%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO883^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 08:48:32 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.29s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 611 ( 50 equ; 0 cnn)
% Maximal formula atoms : 8 ( 23 avg)
% Number of connectives : 664 ( 62 ~; 48 |; 0 &; 552 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 225 ( 225 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 6 con; 0-6 aty)
% Number of variables : 79 ( 40 sgn 25 !; 0 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
f: $i > $i > $i > $i > $i > $i > $i ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db8:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,axiom,
! [X0: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i] :
( ( ( X0 @ a @ b @ c @ c @ c @ c @ c @ c @ c )
!= ( f @ b @ a @ c @ c @ c @ c ) )
| ( ( X0 @ c @ a @ c @ c @ c @ c @ c @ c @ c )
!= ( f @ a @ c @ c @ c @ c @ c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax) ).
thf(f2,plain,
! [X0: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i] :
( ( ( X0 @ c @ a @ c @ c @ c @ c @ c @ c @ c )
!= ( f @ a @ c @ c @ c @ c @ c ) )
| ( ( X0 @ a @ b @ c @ c @ c @ c @ c @ c @ c )
!= ( f @ b @ a @ c @ c @ c @ c ) ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f4,plain,
! [X2: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i,X3: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i,X0: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i,X1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i,X4: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i] :
( ( c
!= ( X4 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) )
| ( a
!= ( X0 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) )
| ( c
!= ( X2 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) )
| ( c
!= ( X3 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) )
| ( ( f @ b @ a @ c @ c @ c @ c )
!= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i,Y4: $i,Y5: $i,Y6: $i,Y7: $i,Y8: $i] :
( f @ ( X0 @ Y0 @ Y1 @ Y2 @ Y3 @ Y4 @ Y5 @ Y6 @ Y7 @ Y8 ) @ ( X1 @ Y0 @ Y1 @ Y2 @ Y3 @ Y4 @ Y5 @ Y6 @ Y7 @ Y8 ) @ ( X2 @ Y0 @ Y1 @ Y2 @ Y3 @ Y4 @ Y5 @ Y6 @ Y7 @ Y8 ) @ ( X3 @ Y0 @ Y1 @ Y2 @ Y3 @ Y4 @ Y5 @ Y6 @ Y7 @ Y8 ) @ ( X4 @ Y0 @ Y1 @ Y2 @ Y3 @ Y4 @ Y5 @ Y6 @ Y7 @ Y8 )
@ ( ^ [Y9: $i,Y10: $i,Y11: $i,Y12: $i,Y13: $i,Y14: $i,Y15: $i,Y16: $i,Y17: $i] : Y11
@ Y0
@ Y1
@ Y2
@ Y3
@ Y4
@ Y5
@ Y6
@ Y7
@ Y8 ) )
@ a
@ b
@ c
@ c
@ c
@ c
@ c
@ c
@ c ) )
| ( c
!= ( X1 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) ) ),
inference(equality_resolution,[],[f2]) ).
thf(f12,plain,
! [X2: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i,X3: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i,X0: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i,X1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i,X4: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i] :
( ( ( f @ b @ a @ c @ c @ c @ c )
!= ( f @ ( X0 @ a @ b @ c @ c @ c @ c @ c @ c @ c ) @ ( X1 @ a @ b @ c @ c @ c @ c @ c @ c @ c ) @ ( X2 @ a @ b @ c @ c @ c @ c @ c @ c @ c ) @ ( X3 @ a @ b @ c @ c @ c @ c @ c @ c @ c ) @ ( X4 @ a @ b @ c @ c @ c @ c @ c @ c @ c ) @ c ) )
| ( c
!= ( X2 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) )
| ( c
!= ( X4 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) )
| ( a
!= ( X0 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) )
| ( c
!= ( X1 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) )
| ( c
!= ( X3 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) ) ),
inference(beta-eta_normalization,[],[f4]) ).
thf(f25,plain,
! [X2: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i,X0: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i,X1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i] :
( ( c
!= ( X2 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) )
| ( a
!= ( X1 @ a @ b @ c @ c @ c @ c @ c @ c @ c ) )
| ( c
!= ( X2 @ a @ b @ c @ c @ c @ c @ c @ c @ c ) )
| ( c
!= ( X0 @ a @ b @ c @ c @ c @ c @ c @ c @ c ) )
| ( c
!= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i,Y4: $i,Y5: $i,Y6: $i,Y7: $i,Y8: $i] : Y6
@ c
@ a
@ c
@ c
@ c
@ c
@ c
@ c
@ c ) )
| ( c
!= ( X0 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) )
| ( a
!= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i,Y4: $i,Y5: $i,Y6: $i,Y7: $i,Y8: $i] : Y1
@ c
@ a
@ c
@ c
@ c
@ c
@ c
@ c
@ c ) )
| ( c
!= ( X1 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) ) ),
inference(equality_resolution,[],[f12]) ).
thf(f67,plain,
! [X2: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i,X0: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i,X1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i] :
( ( c
!= ( X0 @ a @ b @ c @ c @ c @ c @ c @ c @ c ) )
| ( c
!= ( X2 @ a @ b @ c @ c @ c @ c @ c @ c @ c ) )
| ( a
!= ( X1 @ a @ b @ c @ c @ c @ c @ c @ c @ c ) )
| ( c
!= ( X1 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) )
| ( c
!= ( X0 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) )
| ( a != a )
| ( c
!= ( X2 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) )
| ( c != c ) ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f68,plain,
! [X2: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i,X0: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i,X1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i] :
( ( c
!= ( X1 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) )
| ( a
!= ( X1 @ a @ b @ c @ c @ c @ c @ c @ c @ c ) )
| ( c
!= ( X2 @ a @ b @ c @ c @ c @ c @ c @ c @ c ) )
| ( c
!= ( X0 @ a @ b @ c @ c @ c @ c @ c @ c @ c ) )
| ( c
!= ( X0 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) )
| ( c
!= ( X2 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) ) ),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f73,definition,
( spl0_2
<=> ! [X0: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i] :
( ( c
!= ( X0 @ a @ b @ c @ c @ c @ c @ c @ c @ c ) )
| ( c
!= ( X0 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f74,plain,
( ! [X0: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i] :
( ( c
!= ( X0 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) )
| ( c
!= ( X0 @ a @ b @ c @ c @ c @ c @ c @ c @ c ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f73]) ).
