%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM746^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:18:44 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 88 ( 8 unt; 0 typ; 4 def)
% Number of atoms : 470 ( 120 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 564 ( 126 ~; 90 |; 5 &; 296 @)
% ( 4 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 14 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 74 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
frac: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: frac ).
thf(func_def_1,type,
y: frac ).
thf(func_def_2,type,
z: frac ).
thf(func_def_3,type,
lessf: frac > frac > $o ).
thf(func_def_4,type,
eq: frac > frac > $o ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(f1,axiom,
( ~ ( lessf @ x @ y )
=> ( eq @ x @ y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
thf(f2,axiom,
( ~ ( lessf @ y @ z )
=> ( eq @ y @ z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).
thf(f4,axiom,
! [X1: frac,X2: frac,X0: frac] :
( ( eq @ X0 @ X1 )
=> ( ( eq @ X1 @ X2 )
=> ( eq @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz39) ).
thf(f5,axiom,
! [X2: frac,X0: frac,X1: frac] :
( ( lessf @ X0 @ X1 )
=> ( ( ~ ( lessf @ X1 @ X2 )
=> ( eq @ X1 @ X2 ) )
=> ( lessf @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz51b) ).
thf(f6,axiom,
! [X0: frac,X2: frac,X1: frac] :
( ( ~ ( lessf @ X0 @ X1 )
=> ( eq @ X0 @ X1 ) )
=> ( ( lessf @ X1 @ X2 )
=> ( lessf @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz51a) ).
thf(f7,conjecture,
( ~ ( lessf @ x @ z )
=> ( eq @ x @ z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz52) ).
thf(f8,negated_conjecture,
~ ( ~ ( lessf @ x @ z )
=> ( eq @ x @ z ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
~ ( ~ ( lessf @ x @ z )
=> ( eq @ x @ z ) ),
inference(rectify,[],[f8]) ).
thf(f10,plain,
~ ( ( ( lessf @ x @ z )
!= $true )
=> ( ( eq @ x @ z )
= $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ~ ( lessf @ y @ z )
=> ( eq @ y @ z ) ),
inference(rectify,[],[f2]) ).
thf(f12,plain,
( ( ( lessf @ y @ z )
!= $true )
=> ( ( eq @ y @ z )
= $true ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( ~ ( lessf @ x @ y )
=> ( eq @ x @ y ) ),
inference(rectify,[],[f1]) ).
thf(f14,plain,
( ( ( lessf @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ~ ( lessf @ X0 @ X2 )
=> ( eq @ X0 @ X2 ) )
=> ( ( lessf @ X2 @ X1 )
=> ( lessf @ X0 @ X1 ) ) ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( ( lessf @ X0 @ X2 )
!= $true )
=> ( ( eq @ X0 @ X2 )
= $true ) )
=> ( ( ( lessf @ X2 @ X1 )
= $true )
=> ( ( lessf @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( lessf @ X1 @ X2 )
=> ( ( ~ ( lessf @ X2 @ X0 )
=> ( eq @ X2 @ X0 ) )
=> ( lessf @ X1 @ X0 ) ) ),
inference(rectify,[],[f5]) ).
thf(f18,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ X1 @ X2 )
= $true )
=> ( ( ( $true
!= ( lessf @ X2 @ X0 ) )
=> ( $true
= ( eq @ X2 @ X0 ) ) )
=> ( ( lessf @ X1 @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ X2 @ X0 )
=> ( ( eq @ X0 @ X1 )
=> ( eq @ X2 @ X1 ) ) ),
inference(rectify,[],[f4]) ).
thf(f20,plain,
! [X1: frac,X0: frac,X2: frac] :
( ( $true
= ( eq @ X2 @ X0 ) )
=> ( ( ( eq @ X0 @ X1 )
= $true )
=> ( $true
= ( eq @ X2 @ X1 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f23,plain,
~ ( ( ( lessf @ x @ z )
!= $true )
=> ( ( eq @ x @ z )
= $true ) ),
inference(flattening,[],[f10]) ).
thf(f24,plain,
( ( ( lessf @ y @ z )
!= $true )
=> ( ( eq @ y @ z )
= $true ) ),
inference(flattening,[],[f12]) ).
thf(f25,plain,
( ( ( lessf @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(flattening,[],[f14]) ).
thf(f26,plain,
! [X1: frac,X0: frac,X2: frac] :
( ( ( ( lessf @ X0 @ X2 )
!= $true )
=> ( ( eq @ X0 @ X2 )
= $true ) )
=> ( ( ( lessf @ X2 @ X1 )
= $true )
=> ( ( lessf @ X0 @ X1 )
= $true ) ) ),
inference(flattening,[],[f16]) ).
