%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM748^1 : 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 : n019.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 08:18:45 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 19 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 428 ( 10 ~; 0 |; 0 &; 418 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 0 ^; 22 !; 0 ?; 22 :)
% 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,
eq: frac > frac > $o ).
thf(func_def_3,type,
fr: nat > nat > frac ).
thf(func_def_4,type,
pl: nat > nat > nat ).
thf(func_def_5,type,
ts: nat > nat > nat ).
thf(func_def_6,type,
num: frac > nat ).
thf(func_def_7,type,
den: frac > nat ).
thf(f1,axiom,
! [X0: frac] : ( eq @ X0 @ X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz37) ).
thf(f2,axiom,
! [X1: nat,X0: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz29) ).
thf(f3,axiom,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz6) ).
thf(f4,conjecture,
eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz58) ).
thf(f5,negated_conjecture,
~ ( eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
! [X0: frac] : ( eq @ X0 @ X0 ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
! [X0: nat,X1: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
! [X1: nat,X0: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
! [X1: nat,X0: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(fool_elimination,[],[f3]) ).
thf(f11,plain,
~ ( eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f12,plain,
( ( eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
!= $true ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( ( eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
!= $true ),
inference(flattening,[],[f12]) ).
thf(f14,plain,
! [X0: nat,X1: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
inference(rectify,[],[f9]) ).
thf(f15,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(rectify,[],[f10]) ).
thf(f16,plain,
! [X0: nat,X1: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f17,plain,
( ( eq @ ( fr @ ( pl @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f18,plain,
! [X0: nat,X1: nat] :
( ( pl @ X0 @ X1 )
= ( pl @ X1 @ X0 ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f19,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f22,plain,
( ( eq @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
!= $true ),
inference(forward_demodulation,[],[f17,f18]) ).
thf(f23,plain,
( ( eq @ ( fr @ ( pl @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
!= $true ),
inference(forward_demodulation,[],[f22,f16]) ).
thf(f24,plain,
( ( eq @ ( fr @ ( pl @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ y ) @ ( num @ x ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( den @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ y ) @ ( num @ x ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
!= $true ),
inference(forward_demodulation,[],[f23,f16]) ).
thf(f25,plain,
( ( eq @ ( fr @ ( pl @ ( ts @ ( den @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ x ) @ ( num @ y ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( pl @ ( ts @ ( den @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ x ) @ ( num @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
!= $true ),
inference(forward_demodulation,[],[f24,f18]) ).
thf(f26,plain,
( ( eq @ ( fr @ ( pl @ ( ts @ ( den @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ x ) @ ( num @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) @ ( fr @ ( pl @ ( ts @ ( den @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ x ) @ ( num @ y ) ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) )
!= $true ),
inference(forward_demodulation,[],[f25,f16]) ).
thf(f27,plain,
$false,
inference(forward_subsumption_resolution,[],[f26,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM748^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n019.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 12:49:54 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.21/0.27 % (708691)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (708698)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=997501769:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.27 % (708698) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-708691-708698"...
% 0.21/0.27 % (708698)...printing done.
% 0.21/0.27 % (708698)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (708698)------------------------------
% 0.21/0.27 % (708698)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (708698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (708698)CaDiCaL version: 2.1.3
% 0.21/0.27 % (708698)Termination reason: Refutation
% 0.21/0.27 % (708698)Time elapsed: 0.001 s
% 0.21/0.27 % (708698)Peak memory usage: 12 MB
% 0.21/0.27 % (708698)Instructions burned: 4 (million)
% 0.21/0.27 % (708691)Success in time 0.029 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------