%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO314^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 08:49:43 AM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 7 unt; 0 typ; 5 def)
% Number of atoms : 369 ( 114 equ; 0 cnn)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 382 ( 100 ~; 82 |; 57 &; 132 @)
% ( 10 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 12 con; 0-4 aty)
% Number of variables : 111 ( 0 sgn 47 !; 64 ?; 111 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_4,type,
sK0: $i > $o ).
thf(func_def_5,type,
sK1: $i > $o ).
thf(func_def_8,type,
sK4: $i > $o ).
thf(func_def_9,type,
sK5: $i > $o ).
thf(func_def_12,type,
vNOT: $o > $o ).
thf(func_def_14,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_15,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
( ? [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ~ ( X1 @ z )
& ( X1 @ X3 )
& ~ ( X0 @ X3 )
& ( X0 @ X2 ) )
<=> ? [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ~ ( X0 @ X3 )
& ( X0 @ X2 )
& ( X1 @ X3 )
& ~ ( X1 @ z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSILLYWFF2) ).
thf(f2,negated_conjecture,
~ ( ? [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ~ ( X1 @ z )
& ( X1 @ X3 )
& ~ ( X0 @ X3 )
& ( X0 @ X2 ) )
<=> ? [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ~ ( X0 @ X3 )
& ( X0 @ X2 )
& ( X1 @ X3 )
& ~ ( X1 @ z ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ? [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ~ ( X1 @ z )
& ( X1 @ X3 )
& ~ ( X0 @ X3 )
& ( X0 @ X2 ) )
<=> ? [X4: $i > $o,X5: $i > $o,X6: $i,X7: $i] :
( ~ ( X4 @ X7 )
& ( X4 @ X6 )
& ( X5 @ X7 )
& ~ ( X5 @ z ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ? [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ( ( X1 @ z )
!= $true )
& ( ( X1 @ X3 )
= $true )
& ( ( X0 @ X3 )
!= $true )
& ( ( X0 @ X2 )
= $true ) )
<=> ? [X4: $i > $o,X5: $i > $o,X6: $i,X7: $i] :
( ( ( X4 @ X7 )
!= $true )
& ( ( X4 @ X6 )
= $true )
& ( ( X5 @ X7 )
= $true )
& ( ( X5 @ z )
!= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ( ? [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ( ( X1 @ z )
!= $true )
& ( ( X1 @ X3 )
= $true )
& ( ( X0 @ X3 )
!= $true )
& ( ( X0 @ X2 )
= $true ) )
<=> ? [X4: $i > $o,X5: $i > $o,X6: $i,X7: $i] :
( ( ( X4 @ X7 )
!= $true )
& ( ( X4 @ X6 )
= $true )
& ( ( X5 @ X7 )
= $true )
& ( ( X5 @ z )
!= $true ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ? [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ( ( X1 @ z )
!= $true )
& ( ( X1 @ X3 )
= $true )
& ( ( X0 @ X3 )
!= $true )
& ( ( X0 @ X2 )
= $true ) )
<~> ? [X4: $i > $o,X5: $i > $o,X6: $i,X7: $i] :
( ( ( X4 @ X7 )
!= $true )
& ( ( X4 @ X6 )
= $true )
& ( ( X5 @ X7 )
= $true )
& ( ( X5 @ z )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ( ! [X4: $i > $o,X5: $i > $o,X6: $i,X7: $i] :
( ( ( X4 @ X7 )
= $true )
| ( ( X4 @ X6 )
!= $true )
| ( ( X5 @ X7 )
!= $true )
| ( ( X5 @ z )
= $true ) )
| ! [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ( ( X1 @ z )
= $true )
| ( ( X1 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true )
| ( ( X0 @ X2 )
!= $true ) ) )
& ( ? [X4: $i > $o,X5: $i > $o,X6: $i,X7: $i] :
( ( ( X4 @ X7 )
!= $true )
& ( ( X4 @ X6 )
= $true )
& ( ( X5 @ X7 )
= $true )
& ( ( X5 @ z )
!= $true ) )
| ? [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ( ( X1 @ z )
!= $true )
& ( ( X1 @ X3 )
= $true )
& ( ( X0 @ X3 )
!= $true )
& ( ( X0 @ X2 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f6]) ).
