%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM739^1 : 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 : n012.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 08:18:43 AM UTC 2026
% Result : Theorem 0.08s 0.17s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 76 ( 19 unt; 0 typ; 2 def)
% Number of atoms : 376 ( 106 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 420 ( 76 ~; 58 |; 1 &; 256 @)
% ( 2 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 13 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 67 !; 0 ?; 67 :)
% 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,
moref: frac > frac > $o ).
thf(func_def_5,type,
eq: frac > frac > $o ).
thf(func_def_9,type,
vNOT: $o > $o ).
thf(f1,axiom,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(f2,axiom,
eq @ x @ z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e) ).
thf(f3,axiom,
eq @ y @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f) ).
thf(f5,axiom,
! [X1: frac,X0: frac,X2: frac] :
( ( eq @ X0 @ X1 )
=> ( ( eq @ X1 @ X2 )
=> ( eq @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz39) ).
thf(f6,axiom,
! [X0: frac,X1: frac] :
( ( eq @ X0 @ X1 )
=> ( eq @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz38) ).
thf(f7,axiom,
! [X1: frac,X0: frac,X2: frac,X3: frac] :
( ( moref @ X0 @ X1 )
=> ( ( eq @ X0 @ X2 )
=> ( ( eq @ X1 @ X3 )
=> ( moref @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz44) ).
thf(f8,conjecture,
( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz46) ).
thf(f9,negated_conjecture,
~ ( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
thf(f10,plain,
eq @ y @ u,
inference(rectify,[],[f3]) ).
thf(f11,plain,
( ( eq @ y @ u )
= $true ),
inference(fool_elimination,[],[f10]) ).
thf(f14,plain,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
inference(rectify,[],[f1]) ).
thf(f15,plain,
( ( ( moref @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
~ ( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
inference(rectify,[],[f9]) ).
thf(f17,plain,
~ ( ( ( moref @ z @ u )
!= $true )
=> ( ( eq @ z @ u )
= $true ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
! [X0: frac,X1: frac] :
( ( eq @ X0 @ X1 )
=> ( eq @ X1 @ X0 ) ),
inference(rectify,[],[f6]) ).
thf(f19,plain,
! [X1: frac,X0: frac] :
( ( ( eq @ X0 @ X1 )
= $true )
=> ( ( eq @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( moref @ X1 @ X0 )
=> ( ( eq @ X1 @ X2 )
=> ( ( eq @ X0 @ X3 )
=> ( moref @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f21,plain,
! [X3: frac,X0: frac,X1: frac,X2: frac] :
( ( ( moref @ X1 @ X0 )
= $true )
=> ( ( ( eq @ X1 @ X2 )
= $true )
=> ( ( ( eq @ X0 @ X3 )
= $true )
=> ( ( moref @ X2 @ X3 )
= $true ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
eq @ x @ z,
inference(rectify,[],[f2]) ).
thf(f23,plain,
( ( eq @ x @ z )
= $true ),
inference(fool_elimination,[],[f22]) ).
thf(f24,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( eq @ X1 @ X0 )
=> ( ( eq @ X0 @ X2 )
=> ( eq @ X1 @ X2 ) ) ),
inference(rectify,[],[f5]) ).
thf(f25,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X1 @ X0 )
= $true )
=> ( ( ( eq @ X0 @ X2 )
= $true )
=> ( ( eq @ X1 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f27,plain,
( ( ( moref @ x @ y )
!= $true )
=> ( ( eq @ x @ y )
= $true ) ),
inference(flattening,[],[f15]) ).
thf(f28,plain,
~ ( ( ( moref @ z @ u )
!= $true )
=> ( ( eq @ z @ u )
= $true ) ),
inference(flattening,[],[f17]) ).
thf(f29,plain,
! [X3: frac,X0: frac,X1: frac,X2: frac] :
( ( ( moref @ X2 @ X3 )
= $true )
| ( ( eq @ X0 @ X3 )
!= $true )
| ( ( eq @ X1 @ X2 )
!= $true )
| ( ( moref @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f21]) ).
thf(f30,plain,
! [X1: frac,X3: frac,X2: frac,X0: frac] :
( ( ( moref @ X1 @ X0 )
!= $true )
| ( ( moref @ X2 @ X3 )
= $true )
| ( ( eq @ X1 @ X2 )
!= $true )
| ( ( eq @ X0 @ X3 )
!= $true ) ),
inference(flattening,[],[f29]) ).
