%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO111^5 : 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 : n026.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 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 319 ( 84 equ; 0 cnn)
% Maximal formula atoms : 12 ( 11 avg)
% Number of connectives : 323 ( 93 ~; 80 |; 24 &; 119 @)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 15 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 108 ( 0 sgn 70 !; 38 ?; 108 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cG: $i > $o ).
thf(func_def_1,type,
cN: $i > $o ).
thf(func_def_2,type,
cM: $i > $o ).
thf(f1,conjecture,
( ( ~ ( ~ ! [X5: $i] : ( cG @ X5 )
| ! [X4: $i] :
~ ( cN @ X4 ) )
| ~ ( ? [X3: $i] : ( cN @ X3 )
| ! [X2: $i] : ( cM @ X2 ) )
| ? [X1: $i] :
~ ( cG @ X1 )
| ! [X0: $i] : ( cM @ X0 ) )
=> ( ~ ! [X4: $i] :
( ~ ! [X5: $i] : ( cG @ X5 )
| ~ ( cN @ X4 ) )
| ~ ! [X2: $i] :
( ? [X3: $i] : ( cN @ X3 )
| ( cM @ X2 ) )
| ? [X1: $i] :
~ ( cG @ X1 )
| ! [X0: $i] : ( cM @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM80) ).
thf(f2,negated_conjecture,
~ ( ( ~ ( ~ ! [X5: $i] : ( cG @ X5 )
| ! [X4: $i] :
~ ( cN @ X4 ) )
| ~ ( ? [X3: $i] : ( cN @ X3 )
| ! [X2: $i] : ( cM @ X2 ) )
| ? [X1: $i] :
~ ( cG @ X1 )
| ! [X0: $i] : ( cM @ X0 ) )
=> ( ~ ! [X4: $i] :
( ~ ! [X5: $i] : ( cG @ X5 )
| ~ ( cN @ X4 ) )
| ~ ! [X2: $i] :
( ? [X3: $i] : ( cN @ X3 )
| ( cM @ X2 ) )
| ? [X1: $i] :
~ ( cG @ X1 )
| ! [X0: $i] : ( cM @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ~ ( ~ ! [X0: $i] : ( cG @ X0 )
| ! [X1: $i] :
~ ( cN @ X1 ) )
| ~ ( ? [X2: $i] : ( cN @ X2 )
| ! [X3: $i] : ( cM @ X3 ) )
| ? [X4: $i] :
~ ( cG @ X4 )
| ! [X5: $i] : ( cM @ X5 ) )
=> ( ~ ! [X6: $i] :
( ~ ! [X7: $i] : ( cG @ X7 )
| ~ ( cN @ X6 ) )
| ~ ! [X8: $i] :
( ? [X9: $i] : ( cN @ X9 )
| ( cM @ X8 ) )
| ? [X10: $i] :
~ ( cG @ X10 )
| ! [X11: $i] : ( cM @ X11 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ~ ( ~ ! [X0: $i] :
( ( cG @ X0 )
= $true )
| ! [X1: $i] :
( ( cN @ X1 )
!= $true ) )
| ~ ( ? [X2: $i] :
( ( cN @ X2 )
= $true )
| ! [X3: $i] :
( ( cM @ X3 )
= $true ) )
| ? [X4: $i] :
( ( cG @ X4 )
!= $true )
| ! [X5: $i] :
( ( cM @ X5 )
= $true ) )
=> ( ~ ! [X6: $i] :
( ~ ! [X7: $i] :
( ( cG @ X7 )
= $true )
| ( ( cN @ X6 )
!= $true ) )
| ~ ! [X8: $i] :
( ? [X9: $i] :
( ( cN @ X9 )
= $true )
| ( ( cM @ X8 )
= $true ) )
| ? [X10: $i] :
( ( cG @ X10 )
!= $true )
| ! [X11: $i] :
( ( cM @ X11 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ( ( ~ ( ~ ! [X0: $i] :
( ( cG @ X0 )
= $true )
| ! [X1: $i] :
( ( cN @ X1 )
!= $true ) )
| ~ ( ? [X2: $i] :
( ( cN @ X2 )
