%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM730_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 : Tue Sep 29 12:25:31 PM UTC 2026
% Result : Theorem 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 21
% Syntax : Number of formulae : 166 ( 13 unt; 0 typ; 19 def)
% Number of atoms : 679 ( 47 equ)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 625 ( 256 ~; 350 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 144 ( 144 fml; 0 var)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 25 ( 22 usr; 21 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 59 !; 0 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
frac: $tType ).
tff(type_def_6,type,
nat: $tType ).
tff(func_def_0,type,
x: frac ).
tff(func_def_1,type,
y: frac ).
tff(func_def_2,type,
ts: ( nat * nat ) > nat ).
tff(func_def_3,type,
c1x: frac > nat ).
tff(func_def_4,type,
c2y: frac > nat ).
tff(func_def_5,type,
c1y: frac > nat ).
tff(func_def_6,type,
c2x: frac > nat ).
tff(pred_def_1,type,
orec3: ( $o * $o * $o ) > $o ).
tff(pred_def_2,type,
more: ( nat * nat ) > $o ).
tff(pred_def_3,type,
less: ( nat * nat ) > $o ).
tff(f1,axiom,
! [X0: nat,X1: nat] : orec3(X0 = X1,more(X0,X1),less(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10) ).
tff(f2,conjecture,
orec3(ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)),more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x))),less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz41) ).
tff(f3,negated_conjecture,
~ orec3(ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)),more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x))),less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
~ orec3(ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)),more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x))),less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))),
inference(flattening,[],[f3]) ).
tff(f5,plain,
! [X0: nat,X1: nat] :
( ~ less(X0,X1)
| more(X0,X1)
| ( X0 != X1 )
| orec3($true,$false,$true) ),
inference(cnf_transformation,[],[f1]) ).
tff(f6,plain,
! [X0: nat,X1: nat] :
( ~ less(X0,X1)
| more(X0,X1)
| ( X0 = X1 )
| orec3($false,$false,$true) ),
inference(cnf_transformation,[],[f1]) ).
tff(f7,plain,
! [X0: nat,X1: nat] :
( ~ less(X0,X1)
| ~ more(X0,X1)
| ( X0 != X1 )
| orec3($true,$true,$true) ),
inference(cnf_transformation,[],[f1]) ).
tff(f8,plain,
! [X0: nat,X1: nat] :
( ~ less(X0,X1)
| ~ more(X0,X1)
| ( X0 = X1 )
| orec3($false,$true,$true) ),
inference(cnf_transformation,[],[f1]) ).
tff(f9,plain,
! [X0: nat,X1: nat] :
( less(X0,X1)
| more(X0,X1)
| ( X0 != X1 )
| orec3($true,$false,$false) ),
inference(cnf_transformation,[],[f1]) ).
tff(f10,plain,
! [X0: nat,X1: nat] :
( less(X0,X1)
| more(X0,X1)
| ( X0 = X1 )
| orec3($false,$false,$false) ),
inference(cnf_transformation,[],[f1]) ).
tff(f11,plain,
! [X0: nat,X1: nat] :
( less(X0,X1)
| ~ more(X0,X1)
| ( X0 != X1 )
| orec3($true,$true,$false) ),
inference(cnf_transformation,[],[f1]) ).
tff(f12,plain,
! [X0: nat,X1: nat] :
( less(X0,X1)
| ~ more(X0,X1)
| ( X0 = X1 )
| orec3($false,$true,$false) ),
inference(cnf_transformation,[],[f1]) ).
tff(f13,plain,
( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ts(c1x(x),c2y(y)) != ts(c1y(y),c2x(x)) )
| ~ orec3($true,$false,$true) ),
inference(cnf_transformation,[],[f4]) ).
tff(f14,plain,
( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) )
| ~ orec3($false,$false,$true) ),
inference(cnf_transformation,[],[f4]) ).
