%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV167^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 08:39:05 AM UTC 2026
% Result : Theorem 0.08s 0.27s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 3
% Syntax : Number of formulae : 40 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 114 ( 74 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 281 ( 42 ~; 34 |; 11 &; 177 @)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 160 ( 160 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-4 aty)
% Number of variables : 193 ( 59 sgn 55 !; 10 ?; 193 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_2,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
sK0: a > a > a > a > $o ).
thf(func_def_7,type,
sK1: a ).
thf(func_def_8,type,
sK2: a ).
thf(func_def_9,type,
sK3: a ).
thf(func_def_10,type,
sK4: a ).
thf(f1,conjecture,
! [X0: a > a > a > a > $o] :
( ! [X1: ( a > a > a ) > a,X2: ( a > a > a ) > a] :
( ( X0
@ ( X1
@ ^ [X3: a,X4: a] : X3 )
@ ( X1
@ ^ [X3: a,X4: a] : X4 )
@ ( X2
@ ^ [X3: a,X4: a] : X3 )
@ ( X2
@ ^ [X3: a,X4: a] : X4 ) )
=> ( X1 = X2 ) )
=> ! [X5: a,X6: a,X7: a,X8: a] :
( ( X0 @ X5 @ X6 @ X7 @ X8 )
=> ( ( X6 = X8 )
& ( X5 = X7 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM189_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > a > a > $o] :
( ! [X1: ( a > a > a ) > a,X2: ( a > a > a ) > a] :
( ( X0
@ ( X1
@ ^ [X3: a,X4: a] : X3 )
@ ( X1
@ ^ [X3: a,X4: a] : X4 )
@ ( X2
@ ^ [X3: a,X4: a] : X3 )
@ ( X2
@ ^ [X3: a,X4: a] : X4 ) )
=> ( X1 = X2 ) )
=> ! [X5: a,X6: a,X7: a,X8: a] :
( ( X0 @ X5 @ X6 @ X7 @ X8 )
=> ( ( X6 = X8 )
& ( X5 = X7 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > a > a > a > $o] :
( ! [X1: ( a > a > a ) > a,X2: ( a > a > a ) > a] :
( ( X0
@ ( X1
@ ^ [X3: a,X4: a] : X3 )
@ ( X1
@ ^ [X5: a,X6: a] : X6 )
@ ( X2
@ ^ [X7: a,X8: a] : X7 )
@ ( X2
@ ^ [X9: a,X10: a] : X10 ) )
=> ( X1 = X2 ) )
=> ! [X11: a,X12: a,X13: a,X14: a] :
( ( X0 @ X11 @ X12 @ X13 @ X14 )
=> ( ( X12 = X14 )
& ( X11 = X13 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > a > a > a > $o] :
( ! [X1: ( a > a > a ) > a,X2: ( a > a > a ) > a] :
( ( ( X0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 )
@ ( X2
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X2
@ ^ [Y0: a,Y1: a] : Y1 ) )
= $true )
=> ( X1 = X2 ) )
=> ! [X11: a,X12: a,X13: a,X14: a] :
( ( ( X0 @ X11 @ X12 @ X13 @ X14 )
= $true )
=> ( ( X12 = X14 )
& ( X11 = X13 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: a > a > a > a > $o] :
( ! [X1: ( a > a > a ) > a,X2: ( a > a > a ) > a] :
( ( ( X0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 )
@ ( X2
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X2
@ ^ [Y0: a,Y1: a] : Y1 ) )
= $true )
=> ( X1 = X2 ) )
=> ! [X3: a,X4: a,X5: a,X6: a] :
( ( $true
= ( X0 @ X3 @ X4 @ X5 @ X6 ) )
=> ( ( X4 = X6 )
& ( X3 = X5 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
? [X0: a > a > a > a > $o] :
( ? [X3: a,X4: a,X5: a,X6: a] :
( ( ( X4 != X6 )
| ( X3 != X5 ) )
& ( $true
= ( X0 @ X3 @ X4 @ X5 @ X6 ) ) )
& ! [X1: ( a > a > a ) > a,X2: ( a > a > a ) > a] :
( ( X1 = X2 )
| ( ( X0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 )
@ ( X2
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X2
@ ^ [Y0: a,Y1: a] : Y1 ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a > a > a > a > $o] :
( ? [X1: a,X2: a,X3: a,X4: a] :
( ( ( X2 != X4 )
| ( X1 != X3 ) )
& ( $true
= ( X0 @ X1 @ X2 @ X3 @ X4 ) ) )
& ! [X5: ( a > a > a ) > a,X6: ( a > a > a ) > a] :
( ( X5 = X6 )
| ( $true
!= ( X0
@ ( X5
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X5
@ ^ [Y0: a,Y1: a] : Y1 )
@ ( X6
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X6
@ ^ [Y0: a,Y1: a] : Y1 ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ( sK2 != sK4 )
| ( sK1 != sK3 ) )
& ( $true
= ( sK0 @ sK1 @ sK2 @ sK3 @ sK4 ) )
& ! [X5: ( a > a > a ) > a,X6: ( a > a > a ) > a] :
( ( X5 = X6 )
| ( $true
!= ( sK0
@ ( X5
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X5
@ ^ [Y0: a,Y1: a] : Y1 )
@ ( X6
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X6
@ ^ [Y0: a,Y1: a] : Y1 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f7]) ).
