%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET636^5 : 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 : n020.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 08:23:46 AM UTC 2026
% Result : Theorem 0.23s 0.26s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 54 ( 7 unt; 0 typ; 4 def)
% Number of atoms : 282 ( 74 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 285 ( 69 ~; 74 |; 33 &; 100 @)
% ( 8 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 8 con; 0-4 aty)
% Number of variables : 74 ( 21 sgn 20 !; 12 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
vAND: $o > $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_6,type,
sK0: a > $o ).
thf(func_def_7,type,
sK1: a > $o ).
thf(func_def_8,type,
sK2: a ).
thf(func_def_10,type,
sK4: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ~ ? [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) )
<=> ( ( ^ [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= ( ^ [X2: a] : $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_118_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ~ ? [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) )
<=> ( ( ^ [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= ( ^ [X2: a] : $false ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ~ ? [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) )
<=> ( ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X0 @ X3 ) ) )
= ( ^ [X4: a] : $false ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ~ ? [X2: a] :
( ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
= $true ) )
<=> ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( ( X1 @ X2 )
!= $true )
| ( ( X0 @ X2 )
!= $true ) )
<~> ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) )
| ? [X2: a] :
( ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
= $true ) ) )
& ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
| ! [X2: a] :
( ( ( X1 @ X2 )
!= $true )
| ( ( X0 @ X2 )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) )
| ? [X2: a] :
( ( ( X1 @ X2 )
= $true )
& ( ( X0 @ X2 )
= $true ) ) )
& ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
| ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X0 @ X3 )
!= $true ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( ( $true
= ( sK1 @ sK2 ) )
& ( $true
= ( sK0 @ sK2 ) ) ) )
& ( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ! [X3: a] :
( ( $true
!= ( sK1 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f7]) ).
thf(f9,plain,
! [X3: a] :
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( $true
!= ( sK1 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,definition,
( spl3_1
<=> ! [X3: a] :
( ( $true
!= ( sK1 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f16,plain,
( ! [X3: a] :
( ( $true
!= ( sK1 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f15]) ).
thf(f18,definition,
( spl3_2
<=> ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f19,plain,
( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| spl3_2 ),
inference(avatar_component_clause,[],[f18]) ).
thf(f20,plain,
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f18]) ).
thf(f21,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f9,f18,f15]) ).
thf(f23,definition,
( spl3_3
<=> ( $true
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f25,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f26,plain,
( spl3_3
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f10,f18,f23]) ).
thf(f28,definition,
( spl3_4
<=> ( $true
= ( sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f30,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f28]) ).
thf(f31,plain,
( spl3_4
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f11,f18,f28]) ).
thf(f32,plain,
( ! [X1: a] :
( ( ^ [Y0: a] : $false
@ X1 )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 ) )
| ~ spl3_2 ),
inference(argument_congruence,[],[f20]) ).
thf(f33,plain,
( ! [X1: a] :
( ( $true
= ( ^ [Y0: a] : $false
@ X1 ) )
| ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 ) ) )
| ~ spl3_2 ),
inference(iff_proxy_clausification,[],[f32]) ).
thf(f38,plain,
( ! [X1: a] :
( ( $true = $false )
| ( $false
= ( ( sK0 @ X1 )
& ( sK1 @ X1 ) ) ) )
| ~ spl3_2 ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f39,plain,
( ! [X1: a] :
( ( $true = $false )
| ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl3_2 ),
inference(and_proxy_clausification,[],[f38]) ).
thf(f40,plain,
( ! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f39]) ).
thf(f42,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK2 ) )
| ~ spl3_2
| ~ spl3_4 ),
inference(constrained_superposition,[],[f30,f40]) ).
thf(f43,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f45,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_3
| ~ spl3_4 ),
inference(constrained_superposition,[],[f43,f25]) ).
thf(f49,plain,
( $false
| ~ spl3_2
| ~ spl3_3
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f45]) ).
thf(f50,plain,
( ~ spl3_2
| ~ spl3_3
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f49]) ).
thf(f54,plain,
( ( ( ^ [Y0: a] : $false
@ sK4 )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK4 ) )
| spl3_2 ),
inference(negative_extensionality,[],[f19]) ).
thf(f55,plain,
( ( $true
= ( ^ [Y0: a] : $false
@ sK4 ) )
| ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK4 ) )
| spl3_2 ),
inference(xor_proxy_clausification,[],[f54]) ).
thf(f59,plain,
( ( $true = $false )
| ( $true
= ( ( sK0 @ sK4 )
& ( sK1 @ sK4 ) ) )
| spl3_2 ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f60,plain,
( ( $true = $false )
| ( $true
= ( sK1 @ sK4 ) )
| spl3_2 ),
inference(and_proxy_clausification,[],[f59]) ).