thf(f27,plain,
! [X1: frac,X2: frac,X0: frac] :
( ( ( lessf @ X1 @ X2 )
= $true )
=> ( ( ( $true
!= ( lessf @ X2 @ X0 ) )
=> ( $true
= ( eq @ X2 @ X0 ) ) )
=> ( ( lessf @ X1 @ X0 )
= $true ) ) ),
inference(flattening,[],[f18]) ).
thf(f29,plain,
! [X1: frac,X0: frac,X2: frac] :
( ( ( lessf @ X0 @ X1 )
= $true )
| ( ( lessf @ X2 @ X1 )
!= $true )
| ( ( ( eq @ X0 @ X2 )
!= $true )
& ( ( lessf @ X0 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f26]) ).
thf(f30,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( lessf @ X0 @ X1 )
= $true )
| ( ( ( eq @ X0 @ X2 )
!= $true )
& ( ( lessf @ X0 @ X2 )
!= $true ) )
| ( ( lessf @ X2 @ X1 )
!= $true ) ),
inference(flattening,[],[f29]) ).
thf(f31,plain,
! [X1: frac,X2: frac,X0: frac] :
( ( ( lessf @ X1 @ X0 )
= $true )
| ( ( $true
!= ( eq @ X2 @ X0 ) )
& ( $true
!= ( lessf @ X2 @ X0 ) ) )
| ( ( lessf @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f27]) ).
thf(f32,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( $true
!= ( eq @ X2 @ X0 ) )
& ( $true
!= ( lessf @ X2 @ X0 ) ) )
| ( ( lessf @ X1 @ X2 )
!= $true )
| ( ( lessf @ X1 @ X0 )
= $true ) ),
inference(flattening,[],[f31]) ).
thf(f34,plain,
! [X1: frac,X0: frac,X2: frac] :
( ( $true
= ( eq @ X2 @ X1 ) )
| ( ( eq @ X0 @ X1 )
!= $true )
| ( $true
!= ( eq @ X2 @ X0 ) ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f35,plain,
! [X1: frac,X0: frac,X2: frac] :
( ( $true
!= ( eq @ X2 @ X0 ) )
| ( $true
= ( eq @ X2 @ X1 ) )
| ( ( eq @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f34]) ).
thf(f36,plain,
( ( ( lessf @ y @ z )
= $true )
| ( ( eq @ y @ z )
= $true ) ),
inference(ennf_transformation,[],[f24]) ).
thf(f37,plain,
( ( ( lessf @ x @ y )
= $true )
| ( ( eq @ x @ y )
= $true ) ),
inference(ennf_transformation,[],[f25]) ).
thf(f38,plain,
( ( ( eq @ x @ z )
!= $true )
& ( ( lessf @ x @ z )
!= $true ) ),
inference(ennf_transformation,[],[f23]) ).
thf(f39,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( $true
!= ( eq @ X2 @ X1 ) )
| ( $true
= ( eq @ X2 @ X0 ) )
| ( ( eq @ X1 @ X0 )
!= $true ) ),
inference(rectify,[],[f35]) ).
thf(f40,plain,
( ( ( eq @ x @ y )
= $true )
| ( ( lessf @ x @ y )
= $true ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f41,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( eq @ X2 @ X1 ) )
| ( ( eq @ X1 @ X0 )
!= $true )
| ( $true
= ( eq @ X2 @ X0 ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f43,plain,
( ( lessf @ x @ z )
!= $true ),
inference(cnf_transformation,[],[f38]) ).
thf(f44,plain,
( ( eq @ x @ z )
!= $true ),
inference(cnf_transformation,[],[f38]) ).
thf(f45,plain,
( ( ( eq @ y @ z )
= $true )
| ( ( lessf @ y @ z )
= $true ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f46,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( lessf @ X2 @ X0 ) )
| ( ( lessf @ X1 @ X2 )
!= $true )
| ( ( lessf @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f47,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( eq @ X2 @ X0 ) )
| ( ( lessf @ X1 @ X0 )
= $true )
| ( ( lessf @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f49,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ X0 @ X2 )
!= $true )
| ( ( lessf @ X0 @ X1 )
= $true )
| ( ( lessf @ X2 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f54,definition,
( spl0_1
<=> ( ( eq @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f56,plain,
( ( ( eq @ x @ y )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f54]) ).
thf(f58,definition,
( spl0_2
<=> ( ( lessf @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f60,plain,
( ( ( lessf @ x @ y )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f58]) ).
thf(f61,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f40,f58,f54]) ).
thf(f63,definition,
( spl0_3
<=> ( ( eq @ y @ z )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f65,plain,
( ( ( eq @ y @ z )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f63]) ).
thf(f67,definition,
( spl0_4
<=> ( ( lessf @ y @ z )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f69,plain,
( ( ( lessf @ y @ z )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f67]) ).
