%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN998^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 08:42:06 AM UTC 2026
% Result : Theorem 0.25s 0.32s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 62 ( 15 equ; 0 cnn)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 63 ( 8 ~; 0 |; 0 &; 43 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 11 usr; 4 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 22 ( 15 ^; 6 !; 1 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
leibeq: $i > $i > $o ).
thf(func_def_2,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
vIMP: $o > $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
vNOT: $o > $o ).
thf(func_def_12,type,
sK1: $i > $o ).
thf(f1,axiom,
( leibeq
= ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leibeq) ).
thf(f2,conjecture,
! [X0: $i] : ( leibeq @ X0 @ X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f3,negated_conjecture,
~ ! [X0: $i] : ( leibeq @ X0 @ X0 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( leibeq
= ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( leibeq
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ! [X0: $i] : ( leibeq @ X0 @ X0 ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ! [X0: $i] :
( ( leibeq @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X0: $i] :
( ( leibeq @ X0 @ X0 )
!= $true ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( $true
!= ( leibeq @ sK0 @ sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f8]) ).
thf(f10,plain,
( leibeq
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f11,plain,
( $true
!= ( leibeq @ sK0 @ sK0 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f14,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK0
@ sK0 ) ),
inference(definition_unfolding,[],[f11,f10]) ).
thf(f15,plain,
( $true
!= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f14]) ).
thf(f16,plain,
( $false
= ( ^ [Y0: $i > $o] :
( ( Y0 @ sK0 )
=> ( Y0 @ sK0 ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f15]) ).
thf(f17,plain,
( $false
= ( ( sK1 @ sK0 )
=> ( sK1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f18,plain,
( $false
= ( sK1 @ sK0 ) ),
inference(imp_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( $true
= ( sK1 @ sK0 ) ),
inference(imp_proxy_clausification,[],[f17]) ).
thf(f21,plain,
$true = $false,
inference(constrained_superposition,[],[f18,f19]) ).
thf(f22,plain,
$false,
inference(trivial_inequality_removal,[],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN998^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 % Computer : n016.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 16:25:19 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.26 Running first-order model finding
% 0.09/0.26 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
% 0.25/0.32 % (552556)Will run a generic schedule for satisfiability detection.
% 0.25/0.32 % (552561)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2818730257_2999 on theBenchmark for (2999ds/0Mi)
% 0.25/0.32 % Exception at run slice level
% 0.25/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.25/0.32 % (552562)% WARNING: option uhcvi not known.
% 0.25/0.32 % (552564)dis+10_1_sil=32000:sp=arity:random_seed=1354833017:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.25/0.32 % (552562)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=517812677:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.25/0.32 % (552566)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2890164912:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.25/0.32 % (552565)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2687259625:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.25/0.32 % (552563)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1026632897:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.25/0.32 % (552562)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.25/0.32 % (552565)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.25/0.32 % (552567)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=355454336:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.25/0.32 % (552562)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.25/0.32 % (552562) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-552556-552562"...
% 0.25/0.32 % (552566) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-552556-552566"...
% 0.25/0.32 % (552565) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-552556-552565"...
% 0.25/0.32 % (552564) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-552556-552564"...
% 0.25/0.32 % (552563) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-552556-552563"...
% 0.25/0.32 % (552567) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-552556-552567"...
% 0.25/0.32 % (552564)...printing done.
% 0.25/0.32 % (552562)...printing done.
% 0.25/0.32 % (552565)...printing done.
% 0.25/0.32 % (552566)...printing done.
% 0.25/0.32 % (552563)...printing done.
% 0.25/0.32 % (552567)...printing done.
% 0.25/0.32 % (552565)Refutation found. Thanks to Tanya!
% 0.25/0.32 % SZS status Theorem for theBenchmark
% 0.25/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.32 % (552565)------------------------------
% 0.25/0.32 % (552565)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.32 % (552565)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.32 % (552565)CaDiCaL version: 2.1.3
% 0.25/0.32 % (552565)Termination reason: Refutation
% 0.25/0.32 % (552565)Time elapsed: 0.003 s
% 0.25/0.32 % (552565)Peak memory usage: 12 MB
% 0.25/0.32 % (552565)Instructions burned: 1 (million)
% 0.25/0.32 % (552556)Success in time 0.039 s
% 0.25/0.32 % Vampire exiting
%------------------------------------------------------------------------------