%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU617^2 : 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 : n002.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 08:30:21 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 37 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 349 ( 97 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 410 ( 45 ~; 36 |; 20 &; 291 @)
% ( 4 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 12 con; 0-2 aty)
% Number of variables : 87 ( 0 ^; 71 !; 16 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setunion: $i > $i ).
thf(func_def_4,type,
setadjoinIL: $o ).
thf(func_def_6,type,
setunionI: $o ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= setadjoinIL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(f2,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X1 @ ( setunion @ X0 ) ) ) )
= setunionI ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(f3,conjecture,
( setadjoinIL
=> ( setunionI
=> ! [X0: $i,X1: $i] : ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).
thf(f4,negated_conjecture,
~ ( setadjoinIL
=> ( setunionI
=> ! [X0: $i,X1: $i] : ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X0 ) )
= setadjoinIL ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( ( setadjoinIL = $true )
<=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
~ ( setadjoinIL
=> ( setunionI
=> ! [X0: $i,X1: $i] : ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
~ ( ( setadjoinIL = $true )
=> ( ( setunionI = $true )
=> ! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
= $true ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
=> ( ( in @ X0 @ X2 )
=> ( in @ X1 @ ( setunion @ X2 ) ) ) )
= setunionI ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( ( in @ X0 @ X2 )
= $true )
=> ( $true
= ( in @ X1 @ ( setunion @ X2 ) ) ) ) )
<=> ( setunionI = $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ? [X1: $i,X0: $i] :
( ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
!= $true )
& ( setunionI = $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f12,plain,
( ? [X1: $i,X0: $i] :
( ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
!= $true )
& ( setunionI = $true )
& ( setadjoinIL = $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
<=> ( setunionI = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f14,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( $true
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( ( in @ X0 @ X2 )
!= $true ) )
<=> ( setunionI = $true ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
( ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X0 ) )
!= $true ) )
& ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X0 ) )
= $true )
| ( setadjoinIL != $true ) ) ),
inference(nnf_transformation,[],[f6]) ).
thf(f16,plain,
( ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X0 ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( $true
= ( in @ X3 @ ( setadjoin @ X3 @ X2 ) ) )
| ( setadjoinIL != $true ) ) ),
inference(rectify,[],[f15]) ).
thf(f17,plain,
( ( ( setadjoinIL = $true )
| ( $true
!= ( in @ sK1 @ ( setadjoin @ sK1 @ sK0 ) ) ) )
& ( ! [X2: $i,X3: $i] :
( $true
= ( in @ X3 @ ( setadjoin @ X3 @ X2 ) ) )
| ( setadjoinIL != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16]) ).
thf(f18,plain,
( ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( setunionI = $true )
& ( setadjoinIL = $true ) ),
inference(rectify,[],[f12]) ).
thf(f19,plain,
( ( $true
!= ( in @ sK3 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK2 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( setunionI = $true )
& ( setadjoinIL = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f18]) ).
thf(f20,plain,
( ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( $true
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( ( in @ X0 @ X2 )
!= $true ) )
| ( setunionI != $true ) )
& ( ( setunionI = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( $true
!= ( in @ X1 @ ( setunion @ X2 ) ) )
& ( ( in @ X0 @ X2 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f14]) ).
thf(f21,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( setunion @ X1 ) )
= $true )
| ( $true
!= ( in @ X0 @ X1 ) ) )
| ( setunionI != $true ) )
& ( ( setunionI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
& ( $true
!= ( in @ X5 @ ( setunion @ X4 ) ) )
& ( $true
= ( in @ X3 @ X4 ) ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f22,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( setunion @ X1 ) )
= $true )
| ( $true
!= ( in @ X0 @ X1 ) ) )
| ( setunionI != $true ) )
& ( ( setunionI = $true )
| ( ( $true
= ( in @ sK6 @ sK4 ) )
& ( ( in @ sK6 @ ( setunion @ sK5 ) )
!= $true )
& ( $true
= ( in @ sK4 @ sK5 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X3,sK4),skolemize(X4,sK5),skolemize(X5,sK6)],[f21]) ).
thf(f23,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( in @ X3 @ ( setadjoin @ X3 @ X2 ) ) )
| ( setadjoinIL != $true ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f25,plain,
setadjoinIL = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f26,plain,
setunionI = $true,
inference(cnf_transformation,[],[f19]) ).
thf(f27,plain,
( $true
!= ( in @ sK3 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3 @ ( setadjoin @ sK2 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f31,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( ( in @ X2 @ ( setunion @ X1 ) )
= $true )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( setunionI != $true ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f35,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( in @ X3 @ ( setadjoin @ X3 @ X2 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f23,f25]) ).
thf(f36,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setunion @ X1 ) )
= $true )
| ( $true != $true )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( ( in @ X2 @ X0 )
!= $true ) ),
inference(definition_unfolding,[],[f31,f26]) ).
thf(f40,plain,
! [X2: $i,X3: $i] :
( $true
= ( in @ X3 @ ( setadjoin @ X3 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f35]) ).
thf(f41,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( ( in @ X2 @ ( setunion @ X1 ) )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f36]) ).
thf(f42,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( $true
= ( in @ X2 @ ( setunion @ ( setadjoin @ X0 @ X1 ) ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f41,f40]) ).
thf(f43,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
!= $true )
| ( $true
= ( in @ X2 @ ( setunion @ ( setadjoin @ X0 @ X1 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f44,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ X1 ) @ X2 ) ) ) ) ),
inference(constrained_superposition,[],[f43,f40]) ).
thf(f45,plain,
! [X2: $i,X0: $i,X1: $i] :
( $true
= ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ X1 ) @ X2 ) ) ) ),
inference(trivial_inequality_removal,[],[f44]) ).
thf(f84,plain,
$true != $true,
inference(constrained_superposition,[],[f27,f45]) ).
thf(f85,plain,
$false,
inference(trivial_inequality_removal,[],[f84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU617^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n002.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 14:01:07 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 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
% 0.21/0.27 % (1330958)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (1330967)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3127426498:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.27 % (1330967)Refutation not found, incomplete strategy
% 0.21/0.27 % (1330967)------------------------------
% 0.21/0.27 % (1330967)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (1330967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (1330967)CaDiCaL version: 2.1.3
% 0.21/0.27 % (1330967)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.27 % (1330967)Time elapsed: 0.001 s
% 0.21/0.27 % (1330967)Peak memory usage: 12 MB
% 0.21/0.27 % (1330967)Instructions burned: 1 (million)
% 0.21/0.27 % (1330967)------------------------------
% 0.21/0.27 % (1330967)------------------------------
% 0.21/0.27 % (1330971)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.27 % (1330971)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
% 0.21/0.27 % (1330965)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1905248939:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.27 % (1330966)lrs+10_16_si=on:nwc=1.5:random_seed=4020009989:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.27 % (1330969)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3738085382:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.27 % (1330968)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=3107021954: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)
% 0.21/0.27 % (1330965) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1330958-1330965"...
% 0.21/0.27 % (1330970)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1279168827:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.27 % (1330971)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=2978917892:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.27 % (1330965)...printing done.
% 0.21/0.27 % (1330965)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (1330965)------------------------------
% 0.21/0.27 % (1330965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (1330965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (1330965)CaDiCaL version: 2.1.3
% 0.21/0.27 % (1330965)Termination reason: Refutation
% 0.21/0.27 % (1330965)Time elapsed: 0.003 s
% 0.21/0.27 % (1330965)Peak memory usage: 12 MB
% 0.21/0.27 % (1330965)Instructions burned: 10 (million)
% 0.21/0.27 % (1330958)Success in time 0.034 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------