thf(f61,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK4 ) )
| spl3_2 ),
inference(and_proxy_clausification,[],[f59]) ).
thf(f62,plain,
( ( $true
= ( sK0 @ sK4 ) )
| spl3_2 ),
inference(trivial_inequality_removal,[],[f61]) ).
thf(f63,plain,
( ( $true
= ( sK1 @ sK4 ) )
| spl3_2 ),
inference(trivial_inequality_removal,[],[f60]) ).
thf(f64,plain,
( ( $true != $true )
| ( $true
!= ( sK0 @ sK4 ) )
| ~ spl3_1
| spl3_2 ),
inference(constrained_superposition,[],[f16,f63]) ).
thf(f65,plain,
( ( $true
!= ( sK0 @ sK4 ) )
| ~ spl3_1
| spl3_2 ),
inference(trivial_inequality_removal,[],[f64]) ).
thf(f66,plain,
( ( $true != $true )
| ~ spl3_1
| spl3_2 ),
inference(constrained_superposition,[],[f65,f62]) ).
thf(f67,plain,
( $false
| ~ spl3_1
| spl3_2 ),
inference(trivial_inequality_removal,[],[f66]) ).
thf(f68,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_contradiction_clause,[],[f67]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f21]) ).
cnf(s2,plain,
( ~ spl3_2
| spl3_3 ),
inference(sat_conversion,[],[f26]) ).
cnf(s3,plain,
( ~ spl3_2
| spl3_4 ),
inference(sat_conversion,[],[f31]) ).
cnf(s5,plain,
( ~ spl3_2
| ~ spl3_3
| ~ spl3_4 ),
inference(sat_conversion,[],[f50]) ).
cnf(s7,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f68]) ).
cnf(s8,plain,
~ spl3_2,
inference(rat,[],[s5,s2,s3]) ).
cnf(s9,plain,
~ spl3_1,
inference(rat,[],[s7,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s8,s9]) ).
thf(f69,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET636^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n020.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 13:41:05 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 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
% 0.23/0.26 % (1066581)Will run a generic schedule for satisfiability detection.
% 0.23/0.26 % (1066594)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2172087740_2999 on theBenchmark for (2999ds/0Mi)
% 0.23/0.26 % Exception at run slice level
% 0.23/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.26 % (1066595)% WARNING: option uhcvi not known.
% 0.23/0.26 % (1066595)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4191238360:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.23/0.26 % (1066596)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2009210258:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.23/0.26 % (1066595)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.23/0.26 % (1066599)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3980830589:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.23/0.26 % (1066597)dis+10_1_sil=32000:sp=arity:random_seed=3663333513:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.23/0.26 % (1066598)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2686776917:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.23/0.26 % (1066595)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.23/0.26 % (1066601)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4053512771:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.23/0.26 % (1066598)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.23/0.26 % (1066596) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1066581-1066596"...
% 0.23/0.26 % (1066601) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1066581-1066601"...
% 0.23/0.26 % (1066599) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1066581-1066599"...
% 0.23/0.26 % (1066598) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1066581-1066598"...
% 0.23/0.26 % (1066595) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1066581-1066595"...
% 0.23/0.26 % (1066597) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1066581-1066597"...
% 0.23/0.26 % (1066596)...printing done.
% 0.23/0.26 % (1066601)...printing done.
% 0.23/0.26 % (1066599)...printing done.
% 0.23/0.26 % (1066595)...printing done.
% 0.23/0.26 % (1066598)...printing done.
% 0.23/0.26 % (1066597)...printing done.
% 0.23/0.26 % (1066612)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1570085695:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.23/0.26 % Exception at run slice level
% 0.23/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.26 % (1066601)Refutation found. Thanks to Tanya!
% 0.23/0.26 % SZS status Theorem for theBenchmark
% 0.23/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.26 % (1066601)------------------------------
% 0.23/0.26 % (1066601)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.26 % (1066601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.26 % (1066601)CaDiCaL version: 2.1.3
% 0.23/0.26 % (1066601)Termination reason: Refutation
% 0.23/0.26 % (1066601)Time elapsed: 0.004 s
% 0.23/0.26 % (1066601)Peak memory usage: 13 MB
% 0.23/0.26 % (1066601)Instructions burned: 4 (million)
% 0.23/0.26 % (1066581)Success in time 0.04 s
% 0.23/0.26 % Vampire exiting
%------------------------------------------------------------------------------