%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM688^1 : 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 : 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 : Wed Sep 30 08:18:33 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 64 ( 19 unt; 0 typ; 5 def)
% Number of atoms : 240 ( 68 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 367 ( 57 ~; 49 |; 0 &; 240 @)
% ( 5 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 15 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 59 !; 0 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: nat ).
thf(func_def_1,type,
y: nat ).
thf(func_def_2,type,
z: nat ).
thf(func_def_3,type,
u: nat ).
thf(func_def_4,type,
more: nat > nat > $o ).
thf(func_def_6,type,
pl: nat > nat > nat ).
thf(f1,axiom,
more @ x @ y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(f2,axiom,
( ~ ( more @ z @ u )
=> ( z = u ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
thf(f4,axiom,
! [X2: nat,X0: nat,X1: nat,X3: nat] :
( ( X0 = X1 )
=> ( ( more @ X2 @ X3 )
=> ( more @ ( pl @ X2 @ X0 ) @ ( pl @ X3 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19h) ).
thf(f5,axiom,
! [X1: nat,X2: nat,X3: nat,X0: nat] :
( ( more @ X0 @ X1 )
=> ( ( more @ X2 @ X3 )
=> ( more @ ( pl @ X0 @ X2 ) @ ( pl @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz21) ).
thf(f6,conjecture,
more @ ( pl @ x @ z ) @ ( pl @ y @ u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz22b) ).
thf(f7,negated_conjecture,
~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
( ~ ( more @ z @ u )
=> ( z = u ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
( ( ( more @ z @ u )
!= $true )
=> ( z = u ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ),
inference(rectify,[],[f7]) ).
thf(f11,plain,
( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
!= $true ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
more @ x @ y,
inference(rectify,[],[f1]) ).
thf(f13,plain,
( ( more @ x @ y )
= $true ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( more @ X3 @ X0 )
=> ( ( more @ X1 @ X2 )
=> ( more @ ( pl @ X3 @ X1 ) @ ( pl @ X0 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f15,plain,
! [X3: nat,X0: nat,X1: nat,X2: nat] :
( ( $true
= ( more @ X3 @ X0 ) )
=> ( ( $true
= ( more @ X1 @ X2 ) )
=> ( $true
= ( more @ ( pl @ X3 @ X1 ) @ ( pl @ X0 @ X2 ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f18,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( X1 = X2 )
=> ( ( more @ X0 @ X3 )
=> ( more @ ( pl @ X0 @ X1 ) @ ( pl @ X3 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f19,plain,
! [X2: nat,X0: nat,X3: nat,X1: nat] :
( ( X1 = X2 )
=> ( ( $true
= ( more @ X0 @ X3 ) )
=> ( $true
= ( more @ ( pl @ X0 @ X1 ) @ ( pl @ X3 @ X2 ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ( ( more @ z @ u )
!= $true )
=> ( z = u ) ),
inference(flattening,[],[f9]) ).
thf(f21,plain,
( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
!= $true ),
inference(flattening,[],[f11]) ).
thf(f23,plain,
( ( z = u )
| ( ( more @ z @ u )
= $true ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f24,plain,
! [X2: nat,X0: nat,X3: nat,X1: nat] :
( ( $true
= ( more @ ( pl @ X0 @ X1 ) @ ( pl @ X3 @ X2 ) ) )
| ( $true
!= ( more @ X0 @ X3 ) )
| ( X1 != X2 ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f25,plain,
! [X0: nat,X3: nat,X1: nat,X2: nat] :
( ( X1 != X2 )
| ( $true
!= ( more @ X0 @ X3 ) )
| ( $true
= ( more @ ( pl @ X0 @ X1 ) @ ( pl @ X3 @ X2 ) ) ) ),
inference(flattening,[],[f24]) ).
thf(f26,plain,
! [X3: nat,X0: nat,X1: nat,X2: nat] :
( ( $true
= ( more @ ( pl @ X3 @ X1 ) @ ( pl @ X0 @ X2 ) ) )
| ( $true
!= ( more @ X1 @ X2 ) )
| ( $true
!= ( more @ X3 @ X0 ) ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f27,plain,
! [X1: nat,X3: nat,X0: nat,X2: nat] :
( ( $true
!= ( more @ X3 @ X0 ) )
| ( $true
= ( more @ ( pl @ X3 @ X1 ) @ ( pl @ X0 @ X2 ) ) )
| ( $true
!= ( more @ X1 @ X2 ) ) ),
inference(flattening,[],[f26]) ).
thf(f29,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( X2 != X3 )
| ( ( more @ X0 @ X1 )
!= $true )
| ( ( more @ ( pl @ X0 @ X2 ) @ ( pl @ X1 @ X3 ) )
= $true ) ),
inference(rectify,[],[f25]) ).
thf(f30,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true
!= ( more @ X1 @ X2 ) )
| ( $true
= ( more @ ( pl @ X1 @ X0 ) @ ( pl @ X2 @ X3 ) ) )
| ( $true
!= ( more @ X0 @ X3 ) ) ),
inference(rectify,[],[f27]) ).
thf(f31,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( X2 != X3 )
| ( ( more @ X0 @ X1 )
!= $true )
| ( ( more @ ( pl @ X0 @ X2 ) @ ( pl @ X1 @ X3 ) )
= $true ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f32,plain,
( ( z = u )
| ( ( more @ z @ u )
= $true ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f33,plain,
( ( more @ x @ y )
= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f34,plain,
( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
!= $true ),
inference(cnf_transformation,[],[f21]) ).
