%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU727^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 08:33:08 AM UTC 2026
% Result : Theorem 0.08s 0.15s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 3
% Syntax : Number of formulae : 47 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 346 ( 75 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 525 ( 33 ~; 12 |; 15 &; 381 @)
% ( 0 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 8 con; 0-4 aty)
% ( 30 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 105 ( 36 ^; 63 !; 6 ?; 105 :)
% 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,
setminus: $i > $i > $i ).
thf(func_def_3,type,
setminusI: $o ).
thf(func_def_5,type,
setminusER: $o ).
thf(func_def_6,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
vIMP: $o > $o > $o ).
thf(func_def_8,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vNOT: $o > $o ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,axiom,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(f2,axiom,
( setminusER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(f3,conjecture,
( setminusI
=> ( setminusER
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementI1) ).
thf(f4,negated_conjecture,
~ ( setminusI
=> ( setminusER
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( setminusI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( setminusER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( setminusER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) )
=> ~ ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( setminusI
=> ( setminusER
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( setminusI = $true )
=> ( ( setminusER = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
= $true ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
!= $true )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( setminusER = $true )
& ( setminusI = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
!= $true )
& ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( setminusER = $true )
& ( setminusI = $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ( $true
!= ( in @ sK2 @ ( setminus @ sK0 @ ( setminus @ sK0 @ sK1 ) ) ) )
& ( $true
= ( in @ sK2 @ sK1 ) )
& ( $true
= ( in @ sK2 @ sK0 ) )
& ( $true
= ( in @ sK1 @ ( powerset @ sK0 ) ) )
& ( setminusER = $true )
& ( setminusI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f12]) ).
thf(f14,plain,
( setminusI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f15,plain,
( setminusER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) )
=> ~ ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
setminusI = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f17,plain,
setminusER = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f19,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f20,plain,
( $true
= ( in @ sK2 @ sK1 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f21,plain,
( $true
!= ( in @ sK2 @ ( setminus @ sK0 @ ( setminus @ sK0 @ sK1 ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f24,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f14,f16]) ).
thf(f25,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) )
=> ~ ( in @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f15,f17]) ).
thf(f26,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) )
=> ~ ( in @ Y0 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( setminus @ Y1 @ Y0 ) )
=> ~ ( in @ X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( setminus @ Y1 @ Y0 ) )
=> ~ ( in @ X1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( setminus @ Y0 @ X2 ) )
=> ~ ( in @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( setminus @ Y0 @ X2 ) )
=> ~ ( in @ X1 @ X2 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( setminus @ X3 @ X2 ) )
=> ~ ( in @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setminus @ X3 @ X2 ) ) )
| ( $true
= ( ~ ( in @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setminus @ X3 @ X2 ) ) )
| ( $false
= ( in @ X1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f32]) ).
thf(f34,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ~ ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( setminus @ Y2 @ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f24]) ).
thf(f35,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ~ ( in @ X1 @ Y0 )
=> ( in @ X1 @ ( setminus @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ~ ( in @ X1 @ Y0 )
=> ( in @ X1 @ ( setminus @ Y1 @ Y0 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f35]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ~ ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setminus @ Y0 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f38,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ~ ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setminus @ Y0 @ X2 ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f37]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setminus @ X3 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( ~ ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setminus @ X3 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ X3 ) )
| ( $false
= ( ~ ( in @ X1 @ X2 ) ) )
| ( $true
= ( in @ X1 @ ( setminus @ X3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setminus @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( $false
= ( in @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f41]) ).
thf(f45,plain,
( ( $true != $true )
| ( $true
= ( in @ sK2 @ ( setminus @ sK0 @ sK1 ) ) )
| ( ( in @ sK2 @ sK0 )
= $false ) ),
inference(constrained_superposition,[],[f21,f42]) ).
thf(f48,plain,
( ( $true
= ( in @ sK2 @ ( setminus @ sK0 @ sK1 ) ) )
| ( ( in @ sK2 @ sK0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f45]) ).
thf(f50,plain,
( ( $true = $false )
| ( $true
= ( in @ sK2 @ ( setminus @ sK0 @ sK1 ) ) ) ),
inference(forward_demodulation,[],[f48,f19]) ).
thf(f51,plain,
( $true
= ( in @ sK2 @ ( setminus @ sK0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f50]) ).
thf(f64,plain,
( ( $true = $false )
| ( ( in @ sK2 @ sK1 )
= $false ) ),
inference(constrained_superposition,[],[f33,f51]) ).
thf(f65,plain,
( ( in @ sK2 @ sK1 )
= $false ),
inference(trivial_inequality_removal,[],[f64]) ).
thf(f76,plain,
$true = $false,
inference(constrained_superposition,[],[f20,f65]) ).
thf(f77,plain,
$false,
inference(trivial_inequality_removal,[],[f76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU727^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 14:17:18 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.11 Running first-order model finding
% 0.08/0.11 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.15 % (169951)Will run a generic schedule for satisfiability detection.
% 0.08/0.15 % (169957)% WARNING: option uhcvi not known.
% 0.08/0.15 % (169958)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1631686158:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.15 % (169959)dis+10_1_sil=32000:sp=arity:random_seed=2247846822:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.15 % (169956)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1036095882_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.15 % (169957)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2359793933:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.15 % (169960)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=988822306:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.15 % (169961)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2325484355:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.15 % (169962)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1083875161:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.15 % (169957)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.15 % (169960)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.15 % Exception at run slice level
% 0.08/0.15 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.15 % (169957)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.15 % (169959) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-169951-169959"...
% 0.08/0.15 % (169960) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-169951-169960"...
% 0.08/0.15 % (169957) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-169951-169957"...
% 0.08/0.15 % (169961) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-169951-169961"...
% 0.08/0.15 % (169962) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-169951-169962"...
% 0.08/0.15 % (169958) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-169951-169958"...
% 0.08/0.15 % (169959)...printing done.
% 0.08/0.15 % (169960)...printing done.
% 0.08/0.15 % (169957)...printing done.
% 0.08/0.15 % (169961)...printing done.
% 0.08/0.15 % (169962)...printing done.
% 0.08/0.15 % (169959)Refutation found. Thanks to Tanya!
% 0.08/0.15 % SZS status Theorem for theBenchmark
% 0.08/0.15 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.15 % (169959)------------------------------
% 0.08/0.15 % (169959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.15 % (169959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.15 % (169959)CaDiCaL version: 2.1.3
% 0.08/0.15 % (169959)Termination reason: Refutation
% 0.08/0.15 % (169959)Time elapsed: 0.002 s
% 0.08/0.15 % (169959)Peak memory usage: 12 MB
% 0.08/0.15 % (169959)Instructions burned: 7 (million)
% 0.08/0.15 % (169951)Success in time 0.028 s
% 0.08/0.15 % Vampire exiting
%------------------------------------------------------------------------------