%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM757^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 08:18:47 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 70 ( 19 unt; 0 typ; 4 def)
% Number of atoms : 348 ( 93 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 515 ( 97 ~; 50 |; 4 &; 326 @)
% ( 4 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 15 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 78 !; 0 ?; 78 :)
% 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,
pf: frac > frac > frac ).
thf(func_def_6,type,
moref: frac > frac > $o ).
thf(func_def_7,type,
eq: frac > frac > $o ).
thf(f1,axiom,
lessf @ ( pf @ x @ z ) @ ( pf @ y @ z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(f3,axiom,
! [X0: frac,X1: frac] :
~ ( ( ( eq @ X0 @ X1 )
=> ~ ( moref @ X0 @ X1 ) )
=> ~ ~ ( ( ( moref @ X0 @ X1 )
=> ~ ( lessf @ X0 @ X1 ) )
=> ~ ( ( lessf @ X0 @ X1 )
=> ~ ( eq @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz41b) ).
thf(f4,axiom,
! [X1: frac,X2: frac,X0: frac] :
( ( moref @ X0 @ X1 )
=> ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz62a) ).
thf(f5,axiom,
! [X1: frac,X2: frac,X0: frac] :
( ( eq @ X0 @ X1 )
=> ( eq @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz62b) ).
thf(f6,axiom,
! [X0: frac,X1: frac] :
( ~ ( eq @ X0 @ X1 )
=> ( ~ ( moref @ X0 @ X1 )
=> ( lessf @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz41a) ).
thf(f7,conjecture,
lessf @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz63c) ).
thf(f8,negated_conjecture,
~ ( lessf @ x @ y ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ X2 @ X0 )
=> ( eq @ ( pf @ X2 @ X1 ) @ ( pf @ X0 @ X1 ) ) ),
inference(rectify,[],[f5]) ).
thf(f10,plain,
! [X0: frac,X2: frac,X1: frac] :
( ( $true
= ( eq @ X2 @ X0 ) )
=> ( $true
= ( eq @ ( pf @ X2 @ X1 ) @ ( pf @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f13,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( moref @ X2 @ X0 )
=> ( moref @ ( pf @ X2 @ X1 ) @ ( pf @ X0 @ X1 ) ) ),
inference(rectify,[],[f4]) ).
thf(f14,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
= ( moref @ X2 @ X0 ) )
=> ( $true
= ( moref @ ( pf @ X2 @ X1 ) @ ( pf @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
! [X0: frac,X1: frac] :
~ ( ( ( eq @ X0 @ X1 )
=> ~ ( moref @ X0 @ X1 ) )
=> ~ ~ ( ( ( moref @ X0 @ X1 )
=> ~ ( lessf @ X0 @ X1 ) )
=> ~ ( ( lessf @ X0 @ X1 )
=> ~ ( eq @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f16,plain,
! [X0: frac,X1: frac] :
~ ( ( ( ( eq @ X0 @ X1 )
= $true )
=> ( ( moref @ X0 @ X1 )
!= $true ) )
=> ~ ~ ( ( ( ( moref @ X0 @ X1 )
= $true )
=> ( ( lessf @ X0 @ X1 )
!= $true ) )
=> ~ ( ( ( lessf @ X0 @ X1 )
= $true )
=> ( ( eq @ X0 @ X1 )
!= $true ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
~ ( lessf @ x @ y ),
inference(rectify,[],[f8]) ).
thf(f18,plain,
( ( lessf @ x @ y )
!= $true ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
lessf @ ( pf @ x @ z ) @ ( pf @ y @ z ),
inference(rectify,[],[f1]) ).
thf(f20,plain,
( ( lessf @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
= $true ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
! [X0: frac,X1: frac] :
( ~ ( eq @ X0 @ X1 )
=> ( ~ ( moref @ X0 @ X1 )
=> ( lessf @ X0 @ X1 ) ) ),
inference(rectify,[],[f6]) ).
