%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV091^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 08:38:59 AM UTC 2026
% Result : Theorem 0.17s 0.27s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 47 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 447 ( 119 equ; 0 cnn)
% Maximal formula atoms : 12 ( 9 avg)
% Number of connectives : 489 ( 66 ~; 73 |; 40 &; 292 @)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 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 : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 151 ( 0 sgn 139 !; 12 ?; 151 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cQ: $i > $i > $o ).
thf(func_def_1,type,
cP: $i > $i > $o ).
thf(f1,conjecture,
( ( ! [X0: $i,X1: $i] :
( ( cQ @ X0 @ X1 )
| ( cP @ X0 @ X1 ) )
& ! [X0: $i,X1: $i] :
( ( cQ @ X0 @ X1 )
=> ( cQ @ X1 @ X0 ) )
& ! [X0: $i,X1: $i,X2: $i] :
( ( ( cQ @ X1 @ X2 )
& ( cQ @ X0 @ X1 ) )
=> ( cQ @ X0 @ X2 ) )
& ! [X0: $i,X1: $i,X2: $i] :
( ( ( cP @ X1 @ X2 )
& ( cP @ X0 @ X1 ) )
=> ( cP @ X0 @ X2 ) ) )
=> ( ! [X0: $i,X1: $i] : ( cQ @ X0 @ X1 )
| ! [X0: $i,X1: $i] : ( cP @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCADE13_pme) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i,X1: $i] :
( ( cQ @ X0 @ X1 )
| ( cP @ X0 @ X1 ) )
& ! [X0: $i,X1: $i] :
( ( cQ @ X0 @ X1 )
=> ( cQ @ X1 @ X0 ) )
& ! [X0: $i,X1: $i,X2: $i] :
( ( ( cQ @ X1 @ X2 )
& ( cQ @ X0 @ X1 ) )
=> ( cQ @ X0 @ X2 ) )
& ! [X0: $i,X1: $i,X2: $i] :
( ( ( cP @ X1 @ X2 )
& ( cP @ X0 @ X1 ) )
=> ( cP @ X0 @ X2 ) ) )
=> ( ! [X0: $i,X1: $i] : ( cQ @ X0 @ X1 )
| ! [X0: $i,X1: $i] : ( cP @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: $i,X1: $i] :
( ( cQ @ X0 @ X1 )
| ( cP @ X0 @ X1 ) )
& ! [X2: $i,X3: $i] :
( ( cQ @ X2 @ X3 )
=> ( cQ @ X3 @ X2 ) )
& ! [X4: $i,X5: $i,X6: $i] :
( ( ( cQ @ X5 @ X6 )
& ( cQ @ X4 @ X5 ) )
=> ( cQ @ X4 @ X6 ) )
& ! [X7: $i,X8: $i,X9: $i] :
( ( ( cP @ X8 @ X9 )
& ( cP @ X7 @ X8 ) )
=> ( cP @ X7 @ X9 ) ) )
=> ( ! [X10: $i,X11: $i] : ( cQ @ X10 @ X11 )
| ! [X12: $i,X13: $i] : ( cP @ X12 @ X13 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X0: $i,X1: $i] :
( ( ( cQ @ X0 @ X1 )
= $true )
| ( ( cP @ X0 @ X1 )
= $true ) )
& ! [X2: $i,X3: $i] :
( ( ( cQ @ X2 @ X3 )
= $true )
=> ( ( cQ @ X3 @ X2 )
= $true ) )
& ! [X4: $i,X5: $i,X6: $i] :
( ( ( ( cQ @ X5 @ X6 )
= $true )
& ( ( cQ @ X4 @ X5 )
= $true ) )
=> ( ( cQ @ X4 @ X6 )
= $true ) )
& ! [X7: $i,X8: $i,X9: $i] :
( ( ( ( cP @ X8 @ X9 )
= $true )
& ( ( cP @ X7 @ X8 )
= $true ) )
