%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV181^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 08:39:07 AM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 2
% Syntax : Number of formulae : 35 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 174 ( 82 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 286 ( 39 ~; 16 |; 23 &; 183 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 81 ( 81 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 3 con; 0-4 aty)
% ( 0 !!; 15 ??; 0 @@+; 0 @@-)
% Number of variables : 77 ( 38 ^; 36 !; 3 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cD_FOR_X5309: ( ( $i > $o ) > $i ) > $i > $o ).
thf(func_def_2,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
vAND: $o > $o > $o ).
thf(func_def_4,type,
vNOT: $o > $o ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_12,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_13,type,
sK1: $i > $o ).
thf(func_def_14,type,
sK2: $i > $i > $o ).
thf(func_def_15,type,
sK3: $i > $o ).
thf(func_def_17,type,
sK5: $i > $o ).
thf(f1,axiom,
( cD_FOR_X5309
= ( ^ [X0: ( $i > $o ) > $i,X1: $i] :
? [X2: $i > $o] :
( ( X1
= ( X0 @ X2 ) )
& ~ ( X2 @ ( X0 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cD_FOR_X5309_def) ).
thf(f2,conjecture,
! [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
=> ~ ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM143C_pme) ).
thf(f3,negated_conjecture,
~ ! [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
=> ~ ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( cD_FOR_X5309
= ( ^ [X0: ( $i > $o ) > $i,X1: $i] :
? [X2: $i > $o] :
( ( X1
= ( X0 @ X2 ) )
& ~ ( X2 @ ( X0 @ X2 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( cD_FOR_X5309
= ( ^ [Y0: ( $i > $o ) > $i,Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( Y0 @ Y2 ) )
& ( ( Y0 @ Y2 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ! [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
=> ~ ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ! [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X2 )
= ( X0 @ X1 ) )
=> ( X1 = X2 ) )
=> ( ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) )
!= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
~ ! [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X2 )
= ( X0 @ X1 ) )
=> ( X1 = X2 ) )
=> ( ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) )
!= $true ) ),
inference(flattening,[],[f7]) ).
thf(f9,plain,
? [X0: ( $i > $o ) > $i] :
( ( ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) )
= $true )
& ! [X1: $i > $o,X2: $i > $o] :
( ( X1 = X2 )
| ( ( X0 @ X2 )
!= ( X0 @ X1 ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f10,plain,
( ( $true
= ( cD_FOR_X5309 @ sK0 @ ( sK0 @ ( cD_FOR_X5309 @ sK0 ) ) ) )
& ! [X1: $i > $o,X2: $i > $o] :
( ( X1 = X2 )
| ( ( sK0 @ X2 )
!= ( sK0 @ X1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f9]) ).
thf(f11,plain,
( cD_FOR_X5309
= ( ^ [Y0: ( $i > $o ) > $i,Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( Y0 @ Y2 ) )
& ( ( Y0 @ Y2 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f12,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( ( sK0 @ X2 )
!= ( sK0 @ X1 ) )
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f13,plain,
( $true
= ( cD_FOR_X5309 @ sK0 @ ( sK0 @ ( cD_FOR_X5309 @ sK0 ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f16,plain,
( $true
= ( ^ [Y0: ( $i > $o ) > $i,Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( Y0 @ Y2 ) )
& ( ( Y0 @ Y2 )
= Y1 ) ) )
@ sK0
@ ( sK0
@ ( ^ [Y0: ( $i > $o ) > $i,Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( Y0 @ Y2 ) )
& ( ( Y0 @ Y2 )
= Y1 ) ) )
@ sK0 ) ) ) ),
inference(definition_unfolding,[],[f13,f11,f11]) ).
thf(f17,plain,
( $true
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f16]) ).
thf(f18,plain,
( $true
= ( ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( $true
= ( ~ ( sK1 @ ( sK0 @ sK1 ) )
& ( ( sK0 @ sK1 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
( $true
= ( ( sK0 @ sK1 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( $true
= ( ~ ( sK1 @ ( sK0 @ sK1 ) ) ) ),
inference(and_proxy_clausification,[],[f19]) ).
thf(f22,plain,
( $false
= ( sK1 @ ( sK0 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) )
= ( sK0 @ sK1 ) ),
inference(equality_proxy_clausification,[],[f20]) ).
thf(f34,plain,
! [X0: $i > $o] :
( ( ( sK0 @ sK1 )
!= ( sK0 @ X0 ) )
| ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) )
= X0 ) ),
inference(constrained_superposition,[],[f12,f23]) ).
thf(f36,plain,
( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) )
= sK1 ),
inference(equality_resolution,[],[f34]) ).
thf(f37,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) )
@ X1 )
= ( sK1 @ X1 ) ),
inference(argument_congruence,[],[f36]) ).
thf(f39,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) )
@ X1 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f37]) ).
thf(f40,plain,
! [X1: $i] :
( ( $false
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= X1 ) ) ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f41,plain,
! [X2: $i > $o,X1: $i] :
( ( $false
= ( ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= X1 ) )
@ X2 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X2: $i > $o,X1: $i] :
( ( $false
= ( ~ ( X2 @ ( sK0 @ X2 ) )
& ( ( sK0 @ X2 )
= X1 ) ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f43,plain,
! [X2: $i > $o,X1: $i] :
( ( $false
= ( ( sK0 @ X2 )
= X1 ) )
| ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( ~ ( X2 @ ( sK0 @ X2 ) ) ) ) ),
inference(and_proxy_clausification,[],[f42]) ).
thf(f44,plain,
! [X2: $i > $o,X1: $i] :
( ( ( sK0 @ X2 )
!= X1 )
| ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( ~ ( X2 @ ( sK0 @ X2 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X2: $i > $o,X1: $i] :
( ( ( sK0 @ X2 )
!= X1 )
| ( $true
= ( sK1 @ X1 ) )
| ( $true
= ( X2 @ ( sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f44]) ).
thf(f54,plain,
! [X0: $i > $o] :
( ( $true
= ( sK1 @ ( sK0 @ X0 ) ) )
| ( $true
= ( X0 @ ( sK0 @ X0 ) ) ) ),
inference(equality_resolution,[],[f45]) ).
thf(f84,plain,
( ( $true = $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f54,f22]) ).
thf(f120,plain,
$true = $false,
inference(duplicate_literal_removal,[],[f84]) ).
thf(f121,plain,
$false,
inference(trivial_inequality_removal,[],[f120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV181^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n014.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 15:18:46 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 0.09/0.24 % (2794631)Will run a generic schedule for satisfiability detection.
% 0.09/0.24 % (2794640)% WARNING: option uhcvi not known.
% 0.09/0.24 % (2794640)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3060724694:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.09/0.24 % (2794640)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.24 % (2794640)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.24 % (2794640) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2794631-2794640"...
% 0.09/0.24 % (2794640)...printing done.
% 0.09/0.24 % (2794640)Refutation found. Thanks to Tanya!
% 0.09/0.24 % SZS status Theorem for theBenchmark
% 0.09/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.24 % (2794640)------------------------------
% 0.09/0.24 % (2794640)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.24 % (2794640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.24 % (2794640)CaDiCaL version: 2.1.3
% 0.09/0.24 % (2794640)Termination reason: Refutation
% 0.09/0.24 % (2794640)Time elapsed: 0.004 s
% 0.09/0.24 % (2794640)Peak memory usage: 12 MB
% 0.09/0.24 % (2794640)Instructions burned: 8 (million)
% 0.09/0.24 % (2794631)Success in time 0.02 s
% 0.09/0.24 % Vampire exiting
%------------------------------------------------------------------------------