%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO227^5 : 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 : n014.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 08:49:34 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 238 ( 59 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 198 ( 46 ~; 24 |; 24 &; 87 @)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 28 ( 0 sgn 23 !; 5 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
c_less_: $i > $i > $o ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(func_def_8,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
( ! [X0: $i,X1: $i] :
( ( c_less_ @ X0 @ X1 )
=> ( X0 != X1 ) )
=> ( ( ( c_less_ @ b @ c )
& ( c_less_ @ a @ b ) )
=> ? [X2: $i > $o] :
( ~ ( X2 @ c )
& ( X2 @ b )
& ~ ( X2 @ a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBLEDSOE4_W_AX) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i,X1: $i] :
( ( c_less_ @ X0 @ X1 )
=> ( X0 != X1 ) )
=> ( ( ( c_less_ @ b @ c )
& ( c_less_ @ a @ b ) )
=> ? [X2: $i > $o] :
( ~ ( X2 @ c )
& ( X2 @ b )
& ~ ( X2 @ a ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i,X1: $i] :
( ( c_less_ @ X0 @ X1 )
=> ( X0 != X1 ) )
=> ( ( ( c_less_ @ b @ c )
& ( c_less_ @ a @ b ) )
=> ? [X2: $i > $o] :
( ~ ( X2 @ c )
& ( X2 @ b )
& ~ ( X2 @ a ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: $i,X1: $i] :
( ( ( c_less_ @ X0 @ X1 )
= $true )
=> ( X0 != X1 ) )
=> ( ( ( ( c_less_ @ b @ c )
= $true )
& ( ( c_less_ @ a @ b )
= $true ) )
=> ? [X2: $i > $o] :
( ( ( X2 @ c )
!= $true )
& ( ( X2 @ b )
= $true )
& ( ( X2 @ a )
!= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ( ! [X0: $i,X1: $i] :
( ( ( c_less_ @ X0 @ X1 )
= $true )
=> ( X0 != X1 ) )
=> ( ( ( ( c_less_ @ b @ c )
= $true )
& ( ( c_less_ @ a @ b )
= $true ) )
=> ? [X2: $i > $o] :
( ( ( X2 @ c )
!= $true )
& ( ( X2 @ b )
= $true )
& ( ( X2 @ a )
!= $true ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ! [X2: $i > $o] :
( ( ( X2 @ c )
= $true )
| ( ( X2 @ b )
!= $true )
| ( ( X2 @ a )
= $true ) )
& ( ( c_less_ @ b @ c )
= $true )
& ( ( c_less_ @ a @ b )
= $true )
& ! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( ( c_less_ @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ! [X2: $i > $o] :
( ( ( X2 @ c )
= $true )
| ( ( X2 @ b )
!= $true )
| ( ( X2 @ a )
= $true ) )
& ( ( c_less_ @ b @ c )
= $true )
& ( ( c_less_ @ a @ b )
= $true )
& ! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( ( c_less_ @ X0 @ X1 )
!= $true ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ! [X0: $i > $o] :
( ( $true
= ( X0 @ c ) )
| ( $true
!= ( X0 @ b ) )
| ( $true
= ( X0 @ a ) ) )
& ( ( c_less_ @ b @ c )
= $true )
& ( ( c_less_ @ a @ b )
= $true )
& ! [X1: $i,X2: $i] :
( ( X1 != X2 )
| ( $true
!= ( c_less_ @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
! [X2: $i,X1: $i] :
( ( X1 != X2 )
| ( $true
!= ( c_less_ @ X1 @ X2 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( ( c_less_ @ a @ b )
= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( c_less_ @ b @ c )
= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
! [X0: $i > $o] :
( ( $true
!= ( X0 @ b ) )
| ( $true
= ( X0 @ c ) )
| ( $true
= ( X0 @ a ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
! [X2: $i] :
( $true
!= ( c_less_ @ X2 @ X2 ) ),
inference(equality_resolution,[],[f9]) ).
thf(f16,plain,
( ( b = c )
| ( $true
= ( b = a ) ) ),
inference(leibniz_equality_elimination,[],[f12]) ).
thf(f44,plain,
( ( b = c )
| ( a = b ) ),
inference(equality_proxy_clausification,[],[f16]) ).
thf(f50,definition,
( spl0_2
<=> ( b = c ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f52,plain,
( ( b = c )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f50]) ).
thf(f55,definition,
( spl0_3
<=> ( a = b ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f57,plain,
( ( a = b )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f58,plain,
( spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f44,f50,f55]) ).
thf(f60,plain,
( ( $true
= ( c_less_ @ c @ c ) )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f11,f52]) ).
thf(f62,plain,
( ( $true != $true )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f15,f60]) ).
thf(f66,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f62]) ).
thf(f67,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f66]) ).
thf(f69,plain,
( ( $true
= ( c_less_ @ b @ b ) )
| ~ spl0_3 ),
inference(constrained_superposition,[],[f10,f57]) ).
thf(f70,plain,
( ( $true != $true )
| ~ spl0_3 ),
inference(constrained_superposition,[],[f15,f69]) ).
thf(f77,plain,
( $false
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f70]) ).
thf(f78,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f77]) ).
cnf(s2,plain,
( spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f58]) ).
cnf(s3,plain,
~ spl0_2,
inference(sat_conversion,[],[f67]) ).
cnf(s4,plain,
~ spl0_3,
inference(sat_conversion,[],[f78]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s4,s3]) ).
thf(f79,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO227^5 : 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 : n014.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 16:40:00 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 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
% 0.07/0.24 % (2904442)Will run a generic schedule for satisfiability detection.
% 0.07/0.24 % (2904453)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2409173728:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.24 % (2904453) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2904442-2904453"...
% 0.07/0.24 % (2904448)% WARNING: option uhcvi not known.
% 0.07/0.24 % (2904453)...printing done.
% 0.07/0.24 % (2904453)Refutation found. Thanks to Tanya!
% 0.07/0.24 % SZS status Theorem for theBenchmark
% 0.07/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.24 % (2904453)------------------------------
% 0.07/0.24 % (2904453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.24 % (2904453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.24 % (2904453)CaDiCaL version: 2.1.3
% 0.07/0.24 % (2904453)Termination reason: Refutation
% 0.07/0.24 % (2904453)Time elapsed: 0.002 s
% 0.07/0.24 % (2904453)Peak memory usage: 13 MB
% 0.07/0.24 % (2904453)Instructions burned: 4 (million)
% 0.07/0.24 % (2904442)Success in time 0.026 s
% 0.07/0.24 % Vampire exiting
%------------------------------------------------------------------------------