%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET144^5 : 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 : 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 08:23:35 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 7
% Syntax : Number of formulae : 70 ( 15 unt; 0 typ; 6 def)
% Number of atoms : 355 ( 88 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 362 ( 43 ~; 101 |; 34 &; 170 @)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 42 ( 0 sgn 19 !; 3 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
vOR: $o > $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vAND: $o > $o > $o ).
thf(func_def_6,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_7,type,
sK0: a > $o ).
thf(func_def_8,type,
sK1: a > $o ).
thf(func_def_9,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 ) )
=> ( ( ^ [X4: a] :
( ( ( X2 @ X4 )
& ( X1 @ X4 ) )
| ( X0 @ X4 ) ) )
= ( ^ [X3: a] :
( ( X2 @ X3 )
& ( ( X1 @ X3 )
| ( X0 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_44_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) )
=> ( ( ^ [X4: a] :
( ( ( X2 @ X4 )
& ( X1 @ X4 ) )
| ( X0 @ X4 ) ) )
= ( ^ [X3: a] :
( ( X2 @ X3 )
& ( ( X1 @ X3 )
| ( X0 @ 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 ) )
=> ( ( ^ [X4: a] :
( ( ( X2 @ X4 )
& ( X1 @ X4 ) )
| ( X0 @ X4 ) ) )
= ( ^ [X5: a] :
( ( X2 @ X5 )
& ( ( X1 @ X5 )
| ( X0 @ X5 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
=> ( ( X2 @ X3 )
= $true ) )
=> ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
| ( X1 @ Y0 ) )
& ( X2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ( X1 @ Y0 )
& ( X2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
| ( X1 @ Y0 ) )
& ( X2 @ Y0 ) ) ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK2 @ Y0 ) ) ) )
& ! [X3: a] :
( ( $true
= ( sK2 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f5]) ).
thf(f7,plain,
! [X3: a] :
( ( $true
!= ( sK0 @ X3 ) )
| ( $true
= ( sK2 @ X3 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK2 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f20,plain,
( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ sK3 )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK2 @ Y0 ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f8]) ).
thf(f21,plain,
( ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK2 @ Y0 ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK2 @ Y0 ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f20]) ).
thf(f23,plain,
( ( $false
= ( ( sK0 @ sK3 )
| ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK2 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
( ( $false
= ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f23]) ).
thf(f26,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f25]) ).
thf(f28,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f26]) ).
thf(f29,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f28]) ).
thf(f30,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f24]) ).
thf(f31,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f30]) ).
thf(f32,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f31]) ).
thf(f35,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f32]) ).
thf(f36,plain,
( ( $true
= ( ( sK0 @ sK3 )
| ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK2 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f37,plain,
( ( $true
= ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK2 @ sK3 ) ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f36]) ).
thf(f38,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK2 @ sK3 ) ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f37]) ).
thf(f39,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK2 @ sK3 ) ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f37]) ).
thf(f41,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
| ( sK1 @ sK3 ) ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f39]) ).
thf(f42,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f41]) ).
thf(f43,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f42]) ).
thf(f44,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f38]) ).
thf(f48,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f44]) ).
thf(f50,definition,
( spl4_1
<=> ( $false
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f52,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f50]) ).
thf(f54,definition,
( spl4_2
<=> ( $false
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f56,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f54]) ).
thf(f57,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f29,f54,f50]) ).
thf(f59,definition,
( spl4_3
<=> ( $false
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f61,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f59]) ).
thf(f64,plain,
( spl4_3
| spl4_1 ),
inference(avatar_split_clause,[],[f35,f50,f59]) ).
thf(f66,definition,
( spl4_4
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f68,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f66]) ).
thf(f70,definition,
( spl4_5
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f72,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f73,plain,
( spl4_4
| spl4_5 ),
inference(avatar_split_clause,[],[f43,f70,f66]) ).
thf(f76,plain,
( $true
= ( sK2 @ sK3 ) ),
inference(forward_subsumption_resolution,[],[f48,f7]) ).
thf(f78,definition,
( spl4_6
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f80,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f78]) ).
thf(f83,plain,
spl4_6,
inference(avatar_split_clause,[],[f76,f78]) ).
thf(f89,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_4 ),
inference(forward_demodulation,[],[f68,f56]) ).
thf(f90,plain,
( $false
| ~ spl4_2
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f89]) ).
thf(f91,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f90]) ).
thf(f99,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_5 ),
inference(forward_demodulation,[],[f72,f61]) ).
thf(f100,plain,
( $false
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f99]) ).
thf(f101,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f100]) ).
thf(f108,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_6 ),
inference(forward_demodulation,[],[f80,f52]) ).
thf(f109,plain,
( $false
| ~ spl4_1
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f108]) ).
thf(f110,plain,
( ~ spl4_1
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f109]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f57]) ).
cnf(s4,plain,
( spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f64]) ).
cnf(s5,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f73]) ).
cnf(s8,plain,
spl4_6,
inference(sat_conversion,[],[f83]) ).
cnf(s9,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(sat_conversion,[],[f91]) ).
cnf(s12,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(sat_conversion,[],[f101]) ).
cnf(s13,plain,
( ~ spl4_1
| ~ spl4_6 ),
inference(sat_conversion,[],[f110]) ).
cnf(s14,plain,
~ spl4_1,
inference(rat,[],[s13,s8]) ).
cnf(s15,plain,
spl4_3,
inference(rat,[],[s4,s14]) ).
cnf(s16,plain,
~ spl4_5,
inference(rat,[],[s12,s15]) ).
cnf(s17,plain,
spl4_4,
inference(rat,[],[s5,s16]) ).
cnf(s18,plain,
~ spl4_2,
inference(rat,[],[s9,s17]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s1,s18,s14]) ).
thf(f111,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET144^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n020.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:37:49 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.20/0.28 % (1057342)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (1057350)dis+10_1_sil=32000:sp=arity:random_seed=1557192057:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (1057350) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1057342-1057350"...
% 0.20/0.28 % (1057348)% WARNING: option uhcvi not known.
% 0.20/0.28 % (1057350)...printing done.
% 0.20/0.28 % (1057350)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (1057350)------------------------------
% 0.20/0.28 % (1057350)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1057350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1057350)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1057350)Termination reason: Refutation
% 0.20/0.28 % (1057350)Time elapsed: 0.003 s
% 0.20/0.28 % (1057350)Peak memory usage: 12 MB
% 0.20/0.28 % (1057350)Instructions burned: 5 (million)
% 0.20/0.28 % (1057342)Success in time 0.034 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------