%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO383^5 : 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 : n015.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 08:49:50 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 16 unt; 0 typ; 3 def)
% Number of atoms : 348 ( 66 equ; 0 cnn)
% Maximal formula atoms : 23 ( 8 avg)
% Number of connectives : 438 ( 79 ~; 53 |; 35 &; 268 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 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; 9 con; 0-3 aty)
% Number of variables : 89 ( 0 sgn 89 !; 0 ?; 89 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cQ_2: $i > $i > $i > $o ).
thf(func_def_1,type,
f: $i > $i ).
thf(func_def_2,type,
cP_1: $i > $i > $o ).
thf(func_def_3,type,
cQ_1: $i > $i > $i > $o ).
thf(f1,conjecture,
~ ( ! [X0: $i,X1: $i,X2: $i] :
~ ( cQ_2 @ X0 @ X1 @ X2 )
& ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cQ_2 @ X3 @ X4 @ X5 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ~ ( cQ_1 @ X0 @ X1 @ X2 ) )
& ! [X0: $i,X1: $i] :
( ( cP_1 @ ( f @ X0 ) @ X1 )
| ~ ( cP_1 @ X0 @ X1 ) )
& ! [X0: $i] : ( cP_1 @ d @ X0 )
& ( cP_1 @ c @ c )
& ( cP_1 @ b @ b )
& ( cP_1 @ a @ a )
& ( cQ_1 @ a @ b @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM409_1) ).
thf(f2,negated_conjecture,
~ ~ ( ! [X0: $i,X1: $i,X2: $i] :
~ ( cQ_2 @ X0 @ X1 @ X2 )
& ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( cQ_2 @ X3 @ X4 @ X5 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 )
| ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ~ ( cQ_1 @ X0 @ X1 @ X2 ) )
& ! [X0: $i,X1: $i] :
( ( cP_1 @ ( f @ X0 ) @ X1 )
| ~ ( cP_1 @ X0 @ X1 ) )
& ! [X0: $i] : ( cP_1 @ d @ X0 )
& ( cP_1 @ c @ c )
& ( cP_1 @ b @ b )
& ( cP_1 @ a @ a )
& ( cQ_1 @ a @ b @ c ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ~ ( ! [X0: $i,X1: $i,X2: $i] :
~ ( cQ_2 @ X0 @ X1 @ X2 )
& ! [X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( ( cQ_2 @ X6 @ X7 @ X8 )
| ~ ( cP_1 @ ( f @ X5 ) @ X8 )
| ~ ( cP_1 @ ( f @ X4 ) @ X7 )
| ~ ( cP_1 @ ( f @ X3 ) @ X6 )
| ~ ( cQ_1 @ X3 @ X4 @ X5 ) )
& ! [X9: $i,X10: $i] :
( ( cP_1 @ ( f @ X9 ) @ X10 )
| ~ ( cP_1 @ X9 @ X10 ) )
& ! [X11: $i] : ( cP_1 @ d @ X11 )
& ( cP_1 @ c @ c )
& ( cP_1 @ b @ b )
& ( cP_1 @ a @ a )
& ( cQ_1 @ a @ b @ c ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ~ ( ! [X0: $i,X1: $i,X2: $i] :
( ( cQ_2 @ X0 @ X1 @ X2 )
!= $true )
& ! [X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( ( ( cQ_2 @ X6 @ X7 @ X8 )
= $true )
| ( ( cP_1 @ ( f @ X5 ) @ X8 )
!= $true )
| ( ( cP_1 @ ( f @ X4 ) @ X7 )
!= $true )
| ( ( cP_1 @ ( f @ X3 ) @ X6 )
!= $true )
| ( ( cQ_1 @ X3 @ X4 @ X5 )
