 @ (setadjoin @ sK5 @ emptyset) @ sK6))) | ($true != $true)),
% 0.23/0.30 inference(constrained_superposition,[],[f30,f47])).
% 0.23/0.30 thf(f51,plain,(
% 0.23/0.30 (sK5 = ((sK4 @ (setadjoin @ sK5 @ emptyset) @ sK6)))),
% 0.23/0.30 inference(trivial_inequality_removal,[],[f50])).
% 0.23/0.30 thf(f53,plain,(
% 0.23/0.30 (((subset @ (setadjoin @ sK5 @ emptyset) @ sK6)) = $true) | (((in @ sK5 @ sK6)) != $true)),
% 0.23/0.30 inference(constrained_superposition,[],[f42,f51])).
% 0.23/0.30 thf(f54,plain,(
% 0.23/0.30 (((in @ sK5 @ sK6)) != $true)),
% 0.23/0.30 inference(forward_subsumption_resolution,[],[f53,f30])).
% 0.23/0.30 thf(f56,plain,(
% 0.23/0.30 $false),
% 0.23/0.30 inference(forward_subsumption_resolution,[],[f54,f31])).
% 0.23/0.30 % SZS output end Proof for theBenchmark
% 0.23/0.30 % (1097357)------------------------------
% 0.23/0.30 % (1097357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (1097357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (1097357)CaDiCaL version: 2.1.3
% 0.23/0.30 % (1097357)Termination reason: Refutation
% 0.23/0.30 % (1097357)Time elapsed: 0.004 s
% 0.23/0.30 % (1097357)Peak memory usage: 12 MB
% 0.23/0.30 % (1097357)Instructions burned: 5 (million)
% 0.23/0.30 % (1097352)Success in time 0.043 s
% 0.23/0.30 % Vampire exiting
%------------------------------------------------------------------------------