%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU797^2 : 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 : 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 08:33:27 AM UTC 2026
% Result : Theorem 0.09s 0.27s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 2
% Syntax : Number of formulae : 33 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 225 ( 77 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 334 ( 13 ~; 11 |; 25 &; 249 @)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 20 usr; 8 con; 0-4 aty)
% ( 15 !!; 11 ??; 0 @@+; 0 @@-)
% Number of variables : 107 ( 43 ^; 54 !; 10 ?; 107 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
image1: $i > ( $i > $i ) > $i ).
thf(func_def_2,type,
image1Equiv: $o ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vIFF: $o > $o > $o ).
thf(func_def_6,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_9,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_10,type,
vAND: $o > $o > $o ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_17,type,
sK1: $i > $i ).
thf(func_def_20,type,
vNOT: $o > $o ).
thf(func_def_21,type,
sK4: $i > $i > ( $i > $i ) > $i ).
thf(f1,axiom,
( image1Equiv
= ( ! [X0: $i,X1: $i > $i,X2: $i] :
( ( in @ X2
@ ( image1 @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ? [X3: $i] :
( ( X2
= ( X1 @ X3 ) )
& ( in @ X3 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image1Equiv) ).
thf(f2,conjecture,
( image1Equiv
=> ! [X0: $i,X1: $i > $i,X2: $i] :
( ? [X3: $i] :
( ( X2
= ( X1 @ X3 ) )
& ( in @ X3 @ X0 ) )
=> ( in @ X2
@ ( image1 @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image1I) ).
thf(f3,negated_conjecture,
~ ( image1Equiv
=> ! [X0: $i,X1: $i > $i,X2: $i] :
( ? [X3: $i] :
( ( X2
= ( X1 @ X3 ) )
& ( in @ X3 @ X0 ) )
=> ( in @ X2
@ ( image1 @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( image1Equiv
= ( ! [X0: $i,X1: $i > $i,X2: $i] :
( ( in @ X2
@ ( image1 @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ? [X4: $i] :
( ( ( X1 @ X4 )
= X2 )
& ( in @ X4 @ X0 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( image1Equiv
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( image1 @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
= ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( ( Y1 @ Y3 )
= Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( image1Equiv
=> ! [X0: $i,X1: $i > $i,X2: $i] :
( ? [X3: $i] :
( ( X2
= ( X1 @ X3 ) )
& ( in @ X3 @ X0 ) )
=> ( in @ X2
@ ( image1 @ X0
@ ^ [X4: $i] : ( X1 @ X4 ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( image1Equiv = $true )
=> ! [X0: $i,X1: $i > $i,X2: $i] :
( ? [X3: $i] :
( ( ( X1 @ X3 )
= X2 )
& ( ( in @ X3 @ X0 )
= $true ) )
=> ( $true
= ( in @ X2
@ ( image1 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ? [X0: $i,X1: $i > $i,X2: $i] :
( ( $true
!= ( in @ X2
@ ( image1 @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
& ? [X3: $i] :
( ( ( X1 @ X3 )
= X2 )
& ( ( in @ X3 @ X0 )
= $true ) ) )
& ( image1Equiv = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ( $true
!= ( in @ sK2
@ ( image1 @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ) )
& ( sK2
= ( sK1 @ sK3 ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( image1Equiv = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f8]) ).
thf(f10,plain,
( image1Equiv
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( image1 @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
= ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( ( Y1 @ Y3 )
= Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f11,plain,
image1Equiv = $true,
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( $true
= ( in @ sK3 @ sK0 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
( sK2
= ( sK1 @ sK3 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f14,plain,
( $true
!= ( in @ sK2
@ ( image1 @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f17,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( image1 @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
= ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( ( Y1 @ Y3 )
= Y0 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f10,f11]) ).
thf(f18,plain,
( $true
!= ( in @ sK2 @ ( image1 @ sK0 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f14]) ).
thf(f19,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $i )
@ ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0
@ ( image1 @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
= ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y2 )
& ( ( Y1 @ Y3 )
= Y0 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f17]) ).