=> ( ( cP @ X7 @ X9 )
= $true ) ) )
=> ( ! [X10: $i,X11: $i] :
( ( cQ @ X10 @ X11 )
= $true )
| ! [X12: $i,X13: $i] :
( ( cP @ X12 @ X13 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ? [X10: $i,X11: $i] :
( ( cQ @ X10 @ X11 )
!= $true )
& ? [X12: $i,X13: $i] :
( ( cP @ X12 @ X13 )
!= $true )
& ! [X0: $i,X1: $i] :
( ( ( cQ @ X0 @ X1 )
= $true )
| ( ( cP @ X0 @ X1 )
= $true ) )
& ! [X2: $i,X3: $i] :
( ( ( cQ @ X3 @ X2 )
= $true )
| ( ( cQ @ X2 @ X3 )
!= $true ) )
& ! [X4: $i,X5: $i,X6: $i] :
( ( ( cQ @ X4 @ X6 )
= $true )
| ( ( cQ @ X5 @ X6 )
!= $true )
| ( ( cQ @ X4 @ X5 )
!= $true ) )
& ! [X7: $i,X8: $i,X9: $i] :
( ( ( cP @ X7 @ X9 )
= $true )
| ( ( cP @ X8 @ X9 )
!= $true )
| ( ( cP @ X7 @ X8 )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ? [X10: $i,X11: $i] :
( ( cQ @ X10 @ X11 )
!= $true )
& ? [X12: $i,X13: $i] :
( ( cP @ X12 @ X13 )
!= $true )
& ! [X0: $i,X1: $i] :
( ( ( cQ @ X0 @ X1 )
= $true )
| ( ( cP @ X0 @ X1 )
= $true ) )
& ! [X2: $i,X3: $i] :
( ( ( cQ @ X3 @ X2 )
= $true )
| ( ( cQ @ X2 @ X3 )
!= $true ) )
& ! [X4: $i,X5: $i,X6: $i] :
( ( ( cQ @ X4 @ X6 )
= $true )
| ( ( cQ @ X5 @ X6 )
!= $true )
| ( ( cQ @ X4 @ X5 )
!= $true ) )
& ! [X7: $i,X8: $i,X9: $i] :
( ( ( cP @ X7 @ X9 )
= $true )
| ( ( cP @ X8 @ X9 )
!= $true )
| ( ( cP @ X7 @ X8 )
!= $true ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ? [X0: $i,X1: $i] :
( ( cQ @ X0 @ X1 )
!= $true )
& ? [X2: $i,X3: $i] :
( $true
!= ( cP @ X2 @ X3 ) )
& ! [X4: $i,X5: $i] :
( ( ( cQ @ X4 @ X5 )
= $true )
| ( $true
= ( cP @ X4 @ X5 ) ) )
& ! [X6: $i,X7: $i] :
( ( $true
= ( cQ @ X7 @ X6 ) )
| ( $true
!= ( cQ @ X6 @ X7 ) ) )
& ! [X8: $i,X9: $i,X10: $i] :
( ( $true
= ( cQ @ X8 @ X10 ) )
| ( $true
!= ( cQ @ X9 @ X10 ) )
| ( $true
!= ( cQ @ X8 @ X9 ) ) )
& ! [X11: $i,X12: $i,X13: $i] :
( ( $true
= ( cP @ X11 @ X13 ) )
| ( ( cP @ X12 @ X13 )
!= $true )
| ( $true
!= ( cP @ X11 @ X12 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( $true
!= ( cQ @ sK0 @ sK1 ) )
& ( $true
!= ( cP @ sK2 @ sK3 ) )
& ! [X4: $i,X5: $i] :
( ( ( cQ @ X4 @ X5 )
= $true )
| ( $true
= ( cP @ X4 @ X5 ) ) )
& ! [X6: $i,X7: $i] :
( ( $true
= ( cQ @ X7 @ X6 ) )
| ( $true
!= ( cQ @ X6 @ X7 ) ) )
& ! [X8: $i,X9: $i,X10: $i] :
( ( $true
= ( cQ @ X8 @ X10 ) )
| ( $true
!= ( cQ @ X9 @ X10 ) )
| ( $true
!= ( cQ @ X8 @ X9 ) ) )
& ! [X11: $i,X12: $i,X13: $i] :
( ( $true
= ( cP @ X11 @ X13 ) )
| ( ( cP @ X12 @ X13 )
!= $true )
| ( $true
!= ( cP @ X11 @ X12 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f7]) ).
