%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO372^5 : 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 : n020.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 08:47:32 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 9 unt; 0 typ; 4 def)
% Number of atoms : 158 ( 35 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 125 ( 35 ~; 32 |; 1 &; 46 @)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
gtype: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
g: b > $o ).
thf(func_def_1,type,
h: ( b > $o ) > gtype ).
thf(func_def_2,type,
f: b > $o ).
thf(func_def_6,type,
sK0: b ).
thf(f1,conjecture,
( ! [X0: b] :
( ( g @ X0 )
<=> ( f @ X0 ) )
=> ( ( h @ f )
= ( h @ g ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEXT_SET2) ).
thf(f2,negated_conjecture,
~ ( ! [X0: b] :
( ( g @ X0 )
<=> ( f @ X0 ) )
=> ( ( h @ f )
= ( h @ g ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: b] :
( ( g @ X0 )
<=> ( f @ X0 ) )
=> ( ( h @ f )
= ( h @ g ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) )
=> ( ( h @ f )
= ( h @ g ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) )
& ( ( h @ f )
!= ( h @ g ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( h @ f )
!= ( h @ g ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f7,plain,
! [X0: b] :
( ( f @ X0 )
= ( g @ X0 ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f10,plain,
! [X0: b] :
( ( ( f @ X0 )
= $true )
| ( ( g @ X0 )
= $false ) ),
inference(iff_proxy_clausification,[],[f7]) ).
thf(f11,plain,
! [X0: b] :
( ( ( f @ X0 )
= $false )
| ( ( g @ X0 )
= $true ) ),
inference(iff_proxy_clausification,[],[f7]) ).
thf(f12,plain,
f != g,
inference(equality_resolution,[],[f6]) ).
thf(f13,plain,
( ( f @ sK0 )
!= ( g @ sK0 ) ),
inference(negative_extensionality,[],[f12]) ).
thf(f14,plain,
( ( ( g @ sK0 )
= $true )
| ( ( f @ sK0 )
= $true ) ),
inference(xor_proxy_clausification,[],[f13]) ).
thf(f15,plain,
( ( $false
= ( f @ sK0 ) )
| ( $false
= ( g @ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f13]) ).
thf(f17,definition,
( spl1_1
<=> ( $false
= ( g @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f18,plain,
( ( $false
= ( g @ sK0 ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f17]) ).
thf(f20,definition,
( spl1_2
<=> ( $false
= ( f @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f21,plain,
( ( $false
= ( f @ sK0 ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f20]) ).
thf(f22,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f15,f20,f17]) ).
thf(f24,definition,
( spl1_3
<=> ( ( g @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f25,plain,
( ( ( g @ sK0 )
= $true )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f27,definition,
( spl1_4
<=> ( ( f @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
thf(f28,plain,
( ( ( f @ sK0 )
= $true )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f29,plain,
( spl1_3
| spl1_4 ),
inference(avatar_split_clause,[],[f14,f27,f24]) ).
thf(f35,plain,
( ( $false
= ( g @ sK0 ) )
| ( $false = $true )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f10,f21]) ).
thf(f36,plain,
( ( $false
= ( g @ sK0 ) )
| ~ spl1_2 ),
inference(trivial_inequality_removal,[],[f35]) ).
thf(f38,plain,
( spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f36,f20,f17]) ).
thf(f39,plain,
( ( $false = $true )
| ~ spl1_1
| ~ spl1_3 ),
inference(backward_demodulation,[],[f25,f18]) ).
thf(f40,plain,
( $false
| ~ spl1_1
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f39]) ).
thf(f41,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f40]) ).
thf(f46,plain,
( ( ( g @ sK0 )
= $true )
| ( $false = $true )
| ~ spl1_4 ),
inference(constrained_superposition,[],[f11,f28]) ).
thf(f48,plain,
( ( ( g @ sK0 )
= $true )
| ~ spl1_4 ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f52,plain,
( ( $false = $true )
| ~ spl1_1
| ~ spl1_4 ),
inference(forward_demodulation,[],[f48,f18]) ).
thf(f53,plain,
( $false
| ~ spl1_1
| ~ spl1_4 ),
inference(trivial_inequality_removal,[],[f52]) ).
thf(f54,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f53]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s2,plain,
( spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f29]) ).
cnf(s3,plain,
( spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f38]) ).
cnf(s5,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(sat_conversion,[],[f41]) ).
cnf(s8,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(sat_conversion,[],[f54]) ).
cnf(s9,plain,
spl1_1,
inference(rat,[],[s1,s3]) ).
cnf(s10,plain,
~ spl1_4,
inference(rat,[],[s8,s9]) ).
cnf(s11,plain,
~ spl1_3,
inference(rat,[],[s5,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s2,s10,s11]) ).
thf(f55,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO372^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n020.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:50:20 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 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
% 0.19/0.27 % (1298019)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.27 % (1298039)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2543159384:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.27 % (1298039) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1298019-1298039"...
% 0.19/0.27 % (1298039)...printing done.
% 0.19/0.27 % (1298039)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (1298039)------------------------------
% 0.19/0.27 % (1298039)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (1298039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (1298039)CaDiCaL version: 2.1.3
% 0.19/0.27 % (1298039)Termination reason: Refutation
% 0.19/0.27 % (1298039)Time elapsed: 0.002 s
% 0.19/0.27 % (1298039)Peak memory usage: 13 MB
% 0.19/0.27 % (1298039)Instructions burned: 2 (million)
% 0.19/0.27 % (1298019)Success in time 0.037 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------