thf(f9,plain,
! [X6: ( a > a > a ) > a,X5: ( a > a > a ) > a] :
( ( $true
!= ( sK0
@ ( X5
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X5
@ ^ [Y0: a,Y1: a] : Y1 )
@ ( X6
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X6
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ( X5 = X6 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( $true
= ( sK0 @ sK1 @ sK2 @ sK3 @ sK4 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( sK2 != sK4 )
| ( sK1 != sK3 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,definition,
( spl5_1
<=> ( sK1 = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f17,plain,
( ( sK1 != sK3 )
| spl5_1 ),
inference(avatar_component_clause,[],[f15]) ).
thf(f19,definition,
( spl5_2
<=> ( sK2 = sK4 ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f21,plain,
( ( sK2 != sK4 )
| spl5_2 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f22,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f11,f19,f15]) ).
thf(f31,plain,
! [X2: ( a > a > a ) > a,X3: ( a > a > a ) > a] :
( ( $true != $true )
| ( ( ^ [Y0: a > a > a] :
( Y0
@ ( ^ [Y1: a > a > a] : sK1
@ Y0 )
@ ( X2 @ Y0 ) ) )
= X3 )
| ( sK3
!= ( X3
@ ^ [Y0: a,Y1: a] : Y0 ) )
| ( ( X2
@ ^ [Y0: a,Y1: a] : Y1 )
!= sK2 )
| ( sK4
!= ( X3
@ ^ [Y0: a,Y1: a] : Y1 ) ) ),
inference(constrained_superposition,[],[f9,f10]) ).
thf(f34,plain,
! [X2: ( a > a > a ) > a,X3: ( a > a > a ) > a] :
( ( ( ^ [Y0: a > a > a] :
( Y0
@ ( ^ [Y1: a > a > a] : sK1
@ Y0 )
@ ( X2 @ Y0 ) ) )
= X3 )
| ( sK3
!= ( X3
@ ^ [Y0: a,Y1: a] : Y0 ) )
| ( ( X2
@ ^ [Y0: a,Y1: a] : Y1 )
!= sK2 )
| ( sK4
!= ( X3
@ ^ [Y0: a,Y1: a] : Y1 ) ) ),
inference(trivial_inequality_removal,[],[f31]) ).
thf(f35,plain,
! [X2: ( a > a > a ) > a,X3: ( a > a > a ) > a] :
( ( ( X2
@ ^ [Y0: a,Y1: a] : Y1 )
!= sK2 )
| ( sK3
!= ( X3
@ ^ [Y0: a,Y1: a] : Y0 ) )
| ( ( ^ [Y0: a > a > a] : ( Y0 @ sK1 @ ( X2 @ Y0 ) ) )
= X3 )
| ( sK4
!= ( X3
@ ^ [Y0: a,Y1: a] : Y1 ) ) ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f40,plain,
! [X0: ( a > a > a ) > a] :
( ( sK3
!= ( X0
@ ^ [Y0: a,Y1: a] : Y0 ) )
| ( ( ^ [Y0: a > a > a] :
( Y0 @ sK1
@ ( ^ [Y1: a > a > a] : sK2
@ Y0 ) ) )
= X0 )
| ( sK4
!= ( X0
@ ^ [Y0: a,Y1: a] : Y1 ) ) ),
inference(equality_resolution,[],[f35]) ).
thf(f41,plain,
! [X0: ( a > a > a ) > a] :
( ( sK4
!= ( X0
@ ^ [Y0: a,Y1: a] : Y1 ) )
| ( ( ^ [Y0: a > a > a] : ( Y0 @ sK1 @ sK2 ) )
= X0 )
| ( sK3
!= ( X0
@ ^ [Y0: a,Y1: a] : Y0 ) ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f45,plain,
! [X0: ( a > a > a ) > a] :
( ( ( ^ [Y0: a > a > a] : ( Y0 @ sK1 @ sK2 ) )
= ( ^ [Y0: a > a > a] :
( Y0 @ ( X0 @ Y0 )
@ ( ^ [Y1: a > a > a] : sK4
@ Y0 ) ) ) )
| ( sK3
!= ( ^ [Y0: a > a > a] :
( Y0 @ ( X0 @ Y0 )
@ ( ^ [Y1: a > a > a] : sK4
@ Y0 ) )
@ ^ [Y0: a,Y1: a] : Y0 ) ) ),
inference(equality_resolution,[],[f41]) ).
