%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO227^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:47:14 AM UTC 2026
% Result : Theorem 0.24s 0.32s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 230 ( 57 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 192 ( 42 ~; 22 |; 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_ @ a @ b )
& ( c_less_ @ b @ c ) )
=> ? [X2: $i > $o] :
( ~ ( X2 @ c )
& ( X2 @ b )
& ~ ( X2 @ a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBLEDSOE4_W_AX) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i,X1: $i] :
( ( c_less_ @ X0 @ X1 )
=> ( X0 != X1 ) )
=> ( ( ( c_less_ @ a @ b )
& ( c_less_ @ b @ c ) )
=> ? [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_ @ a @ b )
& ( c_less_ @ b @ c ) )
=> ? [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_ @ a @ b )
= $true )
& ( ( c_less_ @ b @ c )
= $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_ @ a @ b )
= $true )
& ( ( c_less_ @ b @ c )
= $true ) )
=> ? [X2: $i > $o] :
( ( ( X2 @ a )
!= $true )
& ( ( X2 @ b )
= $true )
& ( ( X2 @ c )
!= $true ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ! [X2: $i > $o] :
( ( ( X2 @ a )
= $true )
| ( ( X2 @ c )
= $true )
| ( ( X2 @ b )
!= $true ) )
& ( ( c_less_ @ a @ b )
= $true )
& ( ( c_less_ @ b @ c )
= $true )
& ! [X1: $i,X0: $i] :
( ( X0 != X1 )
| ( ( c_less_ @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ! [X1: $i,X0: $i] :
( ( X0 != X1 )
| ( ( c_less_ @ X0 @ X1 )
!= $true ) )
& ( ( c_less_ @ a @ b )
= $true )
& ( ( c_less_ @ b @ c )
= $true )
& ! [X2: $i > $o] :
( ( ( X2 @ a )
= $true )
| ( ( X2 @ c )
= $true )
| ( ( X2 @ b )
!= $true ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( ( c_less_ @ X1 @ X0 )
!= $true ) )
& ( ( c_less_ @ a @ b )
= $true )
& ( ( c_less_ @ b @ c )
= $true )
& ! [X2: $i > $o] :
( ( ( X2 @ a )
= $true )
| ( ( X2 @ c )
= $true )
| ( ( X2 @ b )
!= $true ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
! [X2: $i > $o] :
( ( ( X2 @ b )
!= $true )
| ( ( X2 @ a )
= $true )
| ( ( X2 @ c )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( ( c_less_ @ b @ c )
= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( c_less_ @ a @ b )
= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( ( c_less_ @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
! [X1: $i] :
( $true
!= ( c_less_ @ X1 @ X1 ) ),
inference(equality_resolution,[],[f12]) ).
thf(f16,plain,
( ( ( b = c )
= $true )
| ( a = b ) ),
inference(leibniz_equality_elimination,[],[f9]) ).
thf(f37,plain,
( ( b = c )
| ( a = b ) ),
inference(equality_proxy_clausification,[],[f16]) ).
thf(f44,definition,
( spl0_2
<=> ( a = b ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f46,plain,
( ( a = b )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f44]) ).
thf(f49,definition,
( spl0_3
<=> ( b = c ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f51,plain,
( ( b = c )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f49]) ).
thf(f52,plain,
( spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f37,f44,f49]) ).
thf(f53,plain,
( ( $true
= ( c_less_ @ b @ b ) )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f11,f46]) ).
thf(f54,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f53,f15]) ).
thf(f55,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f54]) ).
thf(f57,plain,
( ( $true
= ( c_less_ @ b @ b ) )
| ~ spl0_3 ),
inference(constrained_superposition,[],[f10,f51]) ).
thf(f58,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f57,f15]) ).
thf(f59,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f58]) ).
cnf(s2,plain,
( spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f52]) ).
cnf(s3,plain,
~ spl0_2,
inference(sat_conversion,[],[f55]) ).
cnf(s4,plain,
~ spl0_3,
inference(sat_conversion,[],[f59]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s4,s3]) ).
thf(f60,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO227^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n008.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 16:40:54 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 Running higher-order theorem proving
% 0.24/0.28 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.32 % (3396302)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.32 % (3396308)lrs+10_16_si=on:nwc=1.5:random_seed=3847193082:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.32 % (3396309)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=589048453:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.32 % (3396307)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=22095925:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.32 % (3396310)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=4022035799:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.24/0.32 % (3396309)Refutation not found, incomplete strategy
% 0.24/0.32 % (3396309)------------------------------
% 0.24/0.32 % (3396309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.32 % (3396309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.32 % (3396309)CaDiCaL version: 2.1.3
% 0.24/0.32 % (3396309)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.32 % (3396309)Time elapsed: 0.002 s
% 0.24/0.32 % (3396309)Peak memory usage: 12 MB
% 0.24/0.32 % (3396309)Instructions burned: 2 (million)
% 0.24/0.32 % (3396307) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3396302-3396307"...
% 0.24/0.32 % (3396308) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3396302-3396308"...
% 0.24/0.32 % (3396310) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3396302-3396310"...
% 0.24/0.32 % (3396309)------------------------------
% 0.24/0.32 % (3396309)------------------------------
% 0.24/0.32 % (3396307)...printing done.
% 0.24/0.32 % (3396308)...printing done.
% 0.24/0.32 % (3396310)...printing done.
% 0.24/0.32 % (3396307)Refutation found. Thanks to Tanya!
% 0.24/0.32 % SZS status Theorem for theBenchmark
% 0.24/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.32 % (3396307)------------------------------
% 0.24/0.32 % (3396307)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.32 % (3396307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.32 % (3396307)CaDiCaL version: 2.1.3
% 0.24/0.32 % (3396307)Termination reason: Refutation
% 0.24/0.32 % (3396307)Time elapsed: 0.003 s
% 0.24/0.32 % (3396307)Peak memory usage: 13 MB
% 0.24/0.32 % (3396307)Instructions burned: 3 (million)
% 0.24/0.32 % (3396302)Success in time 0.038 s
% 0.24/0.32 % Vampire exiting
%------------------------------------------------------------------------------