thf(f31,plain,
( ( ( eq @ x @ y )
= $true )
| ( ( moref @ x @ y )
= $true ) ),
inference(ennf_transformation,[],[f27]) ).
thf(f33,plain,
( ( ( moref @ z @ u )
!= $true )
& ( ( eq @ z @ u )
!= $true ) ),
inference(ennf_transformation,[],[f28]) ).
thf(f34,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X0 @ X1 )
!= $true )
| ( ( eq @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f35,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X1 @ X2 )
= $true )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( ( eq @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f25]) ).
thf(f36,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ X0 @ X2 )
!= $true )
| ( ( eq @ X1 @ X2 )
= $true )
| ( ( eq @ X1 @ X0 )
!= $true ) ),
inference(flattening,[],[f35]) ).
thf(f37,plain,
! [X0: frac,X1: frac,X2: frac] :
( ( ( eq @ X1 @ X0 )
!= $true )
| ( ( eq @ X2 @ X0 )
= $true )
| ( ( eq @ X2 @ X1 )
!= $true ) ),
inference(rectify,[],[f36]) ).
thf(f38,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( moref @ X0 @ X3 )
!= $true )
| ( ( moref @ X2 @ X1 )
= $true )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( ( eq @ X3 @ X1 )
!= $true ) ),
inference(rectify,[],[f30]) ).
thf(f39,plain,
( ( eq @ x @ z )
= $true ),
inference(cnf_transformation,[],[f23]) ).
thf(f40,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X0 @ X1 )
!= $true )
| ( ( eq @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f41,plain,
! [X2: frac,X0: frac,X1: frac] :
( ( ( eq @ X2 @ X1 )
!= $true )
| ( ( eq @ X1 @ X0 )
!= $true )
| ( ( eq @ X2 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f42,plain,
( ( ( moref @ x @ y )
= $true )
| ( ( eq @ x @ y )
= $true ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f44,plain,
( ( eq @ y @ u )
= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f45,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( ( eq @ X3 @ X1 )
!= $true )
| ( ( moref @ X2 @ X1 )
= $true )
| ( ( eq @ X0 @ X2 )
!= $true )
| ( ( moref @ X0 @ X3 )
!= $true ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f46,plain,
( ( eq @ z @ u )
!= $true ),
inference(cnf_transformation,[],[f33]) ).
thf(f47,plain,
( ( moref @ z @ u )
!= $true ),
inference(cnf_transformation,[],[f33]) ).
thf(f52,definition,
( spl0_1
<=> ( ( moref @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f54,plain,
( ( ( moref @ x @ y )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f52]) ).
thf(f56,definition,
( spl0_2
<=> ( ( eq @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f58,plain,
( ( ( eq @ x @ y )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f56]) ).
thf(f59,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f42,f56,f52]) ).
thf(f60,plain,
( ( $true
= ( eq @ z @ x ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f40,f39]) ).
thf(f61,plain,
( ( $true
= ( eq @ y @ x ) )
| ( $true != $true )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f40,f58]) ).
thf(f62,plain,
( ( ( eq @ u @ y )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f40,f44]) ).
thf(f63,plain,
( ( $true
= ( eq @ y @ x ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f61]) ).
thf(f64,plain,
( ( eq @ u @ y )
= $true ),
inference(trivial_inequality_removal,[],[f62]) ).
thf(f65,plain,
( $true
= ( eq @ z @ x ) ),
inference(trivial_inequality_removal,[],[f60]) ).
thf(f76,plain,
! [X0: frac] :
( ( ( eq @ x @ X0 )
!= $true )
| ( $true
= ( eq @ z @ X0 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f41,f65]) ).
thf(f77,plain,
! [X0: frac] :
( ( $true != $true )
| ( ( eq @ u @ X0 )
= $true )
| ( ( eq @ y @ X0 )
!= $true ) ),
inference(constrained_superposition,[],[f41,f64]) ).
thf(f78,plain,
! [X0: frac] :
( ( ( eq @ y @ X0 )
!= $true )
| ( ( eq @ u @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f77]) ).
