%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV177^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 08:37:58 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 12 unt; 0 typ; 2 def)
% Number of atoms : 134 ( 52 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 198 ( 40 ~; 25 |; 16 &; 102 @)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 5 con; 0-4 aty)
% ( 0 !!; 9 ??; 0 @@+; 0 @@-)
% Number of variables : 47 ( 0 sgn 21 !; 5 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
vAND: $o > $o > $o ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_6,type,
vNOT: $o > $o ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
sK0: $i > $o ).
thf(func_def_11,type,
sK1: ( $i > $o ) > $i ).
thf(func_def_13,type,
sK3: $i > $i > $o ).
thf(f1,conjecture,
! [X1: $i > $o,X0: ( $i > $o ) > $i] :
( ( X1
= ( ^ [X2: $i] :
? [X3: $i > $o] :
( ~ ( X3 @ ( X0 @ X3 ) )
& ( X2
= ( X0 @ X3 ) ) ) ) )
=> ( X1 @ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM144_pme) ).
thf(f2,negated_conjecture,
~ ! [X1: $i > $o,X0: ( $i > $o ) > $i] :
( ( X1
= ( ^ [X2: $i] :
? [X3: $i > $o] :
( ~ ( X3 @ ( X0 @ X3 ) )
& ( X2
= ( X0 @ X3 ) ) ) ) )
=> ( X1 @ ( X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: $i > $o,X1: ( $i > $o ) > $i] :
( ( X0
= ( ^ [X2: $i] :
? [X3: $i > $o] :
( ~ ( X3 @ ( X1 @ X3 ) )
& ( ( X1 @ X3 )
= X2 ) ) ) )
=> ( X0 @ ( X1 @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: $i > $o,X1: ( $i > $o ) > $i] :
( ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( X1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( X1 @ Y1 ) ) ) ) )
= X0 )
=> ( ( X0 @ ( X1 @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: $i > $o,X1: ( $i > $o ) > $i] :
( ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( X1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( X1 @ Y1 ) ) ) ) )
= X0 )
& ( ( X0 @ ( X1 @ X0 ) )
!= $true ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK1 @ Y1 ) ) ) ) )
= sK0 )
& ( $true
!= ( sK0 @ ( sK1 @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f5]) ).
thf(f7,plain,
( $true
!= ( sK0 @ ( sK1 @ sK0 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK1 @ Y1 ) ) ) ) )
= sK0 ),
inference(cnf_transformation,[],[f6]) ).
thf(f11,definition,
( spl2_1
<=> ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK1 @ Y1 ) ) ) ) )
= sK0 ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f13,plain,
( ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK1 @ Y1 ) ) ) ) )
= sK0 )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f11]) ).
thf(f14,plain,
spl2_1,
inference(avatar_split_clause,[],[f8,f11]) ).
thf(f16,definition,
( spl2_2
<=> ( $true
= ( sK0 @ ( sK1 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f19,plain,
~ spl2_2,
inference(avatar_split_clause,[],[f7,f16]) ).
thf(f20,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK1 @ Y1 ) ) ) )
@ X1 )
= ( sK0 @ X1 ) )
| ~ spl2_1 ),
inference(argument_congruence,[],[f13]) ).
thf(f22,plain,
( ! [X1: $i] :
( ( $true
= ( sK0 @ X1 ) )
| ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK1 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK1 @ Y1 ) ) ) )
@ X1 )
= $false ) )
| ~ spl2_1 ),
inference(iff_proxy_clausification,[],[f20]) ).
thf(f23,plain,
( ! [X1: $i] :
( ( $true
= ( sK0 @ X1 ) )
| ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( sK1 @ Y0 )
= X1 )
& ~ ( Y0 @ ( sK1 @ Y0 ) ) ) )
= $false ) )
| ~ spl2_1 ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
( ! [X2: $i > $o,X1: $i] :
( ( $true
= ( sK0 @ X1 ) )
| ( ( ^ [Y0: $i > $o] :
( ( ( sK1 @ Y0 )
= X1 )
& ~ ( Y0 @ ( sK1 @ Y0 ) ) )
@ X2 )
= $false ) )
| ~ spl2_1 ),
inference(pi_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ! [X2: $i > $o,X1: $i] :
( ( $true
= ( sK0 @ X1 ) )
| ( ( ( ( sK1 @ X2 )
= X1 )
& ~ ( X2 @ ( sK1 @ X2 ) ) )
= $false ) )
| ~ spl2_1 ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
( ! [X2: $i > $o,X1: $i] :
( ( $true
= ( sK0 @ X1 ) )
| ( ( ~ ( X2 @ ( sK1 @ X2 ) ) )
= $false )
| ( ( ( sK1 @ X2 )
= X1 )
= $false ) )
| ~ spl2_1 ),
inference(and_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( ! [X2: $i > $o,X1: $i] :
( ( ( X2 @ ( sK1 @ X2 ) )
= $true )
| ( ( ( sK1 @ X2 )
= X1 )
= $false )
| ( $true
= ( sK0 @ X1 ) ) )
| ~ spl2_1 ),
inference(not_proxy_clausification,[],[f26]) ).
thf(f28,plain,
( ! [X2: $i > $o,X1: $i] :
( ( ( X2 @ ( sK1 @ X2 ) )
= $true )
| ( ( sK1 @ X2 )
!= X1 )
| ( $true
= ( sK0 @ X1 ) ) )
| ~ spl2_1 ),
inference(equality_proxy_clausification,[],[f27]) ).
thf(f44,plain,
( ( $true
= ( sK0 @ ( sK1 @ sK0 ) ) )
| ( ( sK1 @ sK0 )
!= ( sK1 @ sK0 ) )
| ( $true != $true )
| ~ spl2_1 ),
inference(equality_factoring,[],[f28]) ).
thf(f49,plain,
( ( $true
= ( sK0 @ ( sK1 @ sK0 ) ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f44]) ).
thf(f53,plain,
( spl2_2
| ~ spl2_1 ),
inference(avatar_split_clause,[],[f49,f11,f16]) ).
cnf(s1,plain,
spl2_1,
inference(sat_conversion,[],[f14]) ).
cnf(s2,plain,
~ spl2_2,
inference(sat_conversion,[],[f19]) ).
cnf(s3,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f53]) ).
cnf(s4,plain,
~ spl2_1,
inference(rat,[],[s3,s2]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4]) ).
thf(f54,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV177^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 15:14:07 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.22/0.27 % (450401)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.27 % (450409)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2122716620:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.27 % (450409) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-450401-450409"...
% 0.22/0.27 % (450409)...printing done.
% 0.22/0.27 % (450409)Refutation found. Thanks to Tanya!
% 0.22/0.27 % SZS status Theorem for theBenchmark
% 0.22/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.27 % (450409)------------------------------
% 0.22/0.27 % (450409)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.27 % (450409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.27 % (450409)CaDiCaL version: 2.1.3
% 0.22/0.27 % (450409)Termination reason: Refutation
% 0.22/0.27 % (450409)Time elapsed: 0.002 s
% 0.22/0.27 % (450409)Peak memory usage: 13 MB
% 0.22/0.27 % (450409)Instructions burned: 4 (million)
% 0.22/0.27 % (450401)Success in time 0.027 s
% 0.22/0.27 % Vampire exiting
%------------------------------------------------------------------------------