%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM830^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:19:00 AM UTC 2026
% Result : Theorem 0.22s 0.35s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 89 ( 26 unt; 0 typ; 9 def)
% Number of atoms : 356 ( 123 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 696 ( 112 ~; 104 |; 32 &; 431 @)
% ( 13 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 22 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 52 !; 12 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
n: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
c0: n ).
thf(func_def_1,type,
cS: n > n ).
thf(func_def_2,type,
c_plus: n > n > n ).
thf(func_def_3,type,
c_star: n > n > n ).
thf(func_def_4,type,
cPA_1: $o ).
thf(func_def_5,type,
cPA_2: $o ).
thf(func_def_6,type,
cPA_3: $o ).
thf(func_def_7,type,
cPA_4: $o ).
thf(func_def_11,type,
sK0: n ).
thf(func_def_12,type,
sK1: n ).
thf(func_def_13,type,
sK2: n ).
thf(func_def_14,type,
sK3: n ).
thf(func_def_15,type,
sK4: n ).
thf(func_def_16,type,
sK5: n ).
thf(f1,axiom,
( cPA_1
= ( ! [X0: n] :
( ( c_plus @ X0 @ c0 )
= X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPA_1_def) ).
thf(f2,axiom,
( cPA_2
= ( ! [X0: n,X1: n] :
( ( c_plus @ X0 @ ( cS @ X1 ) )
= ( cS @ ( c_plus @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPA_2_def) ).
thf(f3,axiom,
! [X0: n] :
( ( ( c_star @ X0 @ c0 )
= c0 )
= cPA_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPA_3_def) ).
thf(f4,axiom,
( cPA_4
= ( ! [X1: n,X0: n] :
( ( c_star @ X0 @ ( cS @ X1 ) )
= ( c_plus @ ( c_star @ X0 @ X1 ) @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPA_4_def) ).
thf(f5,conjecture,
( ( cPA_3
& cPA_1
& cPA_4
& cPA_2 )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPA_THM1) ).
thf(f6,negated_conjecture,
~ ( ( cPA_3
& cPA_1
& cPA_4
& cPA_2 )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( ( cPA_1 = $true )
<=> ! [X0: n] :
( ( c_plus @ X0 @ c0 )
= X0 ) ),
inference(fool_elimination,[],[f1]) ).
thf(f8,plain,
( ( cPA_2 = $true )
<=> ! [X0: n,X1: n] :
( ( c_plus @ X0 @ ( cS @ X1 ) )
= ( cS @ ( c_plus @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f9,plain,
( ( cPA_3 = $true )
<=> ! [X0: n] :
( c0
= ( c_star @ X0 @ c0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f10,plain,
~ ( ( cPA_3
& cPA_1
& cPA_4
& cPA_2 )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f11,plain,
~ ( ( ( cPA_3 = $true )
& ( cPA_1 = $true )
& ( cPA_2 = $true )
& ( cPA_4 = $true ) )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( cPA_4
= ( ! [X0: n,X1: n] :
( ( c_plus @ ( c_star @ X1 @ X0 ) @ X1 )
= ( c_star @ X1 @ ( cS @ X0 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f13,plain,
( ( cPA_4 = $true )
<=> ! [X0: n,X1: n] :
( ( c_plus @ ( c_star @ X1 @ X0 ) @ X1 )
= ( c_star @ X1 @ ( cS @ X0 ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) )
& ( cPA_3 = $true )
& ( cPA_1 = $true )
& ( cPA_2 = $true )
& ( cPA_4 = $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f15,plain,
( ( cPA_1 = $true )
& ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) )
& ( cPA_3 = $true )
& ( cPA_4 = $true )
& ( cPA_2 = $true ) ),
inference(flattening,[],[f14]) ).
thf(f16,plain,
( ( ( cPA_4 = $true )
| ? [X0: n,X1: n] :
( ( c_plus @ ( c_star @ X1 @ X0 ) @ X1 )
!= ( c_star @ X1 @ ( cS @ X0 ) ) ) )
& ( ! [X0: n,X1: n] :
( ( c_plus @ ( c_star @ X1 @ X0 ) @ X1 )
= ( c_star @ X1 @ ( cS @ X0 ) ) )
| ( cPA_4 != $true ) ) ),
inference(nnf_transformation,[],[f13]) ).
