%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM753^1 : 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 08:18:46 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 67 ( 27 unt; 0 typ; 3 def)
% Number of atoms : 353 ( 95 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 519 ( 81 ~; 75 |; 0 &; 342 @)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 97 ( 0 sgn 97 !; 0 ?; 97 :)
% 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,
u: frac ).
thf(func_def_4,type,
eq: frac > frac > $o ).
thf(func_def_6,type,
moref: frac > frac > $o ).
thf(func_def_7,type,
pf: frac > frac > frac ).
thf(f1,axiom,
eq @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e) ).
thf(f2,axiom,
moref @ z @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(f3,axiom,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( moref @ X0 @ X1 )
=> ( ( eq @ X0 @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( moref @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz44) ).
thf(f4,axiom,
! [X0: frac,X2: frac,X1: frac] :
( ( moref @ X0 @ X1 )
=> ( moref @ ( pf @ X2 @ X0 ) @ ( pf @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz62d) ).
thf(f5,axiom,
! [X0: frac] : ( eq @ X0 @ X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz37) ).
thf(f6,axiom,
! [X2: frac,X1: frac,X3: frac,X0: frac] :
( ( eq @ X0 @ X1 )
=> ( ( eq @ X2 @ X3 )
=> ( eq @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz56) ).
thf(f7,conjecture,
moref @ ( pf @ x @ z ) @ ( pf @ y @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz62g) ).
thf(f8,negated_conjecture,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
! [X0: frac] : ( eq @ X0 @ X0 ),
inference(rectify,[],[f5]) ).
thf(f10,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( moref @ X0 @ X2 )
=> ( moref @ ( pf @ X1 @ X0 ) @ ( pf @ X1 @ X2 ) ) ),
inference(rectify,[],[f4]) ).
thf(f12,plain,
! [X0: frac,X2: frac,X1: frac] :
( ( $true
= ( moref @ X0 @ X2 ) )
=> ( $true
= ( moref @ ( pf @ X1 @ X0 ) @ ( pf @ X1 @ X2 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( eq @ X3 @ X1 )
=> ( ( eq @ X0 @ X2 )
=> ( eq @ ( pf @ X3 @ X0 ) @ ( pf @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f14,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true
= ( eq @ X3 @ X1 ) )
=> ( ( ( eq @ X0 @ X2 )
= $true )
=> ( $true
= ( eq @ ( pf @ X3 @ X0 ) @ ( pf @ X1 @ X2 ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
moref @ z @ u,
inference(rectify,[],[f2]) ).
thf(f16,plain,
( ( moref @ z @ u )
= $true ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(rectify,[],[f8]) ).
thf(f18,plain,
( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
!= $true ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( moref @ X2 @ X3 )
=> ( ( eq @ X2 @ X0 )
=> ( ( eq @ X3 @ X1 )
=> ( moref @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f20,plain,
! [X0: frac,X3: frac,X1: frac,X2: frac] :
( ( ( moref @ X2 @ X3 )
= $true )
=> ( ( $true
= ( eq @ X2 @ X0 ) )
=> ( ( $true
= ( eq @ X3 @ X1 ) )
=> ( ( moref @ X0 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
eq @ x @ y,
inference(rectify,[],[f1]) ).
thf(f22,plain,
( ( eq @ x @ y )
= $true ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
!= $true ),
inference(flattening,[],[f18]) ).
thf(f24,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true
= ( eq @ ( pf @ X3 @ X0 ) @ ( pf @ X1 @ X2 ) ) )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( $true
!= ( eq @ X3 @ X1 ) ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f25,plain,
! [X3: frac,X0: frac,X2: frac,X1: frac] :
( ( $true
= ( eq @ ( pf @ X3 @ X0 ) @ ( pf @ X1 @ X2 ) ) )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( $true
!= ( eq @ X3 @ X1 ) ) ),
inference(flattening,[],[f24]) ).