!= $true ) )
& ! [X9: $i,X10: $i] :
( ( ( cP_1 @ ( f @ X9 ) @ X10 )
= $true )
| ( ( cP_1 @ X9 @ X10 )
!= $true ) )
& ! [X11: $i] :
( ( cP_1 @ d @ X11 )
= $true )
& ( ( cP_1 @ c @ c )
= $true )
& ( ( cP_1 @ b @ b )
= $true )
& ( ( cP_1 @ a @ a )
= $true )
& ( ( cQ_1 @ a @ b @ c )
= $true ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( cQ_2 @ X0 @ X1 @ X2 )
!= $true )
& ! [X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( ( ( cQ_2 @ X6 @ X7 @ X8 )
= $true )
| ( ( cP_1 @ ( f @ X5 ) @ X8 )
!= $true )
| ( ( cP_1 @ ( f @ X4 ) @ X7 )
!= $true )
| ( ( cP_1 @ ( f @ X3 ) @ X6 )
!= $true )
| ( ( cQ_1 @ X3 @ X4 @ X5 )
!= $true ) )
& ! [X9: $i,X10: $i] :
( ( ( cP_1 @ ( f @ X9 ) @ X10 )
= $true )
| ( ( cP_1 @ X9 @ X10 )
!= $true ) )
& ! [X11: $i] :
( ( cP_1 @ d @ X11 )
= $true )
& ( ( cP_1 @ c @ c )
= $true )
& ( ( cP_1 @ b @ b )
= $true )
& ( ( cP_1 @ a @ a )
= $true )
& ( ( cQ_1 @ a @ b @ c )
= $true ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( cQ_1 @ a @ b @ c )
= $true ),
inference(cnf_transformation,[],[f5]) ).
thf(f7,plain,
( ( cP_1 @ a @ a )
= $true ),
inference(cnf_transformation,[],[f5]) ).
thf(f8,plain,
( ( cP_1 @ b @ b )
= $true ),
inference(cnf_transformation,[],[f5]) ).
thf(f9,plain,
( ( cP_1 @ c @ c )
= $true ),
inference(cnf_transformation,[],[f5]) ).
thf(f11,plain,
! [X10: $i,X9: $i] :
( ( ( cP_1 @ X9 @ X10 )
!= $true )
| ( ( cP_1 @ ( f @ X9 ) @ X10 )
= $true ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f12,plain,
! [X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( cQ_2 @ X6 @ X7 @ X8 )
= $true )
| ( ( cP_1 @ ( f @ X5 ) @ X8 )
!= $true )
| ( ( cP_1 @ ( f @ X4 ) @ X7 )
!= $true )
| ( ( cP_1 @ ( f @ X3 ) @ X6 )
!= $true )
| ( ( cQ_1 @ X3 @ X4 @ X5 )
!= $true ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f13,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( cQ_2 @ X0 @ X1 @ X2 )
!= $true ),
inference(cnf_transformation,[],[f5]) ).
thf(f23,plain,
( ( $true != $true )
| ( $true
= ( cP_1 @ ( f @ c ) @ c ) ) ),
inference(constrained_superposition,[],[f11,f9]) ).
thf(f24,plain,
( ( $true != $true )
| ( $true
= ( cP_1 @ ( f @ b ) @ b ) ) ),
inference(constrained_superposition,[],[f11,f8]) ).
thf(f25,plain,
( ( $true != $true )
| ( $true
= ( cP_1 @ ( f @ a ) @ a ) ) ),
inference(constrained_superposition,[],[f11,f7]) ).
thf(f26,plain,
( $true
= ( cP_1 @ ( f @ a ) @ a ) ),
inference(trivial_inequality_removal,[],[f25]) ).
thf(f27,plain,
( $true
= ( cP_1 @ ( f @ b ) @ b ) ),
inference(trivial_inequality_removal,[],[f24]) ).
thf(f28,plain,
( $true
= ( cP_1 @ ( f @ c ) @ c ) ),
inference(trivial_inequality_removal,[],[f23]) ).