thf(f82,plain,
! [X0: frac] :
( ( ( eq @ x @ X0 )
!= $true )
| ( $true
= ( eq @ z @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f76]) ).
thf(f91,plain,
( ( $true != $true )
| ( $true
= ( eq @ u @ x ) )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f78,f63]) ).
thf(f93,plain,
( ( $true
= ( eq @ u @ x ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f91]) ).
thf(f97,plain,
( ( $true != $true )
| ( ( eq @ x @ u )
= $true )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f40,f93]) ).
thf(f100,plain,
( ( ( eq @ x @ u )
= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f97]) ).
thf(f118,plain,
( ( $true != $true )
| ( ( eq @ z @ u )
= $true )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f82,f100]) ).
thf(f120,plain,
( ( ( eq @ z @ u )
= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f118]) ).
thf(f123,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f120,f46]) ).
thf(f124,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f123]) ).
thf(f130,plain,
! [X0: frac,X1: frac] :
( ( $true != $true )
| ( $true
= ( moref @ X0 @ u ) )
| ( ( moref @ X1 @ y )
!= $true )
| ( ( eq @ X1 @ X0 )
!= $true ) ),
inference(constrained_superposition,[],[f45,f44]) ).
thf(f142,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ X0 )
!= $true )
| ( ( moref @ X1 @ y )
!= $true )
| ( $true
= ( moref @ X0 @ u ) ) ),
inference(trivial_inequality_removal,[],[f130]) ).
thf(f145,plain,
( ( $true != $true )
| ( ( moref @ z @ u )
= $true )
| ( ( moref @ x @ y )
!= $true ) ),
inference(constrained_superposition,[],[f142,f39]) ).
thf(f154,plain,
( ( ( moref @ z @ u )
= $true )
| ( ( moref @ x @ y )
!= $true ) ),
inference(trivial_inequality_removal,[],[f145]) ).
thf(f178,plain,
( ( moref @ x @ y )
!= $true ),
inference(forward_subsumption_resolution,[],[f154,f47]) ).
thf(f192,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f178,f54]) ).
thf(f193,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f192]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f59]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f124]) ).
cnf(s8,plain,
~ spl0_1,
inference(sat_conversion,[],[f193]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s2,s8]) ).
thf(f196,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM739^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 12:46:33 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.13 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
% 0.08/0.17 % (56440)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.17 % (56461)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.17 % (56461)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
% 0.08/0.17 % (56455)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4148447307:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.17 % (56459)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3796777470:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.08/0.17 % (56458)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=122070626: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)
% 0.08/0.17 % (56456)lrs+10_16_si=on:nwc=1.5:random_seed=3180496015:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.17 % (56457)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1141444851:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.08/0.17 % (56460)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2034179262:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.17 % (56461)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=4109718435:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.08/0.17 % (56457)Instruction limit reached!
% 0.08/0.17 % (56457)------------------------------
% 0.08/0.17 % (56457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.17 % (56457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.17 % (56457)CaDiCaL version: 2.1.3
% 0.08/0.17 % (56457)Termination reason: Instruction limit
% 0.08/0.17 % (56457)Termination phase: Saturation
% 0.08/0.17 % (56457)Time elapsed: 0.002 s
% 0.08/0.17 % (56457)Peak memory usage: 12 MB
% 0.08/0.17 % (56457)Instructions burned: 5 (million)
% 0.08/0.17 % (56455) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-56440-56455"...
% 0.08/0.17 % (56456) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-56440-56456"...
% 0.08/0.17 % (56459) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-56440-56459"...
% 0.08/0.17 % (56455)...printing done.
% 0.08/0.17 % (56455)Refutation found. Thanks to Tanya!
% 0.08/0.17 % SZS status Theorem for theBenchmark
% 0.08/0.17 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.17 % (56455)------------------------------
% 0.08/0.17 % (56455)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.17 % (56455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.17 % (56455)CaDiCaL version: 2.1.3
% 0.08/0.17 % (56455)Termination reason: Refutation
% 0.08/0.17 % (56455)Time elapsed: 0.003 s
% 0.08/0.17 % (56455)Peak memory usage: 13 MB
% 0.08/0.17 % (56455)Instructions burned: 10 (million)
% 0.08/0.17 % (56440)Success in time 0.032 s
% 0.08/0.17 % Vampire exiting
%------------------------------------------------------------------------------