thf(f22,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X0 @ X1 )
!= $true )
=> ( ( ( moref @ X0 @ X1 )
!= $true )
=> ( ( lessf @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f24,plain,
! [X1: frac,X0: frac] :
~ ( ( ( ( eq @ X0 @ X1 )
= $true )
=> ( ( moref @ X0 @ X1 )
!= $true ) )
=> ( ( ( ( moref @ X0 @ X1 )
= $true )
=> ( ( lessf @ X0 @ X1 )
!= $true ) )
=> ~ ( ( ( lessf @ X0 @ X1 )
= $true )
=> ( ( eq @ X0 @ X1 )
!= $true ) ) ) ),
inference(flattening,[],[f16]) ).
thf(f25,plain,
( ( lessf @ x @ y )
!= $true ),
inference(flattening,[],[f18]) ).
thf(f26,plain,
! [X1: frac,X0: frac] :
( ( ( eq @ X0 @ X1 )
!= $true )
=> ( ( ( moref @ X0 @ X1 )
!= $true )
=> ( ( lessf @ X0 @ X1 )
= $true ) ) ),
inference(flattening,[],[f22]) ).
thf(f27,plain,
! [X1: frac,X0: frac,X2: frac] :
( ( $true
= ( moref @ ( pf @ X2 @ X1 ) @ ( pf @ X0 @ X1 ) ) )
| ( $true
!= ( moref @ X2 @ X0 ) ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f28,plain,
! [X1: frac,X0: frac] :
( ( ( ( eq @ X0 @ X1 )
!= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) )
& ( ( ( lessf @ X0 @ X1 )
!= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) )
& ( ( ( eq @ X0 @ X1 )
!= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[],[f24]) ).
thf(f29,plain,
! [X0: frac,X1: frac] :
( ( ( ( eq @ X0 @ X1 )
!= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) )
& ( ( ( lessf @ X0 @ X1 )
!= $true )
| ( ( moref @ X0 @ X1 )
!= $true ) )
& ( ( ( eq @ X0 @ X1 )
!= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) ) ),
inference(flattening,[],[f28]) ).
thf(f30,plain,
! [X1: frac,X0: frac] :
( ( ( lessf @ X0 @ X1 )
= $true )
| ( ( moref @ X0 @ X1 )
= $true )
| ( ( eq @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f26]) ).
thf(f31,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X0 @ X1 )
= $true )
| ( ( moref @ X0 @ X1 )
= $true )
| ( ( lessf @ X0 @ X1 )
= $true ) ),
inference(flattening,[],[f30]) ).
thf(f32,plain,
! [X1: frac,X0: frac,X2: frac] :
( ( $true
!= ( eq @ X2 @ X0 ) )
| ( $true
= ( eq @ ( pf @ X2 @ X1 ) @ ( pf @ X0 @ X1 ) ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f34,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( $true
!= ( eq @ X2 @ X1 ) )
| ( $true
= ( eq @ ( pf @ X2 @ X0 ) @ ( pf @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f35,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( $true
= ( moref @ ( pf @ X2 @ X0 ) @ ( pf @ X1 @ X0 ) ) )
| ( ( moref @ X2 @ X1 )
!= $true ) ),
inference(rectify,[],[f27]) ).
thf(f36,plain,
( ( lessf @ x @ y )
!= $true ),
inference(cnf_transformation,[],[f25]) ).
thf(f37,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
= ( eq @ ( pf @ X2 @ X0 ) @ ( pf @ X1 @ X0 ) ) )
| ( $true
!= ( eq @ X2 @ X1 ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f38,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
= ( moref @ ( pf @ X2 @ X0 ) @ ( pf @ X1 @ X0 ) ) )
| ( ( moref @ X2 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f40,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X0 @ X1 )
= $true )
| ( ( moref @ X0 @ X1 )
= $true )
| ( ( lessf @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f41,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X0 @ X1 )
!= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f42,plain,
! [X0: frac,X1: frac] :
( ( ( moref @ X0 @ X1 )
!= $true )
| ( ( lessf @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f44,plain,
( ( lessf @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
= $true ),
inference(cnf_transformation,[],[f20]) ).