thf(f76,definition,
( spl0_3
<=> ! [X1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i] :
( ( c
!= ( X1 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) )
| ( a
!= ( X1 @ a @ b @ c @ c @ c @ c @ c @ c @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f77,plain,
( ! [X1: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i] :
( ( c
!= ( X1 @ c @ a @ c @ c @ c @ c @ c @ c @ c ) )
| ( a
!= ( X1 @ a @ b @ c @ c @ c @ c @ c @ c @ c ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f76]) ).
thf(f93,plain,
( spl0_2
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f68,f76,f73,f73]) ).
thf(f97,plain,
( ( c
!= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i,Y4: $i,Y5: $i,Y6: $i,Y7: $i,Y8: $i] : Y4
@ a
@ b
@ c
@ c
@ c
@ c
@ c
@ c
@ c ) )
| ~ spl0_2 ),
inference(equality_resolution,[],[f74]) ).
thf(f125,plain,
( ( c != c )
| ~ spl0_2 ),
inference(beta-eta_normalization,[],[f97]) ).
thf(f126,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f125]) ).
thf(f127,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f126]) ).
thf(f128,plain,
( ( a
!= ( ^ [Y0: $i,Y1: $i,Y2: $i,Y3: $i,Y4: $i,Y5: $i,Y6: $i,Y7: $i,Y8: $i] : Y0
@ a
@ b
@ c
@ c
@ c
@ c
@ c
@ c
@ c ) )
| ~ spl0_3 ),
inference(equality_resolution,[],[f77]) ).
thf(f138,plain,
( ( a != a )
| ~ spl0_3 ),
inference(beta-eta_normalization,[],[f128]) ).
thf(f139,plain,
( $false
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f138]) ).
thf(f140,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f139]) ).
cnf(s31,plain,
( spl0_2
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f93]) ).
cnf(s32,plain,
( spl0_2
| spl0_3 ),
inference(rat,[],[s31]) ).
cnf(s40,plain,
~ spl0_2,
inference(sat_conversion,[],[f127]) ).
cnf(s41,plain,
~ spl0_3,
inference(sat_conversion,[],[f140]) ).
cnf(s42,plain,
$false,
inference(rat,[],[s32,s41,s40]) ).
thf(f148,plain,
$false,
inference(avatar_sat_refutation,[],[s42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO883^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 17:27:12 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.23/0.29 % (907938)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.29 % (907952)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=449510641:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.29 % (907953)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.29 % (907953)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.23/0.29 % (907947)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3159826504:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.29 % (907948)lrs+10_16_si=on:nwc=1.5:random_seed=3883276139:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.29 % (907951)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=66890572:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.29 % (907953)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=418220202:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.29 % (907950)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=703820990: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)
% 0.23/0.29 % (907949)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1287919616:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.29 % (907952) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-907938-907952"...
% 0.23/0.29 % (907949)Instruction limit reached!
% 0.23/0.29 % (907949)------------------------------
% 0.23/0.29 % (907949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (907949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (907949)CaDiCaL version: 2.1.3
% 0.23/0.29 % (907949)Termination reason: Instruction limit
% 0.23/0.29 % (907949)Termination phase: Saturation
% 0.23/0.29 % (907949)Time elapsed: 0.002 s
% 0.23/0.29 % (907949)Peak memory usage: 11 MB
% 0.23/0.29 % (907949)Instructions burned: 4 (million)
% 0.23/0.29 % (907952)...printing done.
% 0.23/0.29 % (907947)Refutation not found, incomplete strategy
% 0.23/0.29 % (907947)------------------------------
% 0.23/0.29 % (907947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (907947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (907947)CaDiCaL version: 2.1.3
% 0.23/0.29 % (907947)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.29 % (907947)Time elapsed: 0.003 s
% 0.23/0.29 % (907947)Peak memory usage: 12 MB
% 0.23/0.29 % (907947)Instructions burned: 5 (million)
% 0.23/0.29 % (907951)Refutation not found, incomplete strategy
% 0.23/0.29 % (907951)------------------------------
% 0.23/0.29 % (907951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (907951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (907951)CaDiCaL version: 2.1.3
% 0.23/0.29 % (907951)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.29 % (907951)Time elapsed: 0.003 s
% 0.23/0.29 % (907951)Peak memory usage: 11 MB
% 0.23/0.29 % (907951)Instructions burned: 5 (million)
% 0.23/0.29 % (907952)Refutation found. Thanks to Tanya!
% 0.23/0.29 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.29 % (907952)------------------------------
% 0.23/0.29 % (907952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (907952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (907952)CaDiCaL version: 2.1.3
% 0.23/0.29 % (907952)Termination reason: Refutation
% 0.23/0.29 % (907952)Time elapsed: 0.010 s
% 0.23/0.29 % (907952)Peak memory usage: 13 MB
% 0.23/0.29 % (907952)Instructions burned: 40 (million)
% 0.23/0.29 % (907938)Success in time 0.036 s
% 0.23/0.29 % Vampire exiting
%------------------------------------------------------------------------------