%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV116^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 08:37:50 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 2
% Syntax : Number of formulae : 32 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 231 ( 52 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 278 ( 7 ~; 18 |; 22 &; 205 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 102 ( 102 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 5 con; 0-5 aty)
% ( 9 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 67 ( 32 ^; 35 !; 0 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cS: ( $i > $i > $o ) > $o ).
thf(func_def_3,type,
cSTRANGE_HO_ABBR: ( ( $i > $i > $o ) > $o ) > $i > $i > $o ).
thf(func_def_5,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
vIMP: $o > $o > $o ).
thf(func_def_7,type,
vAND: $o > $o > $o ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_16,type,
sK0: $i > ( ( $i > $i > $o ) > $o ) > $i > $i > $i > $o ).
thf(func_def_17,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,axiom,
( ( ^ [X0: ( $i > $i > $o ) > $o,X1: $i,X2: $i] :
! [X3: $i > $i > $o] :
( ( ( X0 @ X3 )
& ( X3 @ X1 @ X2 ) )
=> ( X3 @ X2 @ X1 ) ) )
= cSTRANGE_HO_ABBR ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cSTRANGE_HO_ABBR_def) ).
thf(f2,conjecture,
( ( ( cS @ ( cSTRANGE_HO_ABBR @ cS ) )
& ( cSTRANGE_HO_ABBR @ cS @ x @ y ) )
=> ( cSTRANGE_HO_ABBR @ cS @ y @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cSTRANGE_HO_EXAMPLE) ).
thf(f3,negated_conjecture,
~ ( ( ( cS @ ( cSTRANGE_HO_ABBR @ cS ) )
& ( cSTRANGE_HO_ABBR @ cS @ x @ y ) )
=> ( cSTRANGE_HO_ABBR @ cS @ y @ x ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( ( ^ [X0: ( $i > $i > $o ) > $o,X1: $i,X2: $i] :
! [X3: $i > $i > $o] :
( ( ( X0 @ X3 )
& ( X3 @ X1 @ X2 ) )
=> ( X3 @ X2 @ X1 ) ) )
= cSTRANGE_HO_ABBR ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( cSTRANGE_HO_ABBR
= ( ^ [Y0: ( $i > $i > $o ) > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( Y3 @ Y1 @ Y2 )
& ( Y0 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( ( ( cS @ ( cSTRANGE_HO_ABBR @ cS ) )
& ( cSTRANGE_HO_ABBR @ cS @ x @ y ) )
=> ( cSTRANGE_HO_ABBR @ cS @ y @ x ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( ( ( cSTRANGE_HO_ABBR @ cS @ x @ y )
= $true )
& ( ( cS @ ( cSTRANGE_HO_ABBR @ cS ) )
= $true ) )
=> ( ( cSTRANGE_HO_ABBR @ cS @ y @ x )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ( ( cSTRANGE_HO_ABBR @ cS @ y @ x )
!= $true )
& ( ( cSTRANGE_HO_ABBR @ cS @ x @ y )
= $true )
& ( ( cS @ ( cSTRANGE_HO_ABBR @ cS ) )
= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ( ( cSTRANGE_HO_ABBR @ cS @ x @ y )
= $true )
& ( ( cSTRANGE_HO_ABBR @ cS @ y @ x )
!= $true )
& ( ( cS @ ( cSTRANGE_HO_ABBR @ cS ) )
= $true ) ),
inference(flattening,[],[f8]) ).
thf(f10,plain,
( cSTRANGE_HO_ABBR
= ( ^ [Y0: ( $i > $i > $o ) > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( Y3 @ Y1 @ Y2 )
& ( Y0 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f11,plain,
( ( cS @ ( cSTRANGE_HO_ABBR @ cS ) )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( ( cSTRANGE_HO_ABBR @ cS @ y @ x )
!= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
( ( cSTRANGE_HO_ABBR @ cS @ x @ y )
= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,plain,
! [X1: ( $i > $i > $o ) > $o] :
( ( ^ [Y0: ( $i > $i > $o ) > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( Y3 @ Y1 @ Y2 )
& ( Y0 @ Y3 ) )
=> ( Y3 @ Y2 @ Y1 ) ) )
@ X1 )
= ( cSTRANGE_HO_ABBR @ X1 ) ),
inference(argument_congruence,[],[f10]) ).
thf(f16,plain,
! [X1: ( $i > $i > $o ) > $o] :
( ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ Y0 @ Y1 )
& ( X1 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) ) )
= ( cSTRANGE_HO_ABBR @ X1 ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f17,plain,
! [X2: $i,X1: ( $i > $i > $o ) > $o] :
( ( cSTRANGE_HO_ABBR @ X1 @ X2 )
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( ( Y2 @ Y0 @ Y1 )
& ( X1 @ Y2 ) )
=> ( Y2 @ Y1 @ Y0 ) ) )
@ X2 ) ),
inference(argument_congruence,[],[f16]) ).