= $true )
| ! [X3: $i] :
( ( cM @ X3 )
= $true ) )
| ? [X4: $i] :
( ( cG @ X4 )
!= $true )
| ! [X5: $i] :
( ( cM @ X5 )
= $true ) )
=> ( ~ ! [X6: $i] :
( ~ ! [X7: $i] :
( ( cG @ X7 )
= $true )
| ( ( cN @ X6 )
!= $true ) )
| ~ ! [X8: $i] :
( ? [X9: $i] :
( ( cN @ X9 )
= $true )
| ( ( cM @ X8 )
= $true ) )
| ? [X10: $i] :
( ( cG @ X10 )
!= $true )
| ! [X11: $i] :
( ( cM @ X11 )
= $true ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ! [X6: $i] :
( ? [X7: $i] :
( ( cG @ X7 )
!= $true )
| ( ( cN @ X6 )
!= $true ) )
& ! [X8: $i] :
( ? [X9: $i] :
( ( cN @ X9 )
= $true )
| ( ( cM @ X8 )
= $true ) )
& ! [X10: $i] :
( ( cG @ X10 )
= $true )
& ? [X11: $i] :
( ( cM @ X11 )
!= $true )
& ( ( ! [X0: $i] :
( ( cG @ X0 )
= $true )
& ? [X1: $i] :
( ( cN @ X1 )
= $true ) )
| ( ! [X2: $i] :
( ( cN @ X2 )
!= $true )
& ? [X3: $i] :
( ( cM @ X3 )
!= $true ) )
| ? [X4: $i] :
( ( cG @ X4 )
!= $true )
| ! [X5: $i] :
( ( cM @ X5 )
= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ! [X6: $i] :
( ? [X7: $i] :
( ( cG @ X7 )
!= $true )
| ( ( cN @ X6 )
!= $true ) )
& ! [X8: $i] :
( ? [X9: $i] :
( ( cN @ X9 )
= $true )
| ( ( cM @ X8 )
= $true ) )
& ! [X10: $i] :
( ( cG @ X10 )
= $true )
& ? [X11: $i] :
( ( cM @ X11 )
!= $true )
& ( ( ! [X0: $i] :
( ( cG @ X0 )
= $true )
& ? [X1: $i] :
( ( cN @ X1 )
= $true ) )
| ( ! [X2: $i] :
( ( cN @ X2 )
!= $true )
& ? [X3: $i] :
( ( cM @ X3 )
!= $true ) )
| ? [X4: $i] :
( ( cG @ X4 )
!= $true )
| ! [X5: $i] :
( ( cM @ X5 )
= $true ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ! [X0: $i] :
( ? [X1: $i] :
( ( cG @ X1 )
!= $true )
| ( $true
!= ( cN @ X0 ) ) )
& ! [X2: $i] :
( ? [X3: $i] :
( ( cN @ X3 )
= $true )
| ( ( cM @ X2 )
= $true ) )
& ! [X4: $i] :
( ( cG @ X4 )
= $true )
& ? [X5: $i] :
( ( cM @ X5 )
!= $true )
& ( ( ! [X6: $i] :
( $true
= ( cG @ X6 ) )
& ? [X7: $i] :
( $true
= ( cN @ X7 ) ) )
| ( ! [X8: $i] :
( $true
!= ( cN @ X8 ) )
& ? [X9: $i] :
( $true
!= ( cM @ X9 ) ) )
| ? [X10: $i] :
( ( cG @ X10 )
!= $true )
| ! [X11: $i] :
( ( cM @ X11 )
= $true ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ sK0 ) )
| ( $true
!= ( cN @ X0 ) ) )
& ! [X2: $i] :
( ( $true
= ( cN @ sK1 ) )
| ( ( cM @ X2 )
= $true ) )
& ! [X4: $i] :
( ( cG @ X4 )
= $true )
& ( $true
!= ( cM @ sK2 ) )
& ( ( ! [X6: $i] :
( $true
= ( cG @ X6 ) )
& ( $true
= ( cN @ sK3 ) ) )
| ( ! [X8: $i] :
( $true
!= ( cN @ X8 ) )
& ( $true
!= ( cM @ sK4 ) ) )
| ( $true
!= ( cG @ sK5 ) )
| ! [X11: $i] :
( ( cM @ X11 )
= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X1,sK0),skolemize(X3,sK1),skolemize(X5,sK2),skolemize(X7,sK3),skolemize(X9,sK4),skolemize(X10,sK5)],[f8]) ).