thf(f17,plain,
( ( ( cPA_4 = $true )
| ? [X0: n,X1: n] :
( ( c_plus @ ( c_star @ X1 @ X0 ) @ X1 )
!= ( c_star @ X1 @ ( cS @ X0 ) ) ) )
& ( ! [X2: n,X3: n] :
( ( c_star @ X3 @ ( cS @ X2 ) )
= ( c_plus @ ( c_star @ X3 @ X2 ) @ X3 ) )
| ( cPA_4 != $true ) ) ),
inference(rectify,[],[f16]) ).
thf(f18,plain,
( ( ( cPA_4 = $true )
| ( ( c_star @ sK1 @ ( cS @ sK0 ) )
!= ( c_plus @ ( c_star @ sK1 @ sK0 ) @ sK1 ) ) )
& ( ! [X2: n,X3: n] :
( ( c_star @ X3 @ ( cS @ X2 ) )
= ( c_plus @ ( c_star @ X3 @ X2 ) @ X3 ) )
| ( cPA_4 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f17]) ).
thf(f19,plain,
( ( ( cPA_3 = $true )
| ? [X0: n] :
( c0
!= ( c_star @ X0 @ c0 ) ) )
& ( ! [X0: n] :
( c0
= ( c_star @ X0 @ c0 ) )
| ( cPA_3 != $true ) ) ),
inference(nnf_transformation,[],[f9]) ).
thf(f20,plain,
( ( ( cPA_3 = $true )
| ? [X0: n] :
( c0
!= ( c_star @ X0 @ c0 ) ) )
& ( ! [X1: n] :
( c0
= ( c_star @ X1 @ c0 ) )
| ( cPA_3 != $true ) ) ),
inference(rectify,[],[f19]) ).
thf(f21,plain,
( ( ( cPA_3 = $true )
| ( c0
!= ( c_star @ sK2 @ c0 ) ) )
& ( ! [X1: n] :
( c0
= ( c_star @ X1 @ c0 ) )
| ( cPA_3 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f20]) ).
thf(f22,plain,
( ( ( cPA_2 = $true )
| ? [X0: n,X1: n] :
( ( c_plus @ X0 @ ( cS @ X1 ) )
!= ( cS @ ( c_plus @ X0 @ X1 ) ) ) )
& ( ! [X0: n,X1: n] :
( ( c_plus @ X0 @ ( cS @ X1 ) )
= ( cS @ ( c_plus @ X0 @ X1 ) ) )
| ( cPA_2 != $true ) ) ),
inference(nnf_transformation,[],[f8]) ).
thf(f23,plain,
( ( ( cPA_2 = $true )
| ? [X0: n,X1: n] :
( ( c_plus @ X0 @ ( cS @ X1 ) )
!= ( cS @ ( c_plus @ X0 @ X1 ) ) ) )
& ( ! [X2: n,X3: n] :
( ( c_plus @ X2 @ ( cS @ X3 ) )
= ( cS @ ( c_plus @ X2 @ X3 ) ) )
| ( cPA_2 != $true ) ) ),
inference(rectify,[],[f22]) ).
thf(f24,plain,
( ( ( cPA_2 = $true )
| ( ( cS @ ( c_plus @ sK3 @ sK4 ) )
!= ( c_plus @ sK3 @ ( cS @ sK4 ) ) ) )
& ( ! [X2: n,X3: n] :
( ( c_plus @ X2 @ ( cS @ X3 ) )
= ( cS @ ( c_plus @ X2 @ X3 ) ) )
| ( cPA_2 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f23]) ).
thf(f25,plain,
( ( ( cPA_1 = $true )
| ? [X0: n] :
( ( c_plus @ X0 @ c0 )
!= X0 ) )
& ( ! [X0: n] :
( ( c_plus @ X0 @ c0 )
= X0 )
| ( cPA_1 != $true ) ) ),
inference(nnf_transformation,[],[f7]) ).
thf(f26,plain,
( ( ( cPA_1 = $true )
| ? [X0: n] :
( ( c_plus @ X0 @ c0 )
!= X0 ) )
& ( ! [X1: n] :
( ( c_plus @ X1 @ c0 )
= X1 )
| ( cPA_1 != $true ) ) ),
inference(rectify,[],[f25]) ).