tff(f15,plain,
( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ts(c1x(x),c2y(y)) != ts(c1y(y),c2x(x)) )
| ~ orec3($true,$true,$true) ),
inference(cnf_transformation,[],[f4]) ).
tff(f16,plain,
( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) )
| ~ orec3($false,$true,$true) ),
inference(cnf_transformation,[],[f4]) ).
tff(f17,plain,
( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ts(c1x(x),c2y(y)) != ts(c1y(y),c2x(x)) )
| ~ orec3($true,$false,$false) ),
inference(cnf_transformation,[],[f4]) ).
tff(f18,plain,
( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) )
| ~ orec3($false,$false,$false) ),
inference(cnf_transformation,[],[f4]) ).
tff(f19,plain,
( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ts(c1x(x),c2y(y)) != ts(c1y(y),c2x(x)) )
| ~ orec3($true,$true,$false) ),
inference(cnf_transformation,[],[f4]) ).
tff(f20,plain,
( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) )
| ~ orec3($false,$true,$false) ),
inference(cnf_transformation,[],[f4]) ).
tff(f23,plain,
! [X1: nat] :
( less(X1,X1)
| ~ more(X1,X1)
| orec3($true,$true,$false) ),
inference(equality_resolution,[],[f11]) ).
tff(f24,plain,
! [X1: nat] :
( less(X1,X1)
| more(X1,X1)
| orec3($true,$false,$false) ),
inference(equality_resolution,[],[f9]) ).
tff(f25,plain,
! [X1: nat] :
( ~ less(X1,X1)
| ~ more(X1,X1)
| orec3($true,$true,$true) ),
inference(equality_resolution,[],[f7]) ).
tff(f26,plain,
! [X1: nat] :
( ~ less(X1,X1)
| more(X1,X1)
| orec3($true,$false,$true) ),
inference(equality_resolution,[],[f5]) ).
tff(f27,plain,
! [X0: nat,X1: nat] :
( ~ less(X0,X1)
| more(X0,X1)
| ( X0 = X1 )
| orec3($false,$true,$false) ),
inference(consistent_polarity_flipping,[],[f12]) ).
tff(f28,plain,
! [X1: nat] :
( ~ less(X1,X1)
| more(X1,X1)
| orec3($true,$true,$false) ),
inference(consistent_polarity_flipping,[],[f23]) ).
tff(f29,plain,
! [X0: nat,X1: nat] :
( ~ less(X0,X1)
| ~ more(X0,X1)
| ( X0 = X1 )
| orec3($false,$false,$false) ),
inference(consistent_polarity_flipping,[],[f10]) ).
tff(f30,plain,
! [X1: nat] :
( ~ less(X1,X1)
| ~ more(X1,X1)
| orec3($true,$false,$false) ),
inference(consistent_polarity_flipping,[],[f24]) ).
tff(f31,plain,
! [X0: nat,X1: nat] :
( less(X0,X1)
| more(X0,X1)
| ( X0 = X1 )
| orec3($false,$true,$true) ),
inference(consistent_polarity_flipping,[],[f8]) ).
tff(f32,plain,
! [X1: nat] :
( less(X1,X1)
| more(X1,X1)
| orec3($true,$true,$true) ),
inference(consistent_polarity_flipping,[],[f25]) ).
tff(f33,plain,
! [X0: nat,X1: nat] :
( less(X0,X1)
| ~ more(X0,X1)
| ( X0 = X1 )
| orec3($false,$false,$true) ),
inference(consistent_polarity_flipping,[],[f6]) ).
tff(f34,plain,
! [X1: nat] :
( less(X1,X1)
| ~ more(X1,X1)
| orec3($true,$false,$true) ),
inference(consistent_polarity_flipping,[],[f26]) ).
tff(f35,plain,
( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) )
| ~ orec3($false,$true,$false) ),
inference(consistent_polarity_flipping,[],[f20]) ).