thf(f26,plain,
! [X0: frac,X3: frac,X1: frac,X2: frac] :
( ( ( moref @ X0 @ X1 )
= $true )
| ( $true
!= ( eq @ X3 @ X1 ) )
| ( $true
!= ( eq @ X2 @ X0 ) )
| ( ( moref @ X2 @ X3 )
!= $true ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f27,plain,
! [X0: frac,X2: frac,X3: frac,X1: frac] :
( ( ( moref @ X0 @ X1 )
= $true )
| ( $true
!= ( eq @ X2 @ X0 ) )
| ( $true
!= ( eq @ X3 @ X1 ) )
| ( ( moref @ X2 @ X3 )
!= $true ) ),
inference(flattening,[],[f26]) ).
thf(f28,plain,
! [X1: frac,X2: frac,X0: frac] :
( ( $true
!= ( moref @ X0 @ X2 ) )
| ( $true
= ( moref @ ( pf @ X1 @ X0 ) @ ( pf @ X1 @ X2 ) ) ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f29,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true
= ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X3 @ X2 ) ) )
| ( $true
!= ( eq @ X1 @ X2 ) )
| ( $true
!= ( eq @ X0 @ X3 ) ) ),
inference(rectify,[],[f25]) ).
thf(f30,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( $true
!= ( moref @ X2 @ X1 ) )
| ( $true
= ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f28]) ).
thf(f31,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( $true
= ( moref @ X0 @ X3 ) )
| ( $true
!= ( eq @ X1 @ X0 ) )
| ( ( eq @ X2 @ X3 )
!= $true )
| ( $true
!= ( moref @ X1 @ X2 ) ) ),
inference(rectify,[],[f27]) ).
thf(f32,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f33,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true
= ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ X3 @ X2 ) ) )
| ( $true
!= ( eq @ X1 @ X2 ) )
| ( $true
!= ( eq @ X0 @ X3 ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f34,plain,
( ( moref @ z @ u )
= $true ),
inference(cnf_transformation,[],[f16]) ).
thf(f35,plain,
( ( eq @ x @ y )
= $true ),
inference(cnf_transformation,[],[f22]) ).
thf(f36,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( $true
= ( moref @ ( pf @ X0 @ X2 ) @ ( pf @ X0 @ X1 ) ) )
| ( $true
!= ( moref @ X2 @ X1 ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f37,plain,
( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
!= $true ),
inference(cnf_transformation,[],[f23]) ).
thf(f38,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true
= ( moref @ X0 @ X3 ) )
| ( $true
!= ( moref @ X1 @ X2 ) )
| ( ( eq @ X2 @ X3 )
!= $true )
| ( $true
!= ( eq @ X1 @ X0 ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f41,definition,
( spl0_1
<=> ( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f43,plain,
( ( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
!= $true )
| spl0_1 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f44,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f37,f41]) ).
thf(f46,definition,
( spl0_2
<=> ( ( moref @ z @ u )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f48,plain,
( ( ( moref @ z @ u )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f46]) ).
thf(f49,plain,
spl0_2,
inference(avatar_split_clause,[],[f34,f46]) ).
thf(f51,definition,
( spl0_3
<=> ( ( eq @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f53,plain,
( ( ( eq @ x @ y )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f54,plain,
spl0_3,
inference(avatar_split_clause,[],[f35,f51]) ).
thf(f55,plain,
( ! [X0: frac,X1: frac] :
( ( $true != $true )
| ( ( eq @ X0 @ ( pf @ x @ z ) )
!= $true )
| ( ( moref @ X0 @ X1 )
!= $true )
| ( $true
!= ( eq @ X1 @ ( pf @ y @ u ) ) ) )
| spl0_1 ),
inference(superposition,[],[f43,f38]) ).
thf(f56,plain,
( ! [X0: frac,X1: frac] :
( ( $true
!= ( eq @ X1 @ ( pf @ y @ u ) ) )
| ( ( moref @ X0 @ X1 )
!= $true )
| ( ( eq @ X0 @ ( pf @ x @ z ) )
!= $true ) )
| spl0_1 ),
inference(trivial_inequality_removal,[],[f55]) ).
