%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO547^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 08:50:24 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 97 ( 40 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 156 ( 46 ~; 11 |; 2 &; 89 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 3 con; 0-4 aty)
% Number of variables : 63 ( 28 ^; 25 !; 10 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_2,type,
epscomp: ( $i > $o ) > $i ).
thf(func_def_5,type,
vNOT: $o > $o ).
thf(func_def_6,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_9,type,
sK0: $i > $o ).
thf(func_def_11,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_13,type,
sK3: ( $i > $i > $o ) > $i > $i ).
thf(func_def_14,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK4: ( $i > $i > $o ) > $i > $i ).
thf(func_def_16,type,
sK5: $i > $i ).
thf(f1,axiom,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choiceax) ).
thf(f2,axiom,
( epscomp
= ( ^ [X0: $i > $o] :
( eps
@ ^ [X1: $i] :
~ ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',epscompd) ).
thf(f3,conjecture,
! [X0: $i > $o] :
( ? [X1: $i] :
~ ( X0 @ X1 )
=> ~ ( X0 @ ( epscomp @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choicecomp) ).
thf(f4,negated_conjecture,
~ ! [X0: $i > $o] :
( ? [X1: $i] :
~ ( X0 @ X1 )
=> ~ ( X0 @ ( epscomp @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( epscomp
= ( ^ [X0: $i > $o] :
( eps
@ ^ [X1: $i] :
~ ( X0 @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( epscomp
= ( ^ [Y0: $i > $o] :
( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ! [X0: $i > $o] :
( ? [X1: $i] :
~ ( X0 @ X1 )
=> ~ ( X0 @ ( epscomp @ X0 ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
!= $true )
=> ( ( X0 @ ( epscomp @ X0 ) )
!= $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
~ ! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
!= $true )
=> ( ( X0 @ ( epscomp @ X0 ) )
!= $true ) ),
inference(flattening,[],[f10]) ).
thf(f12,plain,
! [X0: $i > $o] :
( ( ( X0 @ ( eps @ X0 ) )
= $true )
| ! [X1: $i] :
( ( X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f13,plain,
? [X0: $i > $o] :
( ( ( X0 @ ( epscomp @ X0 ) )
= $true )
& ? [X1: $i] :
( ( X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f14,plain,
( ( $true
= ( sK0 @ ( epscomp @ sK0 ) ) )
& ( $true
!= ( sK0 @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f13]) ).
thf(f15,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( eps @ X0 ) )
= $true )
| ( ( X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f16,plain,
( epscomp
= ( ^ [Y0: $i > $o] :
( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f17,plain,
( $true
!= ( sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f18,plain,
( $true
= ( sK0 @ ( epscomp @ sK0 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f21,plain,
( $true
= ( sK0
@ ( ^ [Y0: $i > $o] :
( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f18,f16]) ).
thf(f22,plain,
( $true
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f41,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
~ ( X2 @ Y0 )
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) ) )
| ( $true
!= ( ^ [Y0: $i] :
~ ( X2 @ Y0 )
@ X1 ) ) ),
inference(primitive_instantiation,[],[f15]) ).
thf(f75,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( ~ ( X2
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) ) ) )
| ( $true
!= ( ~ ( X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f76,plain,
! [X2: $i > $o,X1: $i] :
( ( $false
= ( X2
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) ) )
| ( $true
!= ( ~ ( X2 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f75]) ).
thf(f77,plain,
! [X2: $i > $o,X1: $i] :
( ( $false
= ( X2
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) ) )
| ( $true
= ( X2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f76]) ).
thf(f320,plain,
! [X0: $i] :
( ( $true != $true )
| ( $false
= ( ^ [Y0: $i] :
( sK0
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ ( eps
@ ^ [Y0: $i] :
~ ( ^ [Y1: $i] :
( sK0
@ ( ^ [Y2: $i] : Y2
@ Y1 ) )
@ Y0 ) ) ) )
| ( sK1 != X0 ) ),
inference(constrained_superposition,[],[f17,f77]) ).
thf(f344,plain,
! [X0: $i] :
( ( $false
= ( ^ [Y0: $i] :
( sK0
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ ( eps
@ ^ [Y0: $i] :
~ ( ^ [Y1: $i] :
( sK0
@ ( ^ [Y2: $i] : Y2
@ Y1 ) )
@ Y0 ) ) ) )
| ( sK1 != X0 ) ),
inference(trivial_inequality_removal,[],[f320]) ).
thf(f345,plain,
! [X0: $i] :
( ( $false
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) ) ) )
| ( sK1 != X0 ) ),
inference(beta-eta_normalization,[],[f344]) ).
thf(f442,plain,
! [X0: $i] :
( ( $true = $false )
| ( sK1 != X0 ) ),
inference(forward_demodulation,[],[f345,f22]) ).
thf(f443,plain,
! [X0: $i] : ( sK1 != X0 ),
inference(trivial_inequality_removal,[],[f442]) ).
thf(f463,plain,
$false,
inference(equality_resolution,[],[f443]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO547^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n009.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 17:14:45 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.08/0.25 % (97701)Will run a generic schedule for satisfiability detection.
% 0.08/0.25 % (97710)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=847890207:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.25 % (97710)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.25 % (97707)% WARNING: option uhcvi not known.
% 0.08/0.25 % (97709)dis+10_1_sil=32000:sp=arity:random_seed=3718825662:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.25 % (97707)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2412319452:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.25 % (97706)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3511847658_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.25 % (97708)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1852605648:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.25 % (97707)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.25 % (97707)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.25 % Exception at run slice level
% 0.08/0.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.25 % (97710) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-97701-97710"...
% 0.08/0.25 % (97710)...printing done.
% 0.08/0.25 % (97710)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.25 % (97710)------------------------------
% 0.08/0.25 % (97710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (97710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (97710)CaDiCaL version: 2.1.3
% 0.08/0.25 % (97710)Termination reason: Refutation
% 0.08/0.25 % (97710)Time elapsed: 0.009 s
% 0.08/0.25 % (97710)Peak memory usage: 12 MB
% 0.08/0.25 % (97710)Instructions burned: 31 (million)
% 0.08/0.25 % (97701)Success in time 0.039 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------