%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU822^2 : 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 : n004.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 08:31:44 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 24 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 226 ( 66 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 189 ( 41 ~; 22 |; 13 &; 92 @)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 6 con; 0-4 aty)
% Number of variables : 30 ( 0 ^; 25 !; 5 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
nonempty: $i > $o ).
thf(func_def_3,type,
transitiveset: $i > $o ).
thf(func_def_4,type,
stricttotalorderedByIn: $i > $o ).
thf(func_def_6,type,
wellorderedByIn: $i > $o ).
thf(func_def_7,type,
ordinal: $i > $o ).
thf(func_def_8,type,
ordinalIrrefl: $o ).
thf(func_def_11,type,
vAND: $o > $o > $o ).
thf(func_def_12,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_13,type,
vIMP: $o > $o > $o ).
thf(func_def_14,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_18,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vOR: $o > $o > $o ).
thf(func_def_20,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_21,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(f4,axiom,
( ordinalIrrefl
= ( ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ~ ( in @ X1 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinalIrrefl) ).
thf(f5,conjecture,
( ordinalIrrefl
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ~ ( in @ X0 @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinalIrrefl2) ).
thf(f6,negated_conjecture,
~ ( ordinalIrrefl
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ~ ( in @ X0 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
~ ( ordinalIrrefl
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ~ ( in @ X0 @ X0 ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
~ ( ( ordinalIrrefl = $true )
=> ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ( ( in @ X0 @ X0 )
!= $true ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f15,plain,
( ordinalIrrefl
= ( ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ~ ( in @ X1 @ X1 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f16,plain,
( ( ordinalIrrefl = $true )
<=> ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( in @ X1 @ X1 )
!= $true ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
~ ( ( ordinalIrrefl = $true )
=> ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ( ( in @ X0 @ X0 )
!= $true ) ) ),
inference(flattening,[],[f8]) ).
thf(f18,plain,
( ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( in @ X1 @ X1 )
!= $true ) ) )
<=> ( ordinalIrrefl = $true ) ),
inference(flattening,[],[f16]) ).
thf(f19,plain,
( ( ordinalIrrefl = $true )
<=> ! [X0: $i] :
( ! [X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ X1 )
!= $true ) )
| ( ( ordinal @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f18]) ).
thf(f20,plain,
( ? [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
& ( ( in @ X0 @ X0 )
= $true ) )
& ( ordinalIrrefl = $true ) ),
inference(ennf_transformation,[],[f17]) ).
thf(f21,plain,
( ( ( ordinal @ sK0 )
= $true )
& ( $true
= ( in @ sK0 @ sK0 ) )
& ( ordinalIrrefl = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f20]) ).
thf(f22,plain,
( ( ( ordinalIrrefl = $true )
| ? [X0: $i] :
( ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X1 @ X1 )
= $true ) )
& ( ( ordinal @ X0 )
= $true ) ) )
& ( ! [X0: $i] :
( ! [X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ X1 )
!= $true ) )
| ( ( ordinal @ X0 )
!= $true ) )
| ( ordinalIrrefl != $true ) ) ),
inference(nnf_transformation,[],[f19]) ).
thf(f23,plain,
( ( ( ordinalIrrefl = $true )
| ? [X0: $i] :
( ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( ( in @ X1 @ X1 )
= $true ) )
& ( ( ordinal @ X0 )
= $true ) ) )
& ( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X3 @ X3 )
!= $true ) )
| ( ( ordinal @ X2 )
!= $true ) )
| ( ordinalIrrefl != $true ) ) ),
inference(rectify,[],[f22]) ).
thf(f24,plain,
( ( ( ordinalIrrefl = $true )
| ( ( ( in @ sK2 @ sK1 )
= $true )
& ( $true
= ( in @ sK2 @ sK2 ) )
& ( ( ordinal @ sK1 )
= $true ) ) )
& ( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X3 @ X3 )
!= $true ) )
| ( ( ordinal @ X2 )
!= $true ) )
| ( ordinalIrrefl != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f23]) ).
thf(f26,plain,
ordinalIrrefl = $true,
inference(cnf_transformation,[],[f21]) ).
thf(f27,plain,
( $true
= ( in @ sK0 @ sK0 ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f28,plain,
( ( ordinal @ sK0 )
= $true ),
inference(cnf_transformation,[],[f21]) ).
thf(f30,plain,
! [X2: $i,X3: $i] :
( ( ordinalIrrefl != $true )
| ( ( in @ X3 @ X3 )
!= $true )
| ( ( ordinal @ X2 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f49,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X3 @ X3 )
!= $true )
| ( ( ordinal @ X2 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f30,f26]) ).
thf(f50,plain,
( ( $true != $true )
| ( $true != $true )
| ( ( ordinal @ sK0 )
!= $true ) ),
inference(superposition,[],[f49,f27]) ).
thf(f51,plain,
( ( ( ordinal @ sK0 )
!= $true )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[],[f50]) ).
thf(f52,plain,
( ( ordinal @ sK0 )
!= $true ),
inference(trivial_inequality_removal,[],[f51]) ).
thf(f53,plain,
$false,
inference(forward_subsumption_resolution,[],[f52,f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU822^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n004.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 14:34:52 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.20/0.29 % (1372211)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (1372217)lrs+10_16_si=on:nwc=1.5:random_seed=90931077:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (1372217)Instruction limit reached!
% 0.20/0.29 % (1372217)------------------------------
% 0.20/0.29 % (1372217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1372217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1372217)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1372217)Termination reason: Instruction limit
% 0.20/0.29 % (1372217)Termination phase: Saturation
% 0.20/0.29 % (1372217)Time elapsed: 0.005 s
% 0.20/0.29 % (1372217)Peak memory usage: 11 MB
% 0.20/0.29 % (1372217)Instructions burned: 22 (million)
% 0.20/0.29 % (1372216)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=704646945:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (1372218)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=842800002:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (1372219)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=3873607144: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)
% 0.20/0.29 % (1372218)Instruction limit reached!
% 0.20/0.29 % (1372218)------------------------------
% 0.20/0.29 % (1372218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1372218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1372218)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1372218)Termination reason: Instruction limit
% 0.20/0.29 % (1372218)Termination phase: Property scanning
% 0.20/0.29 % (1372218)Time elapsed: 0.002 s
% 0.20/0.29 % (1372218)Peak memory usage: 10 MB
% 0.20/0.29 % (1372218)Instructions burned: 3 (million)
% 0.20/0.29 % (1372220)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=950725783:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (1372222)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (1372220) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1372211-1372220"...
% 0.20/0.29 % (1372222)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
% 0.20/0.29 % (1372219) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1372211-1372219"...
% 0.20/0.29 % (1372220)...printing done.
% 0.20/0.29 % (1372221)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2024819166:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.29 % (1372220)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (1372220)------------------------------
% 0.20/0.29 % (1372220)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1372220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1372220)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1372220)Termination reason: Refutation
% 0.20/0.29 % (1372220)Time elapsed: 0.004 s
% 0.20/0.29 % (1372220)Peak memory usage: 12 MB
% 0.20/0.29 % (1372220)Instructions burned: 5 (million)
% 0.20/0.29 % (1372211)Success in time 0.042 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------