thf(f27,plain,
( ( ( cPA_1 = $true )
| ( sK5
!= ( c_plus @ sK5 @ c0 ) ) )
& ( ! [X1: n] :
( ( c_plus @ X1 @ c0 )
= X1 )
| ( cPA_1 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X0,sK5)],[f26]) ).
thf(f28,plain,
! [X2: n,X3: n] :
( ( cPA_4 != $true )
| ( ( c_star @ X3 @ ( cS @ X2 ) )
= ( c_plus @ ( c_star @ X3 @ X2 ) @ X3 ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f30,plain,
! [X1: n] :
( ( c0
= ( c_star @ X1 @ c0 ) )
| ( cPA_3 != $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f32,plain,
! [X2: n,X3: n] :
( ( cPA_2 != $true )
| ( ( c_plus @ X2 @ ( cS @ X3 ) )
= ( cS @ ( c_plus @ X2 @ X3 ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f34,plain,
cPA_2 = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f35,plain,
cPA_4 = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f36,plain,
cPA_3 = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f37,plain,
( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f38,plain,
cPA_1 = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f39,plain,
! [X1: n] :
( ( cPA_1 != $true )
| ( ( c_plus @ X1 @ c0 )
= X1 ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f43,definition,
( spl6_1
<=> ( cPA_4 = $true ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f47,definition,
( spl6_2
<=> ! [X2: n,X3: n] :
( ( c_star @ X3 @ ( cS @ X2 ) )
= ( c_plus @ ( c_star @ X3 @ X2 ) @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f48,plain,
( ! [X2: n,X3: n] :
( ( c_star @ X3 @ ( cS @ X2 ) )
= ( c_plus @ ( c_star @ X3 @ X2 ) @ X3 ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f47]) ).
thf(f49,plain,
( ~ spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f28,f47,f43]) ).
thf(f51,definition,
( spl6_3
<=> ( cPA_2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f54,plain,
spl6_3,
inference(avatar_split_clause,[],[f34,f51]) ).
thf(f56,definition,
( spl6_4
<=> ( cPA_3 = $true ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f64,plain,
spl6_1,
inference(avatar_split_clause,[],[f35,f43]) ).
thf(f70,definition,
( spl6_7
<=> ( cPA_1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
thf(f75,definition,
( spl6_8
<=> ! [X2: n,X3: n] :
( ( c_plus @ X2 @ ( cS @ X3 ) )
= ( cS @ ( c_plus @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
thf(f76,plain,
( ! [X2: n,X3: n] :
( ( c_plus @ X2 @ ( cS @ X3 ) )
= ( cS @ ( c_plus @ X2 @ X3 ) ) )
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f75]) ).
thf(f77,plain,
( ~ spl6_3
| spl6_8 ),
inference(avatar_split_clause,[],[f32,f75,f51]) ).
thf(f84,definition,
( spl6_10
<=> ! [X1: n] :
( ( c_plus @ X1 @ c0 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition]) ).
thf(f85,plain,
( ! [X1: n] :
( ( c_plus @ X1 @ c0 )
= X1 )
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f84]) ).
thf(f86,plain,
( ~ spl6_7
| spl6_10 ),
inference(avatar_split_clause,[],[f39,f84,f70]) ).
thf(f87,plain,
spl6_7,
inference(avatar_split_clause,[],[f38,f70]) ).
thf(f94,definition,
( spl6_12
<=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_12])],[avatar_definition]) ).
thf(f96,plain,
( ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) )
| spl6_12 ),
inference(avatar_component_clause,[],[f94]) ).
thf(f97,plain,
~ spl6_12,
inference(avatar_split_clause,[],[f37,f94]) ).
thf(f98,plain,
spl6_4,
inference(avatar_split_clause,[],[f36,f56]) ).
thf(f100,definition,
( spl6_13
<=> ! [X1: n] :
( c0
= ( c_star @ X1 @ c0 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_13])],[avatar_definition]) ).
thf(f101,plain,
( ! [X1: n] :
( c0
= ( c_star @ X1 @ c0 ) )
| ~ spl6_13 ),
inference(avatar_component_clause,[],[f100]) ).