thf(f48,definition,
( spl0_1
<=> ( ( lessf @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f50,plain,
( ( ( lessf @ x @ y )
!= $true )
| spl0_1 ),
inference(avatar_component_clause,[],[f48]) ).
thf(f51,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f36,f48]) ).
thf(f53,definition,
( spl0_2
<=> ( ( lessf @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f55,plain,
( ( ( lessf @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f53]) ).
thf(f56,plain,
spl0_2,
inference(avatar_split_clause,[],[f44,f53]) ).
thf(f58,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( lessf @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) ) )
| ( $true != $true )
| ( $true
!= ( eq @ X0 @ X2 ) ) ),
inference(superposition,[],[f41,f37]) ).
thf(f59,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( lessf @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) ) )
| ( $true
!= ( eq @ X0 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f60,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true != $true )
| ( $true
!= ( lessf @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) ) )
| ( ( moref @ X0 @ X2 )
!= $true ) ),
inference(superposition,[],[f42,f38]) ).
thf(f61,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( lessf @ ( pf @ X0 @ X1 ) @ ( pf @ X2 @ X1 ) ) )
| ( ( moref @ X0 @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f60]) ).
thf(f65,plain,
( ( $true
!= ( eq @ x @ y ) )
| ( $true != $true )
| ~ spl0_2 ),
inference(superposition,[],[f59,f55]) ).
thf(f66,plain,
( ( $true
!= ( eq @ x @ y ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f65]) ).
thf(f68,definition,
( spl0_3
<=> ( $true
= ( eq @ x @ y ) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f70,plain,
( ( $true
!= ( eq @ x @ y ) )
| spl0_3 ),
inference(avatar_component_clause,[],[f68]) ).
thf(f71,plain,
( ~ spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f66,f53,f68]) ).
thf(f72,plain,
( ( $true != $true )
| ( $true
!= ( moref @ x @ y ) )
| ~ spl0_2 ),
inference(superposition,[],[f61,f55]) ).
thf(f73,plain,
( ( $true
!= ( moref @ x @ y ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f72]) ).
thf(f75,definition,
( spl0_4
<=> ( $true
= ( moref @ x @ y ) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f78,plain,
( ~ spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f73,f53,f75]) ).
thf(f81,plain,
( ( $true != $true )
| ( ( lessf @ x @ y )
= $true )
| ( $true
= ( moref @ x @ y ) )
| spl0_3 ),
inference(superposition,[],[f70,f40]) ).
thf(f82,plain,
( ( $true
= ( moref @ x @ y ) )
| ( ( lessf @ x @ y )
= $true )
| spl0_3 ),
inference(trivial_inequality_removal,[],[f81]) ).
thf(f83,plain,
( ( $true
= ( moref @ x @ y ) )
| spl0_1
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f82,f50]) ).
thf(f84,plain,
( spl0_4
| spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f83,f68,f48,f75]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f51]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f56]) ).
cnf(s3,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f71]) ).
cnf(s4,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f78]) ).
cnf(s5,plain,
( spl0_1
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f84]) ).
cnf(s6,plain,
~ spl0_4,
inference(rat,[],[s4,s2]) ).
cnf(s7,plain,
~ spl0_3,
inference(rat,[],[s3,s2]) ).
cnf(s8,plain,
spl0_1,
inference(rat,[],[s5,s6,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s8]) ).
thf(f85,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM757^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 12:47:51 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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
% 0.20/0.28 % (286780)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (286788)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=3082007476: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)
% 0.20/0.28 % (286788) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-286780-286788"...
% 0.20/0.28 % (286791)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.28 % (286791)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.28 % (286788)...printing done.
% 0.20/0.28 % (286788)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 % (286788)------------------------------
% 0.20/0.28 % (286788)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (286788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (286788)CaDiCaL version: 2.1.3
% 0.20/0.28 % (286788)Termination reason: Refutation
% 0.20/0.28 % (286788)Time elapsed: 0.003 s
% 0.20/0.28 % (286788)Peak memory usage: 13 MB
% 0.20/0.28 % (286788)Instructions burned: 7 (million)
% 0.20/0.28 % (286780)Success in time 0.03 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------