tff(f36,plain,
( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ts(c1x(x),c2y(y)) != ts(c1y(y),c2x(x)) )
| ~ orec3($true,$true,$false) ),
inference(consistent_polarity_flipping,[],[f19]) ).
tff(f37,plain,
( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) )
| ~ orec3($false,$false,$false) ),
inference(consistent_polarity_flipping,[],[f18]) ).
tff(f38,plain,
( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ts(c1x(x),c2y(y)) != ts(c1y(y),c2x(x)) )
| ~ orec3($true,$false,$false) ),
inference(consistent_polarity_flipping,[],[f17]) ).
tff(f39,plain,
( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) )
| ~ orec3($false,$true,$true) ),
inference(consistent_polarity_flipping,[],[f16]) ).
tff(f40,plain,
( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ts(c1x(x),c2y(y)) != ts(c1y(y),c2x(x)) )
| ~ orec3($true,$true,$true) ),
inference(consistent_polarity_flipping,[],[f15]) ).
tff(f41,plain,
( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) )
| ~ orec3($false,$false,$true) ),
inference(consistent_polarity_flipping,[],[f14]) ).
tff(f42,plain,
( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ts(c1x(x),c2y(y)) != ts(c1y(y),c2x(x)) )
| ~ orec3($true,$false,$true) ),
inference(consistent_polarity_flipping,[],[f13]) ).
tff(f44,definition,
( spl0_1
<=> orec3($true,$false,$true) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f48,definition,
( spl0_2
<=> ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f49,plain,
( ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f48]) ).
tff(f50,plain,
( ( ts(c1x(x),c2y(y)) != ts(c1y(y),c2x(x)) )
| spl0_2 ),
inference(avatar_component_clause,[],[f48]) ).
tff(f52,definition,
( spl0_3
<=> more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f53,plain,
( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f52]) ).
tff(f54,plain,
( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| spl0_3 ),
inference(avatar_component_clause,[],[f52]) ).
tff(f56,definition,
( spl0_4
<=> less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
tff(f57,plain,
( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| spl0_4 ),
inference(avatar_component_clause,[],[f56]) ).
tff(f58,plain,
( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f56]) ).
tff(f59,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f42,f56,f52,f48,f44]) ).
tff(f61,definition,
( spl0_5
<=> orec3($false,$false,$true) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
tff(f64,plain,
( ~ spl0_5
| spl0_2
| ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f41,f56,f52,f48,f61]) ).
tff(f66,definition,
( spl0_6
<=> orec3($true,$true,$true) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
tff(f69,plain,
( ~ spl0_6
| ~ spl0_2
| spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f40,f56,f52,f48,f66]) ).
tff(f71,definition,
( spl0_7
<=> orec3($false,$true,$true) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
tff(f74,plain,
( ~ spl0_7
| spl0_2
| spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f39,f56,f52,f48,f71]) ).
tff(f76,definition,
( spl0_8
<=> orec3($true,$false,$false) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
tff(f79,plain,
( ~ spl0_8
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f38,f56,f52,f48,f76]) ).
tff(f81,definition,
( spl0_9
<=> orec3($false,$false,$false) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
tff(f84,plain,
( ~ spl0_9
| spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f37,f56,f52,f48,f81]) ).
tff(f86,definition,
( spl0_10
<=> orec3($true,$true,$false) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
tff(f89,plain,
( ~ spl0_10
| ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f36,f56,f52,f48,f86]) ).
tff(f91,definition,
( spl0_11
<=> orec3($false,$true,$false) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
tff(f94,plain,
( ~ spl0_11
| spl0_2
| spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f35,f56,f52,f48,f91]) ).
tff(f96,definition,
( spl0_12
<=> ! [X1: nat] :
( less(X1,X1)
| ~ more(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
tff(f97,plain,
( ! [X1: nat] :
( ~ more(X1,X1)
| less(X1,X1) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f96]) ).
tff(f98,plain,
( spl0_1
| spl0_12 ),
inference(avatar_split_clause,[],[f34,f96,f44]) ).