thf(f48,plain,
! [X0: ( a > a > a ) > a] :
( ( sK3
!= ( X0
@ ^ [Y0: a,Y1: a] : Y0 ) )
| ( ( ^ [Y0: a > a > a] : ( Y0 @ sK1 @ sK2 ) )
= ( ^ [Y0: a > a > a] : ( Y0 @ ( X0 @ Y0 ) @ sK4 ) ) ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f82,plain,
( ( ^ [Y0: a > a > a] : ( Y0 @ sK1 @ sK2 ) )
= ( ^ [Y0: a > a > a] :
( Y0
@ ( ^ [Y1: a > a > a] : sK3
@ Y0 )
@ sK4 ) ) ),
inference(equality_resolution,[],[f48]) ).
thf(f83,plain,
( ( ^ [Y0: a > a > a] : ( Y0 @ sK1 @ sK2 ) )
= ( ^ [Y0: a > a > a] : ( Y0 @ sK3 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f82]) ).
thf(f92,plain,
! [X1: a > a > a] :
( ( ^ [Y0: a > a > a] : ( Y0 @ sK1 @ sK2 )
@ X1 )
= ( ^ [Y0: a > a > a] : ( Y0 @ sK3 @ sK4 )
@ X1 ) ),
inference(argument_congruence,[],[f83]) ).
thf(f93,plain,
! [X1: a > a > a] :
( ( X1 @ sK1 @ sK2 )
= ( X1 @ sK3 @ sK4 ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f134,plain,
( ( sK1
!= ( ^ [Y0: a,Y1: a] : Y0
@ sK1
@ sK2 ) )
| spl5_1 ),
inference(constrained_superposition,[],[f17,f93]) ).
thf(f147,plain,
( ( sK1 != sK1 )
| spl5_1 ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f148,plain,
( $false
| spl5_1 ),
inference(trivial_inequality_removal,[],[f147]) ).
thf(f149,plain,
spl5_1,
inference(avatar_contradiction_clause,[],[f148]) ).
thf(f326,plain,
( ( sK2
!= ( ^ [Y0: a,Y1: a] : Y1
@ sK1
@ sK2 ) )
| spl5_2 ),
inference(constrained_superposition,[],[f21,f93]) ).
thf(f327,plain,
( ( sK2 != sK2 )
| spl5_2 ),
inference(beta-eta_normalization,[],[f326]) ).
thf(f328,plain,
( $false
| spl5_2 ),
inference(trivial_inequality_removal,[],[f327]) ).
thf(f329,plain,
spl5_2,
inference(avatar_contradiction_clause,[],[f328]) ).
cnf(s1,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s4,plain,
spl5_1,
inference(sat_conversion,[],[f149]) ).
cnf(s13,plain,
spl5_2,
inference(sat_conversion,[],[f329]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s1,s13,s4]) ).
thf(f330,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV167^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n017.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 15:13:37 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 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
% 0.08/0.27 % (449445)Will run a generic schedule for satisfiability detection.
% 0.08/0.27 % (449454)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3927063278:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.27 % (449454)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.27 % (449451)% WARNING: option uhcvi not known.
% 0.08/0.27 % (449452)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2944115408:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.27 % (449450)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1537461185_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.27 % (449451)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=899968789:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.27 % (449455)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2349529796:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.27 % (449451)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.27 % (449456)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1011993905:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.27 % Exception at run slice level
% 0.08/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.27 % (449451)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.27 % (449452)Refutation not found, incomplete strategy
% 0.08/0.27 % (449452)------------------------------
% 0.08/0.27 % (449452)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.27 % (449452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.27 % (449452)CaDiCaL version: 2.1.3
% 0.08/0.27 % (449452)Termination reason: Refutation not found, incomplete strategy
% 0.08/0.27 % (449452)Time elapsed: 0.010 s
% 0.08/0.27 % (449452)Peak memory usage: 12 MB
% 0.08/0.27 % (449452)Instructions burned: 18 (million)
% 0.08/0.27 % (449452)------------------------------
% 0.08/0.27 % (449452)------------------------------
% 0.08/0.27 % (449453)dis+10_1_sil=32000:sp=arity:random_seed=3971442406:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.27 % (449455) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-449445-449455"...
% 0.08/0.27 % (449463)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3449321385:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.08/0.27 % (449455)...printing done.
% 0.08/0.27 % Exception at run slice level
% 0.08/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.27 % (449455)Refutation found. Thanks to Tanya!
% 0.08/0.27 % SZS status Theorem for theBenchmark
% 0.08/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.27 % (449455)------------------------------
% 0.08/0.27 % (449455)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.27 % (449455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.27 % (449455)CaDiCaL version: 2.1.3
% 0.08/0.27 % (449455)Termination reason: Refutation
% 0.08/0.27 % (449455)Time elapsed: 0.019 s
% 0.08/0.27 % (449455)Peak memory usage: 13 MB
% 0.08/0.27 % (449455)Instructions burned: 37 (million)
% 0.08/0.27 % (449445)Success in time 0.058 s
% 0.08/0.27 % Vampire exiting
%------------------------------------------------------------------------------