%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO103^5 : 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 : n003.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 08:48:58 AM UTC 2026
% Result : Theorem 0.11s 0.27s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 2
% Syntax : Number of formulae : 33 ( 13 unt; 0 typ; 1 def)
% Number of atoms : 201 ( 55 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 437 ( 46 ~; 29 |; 24 &; 337 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 96 ( 0 sgn 91 !; 5 ?; 96 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
imp: $i > $i > $i ).
thf(func_def_1,type,
cT: $i > $o ).
thf(func_def_2,type,
nt: $i > $i ).
thf(f1,conjecture,
~ ( ? [X3: $i] :
~ ( cT @ ( imp @ X3 @ X3 ) )
& ! [X0: $i,X1: $i] : ( cT @ ( imp @ ( imp @ ( nt @ X0 ) @ ( nt @ X1 ) ) @ ( imp @ X1 @ X0 ) ) )
& ! [X0: $i,X1: $i,X2: $i] : ( cT @ ( imp @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) @ ( imp @ ( imp @ X0 @ X1 ) @ ( imp @ X0 @ X2 ) ) ) )
& ! [X0: $i,X1: $i] : ( cT @ ( imp @ X0 @ ( imp @ X1 @ X0 ) ) )
& ! [X0: $i,X1: $i] :
( ( cT @ X1 )
| ~ ( cT @ X0 )
| ~ ( cT @ ( imp @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM147) ).
thf(f2,negated_conjecture,
~ ~ ( ? [X3: $i] :
~ ( cT @ ( imp @ X3 @ X3 ) )
& ! [X0: $i,X1: $i] : ( cT @ ( imp @ ( imp @ ( nt @ X0 ) @ ( nt @ X1 ) ) @ ( imp @ X1 @ X0 ) ) )
& ! [X0: $i,X1: $i,X2: $i] : ( cT @ ( imp @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) @ ( imp @ ( imp @ X0 @ X1 ) @ ( imp @ X0 @ X2 ) ) ) )
& ! [X0: $i,X1: $i] : ( cT @ ( imp @ X0 @ ( imp @ X1 @ X0 ) ) )
& ! [X0: $i,X1: $i] :
( ( cT @ X1 )
| ~ ( cT @ X0 )
| ~ ( cT @ ( imp @ X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ~ ( ? [X0: $i] :
~ ( cT @ ( imp @ X0 @ X0 ) )
& ! [X1: $i,X2: $i] : ( cT @ ( imp @ ( imp @ ( nt @ X1 ) @ ( nt @ X2 ) ) @ ( imp @ X2 @ X1 ) ) )
& ! [X3: $i,X4: $i,X5: $i] : ( cT @ ( imp @ ( imp @ X3 @ ( imp @ X4 @ X5 ) ) @ ( imp @ ( imp @ X3 @ X4 ) @ ( imp @ X3 @ X5 ) ) ) )
& ! [X6: $i,X7: $i] : ( cT @ ( imp @ X6 @ ( imp @ X7 @ X6 ) ) )
& ! [X8: $i,X9: $i] :
( ( cT @ X9 )
| ~ ( cT @ X8 )
| ~ ( cT @ ( imp @ X8 @ X9 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ~ ( ? [X0: $i] :
( ( cT @ ( imp @ X0 @ X0 ) )
!= $true )
& ! [X1: $i,X2: $i] :
( ( cT @ ( imp @ ( imp @ ( nt @ X1 ) @ ( nt @ X2 ) ) @ ( imp @ X2 @ X1 ) ) )
= $true )
& ! [X3: $i,X4: $i,X5: $i] :
( ( cT @ ( imp @ ( imp @ X3 @ ( imp @ X4 @ X5 ) ) @ ( imp @ ( imp @ X3 @ X4 ) @ ( imp @ X3 @ X5 ) ) ) )
= $true )
& ! [X6: $i,X7: $i] :
( ( cT @ ( imp @ X6 @ ( imp @ X7 @ X6 ) ) )
= $true )
& ! [X8: $i,X9: $i] :
( ( ( cT @ X9 )
= $true )
| ( ( cT @ X8 )
!= $true )
| ( ( cT @ ( imp @ X8 @ X9 ) )
!= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ? [X0: $i] :
( ( cT @ ( imp @ X0 @ X0 ) )
!= $true )
& ! [X1: $i,X2: $i] :
( ( cT @ ( imp @ ( imp @ ( nt @ X1 ) @ ( nt @ X2 ) ) @ ( imp @ X2 @ X1 ) ) )
= $true )
& ! [X3: $i,X4: $i,X5: $i] :