tff(f100,definition,
( spl0_13
<=> ! [X0: nat,X1: nat] :
( less(X0,X1)
| ( X0 = X1 )
| ~ more(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
tff(f101,plain,
( ! [X0: nat,X1: nat] :
( less(X0,X1)
| ( X0 = X1 )
| ~ more(X0,X1) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f100]) ).
tff(f102,plain,
( spl0_5
| spl0_13 ),
inference(avatar_split_clause,[],[f33,f100,f61]) ).
tff(f104,definition,
( spl0_14
<=> ! [X1: nat] :
( less(X1,X1)
| more(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
tff(f105,plain,
( ! [X1: nat] :
( less(X1,X1)
| more(X1,X1) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f104]) ).
tff(f106,plain,
( spl0_6
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f104,f66]) ).
tff(f108,definition,
( spl0_15
<=> ! [X0: nat,X1: nat] :
( less(X0,X1)
| ( X0 = X1 )
| more(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
tff(f109,plain,
( ! [X0: nat,X1: nat] :
( less(X0,X1)
| ( X0 = X1 )
| more(X0,X1) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f108]) ).
tff(f110,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f31,f108,f71]) ).
tff(f112,definition,
( spl0_16
<=> ! [X1: nat] :
( ~ less(X1,X1)
| ~ more(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
tff(f113,plain,
( ! [X1: nat] :
( ~ less(X1,X1)
| ~ more(X1,X1) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f112]) ).
tff(f114,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f30,f112,f76]) ).
tff(f116,definition,
( spl0_17
<=> ! [X0: nat,X1: nat] :
( ~ less(X0,X1)
| ( X0 = X1 )
| ~ more(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
tff(f117,plain,
( ! [X0: nat,X1: nat] :
( ~ more(X0,X1)
| ( X0 = X1 )
| ~ less(X0,X1) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f116]) ).
tff(f118,plain,
( spl0_9
| spl0_17 ),
inference(avatar_split_clause,[],[f29,f116,f81]) ).
tff(f120,definition,
( spl0_18
<=> ! [X1: nat] :
( ~ less(X1,X1)
| more(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
tff(f121,plain,
( ! [X1: nat] :
( ~ less(X1,X1)
| more(X1,X1) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f120]) ).
tff(f122,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f28,f120,f86]) ).
tff(f124,definition,
( spl0_19
<=> ! [X0: nat,X1: nat] :
( ~ less(X0,X1)
| ( X0 = X1 )
| more(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
tff(f125,plain,
( ! [X0: nat,X1: nat] :
( ~ less(X0,X1)
| ( X0 = X1 )
| more(X0,X1) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f124]) ).
tff(f126,plain,
( spl0_11
| spl0_19 ),
inference(avatar_split_clause,[],[f27,f124,f91]) ).
tff(f127,plain,
( more(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y)))
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f53,f49]) ).
tff(f128,plain,
( ~ less(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y)))
| ~ spl0_2
| spl0_4 ),
inference(forward_demodulation,[],[f57,f49]) ).
tff(f140,plain,
( less(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y)))
| ~ spl0_2
| ~ spl0_3
| ~ spl0_12 ),
inference(resolution,[],[f97,f127]) ).
tff(f141,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f140,f128]) ).
tff(f142,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f141]) ).
tff(f143,plain,
( less(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y)))
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f58,f49]) ).
tff(f144,plain,
( ! [X1: nat] : ~ more(X1,X1)
| ~ spl0_12
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f113,f97]) ).
tff(f148,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_12
| ~ spl0_16 ),
inference(backward_subsumption_resolution,[],[f127,f144]) ).
tff(f149,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_12
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f148]) ).
tff(f151,plain,
( ~ more(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y)))
| ~ spl0_2
| ~ spl0_4
| ~ spl0_16 ),
inference(resolution,[],[f113,f143]) ).
tff(f152,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f151,f127]) ).