thf(f14,plain,
( $true
!= ( cM @ sK2 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,plain,
! [X4: $i] :
( ( cG @ X4 )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,plain,
! [X2: $i] :
( ( $true
= ( cN @ sK1 ) )
| ( ( cM @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f17,plain,
! [X0: $i] :
( ( $true
!= ( cG @ sK0 ) )
| ( $true
!= ( cN @ X0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f21,definition,
( spl6_1
<=> ! [X0: $i] :
( $true
!= ( cN @ X0 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f22,plain,
( ! [X0: $i] :
( $true
!= ( cN @ X0 ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f21]) ).
thf(f24,definition,
( spl6_2
<=> ( $true
= ( cG @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f26,plain,
( ( $true
!= ( cG @ sK0 ) )
| spl6_2 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f27,plain,
( spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f17,f24,f21]) ).
thf(f28,plain,
( ! [X2: $i] :
( ( cM @ X2 )
= $true )
| ~ spl6_1 ),
inference(forward_subsumption_resolution,[],[f16,f22]) ).
thf(f29,plain,
( ( $true != $true )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f14,f28]) ).
thf(f30,plain,
( $false
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f31,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[],[f30]) ).
thf(f32,plain,
( $false
| spl6_2 ),
inference(forward_subsumption_resolution,[],[f26,f15]) ).
thf(f33,plain,
spl6_2,
inference(avatar_contradiction_clause,[],[f32]) ).
cnf(s13,plain,
( spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f27]) ).
cnf(s20,plain,
~ spl6_1,
inference(sat_conversion,[],[f31]) ).
cnf(s21,plain,
spl6_2,
inference(sat_conversion,[],[f33]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s13,s21,s20]) ).
thf(f34,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO111^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n026.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 16:36:58 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
% 0.20/0.28 % (825445)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (825464)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3720603414_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % Exception at run slice level
% 0.20/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.28 % (825465)% WARNING: option uhcvi not known.
% 0.20/0.28 % (825468)dis+10_1_sil=32000:sp=arity:random_seed=2968637247:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (825465)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=945615193:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (825467)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2239474278:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (825470)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2605187957:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (825471)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=585083964:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % (825469)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=551881743:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (825465)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (825469)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (825465)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.28 % (825468) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-825445-825468"...
% 0.20/0.28 % (825467) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-825445-825467"...
% 0.20/0.28 % (825470) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-825445-825470"...
% 0.20/0.28 % (825465) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-825445-825465"...
% 0.20/0.28 % (825469) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-825445-825469"...
% 0.20/0.28 % (825471) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-825445-825471"...
% 0.20/0.28 % (825480)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1025153647:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.28 % Exception at run slice level
% 0.20/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.28 % (825467)...printing done.
% 0.20/0.28 % (825468)...printing done.
% 0.20/0.28 % (825470)...printing done.
% 0.20/0.28 % (825465)...printing done.
% 0.20/0.28 % (825469)...printing done.
% 0.20/0.28 % (825471)...printing done.
% 0.20/0.28 % (825467)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (825467)------------------------------
% 0.20/0.28 % (825467)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (825467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (825467)CaDiCaL version: 2.1.3
% 0.20/0.28 % (825467)Termination reason: Refutation
% 0.20/0.28 % (825467)Time elapsed: 0.003 s
% 0.20/0.28 % (825467)Peak memory usage: 12 MB
% 0.20/0.28 % (825467)Instructions burned: 3 (million)
% 0.20/0.28 % (825445)Success in time 0.048 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------