thf(f9,plain,
! [X11: $i,X12: $i,X13: $i] :
( ( $true
!= ( cP @ X11 @ X12 ) )
| ( ( cP @ X12 @ X13 )
!= $true )
| ( $true
= ( cP @ X11 @ X13 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
! [X10: $i,X8: $i,X9: $i] :
( ( $true
!= ( cQ @ X9 @ X10 ) )
| ( $true
= ( cQ @ X8 @ X10 ) )
| ( $true
!= ( cQ @ X8 @ X9 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
! [X6: $i,X7: $i] :
( ( $true
!= ( cQ @ X6 @ X7 ) )
| ( $true
= ( cQ @ X7 @ X6 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
! [X4: $i,X5: $i] :
( ( $true
= ( cP @ X4 @ X5 ) )
| ( ( cQ @ X4 @ X5 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
( $true
!= ( cP @ sK2 @ sK3 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
( $true
!= ( cQ @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f18,definition,
( spl4_1
<=> ! [X6: $i,X7: $i] :
( $true
= ( cQ @ X7 @ X6 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f19,plain,
( ! [X6: $i,X7: $i] :
( $true
= ( cQ @ X7 @ X6 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f18]) ).
thf(f32,plain,
( ( $true != $true )
| ( $true
= ( cQ @ sK2 @ sK3 ) ) ),
inference(constrained_superposition,[],[f13,f12]) ).
thf(f33,plain,
( $true
= ( cQ @ sK2 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f32]) ).
thf(f34,plain,
( ( $true != $true )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f14,f19]) ).
thf(f37,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f34]) ).
thf(f38,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f37]) ).
thf(f49,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( cP @ X1 @ X2 )
!= $true )
| ( ( cP @ X0 @ X2 )
= $true )
| ( ( cQ @ X0 @ X1 )
= $true ) ),
inference(constrained_superposition,[],[f9,f12]) ).
thf(f50,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( cP @ X1 @ X2 )
!= $true )
| ( ( cP @ X0 @ X2 )
= $true )
| ( ( cQ @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f49]) ).
thf(f54,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( cQ @ X0 @ sK3 ) )
| ( $true
!= ( cQ @ X0 @ sK2 ) ) ),
inference(constrained_superposition,[],[f10,f33]) ).
thf(f57,plain,
! [X0: $i] :
( ( $true
!= ( cQ @ X0 @ sK2 ) )
| ( $true
= ( cQ @ X0 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f54]) ).
thf(f59,definition,
( spl4_5
<=> ! [X0: $i] :
( $true
= ( cQ @ X0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f60,plain,
( ! [X0: $i] :
( $true
= ( cQ @ X0 @ sK3 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f59]) ).
thf(f70,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
= ( cQ @ sK3 @ X0 ) ) )
| ~ spl4_5 ),
inference(constrained_superposition,[],[f11,f60]) ).
thf(f71,plain,
( ! [X0: $i] :
( $true
= ( cQ @ sK3 @ X0 ) )
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f70]) ).
thf(f73,plain,
( ! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( cQ @ X1 @ X0 )
= $true )
| ( $true
!= ( cQ @ X1 @ sK3 ) ) )
| ~ spl4_5 ),
inference(constrained_superposition,[],[f10,f71]) ).
thf(f78,plain,
( ! [X0: $i,X1: $i] :
( ( ( cQ @ X1 @ X0 )
= $true )
| ( $true
!= ( cQ @ X1 @ sK3 ) ) )
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f73]) ).
thf(f79,plain,
( ! [X0: $i,X1: $i] :
( ( cQ @ X1 @ X0 )
= $true )
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f78,f60]) ).