thf(f70,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f45,f67,f63]) ).
thf(f75,plain,
( ! [X0: frac] :
( ( $true != $true )
| ( ( lessf @ X0 @ y )
!= $true )
| ( ( lessf @ X0 @ z )
= $true ) )
| ~ spl0_3 ),
inference(constrained_superposition,[],[f47,f65]) ).
thf(f76,plain,
( ! [X0: frac] :
( ( ( lessf @ X0 @ y )
!= $true )
| ( ( lessf @ X0 @ z )
= $true ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f75]) ).
thf(f77,plain,
( ( ( lessf @ x @ z )
= $true )
| ( $true != $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(constrained_superposition,[],[f76,f60]) ).
thf(f78,plain,
( ( ( lessf @ x @ z )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f77]) ).
thf(f79,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f78,f43]) ).
thf(f80,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f79]) ).
thf(f82,plain,
( ! [X0: frac] :
( ( ( eq @ y @ X0 )
!= $true )
| ( ( eq @ x @ X0 )
= $true )
| ( $true != $true ) )
| ~ spl0_1 ),
inference(constrained_superposition,[],[f41,f56]) ).
thf(f84,plain,
( ! [X0: frac] :
( ( ( eq @ y @ X0 )
!= $true )
| ( ( eq @ x @ X0 )
= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f82]) ).
thf(f85,plain,
( ( ( eq @ x @ z )
= $true )
| ( $true != $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(constrained_superposition,[],[f84,f65]) ).
thf(f86,plain,
( ( ( eq @ x @ z )
= $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f85]) ).
thf(f87,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f86,f44]) ).
thf(f88,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f87]) ).
thf(f91,plain,
( ! [X0: frac] :
( ( ( lessf @ X0 @ y )
!= $true )
| ( $true != $true )
| ( ( lessf @ X0 @ z )
= $true ) )
| ~ spl0_4 ),
inference(constrained_superposition,[],[f46,f69]) ).
thf(f92,plain,
( ! [X0: frac] :
( ( ( lessf @ X0 @ y )
!= $true )
| ( ( lessf @ X0 @ z )
= $true ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f91]) ).
thf(f93,plain,
( ( ( lessf @ x @ z )
= $true )
| ( $true != $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(constrained_superposition,[],[f92,f60]) ).
thf(f94,plain,
( ( ( lessf @ x @ z )
= $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f93]) ).
thf(f95,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f94,f43]) ).
thf(f96,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f95]) ).
thf(f97,plain,
( ! [X0: frac] :
( ( $true != $true )
| ( ( lessf @ y @ X0 )
!= $true )
| ( ( lessf @ x @ X0 )
= $true ) )
| ~ spl0_1 ),
inference(constrained_superposition,[],[f49,f56]) ).
thf(f102,plain,
( ! [X0: frac] :
( ( ( lessf @ y @ X0 )
!= $true )
| ( ( lessf @ x @ X0 )
= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f97]) ).
thf(f103,plain,
( ( $true != $true )
| ( ( lessf @ x @ z )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(constrained_superposition,[],[f102,f69]) ).
thf(f104,plain,
( ( ( lessf @ x @ z )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f103]) ).
thf(f105,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f104,f43]) ).
thf(f106,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f105]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f61]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f70]) ).
cnf(s3,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f80]) ).
cnf(s4,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f88]) ).
cnf(s5,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f96]) ).
cnf(s6,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f106]) ).
cnf(s7,plain,
~ spl0_2,
inference(rat,[],[s2,s3,s5]) ).
cnf(s8,plain,
spl0_1,
inference(rat,[],[s1,s7]) ).
cnf(s9,plain,
~ spl0_4,
inference(rat,[],[s6,s8]) ).
cnf(s10,plain,
~ spl0_3,
inference(rat,[],[s4,s8]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s2,s9,s10]) ).
thf(f107,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM746^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n001.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 12:53:51 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.27 % (1189022)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (1189038)lrs+10_16_si=on:nwc=1.5:random_seed=631362977:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.27 % (1189038) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1189022-1189038"...
% 0.21/0.27 % (1189038)...printing done.
% 0.21/0.27 % (1189038)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (1189038)------------------------------
% 0.21/0.27 % (1189038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (1189038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (1189038)CaDiCaL version: 2.1.3
% 0.21/0.27 % (1189038)Termination reason: Refutation
% 0.21/0.27 % (1189038)Time elapsed: 0.003 s
% 0.21/0.27 % (1189038)Peak memory usage: 13 MB
% 0.21/0.27 % (1189038)Instructions burned: 8 (million)
% 0.21/0.27 % (1189022)Success in time 0.03 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------