thf(f8,plain,
( ( ! [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ( ( X0 @ X3 )
= $true )
| ( ( X0 @ X2 )
!= $true )
| ( ( X1 @ X3 )
!= $true )
| ( ( X1 @ z )
= $true ) )
| ! [X4: $i > $o,X5: $i > $o,X6: $i,X7: $i] :
( ( ( X5 @ z )
= $true )
| ( ( X5 @ X7 )
!= $true )
| ( ( X4 @ X7 )
= $true )
| ( ( X4 @ X6 )
!= $true ) ) )
& ( ? [X8: $i > $o,X9: $i > $o,X10: $i,X11: $i] :
( ( $true
!= ( X8 @ X11 ) )
& ( $true
= ( X8 @ X10 ) )
& ( $true
= ( X9 @ X11 ) )
& ( $true
!= ( X9 @ z ) ) )
| ? [X12: $i > $o,X13: $i > $o,X14: $i,X15: $i] :
( ( $true
!= ( X13 @ z ) )
& ( $true
= ( X13 @ X15 ) )
& ( $true
!= ( X12 @ X15 ) )
& ( $true
= ( X12 @ X14 ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ( ! [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ( ( X0 @ X3 )
= $true )
| ( ( X0 @ X2 )
!= $true )
| ( ( X1 @ X3 )
!= $true )
| ( ( X1 @ z )
= $true ) )
| ! [X4: $i > $o,X5: $i > $o,X6: $i,X7: $i] :
( ( ( X5 @ z )
= $true )
| ( ( X5 @ X7 )
!= $true )
| ( ( X4 @ X7 )
= $true )
| ( ( X4 @ X6 )
!= $true ) ) )
& ( ( ( $true
!= ( sK0 @ sK3 ) )
& ( $true
= ( sK0 @ sK2 ) )
& ( $true
= ( sK1 @ sK3 ) )
& ( $true
!= ( sK1 @ z ) ) )
| ( ( $true
!= ( sK5 @ z ) )
& ( $true
= ( sK5 @ sK7 ) )
& ( $true
!= ( sK4 @ sK7 ) )
& ( $true
= ( sK4 @ sK6 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(X8,sK0),skolemize(X9,sK1),skolemize(X10,sK2),skolemize(X11,sK3),skolemize(X12,sK4),skolemize(X13,sK5),skolemize(X14,sK6),skolemize(X15,sK7)],[f8]) ).
thf(f12,plain,
( ( $true
!= ( sK1 @ z ) )
| ( $true
= ( sK5 @ sK7 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
( ( $true
!= ( sK1 @ z ) )
| ( $true
!= ( sK5 @ z ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK5 @ sK7 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f17,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
!= ( sK5 @ z ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f26,plain,
! [X2: $i,X3: $i,X0: $i > $o,X1: $i > $o,X6: $i,X7: $i,X4: $i > $o,X5: $i > $o] :
( ( ( X0 @ X3 )
= $true )
| ( ( X0 @ X2 )
!= $true )
| ( ( X1 @ X3 )
!= $true )
| ( ( X1 @ z )
= $true )
| ( ( X5 @ z )
= $true )
| ( ( X5 @ X7 )
!= $true )
| ( ( X4 @ X7 )
= $true )
| ( ( X4 @ X6 )
!= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f34,definition,
( spl8_2
<=> ( $true
= ( sK1 @ z ) ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f36,plain,
( ( $true
!= ( sK1 @ z ) )
| spl8_2 ),
inference(avatar_component_clause,[],[f34]) ).
thf(f44,definition,
( spl8_4
<=> ( $true
= ( sK5 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
thf(f46,plain,
( ( $true
= ( sK5 @ sK7 ) )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f44]) ).
thf(f47,plain,
( spl8_4
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f12,f34,f44]) ).
thf(f49,definition,
( spl8_5
<=> ( $true
= ( sK5 @ z ) ) ),
introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition]) ).
thf(f51,plain,
( ( $true
!= ( sK5 @ z ) )
| spl8_5 ),
inference(avatar_component_clause,[],[f49]) ).
thf(f52,plain,
( ~ spl8_5
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f13,f34,f49]) ).
thf(f54,definition,
( spl8_6
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition]) ).
thf(f56,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f54]) ).
thf(f59,plain,
( spl8_4
| spl8_6 ),
inference(avatar_split_clause,[],[f16,f54,f44]) ).
thf(f60,plain,
( ~ spl8_5
| spl8_6 ),
inference(avatar_split_clause,[],[f17,f54,f49]) ).
thf(f78,definition,
( spl8_9
<=> ! [X5: $i > $o,X4: $i > $o,X7: $i,X6: $i] :
( ( ( X5 @ z )
= $true )
| ( ( X4 @ X6 )
!= $true )
| ( ( X4 @ X7 )
= $true )
| ( ( X5 @ X7 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
thf(f79,plain,
( ! [X6: $i,X7: $i,X4: $i > $o,X5: $i > $o] :
( ( ( X4 @ X6 )
!= $true )
| ( ( X5 @ z )
= $true )
| ( ( X4 @ X7 )
= $true )
| ( ( X5 @ X7 )
!= $true ) )
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f78]) ).
thf(f80,plain,
( spl8_9
| spl8_9 ),
inference(avatar_split_clause,[],[f26,f78,f78]) ).
