%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM730^1 : 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 : n005.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 08:18:42 AM UTC 2026
% Result : Theorem 0.19s 0.30s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 60 ( 18 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 227 ( 6 ~; 0 |; 0 &; 221 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
frac: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
nat: $tType ).
thf(func_def_0,type,
x: frac ).
thf(func_def_1,type,
y: frac ).
thf(func_def_2,type,
orec3: $o > $o > $o > $o ).
thf(func_def_3,type,
ts: nat > nat > nat ).
thf(func_def_4,type,
c1x: frac > nat ).
thf(func_def_5,type,
c2y: frac > nat ).
thf(func_def_6,type,
c1y: frac > nat ).
thf(func_def_7,type,
c2x: frac > nat ).
thf(func_def_8,type,
more: nat > nat > $o ).
thf(func_def_9,type,
less: nat > nat > $o ).
thf(func_def_11,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,axiom,
! [X0: nat,X1: nat] : ( orec3 @ ( X0 = X1 ) @ ( more @ X0 @ X1 ) @ ( less @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10) ).
thf(f2,conjecture,
( orec3
@ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
= ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz41) ).
thf(f3,negated_conjecture,
~ ( orec3
@ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
= ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
! [X0: nat,X1: nat] : ( orec3 @ ( X0 = X1 ) @ ( more @ X0 @ X1 ) @ ( less @ X0 @ X1 ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
! [X1: nat,X0: nat] :
( $true
= ( orec3 @ ( X0 = X1 ) @ ( more @ X0 @ X1 ) @ ( less @ X0 @ X1 ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( orec3
@ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
= ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
( $true
!= ( orec3
@ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
= ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( $true
!= ( orec3
@ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
= ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) ) ),
inference(flattening,[],[f7]) ).
thf(f9,plain,
! [X0: nat,X1: nat] :
( $true
= ( orec3 @ ( X1 = X0 ) @ ( more @ X1 @ X0 ) @ ( less @ X1 @ X0 ) ) ),
inference(rectify,[],[f5]) ).
thf(f10,plain,
! [X0: nat,X1: nat] :
( $true
= ( orec3 @ ( X1 = X0 ) @ ( more @ X1 @ X0 ) @ ( less @ X1 @ X0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
( $true
!= ( orec3
@ ( ( ts @ ( c1x @ x ) @ ( c2y @ y ) )
= ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( more @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) )
@ ( less @ ( ts @ ( c1x @ x ) @ ( c2y @ y ) ) @ ( ts @ ( c1y @ y ) @ ( c2x @ x ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
$true != $true,
inference(constrained_superposition,[],[f11,f10]) ).
thf(f15,plain,
$false,
inference(trivial_inequality_removal,[],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM730^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.19 % Computer : n005.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Sep 29 12:45:46 UTC 2026
% 0.06/0.20 % CPUTime :
% 0.06/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.23 Running higher-order theorem proving
% 0.06/0.24 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
% 0.19/0.30 % (1615947)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.30 % (1615966)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2876605706:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.30 % (1615966)Refutation not found, incomplete strategy
% 0.19/0.30 % (1615966)------------------------------
% 0.19/0.30 % (1615966)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (1615966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (1615966)CaDiCaL version: 2.1.3
% 0.19/0.30 % (1615966)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.30 % (1615966)Time elapsed: 0.001 s
% 0.19/0.30 % (1615966)Peak memory usage: 11 MB
% 0.19/0.30 % (1615966)Instructions burned: 1 (million)
% 0.19/0.30 % (1615966)------------------------------
% 0.19/0.30 % (1615966)------------------------------
% 0.19/0.30 % (1615968)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.30 % (1615968)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
% 0.19/0.30 % (1615962)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2125358595:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.30 % (1615963)lrs+10_16_si=on:nwc=1.5:random_seed=3796035050:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.30 % (1615965)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=1759639688: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)
% 0.19/0.30 % (1615964)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=923122164:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.30 % (1615968)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=2233874736:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.30 % (1615967)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=638299745:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.30 % (1615962)Refutation not found, incomplete strategy
% 0.19/0.30 % (1615962)------------------------------
% 0.19/0.30 % (1615962)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (1615962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (1615962)CaDiCaL version: 2.1.3
% 0.19/0.30 % (1615962)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.30 % (1615962)Time elapsed: 0.001 s
% 0.19/0.30 % (1615962)Peak memory usage: 12 MB
% 0.19/0.30 % (1615962)Instructions burned: 1 (million)
% 0.19/0.30 % (1615963)Refutation not found, incomplete strategy
% 0.19/0.30 % (1615963)------------------------------
% 0.19/0.30 % (1615963)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (1615963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (1615963)CaDiCaL version: 2.1.3
% 0.19/0.30 % (1615963)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.30 % (1615963)Time elapsed: 0.001 s
% 0.19/0.30 % (1615963)Peak memory usage: 12 MB
% 0.19/0.30 % (1615963)Instructions burned: 1 (million)
% 0.19/0.30 % (1615964) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1615947-1615964"...
% 0.19/0.30 % (1615962)------------------------------
% 0.19/0.30 % (1615962)------------------------------
% 0.19/0.30 % (1615963)------------------------------
% 0.19/0.30 % (1615963)------------------------------
% 0.19/0.30 % (1615964)...printing done.
% 0.19/0.30 % (1615964)Refutation found. Thanks to Tanya!
% 0.19/0.30 % SZS status Theorem for theBenchmark
% 0.19/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.30 % (1615964)------------------------------
% 0.19/0.30 % (1615964)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (1615964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (1615964)CaDiCaL version: 2.1.3
% 0.19/0.30 % (1615964)Termination reason: Refutation
% 0.19/0.30 % (1615964)Time elapsed: 0.002 s
% 0.19/0.30 % (1615964)Peak memory usage: 12 MB
% 0.19/0.30 % (1615964)Instructions burned: 2 (million)
% 0.19/0.30 % (1615947)Success in time 0.041 s
% 0.19/0.30 % Vampire exiting
%------------------------------------------------------------------------------