thf(f102,plain,
( ~ spl6_4
| spl6_13 ),
inference(avatar_split_clause,[],[f30,f100,f56]) ).
thf(f107,plain,
( ! [X0: n] :
( ( c_plus @ c0 @ X0 )
= ( c_star @ X0 @ ( cS @ c0 ) ) )
| ~ spl6_2
| ~ spl6_13 ),
inference(superposition,[],[f48,f101]) ).
thf(f112,plain,
( ! [X0: n] :
( ( c_star @ X0 @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( c_plus @ c0 @ X0 ) @ X0 ) )
| ~ spl6_2
| ~ spl6_13 ),
inference(superposition,[],[f48,f107]) ).
thf(f145,plain,
( ( ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( c_plus @ ( c_plus @ c0 @ ( cS @ ( cS @ c0 ) ) ) @ ( cS @ ( cS @ c0 ) ) ) )
| ~ spl6_2
| spl6_12
| ~ spl6_13 ),
inference(superposition,[],[f96,f112]) ).
thf(f150,plain,
( ( ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( cS @ ( c_plus @ ( c_plus @ c0 @ ( cS @ ( cS @ c0 ) ) ) @ ( cS @ c0 ) ) ) )
| ~ spl6_2
| ~ spl6_8
| spl6_12
| ~ spl6_13 ),
inference(forward_demodulation,[],[f145,f76]) ).
thf(f156,plain,
( ( ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( cS @ ( cS @ ( c_plus @ ( c_plus @ c0 @ ( cS @ ( cS @ c0 ) ) ) @ c0 ) ) ) )
| ~ spl6_2
| ~ spl6_8
| spl6_12
| ~ spl6_13 ),
inference(forward_demodulation,[],[f150,f76]) ).
thf(f160,plain,
( ( ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( cS @ ( cS @ ( c_plus @ c0 @ ( cS @ ( cS @ c0 ) ) ) ) ) )
| ~ spl6_2
| ~ spl6_8
| ~ spl6_10
| spl6_12
| ~ spl6_13 ),
inference(forward_demodulation,[],[f156,f85]) ).
thf(f163,plain,
( ( ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( cS @ ( cS @ ( cS @ ( c_plus @ c0 @ ( cS @ c0 ) ) ) ) ) )
| ~ spl6_2
| ~ spl6_8
| ~ spl6_10
| spl6_12
| ~ spl6_13 ),
inference(forward_demodulation,[],[f160,f76]) ).
thf(f166,plain,
( ( ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( cS @ ( cS @ ( cS @ ( cS @ ( c_plus @ c0 @ c0 ) ) ) ) ) )
| ~ spl6_2
| ~ spl6_8
| ~ spl6_10
| spl6_12
| ~ spl6_13 ),
inference(forward_demodulation,[],[f163,f76]) ).
thf(f167,plain,
( ( ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) )
| ~ spl6_2
| ~ spl6_8
| ~ spl6_10
| spl6_12
| ~ spl6_13 ),
inference(forward_demodulation,[],[f166,f85]) ).
thf(f168,plain,
( ( ( cS @ ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ c0 ) ) )
!= ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) )
| ~ spl6_2
| ~ spl6_8
| ~ spl6_10
| spl6_12
| ~ spl6_13 ),
inference(forward_demodulation,[],[f167,f76]) ).
thf(f169,plain,
( ( ( cS @ ( cS @ ( c_plus @ ( cS @ ( cS @ c0 ) ) @ c0 ) ) )
!= ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) )
| ~ spl6_2
| ~ spl6_8
| ~ spl6_10
| spl6_12
| ~ spl6_13 ),
inference(forward_demodulation,[],[f168,f76]) ).
thf(f170,plain,
( ( ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) )
!= ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) )
| ~ spl6_2
| ~ spl6_8
| ~ spl6_10
| spl6_12
| ~ spl6_13 ),
inference(forward_demodulation,[],[f169,f85]) ).
thf(f171,plain,
( $false
| ~ spl6_2
| ~ spl6_8
| ~ spl6_10
| spl6_12
| ~ spl6_13 ),
inference(trivial_inequality_removal,[],[f170]) ).
