%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET173^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 08:23:36 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 17 unt; 0 typ; 2 def)
% Number of atoms : 118 ( 31 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 121 ( 18 ~; 30 |; 12 &; 59 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 20 ( 0 sgn 8 !; 2 ?; 20 :)
% 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,
vOR: $o > $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_9,type,
sK2: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( ( X1 @ X2 )
| ( X0 @ X2 ) )
& ( X0 @ X2 ) ) )
= X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_68_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( ( X1 @ X2 )
| ( X0 @ X2 ) )
& ( X0 @ X2 ) ) )
= X0 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [X2: a] :
( ( ( X1 @ X2 )
| ( X0 @ X2 ) )
& ( X0 @ X2 ) ) )
= X0 ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( ( X0 @ Y0 )
| ( X1 @ Y0 ) ) ) )
= X0 ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( ( X0 @ Y0 )
| ( X1 @ Y0 ) ) ) )
!= X0 ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( sK0
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f5]) ).
thf(f7,plain,
( sK0
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f10,plain,
( ( sK0 @ sK2 )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) )
@ sK2 ) ),
inference(negative_extensionality,[],[f7]) ).
thf(f11,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f10]) ).
thf(f12,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f10]) ).
thf(f13,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( ( sK0 @ sK2 )
& ( ( sK0 @ sK2 )
| ( sK1 @ sK2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f12]) ).
thf(f14,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( ( sK0 @ sK2 )
| ( sK1 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f13]) ).
thf(f16,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f14]) ).
thf(f17,plain,
( $false
= ( sK0 @ sK2 ) ),
inference(duplicate_literal_removal,[],[f16]) ).
thf(f19,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( ( sK0 @ sK2 )
& ( ( sK0 @ sK2 )
| ( sK1 @ sK2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f11]) ).
thf(f21,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f19]) ).
thf(f22,plain,
( $true
= ( sK0 @ sK2 ) ),
inference(duplicate_literal_removal,[],[f21]) ).
thf(f30,definition,
( spl3_2
<=> ( $false
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f32,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f39,definition,
( spl3_4
<=> ( $true
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f41,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f50,plain,
spl3_2,
inference(avatar_split_clause,[],[f17,f30]) ).
thf(f51,plain,
spl3_4,
inference(avatar_split_clause,[],[f22,f39]) ).
thf(f54,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_4 ),
inference(forward_demodulation,[],[f41,f32]) ).
thf(f55,plain,
( $false
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f54]) ).
thf(f56,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f55]) ).
cnf(s3,plain,
spl3_2,
inference(sat_conversion,[],[f50]) ).
cnf(s4,plain,
spl3_4,
inference(sat_conversion,[],[f51]) ).
cnf(s5,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(sat_conversion,[],[f56]) ).
cnf(s6,plain,
~ spl3_2,
inference(rat,[],[s5,s4]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s3,s6]) ).
thf(f57,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET173^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n015.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 13:40:33 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.26 % (3532119)Will run a generic schedule for satisfiability detection.
% 0.08/0.26 % (3532125)% WARNING: option uhcvi not known.
% 0.08/0.26 % (3532125)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=647410407:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.26 % (3532125)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.26 % (3532125)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.26 % (3532125) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3532119-3532125"...
% 0.08/0.26 % (3532125)...printing done.
% 0.08/0.26 % (3532125)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.26 % (3532125)------------------------------
% 0.08/0.26 % (3532125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (3532125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (3532125)CaDiCaL version: 2.1.3
% 0.08/0.26 % (3532125)Termination reason: Refutation
% 0.08/0.26 % (3532125)Time elapsed: 0.002 s
% 0.08/0.26 % (3532125)Peak memory usage: 13 MB
% 0.08/0.26 % (3532125)Instructions burned: 2 (million)
% 0.08/0.26 % (3532119)Success in time 0.037 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------