thf(f44,plain,
! [X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( cQ_1 @ X3 @ X4 @ X5 )
!= $true )
| ( ( cP_1 @ ( f @ X4 ) @ X7 )
!= $true )
| ( ( cP_1 @ ( f @ X3 ) @ X6 )
!= $true )
| ( ( cP_1 @ ( f @ X5 ) @ X8 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f12,f13]) ).
thf(f57,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( cP_1 @ ( f @ b ) @ X0 ) )
| ( $true
!= ( cP_1 @ ( f @ a ) @ X1 ) )
| ( $true
!= ( cP_1 @ ( f @ c ) @ X2 ) ) ),
inference(constrained_superposition,[],[f44,f6]) ).
thf(f58,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( cP_1 @ ( f @ b ) @ X0 ) )
| ( $true
!= ( cP_1 @ ( f @ a ) @ X1 ) )
| ( $true
!= ( cP_1 @ ( f @ c ) @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f57]) ).
thf(f65,definition,
( spl0_5
<=> ! [X2: $i] :
( $true
!= ( cP_1 @ ( f @ c ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
thf(f66,plain,
( ! [X2: $i] :
( $true
!= ( cP_1 @ ( f @ c ) @ X2 ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f65]) ).
thf(f68,definition,
( spl0_6
<=> ! [X1: $i] :
( $true
!= ( cP_1 @ ( f @ a ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
thf(f69,plain,
( ! [X1: $i] :
( $true
!= ( cP_1 @ ( f @ a ) @ X1 ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f68]) ).
thf(f71,definition,
( spl0_7
<=> ! [X0: $i] :
( $true
!= ( cP_1 @ ( f @ b ) @ X0 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
thf(f72,plain,
( ! [X0: $i] :
( $true
!= ( cP_1 @ ( f @ b ) @ X0 ) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f71]) ).
thf(f73,plain,
( spl0_5
| spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f58,f71,f68,f65]) ).
thf(f78,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f28,f66]) ).
thf(f79,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f78]) ).
thf(f80,plain,
( ( $true != $true )
| ~ spl0_6 ),
inference(constrained_superposition,[],[f69,f26]) ).
thf(f81,plain,
( $false
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f82,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f81]) ).
thf(f83,plain,
( ( $true != $true )
| ~ spl0_7 ),
inference(constrained_superposition,[],[f72,f27]) ).
thf(f84,plain,
( $false
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f85,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f84]) ).
cnf(s50,plain,
( spl0_5
| spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f73]) ).
cnf(s57,plain,
~ spl0_5,
inference(sat_conversion,[],[f79]) ).
cnf(s61,plain,
~ spl0_6,
inference(sat_conversion,[],[f82]) ).
cnf(s64,plain,
~ spl0_7,
inference(sat_conversion,[],[f85]) ).
cnf(s65,plain,
$false,
inference(rat,[],[s50,s64,s61,s57]) ).
thf(f86,plain,
$false,
inference(avatar_sat_refutation,[],[s65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO383^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n015.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 16:53:18 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 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
% 0.07/0.25 % (3787603)Will run a generic schedule for satisfiability detection.
% 0.07/0.25 % (3787610)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1966690626:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.25 % (3787610) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3787603-3787610"...
% 0.07/0.25 % (3787609)% WARNING: option uhcvi not known.
% 0.07/0.25 % (3787610)...printing done.
% 0.07/0.25 % (3787610)Refutation found. Thanks to Tanya!
% 0.07/0.25 % SZS status Theorem for theBenchmark
% 0.07/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.26 % (3787610)------------------------------
% 0.07/0.26 % (3787610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (3787610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (3787610)CaDiCaL version: 2.1.3
% 0.07/0.26 % (3787610)Termination reason: Refutation
% 0.07/0.26 % (3787610)Time elapsed: 0.003 s
% 0.07/0.26 % (3787610)Peak memory usage: 12 MB
% 0.07/0.26 % (3787610)Instructions burned: 8 (million)
% 0.07/0.26 % (3787603)Success in time 0.035 s
% 0.07/0.26 % Vampire exiting
%------------------------------------------------------------------------------