( ( cT @ ( imp @ ( imp @ X3 @ ( imp @ X4 @ X5 ) ) @ ( imp @ ( imp @ X3 @ X4 ) @ ( imp @ X3 @ X5 ) ) ) )
= $true )
& ! [X6: $i,X7: $i] :
( ( cT @ ( imp @ X6 @ ( imp @ X7 @ X6 ) ) )
= $true )
& ! [X8: $i,X9: $i] :
( ( ( cT @ X9 )
= $true )
| ( ( cT @ X8 )
!= $true )
| ( ( cT @ ( imp @ X8 @ X9 ) )
!= $true ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( $true
!= ( cT @ ( imp @ sK0 @ sK0 ) ) )
& ! [X1: $i,X2: $i] :
( ( cT @ ( imp @ ( imp @ ( nt @ X1 ) @ ( nt @ X2 ) ) @ ( imp @ X2 @ X1 ) ) )
= $true )
& ! [X3: $i,X4: $i,X5: $i] :
( ( cT @ ( imp @ ( imp @ X3 @ ( imp @ X4 @ X5 ) ) @ ( imp @ ( imp @ X3 @ X4 ) @ ( imp @ X3 @ X5 ) ) ) )
= $true )
& ! [X6: $i,X7: $i] :
( ( cT @ ( imp @ X6 @ ( imp @ X7 @ X6 ) ) )
= $true )
& ! [X8: $i,X9: $i] :
( ( ( cT @ X9 )
= $true )
| ( ( cT @ X8 )
!= $true )
| ( ( cT @ ( imp @ X8 @ X9 ) )
!= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f5]) ).
thf(f7,plain,
! [X8: $i,X9: $i] :
( ( ( cT @ ( imp @ X8 @ X9 ) )
!= $true )
| ( ( cT @ X8 )
!= $true )
| ( ( cT @ X9 )
= $true ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
! [X6: $i,X7: $i] :
( ( cT @ ( imp @ X6 @ ( imp @ X7 @ X6 ) ) )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( cT @ ( imp @ ( imp @ X3 @ ( imp @ X4 @ X5 ) ) @ ( imp @ ( imp @ X3 @ X4 ) @ ( imp @ X3 @ X5 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f10,plain,
! [X2: $i,X1: $i] :
( ( cT @ ( imp @ ( imp @ ( nt @ X1 ) @ ( nt @ X2 ) ) @ ( imp @ X2 @ X1 ) ) )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f11,plain,
( $true
!= ( cT @ ( imp @ sK0 @ sK0 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f23,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( cT @ X0 )
!= $true )
| ( $true
= ( cT @ ( imp @ X1 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f7,f8]) ).
thf(f24,plain,
! [X0: $i,X1: $i] :
( ( ( cT @ X0 )
!= $true )
| ( $true
= ( cT @ ( imp @ X1 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f23]) ).
thf(f53,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( cT @ ( imp @ X2 @ ( imp @ ( imp @ ( nt @ X0 ) @ ( nt @ X1 ) ) @ ( imp @ X1 @ X0 ) ) ) ) ) ),
inference(constrained_superposition,[],[f24,f10]) ).
thf(f54,plain,
! [X2: $i,X0: $i,X1: $i] :
( $true
= ( cT @ ( imp @ X2 @ ( imp @ ( imp @ ( nt @ X0 ) @ ( nt @ X1 ) ) @ ( imp @ X1 @ X0 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f53]) ).
thf(f75,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( cT @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) ) )
| ( $true
= ( cT @ ( imp @ ( imp @ X0 @ X1 ) @ ( imp @ X0 @ X2 ) ) ) ) ),
inference(constrained_superposition,[],[f7,f9]) ).
thf(f78,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( cT @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) ) )
| ( $true
= ( cT @ ( imp @ ( imp @ X0 @ X1 ) @ ( imp @ X0 @ X2 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f75]) ).
thf(f85,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( cT @ ( imp @ ( imp @ X0 @ X1 ) @ ( imp @ X0 @ X0 ) ) ) ) ),
inference(constrained_superposition,[],[f78,f8]) ).
