%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU809^2 : 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 : 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 08:31:35 AM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 201 ( 46 equ; 0 cnn)
% Maximal formula atoms : 6 ( 9 avg)
% Number of connectives : 177 ( 22 ~; 14 |; 10 &; 118 @)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 16 ( 0 ^; 13 !; 3 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
omegaSAx: $o ).
thf(f1,axiom,
( omegaSAx
= ( ! [X0: $i] :
( ( in @ X0 @ omega )
=> ( in @ ( setadjoin @ X0 @ X0 ) @ omega ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(f2,conjecture,
( omegaSAx
=> ! [X0: $i] :
( ( in @ X0 @ omega )
=> ( in @ ( setadjoin @ X0 @ X0 ) @ omega ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSclos) ).
thf(f3,negated_conjecture,
~ ( omegaSAx
=> ! [X0: $i] :
( ( in @ X0 @ omega )
=> ( in @ ( setadjoin @ X0 @ X0 ) @ omega ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( omegaSAx
= ( ! [X0: $i] :
( ( in @ X0 @ omega )
=> ( in @ ( setadjoin @ X0 @ X0 ) @ omega ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ omega )
= $true )
=> ( ( in @ ( setadjoin @ X0 @ X0 ) @ omega )
= $true ) )
<=> ( omegaSAx = $true ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( omegaSAx
=> ! [X0: $i] :
( ( in @ X0 @ omega )
=> ( in @ ( setadjoin @ X0 @ X0 ) @ omega ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( omegaSAx = $true )
=> ! [X0: $i] :
( ( ( in @ X0 @ omega )
= $true )
=> ( ( in @ ( setadjoin @ X0 @ X0 ) @ omega )
= $true ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ( omegaSAx = $true )
<=> ! [X0: $i] :
( ( ( in @ ( setadjoin @ X0 @ X0 ) @ omega )
= $true )
| ( ( in @ X0 @ omega )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f9,plain,
( ? [X0: $i] :
( ( ( in @ ( setadjoin @ X0 @ X0 ) @ omega )
!= $true )
& ( ( in @ X0 @ omega )
= $true ) )
& ( omegaSAx = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f10,plain,
( ( ( omegaSAx = $true )
| ? [X0: $i] :
( ( ( in @ ( setadjoin @ X0 @ X0 ) @ omega )
!= $true )
& ( ( in @ X0 @ omega )
= $true ) ) )
& ( ! [X0: $i] :
( ( ( in @ ( setadjoin @ X0 @ X0 ) @ omega )
= $true )
| ( ( in @ X0 @ omega )
!= $true ) )
| ( omegaSAx != $true ) ) ),
inference(nnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( ( omegaSAx = $true )
| ? [X0: $i] :
( ( ( in @ ( setadjoin @ X0 @ X0 ) @ omega )
!= $true )
& ( ( in @ X0 @ omega )
= $true ) ) )
& ( ! [X1: $i] :
( ( $true
= ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
| ( ( in @ X1 @ omega )
!= $true ) )
| ( omegaSAx != $true ) ) ),
inference(rectify,[],[f10]) ).
thf(f12,plain,
( ( ( omegaSAx = $true )
| ( ( $true
!= ( in @ ( setadjoin @ sK0 @ sK0 ) @ omega ) )
& ( ( in @ sK0 @ omega )
= $true ) ) )
& ( ! [X1: $i] :
( ( $true
= ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
| ( ( in @ X1 @ omega )
!= $true ) )
| ( omegaSAx != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f11]) ).
thf(f13,plain,
( ( ( in @ ( setadjoin @ sK1 @ sK1 ) @ omega )
!= $true )
& ( ( in @ sK1 @ omega )
= $true )
& ( omegaSAx = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f9]) ).
thf(f14,plain,
! [X1: $i] :
( ( $true
= ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
| ( ( in @ X1 @ omega )
!= $true )
| ( omegaSAx != $true ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f17,plain,
omegaSAx = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f18,plain,
( ( in @ sK1 @ omega )
= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f19,plain,
( ( in @ ( setadjoin @ sK1 @ sK1 ) @ omega )
!= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f22,plain,
! [X1: $i] :
( ( $true
= ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
| ( ( in @ X1 @ omega )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f14,f17]) ).
thf(f23,plain,
( ( ( in @ sK1 @ omega )
!= $true )
| ( $true != $true ) ),
inference(superposition,[],[f19,f22]) ).
thf(f24,plain,
( ( in @ sK1 @ omega )
!= $true ),
inference(trivial_inequality_removal,[],[f23]) ).
thf(f25,plain,
$false,
inference(forward_subsumption_resolution,[],[f24,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU809^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n026.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 14:35:57 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.25 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
% 0.21/0.31 % (684452)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.31 % (684461)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1896532325:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.31 % (684457)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1624048103:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.31 % (684459)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1416018718:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.31 % (684458)lrs+10_16_si=on:nwc=1.5:random_seed=3085925182:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.31 % (684460)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=3750561564: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)
% 0.21/0.31 % (684459)Refutation not found, incomplete strategy
% 0.21/0.31 % (684459)------------------------------
% 0.21/0.31 % (684459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (684459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (684459)CaDiCaL version: 2.1.3
% 0.21/0.31 % (684459)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.31 % (684459)Time elapsed: 0.001 s
% 0.21/0.31 % (684457) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-684452-684457"...
% 0.21/0.31 % (684459)Peak memory usage: 12 MB
% 0.21/0.31 % (684459)Instructions burned: 1 (million)
% 0.21/0.31 % (684461) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-684452-684461"...
% 0.21/0.31 % (684458) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-684452-684458"...
% 0.21/0.31 % (684459)------------------------------
% 0.21/0.31 % (684459)------------------------------
% 0.21/0.31 % (684460) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-684452-684460"...
% 0.21/0.31 % (684461)...printing done.
% 0.21/0.31 % (684457)...printing done.
% 0.21/0.31 % (684458)...printing done.
% 0.21/0.31 % (684461)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.31 % (684461)------------------------------
% 0.21/0.31 % (684461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (684461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (684461)CaDiCaL version: 2.1.3
% 0.21/0.31 % (684461)Termination reason: Refutation
% 0.21/0.31 % (684461)Time elapsed: 0.002 s
% 0.21/0.31 % (684461)Peak memory usage: 12 MB
% 0.21/0.31 % (684461)Instructions burned: 2 (million)
% 0.21/0.31 % (684452)Success in time 0.048 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------