%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET634^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:23:25 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 69 ( 22 unt; 0 typ; 6 def)
% Number of atoms : 342 ( 83 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 380 ( 82 ~; 64 |; 67 &; 161 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 35 ( 0 sgn 12 !; 3 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vAND: $o > $o > $o ).
thf(func_def_2,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_3,type,
vNOT: $o > $o ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_5,type,
sK0: a > $o ).
thf(func_def_6,type,
sK1: a > $o ).
thf(func_def_7,type,
sK2: a > $o ).
thf(func_def_10,type,
sK3: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( X0 @ X3 )
& ~ ( X2 @ X3 )
& ( X1 @ X3 ) ) )
= ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X0 @ X3 )
& ~ ( X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_116_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( X0 @ X3 )
& ~ ( X2 @ X3 )
& ( X1 @ X3 ) ) )
= ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X0 @ X3 )
& ~ ( X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( X0 @ X3 )
& ~ ( X2 @ X3 )
& ( X1 @ X3 ) ) )
= ( ^ [X4: a] :
( ( X1 @ X4 )
& ( X0 @ X4 )
& ~ ( X2 @ X4 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ~ ( X2 @ Y0 )
& ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ~ ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ~ ( X2 @ Y0 )
& ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ~ ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f10,plain,
( ( ^ [Y0: a] :
( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK3 )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f7]) ).
thf(f11,plain,
( ( ( ^ [Y0: a] :
( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK3 )
= $true )
| ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
@ sK3 )
= $true ) ),
inference(xor_proxy_clausification,[],[f10]) ).
thf(f12,plain,
( ( ( ^ [Y0: a] :
( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK3 )
= $false )
| ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
@ sK3 )
= $false ) ),
inference(xor_proxy_clausification,[],[f10]) ).
thf(f13,plain,
( ( $false
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $false
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f12]) ).
thf(f14,plain,
( ( $false
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $false
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f13]) ).
thf(f15,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( $false
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( ( sK0 @ sK3 )
= $false )
| ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f14]) ).
thf(f16,plain,
( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f15]) ).
thf(f17,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( ( ~ ( sK2 @ sK3 ) )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK0 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( ( sK1 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(duplicate_literal_removal,[],[f18]) ).
thf(f20,plain,
( ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f11]) ).
thf(f21,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f20]) ).
thf(f23,plain,
( ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f22]) ).
thf(f25,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f24]) ).
thf(f30,plain,
( ( sK1 @ sK3 )
= $true ),
inference(duplicate_literal_removal,[],[f25]) ).
thf(f31,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f23]) ).
thf(f33,plain,
( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f31]) ).
thf(f35,plain,
( ( ( ~ ( sK2 @ sK3 ) )
= $true )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(and_proxy_clausification,[],[f33]) ).
thf(f36,plain,
( ( ( sK2 @ sK3 )
= $false )
| ( ( sK2 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f35]) ).
thf(f37,plain,
( ( sK2 @ sK3 )
= $false ),
inference(duplicate_literal_removal,[],[f36]) ).
thf(f39,plain,
( ( ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f21]) ).
thf(f40,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f39]) ).
thf(f43,plain,
( ( sK0 @ sK3 )
= $true ),
inference(duplicate_literal_removal,[],[f40]) ).
thf(f45,definition,
( spl4_1
<=> ( ( sK2 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f47,plain,
( ( ( sK2 @ sK3 )
= $true )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f45]) ).
thf(f49,definition,
( spl4_2
<=> ( ( sK0 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f51,plain,
( ( ( sK0 @ sK3 )
= $false )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f49]) ).
thf(f53,definition,
( spl4_3
<=> ( ( sK1 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f55,plain,
( ( ( sK1 @ sK3 )
= $false )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f53]) ).
thf(f56,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f19,f53,f49,f45]) ).
thf(f58,definition,
( spl4_4
<=> ( ( sK1 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f60,plain,
( ( ( sK1 @ sK3 )
= $true )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f58]) ).
thf(f62,definition,
( spl4_5
<=> ( ( sK2 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f64,plain,
( ( ( sK2 @ sK3 )
= $false )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f67,definition,
( spl4_6
<=> ( ( sK0 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f69,plain,
( ( ( sK0 @ sK3 )
= $true )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f67]) ).
thf(f71,plain,
spl4_4,
inference(avatar_split_clause,[],[f30,f58]) ).
thf(f72,plain,
spl4_5,
inference(avatar_split_clause,[],[f37,f62]) ).
thf(f76,plain,
spl4_6,
inference(avatar_split_clause,[],[f43,f67]) ).
thf(f78,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_6 ),
inference(forward_demodulation,[],[f69,f51]) ).
thf(f79,plain,
( $false
| ~ spl4_2
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f78]) ).
thf(f80,plain,
( ~ spl4_2
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f79]) ).
thf(f81,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_4 ),
inference(forward_demodulation,[],[f55,f60]) ).
thf(f82,plain,
( $false
| ~ spl4_3
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f81]) ).
thf(f83,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f82]) ).
thf(f85,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_5 ),
inference(forward_demodulation,[],[f47,f64]) ).
thf(f86,plain,
( $false
| ~ spl4_1
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f85]) ).
thf(f87,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f86]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f56]) ).
cnf(s4,plain,
spl4_4,
inference(sat_conversion,[],[f71]) ).
cnf(s5,plain,
spl4_5,
inference(sat_conversion,[],[f72]) ).
cnf(s9,plain,
spl4_6,
inference(sat_conversion,[],[f76]) ).
cnf(s11,plain,
( ~ spl4_2
| ~ spl4_6 ),
inference(sat_conversion,[],[f80]) ).
cnf(s12,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f83]) ).
cnf(s13,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(sat_conversion,[],[f87]) ).
cnf(s14,plain,
~ spl4_2,
inference(rat,[],[s11,s9]) ).
cnf(s15,plain,
~ spl4_1,
inference(rat,[],[s13,s5]) ).
cnf(s16,plain,
~ spl4_3,
inference(rat,[],[s12,s4]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s1,s16,s14,s15]) ).
thf(f89,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET634^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n019.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 13:40:18 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.30 % (778424)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (778430)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1655870702:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (778430) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-778424-778430"...
% 0.21/0.30 % (778430)...printing done.
% 0.21/0.30 % (778430)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (778430)------------------------------
% 0.21/0.30 % (778430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (778430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (778430)CaDiCaL version: 2.1.3
% 0.21/0.30 % (778430)Termination reason: Refutation
% 0.21/0.30 % (778430)Time elapsed: 0.002 s
% 0.21/0.30 % (778430)Peak memory usage: 13 MB
% 0.21/0.30 % (778430)Instructions burned: 4 (million)
% 0.21/0.30 % (778424)Success in time 0.044 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------