thf(f58,plain,
( ! [X2: frac,X0: frac,X1: frac] :
( ( $true != $true )
| ( $true
!= ( eq @ X1 @ u ) )
| ( $true
!= ( eq @ X2 @ ( pf @ x @ z ) ) )
| ( $true
!= ( moref @ X2 @ ( pf @ X0 @ X1 ) ) )
| ( $true
!= ( eq @ X0 @ y ) ) )
| spl0_1 ),
inference(superposition,[],[f56,f33]) ).
thf(f60,plain,
( ! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( moref @ X2 @ ( pf @ X0 @ X1 ) ) )
| ( $true
!= ( eq @ X1 @ u ) )
| ( $true
!= ( eq @ X2 @ ( pf @ x @ z ) ) )
| ( $true
!= ( eq @ X0 @ y ) ) )
| spl0_1 ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f65,plain,
( ! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ x @ z ) ) )
| ( $true
!= ( eq @ X2 @ u ) )
| ( $true != $true )
| ( $true
!= ( moref @ X1 @ X2 ) )
| ( $true
!= ( eq @ X0 @ y ) ) )
| spl0_1 ),
inference(superposition,[],[f60,f36]) ).
thf(f68,plain,
( ! [X2: frac,X0: frac,X1: frac] :
( ( $true
!= ( eq @ ( pf @ X0 @ X1 ) @ ( pf @ x @ z ) ) )
| ( $true
!= ( eq @ X0 @ y ) )
| ( $true
!= ( moref @ X1 @ X2 ) )
| ( $true
!= ( eq @ X2 @ u ) ) )
| spl0_1 ),
inference(trivial_inequality_removal,[],[f65]) ).
thf(f84,plain,
( ! [X0: frac] :
( ( $true
!= ( moref @ z @ X0 ) )
| ( ( eq @ x @ y )
!= $true )
| ( $true
!= ( eq @ X0 @ u ) )
| ( $true != $true ) )
| spl0_1 ),
inference(superposition,[],[f68,f32]) ).
thf(f86,plain,
( ! [X0: frac] :
( ( $true
!= ( moref @ z @ X0 ) )
| ( $true
!= ( eq @ X0 @ u ) )
| ( ( eq @ x @ y )
!= $true ) )
| spl0_1 ),
inference(trivial_inequality_removal,[],[f84]) ).
thf(f94,plain,
( ! [X0: frac] :
( ( $true
!= ( moref @ z @ X0 ) )
| ( $true
!= ( eq @ X0 @ u ) ) )
| spl0_1
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f86,f53]) ).
thf(f99,plain,
( ( $true != $true )
| ( $true
!= ( eq @ u @ u ) )
| spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f94,f48]) ).
thf(f101,plain,
( ( $true
!= ( eq @ u @ u ) )
| spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f99]) ).
thf(f103,plain,
( $false
| spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f101,f32]) ).
thf(f104,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f103]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f44]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f49]) ).
cnf(s3,plain,
spl0_3,
inference(sat_conversion,[],[f54]) ).
cnf(s6,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f104]) ).
cnf(s7,plain,
spl0_1,
inference(rat,[],[s6,s3,s2]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7]) ).
thf(f105,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM753^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n017.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 12:46:07 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 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
% 0.22/0.28 % (286357)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (286365)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=4164277190: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)
% 0.22/0.28 % (286365) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-286357-286365"...
% 0.22/0.28 % (286368)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.28 % (286368)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
% 0.22/0.28 % (286365)...printing done.
% 0.22/0.28 % (286365)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (286365)------------------------------
% 0.22/0.29 % (286365)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (286365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (286365)CaDiCaL version: 2.1.3
% 0.22/0.29 % (286365)Termination reason: Refutation
% 0.22/0.29 % (286365)Time elapsed: 0.004 s
% 0.22/0.29 % (286365)Peak memory usage: 13 MB
% 0.22/0.29 % (286365)Instructions burned: 11 (million)
% 0.22/0.29 % (286357)Success in time 0.036 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------