thf(f20,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( image1 @ Y1 @ Y0 ) )
= ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( ( Y0 @ Y2 )
= X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
! [X2: $i > $i,X1: $i] :
( $true
= ( ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( image1 @ Y1 @ Y0 ) )
= ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( ( Y0 @ Y2 )
= X1 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f20]) ).
thf(f22,plain,
! [X2: $i > $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( image1 @ Y0 @ X2 ) )
= ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( X2 @ Y1 )
= X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f23,plain,
! [X2: $i > $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( image1 @ Y0 @ X2 ) )
= ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( X2 @ Y1 )
= X1 ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f24,plain,
! [X2: $i > $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( image1 @ X3 @ X2 ) )
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
& ( ( X2 @ Y0 )
= X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f25,plain,
! [X2: $i > $i,X3: $i,X1: $i] :
( ( in @ X1 @ ( image1 @ X3 @ X2 ) )
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
& ( ( X2 @ Y0 )
= X1 ) ) ) ),
inference(iff_proxy_clausification,[],[f24]) ).
thf(f26,plain,
! [X2: $i > $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( image1 @ X3 @ X2 ) ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
& ( ( X2 @ Y0 )
= X1 ) ) ) ) ),
inference(iff_proxy_clausification,[],[f25]) ).
thf(f33,plain,
! [X2: $i > $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ X1 @ ( image1 @ X3 @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
& ( ( X2 @ Y0 )
= X1 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f26]) ).
thf(f34,plain,
! [X2: $i > $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ X1 @ ( image1 @ X3 @ X2 ) ) )
| ( $false
= ( ( in @ X4 @ X3 )
& ( ( X2 @ X4 )
= X1 ) ) ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
! [X2: $i > $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ X1 @ ( image1 @ X3 @ X2 ) ) )
| ( $false
= ( ( X2 @ X4 )
= X1 ) )
| ( $false
= ( in @ X4 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f34]) ).
thf(f36,plain,
! [X2: $i > $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( in @ X1 @ ( image1 @ X3 @ X2 ) ) )
| ( $false
= ( in @ X4 @ X3 ) )
| ( ( X2 @ X4 )
!= X1 ) ),
inference(equality_proxy_clausification,[],[f35]) ).
thf(f39,plain,
! [X0: $i] :
( ( $true != $true )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( sK2
!= ( sK1 @ X0 ) ) ),
inference(constrained_superposition,[],[f18,f36]) ).
thf(f40,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ sK0 ) )
| ( sK2
!= ( sK1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f39]) ).
thf(f56,plain,
( ( $true = $false )
| ( sK2
!= ( sK1 @ sK3 ) ) ),
inference(constrained_superposition,[],[f12,f40]) ).
thf(f57,plain,
( sK2
!= ( sK1 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f56]) ).
thf(f60,plain,
$false,
inference(forward_subsumption_resolution,[],[f57,f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU797^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n006.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:31:25 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.09/0.27 % (805562)Will run a generic schedule for satisfiability detection.
% 0.09/0.27 % (805570)% WARNING: option uhcvi not known.
% 0.09/0.27 % (805573)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3961914604:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.09/0.27 % (805573)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.27 % (805572)dis+10_1_sil=32000:sp=arity:random_seed=1467462614:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.09/0.27 % (805570)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=499658517:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.09/0.27 % (805571)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2306044950:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.09/0.27 % (805573) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-805562-805573"...
% 0.09/0.27 % (805570)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.27 % (805570)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.27 % (805573)...printing done.
% 0.09/0.27 % (805573)Refutation found. Thanks to Tanya!
% 0.09/0.27 % SZS status Theorem for theBenchmark
% 0.09/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.28 % (805573)------------------------------
% 0.09/0.28 % (805573)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.28 % (805573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.28 % (805573)CaDiCaL version: 2.1.3
% 0.09/0.28 % (805573)Termination reason: Refutation
% 0.09/0.28 % (805573)Time elapsed: 0.005 s
% 0.09/0.28 % (805573)Peak memory usage: 12 MB
% 0.09/0.28 % (805573)Instructions burned: 6 (million)
% 0.09/0.28 % (805562)Success in time 0.037 s
% 0.09/0.28 % Vampire exiting
%------------------------------------------------------------------------------