%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM729^1 : 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 : n006.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 08:18:41 AM UTC 2026
% Result : Theorem 0.23s 0.33s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 16 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 165 ( 9 ~; 3 |; 0 &; 150 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 31 ( 0 ^; 31 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
frac: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x1: nat ).
thf(func_def_1,type,
x2: nat ).
thf(func_def_2,type,
n: nat ).
thf(func_def_3,type,
eq: frac > frac > $o ).
thf(func_def_4,type,
fr: nat > nat > frac ).
thf(func_def_5,type,
ts: nat > nat > nat ).
thf(f1,axiom,
! [X1: frac,X0: frac] :
( ( eq @ X0 @ X1 )
=> ( eq @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz38) ).
thf(f2,axiom,
! [X2: nat,X0: nat,X1: nat] : ( eq @ ( fr @ X0 @ X1 ) @ ( fr @ ( ts @ X0 @ X2 ) @ ( ts @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz40b) ).
thf(f3,conjecture,
eq @ ( fr @ ( ts @ x1 @ n ) @ ( ts @ x2 @ n ) ) @ ( fr @ x1 @ x2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz40c) ).
thf(f4,negated_conjecture,
~ ( eq @ ( fr @ ( ts @ x1 @ n ) @ ( ts @ x2 @ n ) ) @ ( fr @ x1 @ x2 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: nat,X1: nat,X2: nat] : ( eq @ ( fr @ X1 @ X2 ) @ ( fr @ ( ts @ X1 @ X0 ) @ ( ts @ X2 @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f6,plain,
! [X2: nat,X1: nat,X0: nat] :
( ( eq @ ( fr @ X1 @ X2 ) @ ( fr @ ( ts @ X1 @ X0 ) @ ( ts @ X2 @ X0 ) ) )
= $true ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: frac,X1: frac] :
( ( eq @ X1 @ X0 )
=> ( eq @ X0 @ X1 ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
! [X1: frac,X0: frac] :
( ( ( eq @ X1 @ X0 )
= $true )
=> ( ( eq @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( eq @ ( fr @ ( ts @ x1 @ n ) @ ( ts @ x2 @ n ) ) @ ( fr @ x1 @ x2 ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
( ( eq @ ( fr @ ( ts @ x1 @ n ) @ ( ts @ x2 @ n ) ) @ ( fr @ x1 @ x2 ) )
!= $true ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( eq @ ( fr @ ( ts @ x1 @ n ) @ ( ts @ x2 @ n ) ) @ ( fr @ x1 @ x2 ) )
!= $true ),
inference(flattening,[],[f10]) ).
thf(f12,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ X0 )
!= $true )
| ( ( eq @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f13,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( eq @ ( fr @ X1 @ X0 ) @ ( fr @ ( ts @ X1 @ X2 ) @ ( ts @ X0 @ X2 ) ) )
= $true ),
inference(rectify,[],[f6]) ).
thf(f14,plain,
! [X0: frac,X1: frac] :
( ( ( eq @ X1 @ X0 )
!= $true )
| ( ( eq @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f15,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( eq @ ( fr @ X1 @ X0 ) @ ( fr @ ( ts @ X1 @ X2 ) @ ( ts @ X0 @ X2 ) ) )
= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f16,plain,
( ( eq @ ( fr @ ( ts @ x1 @ n ) @ ( ts @ x2 @ n ) ) @ ( fr @ x1 @ x2 ) )
!= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f19,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true != $true )
| ( ( eq @ ( fr @ ( ts @ X0 @ X2 ) @ ( ts @ X1 @ X2 ) ) @ ( fr @ X0 @ X1 ) )
= $true ) ),
inference(constrained_superposition,[],[f14,f15]) ).
thf(f20,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( eq @ ( fr @ ( ts @ X0 @ X2 ) @ ( ts @ X1 @ X2 ) ) @ ( fr @ X0 @ X1 ) )
= $true ),
inference(trivial_inequality_removal,[],[f19]) ).
thf(f21,plain,
$true != $true,
inference(constrained_superposition,[],[f16,f20]) ).
thf(f23,plain,
$false,
inference(trivial_inequality_removal,[],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM729^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n006.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 12:45:40 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.26 Running higher-order theorem proving
% 0.23/0.27 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
% 0.23/0.33 % (664920)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.33 % (664927)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2405870413:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.33 % (664926)lrs+10_16_si=on:nwc=1.5:random_seed=557646624:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.33 % (664928)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=3885867150: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)
% 0.23/0.33 % (664927) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-664920-664927"...
% 0.23/0.33 % (664926) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-664920-664926"...
% 0.23/0.33 % (664928) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-664920-664928"...
% 0.23/0.33 % (664927)...printing done.
% 0.23/0.33 % (664926)...printing done.
% 0.23/0.33 % (664928)...printing done.
% 0.23/0.33 % (664927)Refutation found. Thanks to Tanya!
% 0.23/0.33 % SZS status Theorem for theBenchmark
% 0.23/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.33 % (664927)------------------------------
% 0.23/0.33 % (664927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.33 % (664927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.33 % (664927)CaDiCaL version: 2.1.3
% 0.23/0.33 % (664927)Termination reason: Refutation
% 0.23/0.33 % (664927)Time elapsed: 0.003 s
% 0.23/0.33 % (664927)Peak memory usage: 12 MB
% 0.23/0.33 % (664927)Instructions burned: 2 (million)
% 0.23/0.33 % (664920)Success in time 0.048 s
% 0.23/0.33 % Vampire exiting
%------------------------------------------------------------------------------