thf(f82,plain,
( ! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
!= ( X2 @ X1 ) )
| ( $true
= ( X2 @ z ) )
| ( X0 = X1 ) )
| ~ spl8_9 ),
inference(leibniz_equality_elimination,[],[f79]) ).
thf(f166,plain,
( ! [X0: $i,X1: $i] :
( ( z = X0 )
| ( X0 = X1 ) )
| ~ spl8_9 ),
inference(leibniz_equality_elimination,[],[f82]) ).
thf(f254,plain,
( ! [X0: $i] :
( ( X0 != X0 )
| ( z = X0 ) )
| ~ spl8_9 ),
inference(equality_factoring,[],[f166]) ).
thf(f255,plain,
( ! [X0: $i] : ( z = X0 )
| ~ spl8_9 ),
inference(trivial_inequality_removal,[],[f254]) ).
thf(f283,plain,
( ( $true
= ( sK1 @ z ) )
| ~ spl8_6
| ~ spl8_9 ),
inference(constrained_superposition,[],[f56,f255]) ).
thf(f286,plain,
( ( $true
= ( sK5 @ z ) )
| ~ spl8_4
| ~ spl8_9 ),
inference(constrained_superposition,[],[f46,f255]) ).
thf(f288,plain,
( $false
| ~ spl8_4
| spl8_5
| ~ spl8_9 ),
inference(forward_subsumption_resolution,[],[f286,f51]) ).
thf(f289,plain,
( ~ spl8_4
| spl8_5
| ~ spl8_9 ),
inference(avatar_contradiction_clause,[],[f288]) ).
thf(f291,plain,
( $false
| spl8_2
| ~ spl8_6
| ~ spl8_9 ),
inference(forward_subsumption_resolution,[],[f283,f36]) ).
thf(f292,plain,
( spl8_2
| ~ spl8_6
| ~ spl8_9 ),
inference(avatar_contradiction_clause,[],[f291]) ).
cnf(s3,plain,
( ~ spl8_2
| spl8_4 ),
inference(sat_conversion,[],[f47]) ).
cnf(s4,plain,
( ~ spl8_2
| ~ spl8_5 ),
inference(sat_conversion,[],[f52]) ).
cnf(s7,plain,
( spl8_4
| spl8_6 ),
inference(sat_conversion,[],[f59]) ).
cnf(s8,plain,
( ~ spl8_5
| spl8_6 ),
inference(sat_conversion,[],[f60]) ).
cnf(s17,plain,
( spl8_9
| spl8_9 ),
inference(sat_conversion,[],[f80]) ).
cnf(s18,plain,
spl8_9,
inference(rat,[],[s17]) ).
cnf(s29,plain,
( ~ spl8_4
| spl8_5
| ~ spl8_9 ),
inference(sat_conversion,[],[f289]) ).
cnf(s31,plain,
( spl8_2
| ~ spl8_6
| ~ spl8_9 ),
inference(sat_conversion,[],[f292]) ).
cnf(s39,plain,
spl8_6,
inference(rat,[],[s29,s7,s8,s18]) ).
cnf(s40,plain,
spl8_2,
inference(rat,[],[s31,s18,s39]) ).
cnf(s42,plain,
~ spl8_5,
inference(rat,[],[s4,s40]) ).
cnf(s43,plain,
spl8_4,
inference(rat,[],[s3,s40]) ).
cnf(s45,plain,
$false,
inference(rat,[],[s29,s18,s42,s43]) ).
thf(f294,plain,
$false,
inference(avatar_sat_refutation,[],[s45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO314^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n006.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 16:44:55 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 Running first-order model finding
% 0.09/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.24 % (998019)Will run a generic schedule for satisfiability detection.
% 0.09/0.24 % (998029)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1413873847:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.24 % (998029) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-998019-998029"...
% 0.09/0.24 % (998029)...printing done.
% 0.09/0.24 % (998024)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=270580093_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.24 % (998026)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=340910068:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.24 % (998027)dis+10_1_sil=32000:sp=arity:random_seed=2143478699:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.24 % (998028)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=73859888:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.24 % (998029)Refutation found. Thanks to Tanya!
% 0.09/0.24 % SZS status Theorem for theBenchmark
% 0.09/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.24 % (998029)------------------------------
% 0.09/0.24 % (998029)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.24 % (998029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.24 % (998029)CaDiCaL version: 2.1.3
% 0.09/0.24 % (998029)Termination reason: Refutation
% 0.09/0.24 % (998029)Time elapsed: 0.004 s
% 0.09/0.24 % (998029)Peak memory usage: 12 MB
% 0.09/0.24 % (998029)Instructions burned: 12 (million)
% 0.09/0.24 % (998019)Success in time 0.032 s
% 0.09/0.24 % Vampire exiting
%------------------------------------------------------------------------------