tff(f153,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f152]) ).
tff(f154,plain,
( ~ more(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y)))
| ~ spl0_2
| spl0_3 ),
inference(forward_demodulation,[],[f54,f49]) ).
tff(f160,plain,
( more(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y)))
| ~ spl0_2
| ~ spl0_4
| ~ spl0_18 ),
inference(resolution,[],[f121,f143]) ).
tff(f161,plain,
( $false
| ~ spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f160,f154]) ).
tff(f162,plain,
( ~ spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f161]) ).
tff(f166,plain,
( more(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y)))
| ~ spl0_2
| spl0_4
| ~ spl0_14 ),
inference(resolution,[],[f105,f128]) ).
tff(f167,plain,
( $false
| ~ spl0_2
| spl0_3
| spl0_4
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f166,f154]) ).
tff(f168,plain,
( ~ spl0_2
| spl0_3
| spl0_4
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f167]) ).
tff(f170,plain,
( ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) )
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| spl0_4
| ~ spl0_15 ),
inference(resolution,[],[f109,f57]) ).
tff(f171,plain,
( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| spl0_2
| spl0_4
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f170,f50]) ).
tff(f172,plain,
( $false
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f171,f54]) ).
tff(f173,plain,
( spl0_2
| spl0_3
| spl0_4
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f172]) ).
tff(f181,plain,
( ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) )
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ spl0_4
| ~ spl0_19 ),
inference(resolution,[],[f125,f58]) ).
tff(f183,plain,
( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| spl0_2
| ~ spl0_4
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f181,f50]) ).
tff(f184,plain,
( $false
| spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f183,f54]) ).
tff(f185,plain,
( spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f184]) ).
tff(f188,plain,
( ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) )
| ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| spl0_4
| ~ spl0_13 ),
inference(resolution,[],[f101,f57]) ).
tff(f189,plain,
( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| spl0_2
| spl0_4
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f188,f50]) ).
tff(f190,plain,
( $false
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f189,f53]) ).
tff(f191,plain,
( spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f190]) ).
tff(f202,plain,
( ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) )
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ spl0_3
| ~ spl0_17 ),
inference(resolution,[],[f117,f53]) ).
tff(f203,plain,
( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| spl0_2
| ~ spl0_3
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f202,f50]) ).
tff(f204,plain,
( $false
| spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f203,f58]) ).
tff(f205,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f204]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f59]) ).
cnf(s2,plain,
( spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f64]) ).
cnf(s3,plain,
( ~ spl0_2
| spl0_3
| spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f69]) ).
cnf(s4,plain,
( spl0_2
| spl0_3
| spl0_4
| ~ spl0_7 ),
inference(sat_conversion,[],[f74]) ).
cnf(s5,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8 ),
inference(sat_conversion,[],[f79]) ).
cnf(s6,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_9 ),
inference(sat_conversion,[],[f84]) ).
cnf(s7,plain,
( ~ spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_10 ),
inference(sat_conversion,[],[f89]) ).
cnf(s8,plain,
( spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_11 ),
inference(sat_conversion,[],[f94]) ).
cnf(s9,plain,
( spl0_1
| spl0_12 ),
inference(sat_conversion,[],[f98]) ).
cnf(s10,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f102]) ).
cnf(s11,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f106]) ).
cnf(s12,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f110]) ).
cnf(s13,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f114]) ).
cnf(s14,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f118]) ).
cnf(s15,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f122]) ).
cnf(s16,plain,
( spl0_11
| spl0_19 ),
inference(sat_conversion,[],[f126]) ).
cnf(s17,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_12 ),
inference(sat_conversion,[],[f142]) ).
cnf(s18,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_12
| ~ spl0_16 ),
inference(sat_conversion,[],[f149]) ).
cnf(s19,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_16 ),
inference(sat_conversion,[],[f153]) ).
cnf(s21,plain,
( ~ spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_18 ),
inference(sat_conversion,[],[f162]) ).