thf(f18,plain,
! [X2: $i,X1: ( $i > $i > $o ) > $o] :
( ( cSTRANGE_HO_ABBR @ X1 @ X2 )
= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( Y1 @ X2 @ Y0 )
& ( X1 @ Y1 ) )
=> ( Y1 @ Y0 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
! [X2: $i,X3: $i,X1: ( $i > $i > $o ) > $o] :
( ( cSTRANGE_HO_ABBR @ X1 @ X2 @ X3 )
= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( Y1 @ X2 @ Y0 )
& ( X1 @ Y1 ) )
=> ( Y1 @ Y0 @ X2 ) ) )
@ X3 ) ),
inference(argument_congruence,[],[f18]) ).
thf(f21,plain,
! [X2: $i,X3: $i,X1: ( $i > $i > $o ) > $o] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( ( Y1 @ X2 @ Y0 )
& ( X1 @ Y1 ) )
=> ( Y1 @ Y0 @ X2 ) ) )
@ X3 ) )
| ( ( cSTRANGE_HO_ABBR @ X1 @ X2 @ X3 )
= $false ) ),
inference(iff_proxy_clausification,[],[f19]) ).
thf(f22,plain,
! [X2: $i,X3: $i,X1: ( $i > $i > $o ) > $o] :
( ( ( cSTRANGE_HO_ABBR @ X1 @ X2 @ X3 )
= $false )
| ( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( Y0 @ X2 @ X3 )
& ( X1 @ Y0 ) )
=> ( Y0 @ X3 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f23,plain,
! [X2: $i,X3: $i,X1: ( $i > $i > $o ) > $o,X4: $i > $i > $o] :
( ( ( cSTRANGE_HO_ABBR @ X1 @ X2 @ X3 )
= $false )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( ( ( Y0 @ X2 @ X3 )
& ( X1 @ Y0 ) )
=> ( Y0 @ X3 @ X2 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f24,plain,
! [X2: $i,X3: $i,X1: ( $i > $i > $o ) > $o,X4: $i > $i > $o] :
( ( $true
= ( ( ( X4 @ X2 @ X3 )
& ( X1 @ X4 ) )
=> ( X4 @ X3 @ X2 ) ) )
| ( ( cSTRANGE_HO_ABBR @ X1 @ X2 @ X3 )
= $false ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f25,plain,
! [X2: $i,X3: $i,X1: ( $i > $i > $o ) > $o,X4: $i > $i > $o] :
( ( ( X4 @ X3 @ X2 )
= $true )
| ( $false
= ( ( X4 @ X2 @ X3 )
& ( X1 @ X4 ) ) )
| ( ( cSTRANGE_HO_ABBR @ X1 @ X2 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f24]) ).
thf(f26,plain,
! [X2: $i,X3: $i,X1: ( $i > $i > $o ) > $o,X4: $i > $i > $o] :
( ( ( X1 @ X4 )
= $false )
| ( ( cSTRANGE_HO_ABBR @ X1 @ X2 @ X3 )
= $false )
| ( ( X4 @ X2 @ X3 )
= $false )
| ( ( X4 @ X3 @ X2 )
= $true ) ),
inference(and_proxy_clausification,[],[f25]) ).
thf(f47,plain,
! [X0: $i > $i > $o] :
( ( ( cS @ X0 )
= $false )
| ( ( X0 @ y @ x )
= $true )
| ( ( X0 @ x @ y )
= $false )
| ( $true = $false ) ),
inference(superposition,[],[f26,f13]) ).
thf(f65,plain,
! [X0: $i > $i > $o] :
( ( ( X0 @ y @ x )
= $true )
| ( ( X0 @ x @ y )
= $false )
| ( ( cS @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f47]) ).
thf(f110,plain,
( ( ( cS @ ( cSTRANGE_HO_ABBR @ cS ) )
= $false )
| ( ( cSTRANGE_HO_ABBR @ cS @ x @ y )
= $false )
| ( $true != $true ) ),
inference(superposition,[],[f12,f65]) ).
thf(f126,plain,
( ( ( cSTRANGE_HO_ABBR @ cS @ x @ y )
= $false )
| ( ( cS @ ( cSTRANGE_HO_ABBR @ cS ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f110]) ).
thf(f131,plain,
( ( $true = $false )
| ( ( cS @ ( cSTRANGE_HO_ABBR @ cS ) )
= $false ) ),
inference(forward_demodulation,[],[f126,f13]) ).
thf(f132,plain,
( ( cS @ ( cSTRANGE_HO_ABBR @ cS ) )
= $false ),
inference(trivial_inequality_removal,[],[f131]) ).
thf(f134,plain,
$true = $false,
inference(superposition,[],[f11,f132]) ).
thf(f135,plain,
$false,
inference(trivial_inequality_removal,[],[f134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV116^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n016.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 15:16:19 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 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
% 0.22/0.29 % (471154)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (471163)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1469237788:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.29 % (471163) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-471154-471163"...
% 0.22/0.29 % (471165)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.29 % (471165)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
% 0.22/0.29 % (471163)...printing done.
% 0.22/0.29 % (471163)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (471163)------------------------------
% 0.22/0.29 % (471163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (471163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (471163)CaDiCaL version: 2.1.3
% 0.22/0.29 % (471163)Termination reason: Refutation
% 0.22/0.29 % (471163)Time elapsed: 0.004 s
% 0.22/0.29 % (471163)Peak memory usage: 12 MB
% 0.22/0.29 % (471163)Instructions burned: 10 (million)
% 0.22/0.29 % (471154)Success in time 0.044 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------