%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU535^2 : 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 : n016.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 08:29:58 AM UTC 2026
% Result : Theorem 0.23s 0.31s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 23 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 168 ( 50 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 109 ( 22 ~; 14 |; 12 &; 48 @)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 36 ( 0 ^; 28 !; 8 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
emptysetE: $o ).
thf(func_def_7,type,
sK1: $i > $o ).
thf(func_def_9,type,
sK3: $o ).
thf(func_def_10,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: $i] :
( ( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 )
= emptysetE ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(f2,conjecture,
( emptysetE
=> ! [X0: $i > $o,X1: $i] :
( ( in @ X1 @ emptyset )
=> ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(f3,negated_conjecture,
~ ( emptysetE
=> ! [X0: $i > $o,X1: $i] :
( ( in @ X1 @ emptyset )
=> ( X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
~ ( emptysetE
=> ! [X0: $i > $o,X1: $i] :
( ( in @ X1 @ emptyset )
=> ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f5,plain,
~ ( ( emptysetE = $true )
=> ! [X1: $i,X0: $i > $o] :
( ( ( in @ X1 @ emptyset )
= $true )
=> ( ( X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
! [X0: $i] :
( ( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 )
= emptysetE ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( ( emptysetE = $true )
<=> ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
=> ! [X1: $o] : ( $true = X1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ! [X1: $o] : ( $true = X1 ) )
<=> ( emptysetE = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ? [X1: $i,X0: $i > $o] :
( ( ( in @ X1 @ emptyset )
= $true )
& ( ( X0 @ X1 )
!= $true ) )
& ( emptysetE = $true ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i > $o] :
( ( ( in @ X0 @ emptyset )
= $true )
& ( ( X1 @ X0 )
!= $true ) )
& ( emptysetE = $true ) ),
inference(rectify,[],[f9]) ).
thf(f11,plain,
( ( $true
= ( in @ sK0 @ emptyset ) )
& ( ( sK1 @ sK0 )
!= $true )
& ( emptysetE = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f10]) ).
thf(f12,plain,
( ( ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ! [X1: $o] : ( $true = X1 ) )
| ( emptysetE != $true ) )
& ( ( emptysetE = $true )
| ? [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
& ? [X1: $o] : ( $true != X1 ) ) ) ),
inference(nnf_transformation,[],[f8]) ).
thf(f13,plain,
( ( ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ! [X1: $o] : ( $true = X1 ) )
| ( emptysetE != $true ) )
& ( ( emptysetE = $true )
| ? [X2: $i] :
( ( ( in @ X2 @ emptyset )
= $true )
& ? [X3: $o] : ( $true != X3 ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f14,plain,
( ( ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ! [X1: $o] : ( $true = X1 ) )
| ( emptysetE != $true ) )
& ( ( emptysetE = $true )
| ( ( ( in @ sK2 @ emptyset )
= $true )
& ( sK3 != $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X2,sK2),skolemize(X3,sK3)],[f13]) ).
thf(f15,plain,
emptysetE = $true,
inference(cnf_transformation,[],[f11]) ).
thf(f16,plain,
( ( sK1 @ sK0 )
!= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f17,plain,
( $true
= ( in @ sK0 @ emptyset ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f20,plain,
! [X0: $i,X1: $o] :
( ( $true = X1 )
| ( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetE != $true ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f23,plain,
! [X0: $i,X1: $o] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ( $true = X1 ) ),
inference(forward_subsumption_resolution,[],[f20,f15]) ).
thf(f24,plain,
! [X0: $o] :
( ( $true != $true )
| ( $true = X0 ) ),
inference(superposition,[],[f23,f17]) ).
thf(f25,plain,
! [X0: $o] : ( $true = X0 ),
inference(trivial_inequality_removal,[],[f24]) ).
thf(f28,plain,
$true != $true,
inference(superposition,[],[f16,f25]) ).
thf(f33,plain,
$false,
inference(trivial_inequality_removal,[],[f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU535^2 : 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 : n016.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 13:53:50 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.26 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
% 0.23/0.31 % (384099)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.31 % (384106)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=455727649:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.31 % (384105)lrs+10_16_si=on:nwc=1.5:random_seed=32110983:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.31 % (384107)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=3011603160: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)
% 0.23/0.31 % (384108)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=313594206:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.31 % (384106)Refutation not found, incomplete strategy
% 0.23/0.31 % (384106)------------------------------
% 0.23/0.31 % (384106)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (384106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (384106)CaDiCaL version: 2.1.3
% 0.23/0.31 % (384106)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.31 % (384106)Time elapsed: 0.001 s
% 0.23/0.31 % (384106)Peak memory usage: 12 MB
% 0.23/0.31 % (384104)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2130646033:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.31 % (384108) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-384099-384108"...
% 0.23/0.31 % (384105) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-384099-384105"...
% 0.23/0.31 % (384106)------------------------------
% 0.23/0.31 % (384106)------------------------------
% 0.23/0.31 % (384107) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-384099-384107"...
% 0.23/0.31 % (384108)...printing done.
% 0.23/0.31 % (384105)...printing done.
% 0.23/0.31 % (384104) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-384099-384104"...
% 0.23/0.31 % (384108)Refutation found. Thanks to Tanya!
% 0.23/0.31 % SZS status Theorem for theBenchmark
% 0.23/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.31 % (384108)------------------------------
% 0.23/0.31 % (384108)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (384108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (384108)CaDiCaL version: 2.1.3
% 0.23/0.31 % (384108)Termination reason: Refutation
% 0.23/0.31 % (384108)Time elapsed: 0.002 s
% 0.23/0.31 % (384108)Peak memory usage: 12 MB
% 0.23/0.31 % (384108)Instructions burned: 2 (million)
% 0.23/0.31 % (384099)Success in time 0.046 s
% 0.23/0.31 % Vampire exiting
%------------------------------------------------------------------------------