%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV446^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:38:38 AM UTC 2026
% Result : Theorem 0.26s 0.35s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 176 ( 61 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 260 ( 26 ~; 25 |; 6 &; 200 @)
% ( 2 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 56 ( 0 ^; 50 !; 6 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/INSERT':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_6,type,
sK1: sK0 ).
thf(func_def_7,type,
sK2: sK0 ).
thf(f1,axiom,
! [X0: $tType,X1: X0] :
~ ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/NOT_IN_EMPTY_') ).
thf(f2,axiom,
! [X0: $tType,X3: X0 > $o,X2: X0,X1: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X3 ) )
= ( X1 = X2 ) )
| ( 'const/sets/IN' @ X0 @ X1 @ X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_INSERT_') ).
thf(f3,conjecture,
! [X0: $tType,X1: X0,X2: X0] :
( ( X1 = X2 )
= ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/IN_SING_') ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: X0,X2: X0] :
( ( X1 = X2 )
= ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: $tType,X1: X0] :
~ ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $tType,X1: X0 > $o,X2: X0,X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X1 ) )
= ( X2 = X3 ) )
| ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
! [X0: $tType,X1: X0 > $o,X2: X0,X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X1 ) )
= $true )
<=> ( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $true )
| ( X2 = X3 ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ! [X0: $tType,X1: X0,X2: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) )
= $true )
<=> ( X1 = X2 ) ),
inference(fool_elimination,[],[f4]) ).
thf(f10,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(flattening,[],[f6]) ).
thf(f11,plain,
? [X0: $tType,X1: X0,X2: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) )
= $true )
<~> ( X1 = X2 ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f12,plain,
! [X0: $tType,X1: X0 > $o,X2: X0,X3: X0] :
( ( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X1 ) )
= $true )
| ( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= $true )
& ( X2 != X3 ) ) )
& ( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $true )
| ( X2 = X3 )
| ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X1 ) )
!= $true ) ) ),
inference(nnf_transformation,[],[f8]) ).
thf(f13,plain,
! [X0: $tType,X1: X0 > $o,X2: X0,X3: X0] :
( ( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X1 ) )
= $true )
| ( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= $true )
& ( X2 != X3 ) ) )
& ( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $true )
| ( X2 = X3 )
| ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X1 ) )
!= $true ) ) ),
inference(flattening,[],[f12]) ).
thf(f14,plain,
? [X0: $tType,X1: X0,X2: X0] :
( ( ( X1 != X2 )
| ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) )
!= $true ) )
& ( ( X1 = X2 )
| ( ( 'const/sets/IN' @ X0 @ X1 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) )
= $true ) ) ),
inference(nnf_transformation,[],[f11]) ).
thf(f15,plain,
( ( ( sK2 != sK1 )
| ( ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) )
!= $true ) )
& ( ( sK2 = sK1 )
| ( ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) )
= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f14]) ).
thf(f16,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X1 ) )
!= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $true )
| ( X2 = X3 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f17,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/INSERT' @ X0 @ X2 @ X1 ) )
= $true )
| ( X2 != X3 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f19,plain,
! [X0: $tType,X1: X0] :
( ( 'const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0 )
!= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f20,plain,
( ( ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) )
= $true )
| ( sK2 = sK1 ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f21,plain,
( ( ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK2 @ 'const/sets/EMPTY' @ sK0 ) )
!= $true )
| ( sK2 != sK1 ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f23,plain,
! [X0: $tType,X3: X0,X1: X0 > $o] :
( $true
= ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/INSERT' @ X0 @ X3 @ X1 ) ) ),
inference(equality_resolution,[],[f17]) ).
thf(f27,plain,
( ( sK2 = sK1 )
| ( $true != $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0 ) )
| ( sK2 = sK1 ) ),
inference(superposition,[],[f16,f20]) ).
thf(f29,plain,
( ( $true != $true )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0 ) )
| ( sK2 = sK1 ) ),
inference(duplicate_literal_removal,[],[f27]) ).
thf(f30,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0 ) )
| ( sK2 = sK1 ) ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f31,plain,
sK2 = sK1,
inference(forward_subsumption_resolution,[],[f30,f19]) ).
thf(f32,plain,
( ( ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0 ) )
!= $true )
| ( sK1 != sK1 ) ),
inference(superposition,[],[f21,f31]) ).
thf(f33,plain,
( ( 'const/sets/IN' @ sK0 @ sK1 @ ( 'const/sets/INSERT' @ sK0 @ sK1 @ 'const/sets/EMPTY' @ sK0 ) )
!= $true ),
inference(trivial_inequality_removal,[],[f32]) ).
thf(f34,plain,
$false,
inference(forward_subsumption_resolution,[],[f33,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV446^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 % Computer : n006.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Tue Sep 29 15:46:54 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.28 Running higher-order theorem proving
% 0.26/0.29 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
% 0.26/0.35 % (895709)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.26/0.35 % (895716)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3485251980:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.26/0.35 % (895714)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4227979456:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.26/0.35 % (895716)Instruction limit reached!
% 0.26/0.35 % (895716)------------------------------
% 0.26/0.35 % (895716)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.35 % (895716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.35 % (895716)CaDiCaL version: 2.1.3
% 0.26/0.35 % (895716)Termination reason: Instruction limit
% 0.26/0.35 % (895716)Termination phase: Saturation
% 0.26/0.35 % (895716)Time elapsed: 0.003 s
% 0.26/0.35 % (895716)Peak memory usage: 12 MB
% 0.26/0.35 % (895716)Instructions burned: 5 (million)
% 0.26/0.35 % (895720)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.26/0.35 % (895720)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
% 0.26/0.35 % (895715)lrs+10_16_si=on:nwc=1.5:random_seed=227993543:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.26/0.35 % (895719)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1639866011:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.26/0.35 % (895718)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2521154372:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.26/0.35 % (895720)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=299226449:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.26/0.35 % (895717)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=3287009981: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)
% 0.26/0.35 % (895718) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-895709-895718"...
% 0.26/0.35 % (895717) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-895709-895717"...
% 0.26/0.35 % (895723)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=467328252:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.26/0.35 % (895718)...printing done.
% 0.26/0.35 % (895720) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-895709-895720"...
% 0.26/0.35 % (895718)Refutation found. Thanks to Tanya!
% 0.26/0.35 % SZS status Theorem for theBenchmark
% 0.26/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.36 % (895718)------------------------------
% 0.26/0.36 % (895718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.36 % (895718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.36 % (895718)CaDiCaL version: 2.1.3
% 0.26/0.36 % (895718)Termination reason: Refutation
% 0.26/0.36 % (895718)Time elapsed: 0.005 s
% 0.26/0.36 % (895718)Peak memory usage: 12 MB
% 0.26/0.36 % (895718)Instructions burned: 4 (million)
% 0.26/0.36 % (895709)Success in time 0.045 s
% 0.26/0.36 % Vampire exiting
%------------------------------------------------------------------------------