thf(f35,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true
= ( more @ ( pl @ X1 @ X0 ) @ ( pl @ X2 @ X3 ) ) )
| ( $true
!= ( more @ X1 @ X2 ) )
| ( $true
!= ( more @ X0 @ X3 ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f38,plain,
! [X3: nat,X0: nat,X1: nat] :
( ( $true
= ( more @ ( pl @ X0 @ X3 ) @ ( pl @ X1 @ X3 ) ) )
| ( ( more @ X0 @ X1 )
!= $true ) ),
inference(equality_resolution,[],[f31]) ).
thf(f41,definition,
( spl0_1
<=> ( z = u ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f43,plain,
( ( z = u )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f45,definition,
( spl0_2
<=> ( ( more @ z @ u )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f48,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f32,f45,f41]) ).
thf(f50,definition,
( spl0_3
<=> ( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f52,plain,
( ( ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
!= $true )
| spl0_3 ),
inference(avatar_component_clause,[],[f50]) ).
thf(f53,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f34,f50]) ).
thf(f55,definition,
( spl0_4
<=> ( ( more @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f57,plain,
( ( ( more @ x @ y )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f58,plain,
spl0_4,
inference(avatar_split_clause,[],[f33,f55]) ).
thf(f59,plain,
( ( ( more @ x @ y )
!= $true )
| ( $true != $true )
| ( ( more @ z @ u )
!= $true )
| spl0_3 ),
inference(superposition,[],[f52,f35]) ).
thf(f60,plain,
( ( ( more @ x @ y )
!= $true )
| ( ( more @ z @ u )
!= $true )
| spl0_3 ),
inference(trivial_inequality_removal,[],[f59]) ).
thf(f64,plain,
( ( ( more @ z @ u )
!= $true )
| spl0_3
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f60,f57]) ).
thf(f65,plain,
( ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f64,f55,f50,f45]) ).
thf(f66,plain,
( ( $true
!= ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) ) )
| ~ spl0_1
| spl0_3 ),
inference(superposition,[],[f52,f43]) ).
thf(f68,definition,
( spl0_5
<=> ( $true
= ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
thf(f70,plain,
( ( $true
!= ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) ) )
| spl0_5 ),
inference(avatar_component_clause,[],[f68]) ).
thf(f71,plain,
( ~ spl0_5
| ~ spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f66,f50,f41,f68]) ).
thf(f78,plain,
( ( ( more @ x @ y )
!= $true )
| ( $true != $true )
| spl0_5 ),
inference(superposition,[],[f70,f38]) ).
thf(f81,plain,
( ( ( more @ x @ y )
!= $true )
| spl0_5 ),
inference(trivial_inequality_removal,[],[f78]) ).
thf(f82,plain,
( $false
| ~ spl0_4
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f81,f57]) ).
thf(f83,plain,
( ~ spl0_4
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f82]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f48]) ).
cnf(s2,plain,
~ spl0_3,
inference(sat_conversion,[],[f53]) ).
cnf(s3,plain,
spl0_4,
inference(sat_conversion,[],[f58]) ).
cnf(s5,plain,
( ~ spl0_2
| spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f65]) ).
cnf(s6,plain,
( ~ spl0_1
| spl0_3
| ~ spl0_5 ),
inference(sat_conversion,[],[f71]) ).
cnf(s8,plain,
( ~ spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f83]) ).
cnf(s9,plain,
spl0_5,
inference(rat,[],[s8,s3]) ).
cnf(s10,plain,
~ spl0_1,
inference(rat,[],[s6,s9,s2]) ).
cnf(s11,plain,
~ spl0_2,
inference(rat,[],[s5,s3,s2]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s11,s10]) ).
thf(f84,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM688^1 : 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 : n016.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 12:44:11 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.23/0.29 % (288371)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.29 % (288382)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.29 % (288382)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
% 0.23/0.29 % (288376)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3765606595:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.29 % (288377)lrs+10_16_si=on:nwc=1.5:random_seed=3783903459:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.29 % (288378)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1376224788:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.29 % (288381)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1689868331:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.29 % (288380)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2285413789:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.29 % (288379)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=634017533: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)
% 0.23/0.29 % (288382)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=954671786:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.29 % (288380) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-288371-288380"...
% 0.23/0.29 % (288378)Instruction limit reached!
% 0.23/0.29 % (288378)------------------------------
% 0.23/0.29 % (288378)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (288378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (288378)CaDiCaL version: 2.1.3
% 0.23/0.29 % (288378)Termination reason: Instruction limit
% 0.23/0.29 % (288378)Termination phase: Saturation
% 0.23/0.29 % (288378)Time elapsed: 0.002 s
% 0.23/0.29 % (288378)Peak memory usage: 12 MB
% 0.23/0.29 % (288378)Instructions burned: 3 (million)
% 0.23/0.29 % (288379) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-288371-288379"...
% 0.23/0.29 % (288376) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-288371-288376"...
% 0.23/0.29 % (288380)...printing done.
% 0.23/0.29 % (288377) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-288371-288377"...
% 0.23/0.29 % (288379)...printing done.
% 0.23/0.29 % (288381) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-288371-288381"...
% 0.23/0.29 % (288376)...printing done.
% 0.23/0.29 % (288379)Refutation found. Thanks to Tanya!
% 0.23/0.29 % SZS status Theorem for theBenchmark
% 0.23/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.29 % (288379)------------------------------
% 0.23/0.29 % (288379)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (288379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (288379)CaDiCaL version: 2.1.3
% 0.23/0.29 % (288379)Termination reason: Refutation
% 0.23/0.29 % (288379)Time elapsed: 0.004 s
% 0.23/0.29 % (288379)Peak memory usage: 13 MB
% 0.23/0.29 % (288379)Instructions burned: 5 (million)
% 0.23/0.29 % (288371)Success in time 0.042 s
% 0.23/0.29 % Vampire exiting
%------------------------------------------------------------------------------