cnf(s22,plain,
( ~ spl0_2
| spl0_3
| spl0_4
| ~ spl0_14 ),
inference(sat_conversion,[],[f168]) ).
cnf(s23,plain,
( spl0_2
| spl0_3
| spl0_4
| ~ spl0_15 ),
inference(sat_conversion,[],[f173]) ).
cnf(s25,plain,
( spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_19 ),
inference(sat_conversion,[],[f185]) ).
cnf(s26,plain,
( spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_13 ),
inference(sat_conversion,[],[f191]) ).
cnf(s28,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_17 ),
inference(sat_conversion,[],[f205]) ).
cnf(s29,plain,
( spl0_4
| spl0_3
| spl0_2 ),
inference(rat,[],[s12,s23,s4]) ).
cnf(s30,plain,
( ~ spl0_4
| spl0_3
| spl0_2 ),
inference(rat,[],[s16,s25,s8]) ).
cnf(s31,plain,
( spl0_3
| spl0_2 ),
inference(rat,[],[s30,s29]) ).
cnf(s32,plain,
( spl0_4
| ~ spl0_3
| spl0_2 ),
inference(rat,[],[s10,s2,s26]) ).
cnf(s33,plain,
( ~ spl0_4
| ~ spl0_3
| spl0_2 ),
inference(rat,[],[s14,s6,s28]) ).
cnf(s34,plain,
( ~ spl0_3
| spl0_2 ),
inference(rat,[],[s33,s32]) ).
cnf(s35,plain,
spl0_2,
inference(rat,[],[s34,s31]) ).
cnf(s36,plain,
( spl0_4
| spl0_3 ),
inference(rat,[],[s11,s22,s3,s35]) ).
cnf(s37,plain,
( ~ spl0_4
| spl0_3 ),
inference(rat,[],[s15,s7,s21,s35]) ).
cnf(s38,plain,
spl0_3,
inference(rat,[],[s37,s36]) ).
cnf(s39,plain,
~ spl0_12,
inference(rat,[],[s5,s13,s17,s18,s35,s38]) ).
cnf(s40,plain,
spl0_1,
inference(rat,[],[s9,s39]) ).
cnf(s41,plain,
spl0_4,
inference(rat,[],[s1,s35,s38,s40]) ).
cnf(s42,plain,
~ spl0_16,
inference(rat,[],[s19,s38,s35,s41]) ).
cnf(s43,plain,
~ spl0_8,
inference(rat,[],[s5,s38,s35,s41]) ).
cnf(s44,plain,
$false,
inference(rat,[],[s13,s42,s43]) ).
tff(f206,plain,
$false,
inference(avatar_sat_refutation,[],[s44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM730_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 % Computer : n016.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 21:18:18 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.45 Running first-order model finding
% 0.12/0.45 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.49 % (2997340)Will run a generic schedule for satisfiability detection.
% 0.20/0.49 % (2997346)% WARNING: option uhcvi not known.
% 0.20/0.49 % (2997346)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2729782605:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.49 % (2997346) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2997340-2997346"...
% 0.20/0.49 % (2997346)...printing done.
% 0.20/0.49 % (2997346)Refutation found. Thanks to Tanya!
% 0.20/0.49 % SZS status Theorem for theBenchmark
% 0.20/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49 % (2997346)------------------------------
% 0.20/0.49 % (2997346)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.49 % (2997346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.49 % (2997346)CaDiCaL version: 2.1.3
% 0.20/0.49 % (2997346)Termination reason: Refutation
% 0.20/0.49 % (2997346)Time elapsed: 0.007 s
% 0.20/0.49 % (2997346)Peak memory usage: 12 MB
% 0.20/0.49 % (2997346)Instructions burned: 10 (million)
% 0.20/0.49 % (2997340)Success in time 0.03 s
% 0.20/0.49 % Vampire exiting
%------------------------------------------------------------------------------