thf(f172,plain,
( ~ spl6_2
| ~ spl6_8
| ~ spl6_10
| spl6_12
| ~ spl6_13 ),
inference(avatar_contradiction_clause,[],[f171]) ).
cnf(s1,plain,
( ~ spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f49]) ).
cnf(s2,plain,
spl6_3,
inference(sat_conversion,[],[f54]) ).
cnf(s4,plain,
spl6_1,
inference(sat_conversion,[],[f64]) ).
cnf(s6,plain,
( ~ spl6_3
| spl6_8 ),
inference(sat_conversion,[],[f77]) ).
cnf(s8,plain,
( ~ spl6_7
| spl6_10 ),
inference(sat_conversion,[],[f86]) ).
cnf(s9,plain,
spl6_7,
inference(sat_conversion,[],[f87]) ).
cnf(s11,plain,
~ spl6_12,
inference(sat_conversion,[],[f97]) ).
cnf(s12,plain,
spl6_4,
inference(sat_conversion,[],[f98]) ).
cnf(s13,plain,
( ~ spl6_4
| spl6_13 ),
inference(sat_conversion,[],[f102]) ).
cnf(s14,plain,
( ~ spl6_2
| ~ spl6_8
| ~ spl6_10
| spl6_12
| ~ spl6_13 ),
inference(sat_conversion,[],[f172]) ).
cnf(s15,plain,
spl6_13,
inference(rat,[],[s13,s12]) ).
cnf(s16,plain,
spl6_10,
inference(rat,[],[s8,s9]) ).
cnf(s17,plain,
spl6_8,
inference(rat,[],[s6,s2]) ).
cnf(s18,plain,
~ spl6_2,
inference(rat,[],[s14,s15,s11,s16,s17]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s1,s18,s4]) ).
thf(f173,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM830^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 % Computer : n016.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 13:08:34 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 Running higher-order theorem proving
% 0.11/0.24 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
% 0.22/0.35 % (311076)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.35 % (311082)lrs+10_16_si=on:nwc=1.5:random_seed=1493473650:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.35 % (311082)Instruction limit reached!
% 0.22/0.35 % (311082)------------------------------
% 0.22/0.35 % (311082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (311082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (311082)CaDiCaL version: 2.1.3
% 0.22/0.35 % (311082)Termination reason: Instruction limit
% 0.22/0.35 % (311082)Termination phase: Saturation
% 0.22/0.35 % (311082)Time elapsed: 0.018 s
% 0.22/0.35 % (311082)Peak memory usage: 12 MB
% 0.22/0.35 % (311082)Instructions burned: 19 (million)
% 0.22/0.35 % (311083)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1718259566:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.35 % (311081)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3875877559:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.35 % (311083)Refutation not found, incomplete strategy
% 0.22/0.35 % (311083)------------------------------
% 0.22/0.35 % (311083)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (311083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (311083)CaDiCaL version: 2.1.3
% 0.22/0.35 % (311083)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.35 % (311083)Time elapsed: 0.003 s
% 0.22/0.35 % (311083)Peak memory usage: 12 MB
% 0.22/0.35 % (311083)Instructions burned: 2 (million)
% 0.22/0.35 % (311083)------------------------------
% 0.22/0.35 % (311083)------------------------------
% 0.22/0.35 % (311084)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=2541858977: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)
% 0.22/0.35 % (311081) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-311076-311081"...
% 0.22/0.35 % (311084) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-311076-311084"...
% 0.22/0.35 % (311084)...printing done.
% 0.22/0.35 % (311081)...printing done.
% 0.22/0.35 % (311084)Refutation found. Thanks to Tanya!
% 0.22/0.35 % SZS status Theorem for theBenchmark
% 0.22/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.35 % (311084)------------------------------
% 0.22/0.35 % (311084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (311084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (311084)CaDiCaL version: 2.1.3
% 0.22/0.35 % (311084)Termination reason: Refutation
% 0.22/0.35 % (311084)Time elapsed: 0.007 s
% 0.22/0.35 % (311084)Peak memory usage: 13 MB
% 0.22/0.35 % (311084)Instructions burned: 13 (million)
% 0.22/0.35 % (311076)Success in time 0.097 s
% 0.22/0.35 % Vampire exiting
%------------------------------------------------------------------------------