%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO303^5 : 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 : n002.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 08:49:42 AM UTC 2026
% Result : Theorem 0.22s 0.37s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 37 ( 14 unt; 0 typ; 2 def)
% Number of atoms : 209 ( 48 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 154 ( 35 ~; 28 |; 16 &; 68 @)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 35 ( 0 sgn 27 !; 0 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
cS: $i > $o ).
thf(func_def_3,type,
cT: $i > $o ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(func_def_10,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_11,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
( ! [X0: $i > $o] :
( ! [X1: $i] : ( X0 @ X1 )
| ~ ( X0 @ c0 ) )
=> ( ( ( cS @ b )
& ( cT @ a ) )
| ~ ( ( cT @ c0 )
& ( cS @ c0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cMIN_QUAN_BUG) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i > $o] :
( ! [X1: $i] : ( X0 @ X1 )
| ~ ( X0 @ c0 ) )
=> ( ( ( cS @ b )
& ( cT @ a ) )
| ~ ( ( cT @ c0 )
& ( cS @ c0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i > $o] :
( ! [X1: $i] : ( X0 @ X1 )
| ~ ( X0 @ c0 ) )
=> ( ( ( cS @ b )
& ( cT @ a ) )
| ~ ( ( cT @ c0 )
& ( cS @ c0 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
= $true )
| ( ( X0 @ c0 )
!= $true ) )
=> ( ( ( ( cS @ b )
= $true )
& ( ( cT @ a )
= $true ) )
| ~ ( ( ( cT @ c0 )
= $true )
& ( ( cS @ c0 )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ( ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
= $true )
| ( ( X0 @ c0 )
!= $true ) )
=> ( ( ( ( cS @ b )
= $true )
& ( ( cT @ a )
= $true ) )
| ~ ( ( ( cT @ c0 )
= $true )
& ( ( cS @ c0 )
= $true ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( ( ( cS @ b )
!= $true )
| ( ( cT @ a )
!= $true ) )
& ( ( cT @ c0 )
= $true )
& ( ( cS @ c0 )
= $true )
& ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
= $true )
| ( ( X0 @ c0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ( ( ( cS @ b )
!= $true )
| ( ( cT @ a )
!= $true ) )
& ( ( cT @ c0 )
= $true )
& ( ( cS @ c0 )
= $true )
& ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
= $true )
| ( ( X0 @ c0 )
!= $true ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ c0 )
!= $true )
| ( ( X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( ( cS @ c0 )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( ( cT @ c0 )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( ( ( cS @ b )
!= $true )
| ( ( cT @ a )
!= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f15,definition,
( spl0_1
<=> ( ( cT @ a )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f17,plain,
( ( ( cT @ a )
!= $true )
| spl0_1 ),
inference(avatar_component_clause,[],[f15]) ).
thf(f19,definition,
( spl0_2
<=> ( ( cS @ b )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f21,plain,
( ( ( cS @ b )
!= $true )
| spl0_2 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f22,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f11,f19,f15]) ).
thf(f24,plain,
! [X0: $i] : ( c0 = X0 ),
inference(leibniz_equality_elimination,[],[f8]) ).
thf(f28,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( ^ [Y0: $i] :
( cS
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ X0 ) ) ),
inference(constrained_superposition,[],[f8,f9]) ).
thf(f30,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( ^ [Y0: $i] :
( cT
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ X0 ) ) ),
inference(constrained_superposition,[],[f8,f10]) ).
thf(f36,plain,
! [X0: $i] :
( $true
= ( ^ [Y0: $i] :
( cT
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ X0 ) ),
inference(trivial_inequality_removal,[],[f30]) ).
thf(f37,plain,
! [X0: $i] :
( $true
= ( cT @ X0 ) ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f40,plain,
! [X0: $i] :
( $true
= ( ^ [Y0: $i] :
( cS
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ X0 ) ),
inference(trivial_inequality_removal,[],[f28]) ).
thf(f41,plain,
! [X0: $i] :
( $true
= ( cS @ X0 ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f47,plain,
! [X0: $i,X1: $i] : ( X0 = X1 ),
inference(constrained_superposition,[],[f24,f24]) ).
thf(f52,plain,
( ! [X0: $i] :
( $true
!= ( cS @ X0 ) )
| spl0_2 ),
inference(constrained_superposition,[],[f21,f47]) ).
thf(f53,plain,
( ! [X0: $i] :
( $true
!= ( cT @ X0 ) )
| spl0_1 ),
inference(constrained_superposition,[],[f17,f47]) ).
thf(f61,plain,
( ( $true != $true )
| spl0_2 ),
inference(constrained_superposition,[],[f52,f41]) ).
thf(f62,plain,
( $false
| spl0_2 ),
inference(trivial_inequality_removal,[],[f61]) ).
thf(f63,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f62]) ).
thf(f64,plain,
( ( $true != $true )
| spl0_1 ),
inference(constrained_superposition,[],[f53,f37]) ).
thf(f65,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[],[f64]) ).
thf(f66,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f65]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f63]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f66]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f67,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO303^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.22/0.27 % Computer : n002.cluster.edu
% 0.22/0.27 % Model : x86_64 x86_64
% 0.22/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.27 % Memory : 8046.5625MB
% 0.22/0.27 % OS : Linux 6.8.0-71-generic
% 0.22/0.27 % CPULimit : 300
% 0.22/0.28 % WCLimit : 300
% 0.22/0.28 % DateTime : Tue Sep 29 16:47:07 UTC 2026
% 0.22/0.28 % CPUTime :
% 0.22/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.22/0.32 Running first-order model finding
% 0.22/0.32 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
% 0.22/0.37 % (1535891)Will run a generic schedule for satisfiability detection.
% 0.22/0.37 % (1535896)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3516635527_3000 on theBenchmark for (3000ds/0Mi)
% 0.22/0.37 % Exception at run slice level
% 0.22/0.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.37 % (1535897)% WARNING: option uhcvi not known.
% 0.22/0.37 % (1535902)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3871110824:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.22/0.37 % (1535902) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1535891-1535902"...
% 0.22/0.37 % (1535899)dis+10_1_sil=32000:sp=arity:random_seed=1050652328:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.22/0.37 % (1535900)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1299611838:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.22/0.37 % (1535897)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1875057576:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.22/0.37 % (1535898)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4025499290:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.22/0.37 % (1535901)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2892423674:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.22/0.37 % (1535897)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.37 % (1535900)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.37 % (1535902)...printing done.
% 0.22/0.37 % (1535897)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.37 % (1535902)Refutation found. Thanks to Tanya!
% 0.22/0.37 % SZS status Theorem for theBenchmark
% 0.22/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.37 % (1535902)------------------------------
% 0.22/0.37 % (1535902)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.37 % (1535902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.37 % (1535902)CaDiCaL version: 2.1.3
% 0.22/0.37 % (1535902)Termination reason: Refutation
% 0.22/0.37 % (1535902)Time elapsed: 0.003 s
% 0.22/0.37 % (1535902)Peak memory usage: 12 MB
% 0.22/0.37 % (1535902)Instructions burned: 3 (million)
% 0.22/0.37 % (1535891)Success in time 0.034 s
% 0.22/0.37 % Vampire exiting
%------------------------------------------------------------------------------