thf(f100,plain,
! [X0: $i,X1: $i] :
( $true
= ( cT @ ( imp @ ( imp @ X0 @ X1 ) @ ( imp @ X0 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f85]) ).
thf(f151,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( cT @ ( imp @ X0 @ X1 ) )
!= $true )
| ( ( cT @ ( imp @ X0 @ X0 ) )
= $true ) ),
inference(constrained_superposition,[],[f7,f100]) ).
thf(f154,plain,
! [X0: $i,X1: $i] :
( ( ( cT @ ( imp @ X0 @ X1 ) )
!= $true )
| ( ( cT @ ( imp @ X0 @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f151]) ).
thf(f157,definition,
( spl1_8
<=> ! [X0: $i] :
( ( cT @ ( imp @ X0 @ X0 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
thf(f158,plain,
( ! [X0: $i] :
( ( cT @ ( imp @ X0 @ X0 ) )
= $true )
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f157]) ).
thf(f165,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( cT @ ( imp @ X0 @ X0 ) )
= $true ) ),
inference(constrained_superposition,[],[f154,f54]) ).
thf(f170,plain,
! [X0: $i] :
( ( cT @ ( imp @ X0 @ X0 ) )
= $true ),
inference(trivial_inequality_removal,[],[f165]) ).
thf(f177,plain,
( ( $true != $true )
| ~ spl1_8 ),
inference(constrained_superposition,[],[f11,f158]) ).
thf(f188,plain,
( $false
| ~ spl1_8 ),
inference(trivial_inequality_removal,[],[f177]) ).
thf(f189,plain,
~ spl1_8,
inference(avatar_contradiction_clause,[],[f188]) ).
thf(f190,plain,
spl1_8,
inference(avatar_split_clause,[],[f170,f157]) ).
cnf(s96,plain,
~ spl1_8,
inference(sat_conversion,[],[f189]) ).
cnf(s100,plain,
spl1_8,
inference(sat_conversion,[],[f190]) ).
cnf(s101,plain,
$false,
inference(rat,[],[s96,s100]) ).
thf(f191,plain,
$false,
inference(avatar_sat_refutation,[],[s101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO103^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.18 % Computer : n003.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 16:35:49 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.21 Running first-order model finding
% 0.11/0.21 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
% 0.11/0.27 % (2713044)Will run a generic schedule for satisfiability detection.
% 0.11/0.27 % (2713061)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3527653196_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.27 % Exception at run slice level
% 0.11/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.27 % (2713062)% WARNING: option uhcvi not known.
% 0.11/0.27 % (2713063)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1043495947:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.27 % (2713062)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=770069221:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.27 % (2713066)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2740928135:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.27 % (2713065)dis+10_1_sil=32000:sp=arity:random_seed=2038726523:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.27 % (2713069)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2502155788:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.27 % (2713062)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.11/0.27 % (2713066)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.11/0.27 % (2713062)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.11/0.27 % (2713068)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=785786373:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.27 % (2713071)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=33186314:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.11/0.27 % Exception at run slice level
% 0.11/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.11/0.27 % (2713063) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2713044-2713063"...
% 0.11/0.27 % (2713066) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2713044-2713066"...
% 0.11/0.27 % (2713083)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4065742025:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.27 % (2713063)...printing done.
% 0.11/0.27 % (2713062) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2713044-2713062"...
% 0.11/0.27 % (2713065) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2713044-2713065"...
% 0.11/0.27 % (2713063)Refutation found. Thanks to Tanya!
% 0.11/0.27 % SZS status Theorem for theBenchmark
% 0.11/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.27 % (2713063)------------------------------
% 0.11/0.27 % (2713063)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.27 % (2713063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.27 % (2713063)CaDiCaL version: 2.1.3
% 0.11/0.27 % (2713063)Termination reason: Refutation
% 0.11/0.27 % (2713063)Time elapsed: 0.012 s
% 0.11/0.27 % (2713063)Peak memory usage: 12 MB
% 0.11/0.27 % (2713063)Instructions burned: 19 (million)
% 0.11/0.27 % (2713044)Success in time 0.048 s
% 0.11/0.27 % Vampire exiting
%------------------------------------------------------------------------------