thf(f80,plain,
( spl4_1
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f79,f59,f18]) ).
thf(f108,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( cP @ X2 @ X1 ) )
| ( $true
= ( cQ @ X2 @ X0 ) )
| ( ( cQ @ X0 @ X1 )
= $true ) ),
inference(constrained_superposition,[],[f50,f12]) ).
thf(f109,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( cP @ X2 @ X1 ) )
| ( $true
= ( cQ @ X2 @ X0 ) )
| ( ( cQ @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f108]) ).
thf(f110,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( cQ @ sK2 @ X0 ) )
| ( $true
= ( cQ @ X0 @ sK3 ) ) ),
inference(constrained_superposition,[],[f13,f109]) ).
thf(f127,plain,
! [X0: $i] :
( ( $true
= ( cQ @ sK2 @ X0 ) )
| ( $true
= ( cQ @ X0 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f110]) ).
thf(f132,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
= ( cQ @ X0 @ sK2 ) )
| ( $true
= ( cQ @ X0 @ sK3 ) ) ),
inference(constrained_superposition,[],[f11,f127]) ).
thf(f139,plain,
! [X0: $i] :
( ( $true
= ( cQ @ X0 @ sK2 ) )
| ( $true
= ( cQ @ X0 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f132]) ).
thf(f142,plain,
! [X0: $i] :
( $true
= ( cQ @ X0 @ sK3 ) ),
inference(forward_subsumption_resolution,[],[f139,f57]) ).
thf(f152,plain,
spl4_5,
inference(avatar_split_clause,[],[f142,f59]) ).
cnf(s26,plain,
~ spl4_1,
inference(sat_conversion,[],[f38]) ).
cnf(s53,plain,
( spl4_1
| ~ spl4_5 ),
inference(sat_conversion,[],[f80]) ).
cnf(s94,plain,
spl4_5,
inference(sat_conversion,[],[f152]) ).
cnf(s95,plain,
spl4_1,
inference(rat,[],[s53,s94]) ).
cnf(s96,plain,
$false,
inference(rat,[],[s26,s95]) ).
thf(f153,plain,
$false,
inference(avatar_sat_refutation,[],[s96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV091^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n002.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 15:12:06 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.27 % (1412843)Will run a generic schedule for satisfiability detection.
% 0.17/0.27 % (1412848)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1131317484_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.27 % Exception at run slice level
% 0.17/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.27 % (1412849)% WARNING: option uhcvi not known.
% 0.17/0.27 % (1412849)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3668045176:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.27 % (1412850)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2146995339:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.27 % (1412851)dis+10_1_sil=32000:sp=arity:random_seed=4158643631:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.27 % (1412849)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.17/0.27 % (1412852)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2232645048:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.27 % (1412849)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.17/0.27 % (1412854)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3858281422:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.27 % (1412853)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3075142862:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.27 % (1412852)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.17/0.27 % (1412856)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2915273631:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.17/0.27 % Exception at run slice level
% 0.17/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.27 % (1412850) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1412843-1412850"...
% 0.17/0.27 % (1412854) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1412843-1412854"...
% 0.17/0.27 % (1412850)...printing done.
% 0.17/0.27 % (1412850)Refutation found. Thanks to Tanya!
% 0.17/0.27 % SZS status Theorem for theBenchmark
% 0.17/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.27 % (1412850)------------------------------
% 0.17/0.27 % (1412850)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.27 % (1412850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.27 % (1412850)CaDiCaL version: 2.1.3
% 0.17/0.27 % (1412850)Termination reason: Refutation
% 0.17/0.27 % (1412850)Time elapsed: 0.009 s
% 0.17/0.27 % (1412850)Peak memory usage: 12 MB
% 0.17/0.27 % (1412850)Instructions burned: 13 (million)
% 0.17/0.27 % (1412843)Success in time 0.046 s
% 0.17/0.27 % Vampire exiting
%------------------------------------------------------------------------------