%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA109^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 07:46:04 AM UTC 2026
% Result : Theorem 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 11 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 71 ( 5 ~; 0 |; 0 &; 66 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 2 con; 0-4 aty)
% Number of variables : 16 ( 0 ^; 14 !; 2 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
'const/sets/INSERT':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_1,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_2,type,
'const/iterate/sum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/realax/real' ) > 'type/realax/real' ) ).
thf(func_def_3,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_5,type,
sK0: 'type/nums/num' > 'type/realax/real' ).
thf(func_def_6,type,
sK1: 'type/nums/num' ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > 'type/realax/real',X2: X0] :
( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) @ X1 )
= ( X1 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_SING_') ).
thf(f2,axiom,
! [X0: 'type/nums/num'] :
( ( 'const/iterate/..' @ X0 @ X0 )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ X0 @ 'const/sets/EMPTY' @ 'type/nums/num' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/NUMSEG_SING_') ).
thf(f3,conjecture,
! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X1 ) @ X0 )
= ( X0 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_SING_NUMSEG_') ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X1 ) @ X0 )
= ( X0 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
? [X0: 'type/nums/num' > 'type/realax/real',X1: 'type/nums/num'] :
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X1 ) @ X0 )
!= ( X0 @ X1 ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK1 ) @ sK0 )
!= ( sK0 @ sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f5]) ).
thf(f7,plain,
! [X0: $tType,X2: X0,X1: X0 > 'type/realax/real'] :
( ( 'const/iterate/sum' @ X0 @ ( 'const/sets/INSERT' @ X0 @ X2 @ 'const/sets/EMPTY' @ X0 ) @ X1 )
= ( X1 @ X2 ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f8,plain,
! [X0: 'type/nums/num'] :
( ( 'const/iterate/..' @ X0 @ X0 )
= ( 'const/sets/INSERT' @ 'type/nums/num' @ X0 @ 'const/sets/EMPTY' @ 'type/nums/num' ) ),
inference(cnf_transformation,[],[f2]) ).
thf(f9,plain,
( ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK1 @ sK1 ) @ sK0 )
!= ( sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f50,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num' > 'type/realax/real'] :
( ( X1 @ X0 )
= ( 'const/iterate/sum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X0 ) @ X1 ) ),
inference(constrained_superposition,[],[f7,f8]) ).
thf(f52,plain,
( ( sK0 @ sK1 )
!= ( sK0 @ sK1 ) ),
inference(constrained_superposition,[],[f9,f50]) ).
thf(f53,plain,
$false,
inference(trivial_inequality_removal,[],[f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA109^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n019.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 17:44:54 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.26 % (1138310)Will run a generic schedule for satisfiability detection.
% 0.19/0.26 % (1138317)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=952357030:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.26 % (1138317) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1138310-1138317"...
% 0.19/0.26 % (1138317)...printing done.
% 0.19/0.26 % (1138317)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.26 % (1138317)------------------------------
% 0.19/0.26 % (1138317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.26 % (1138317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.26 % (1138317)CaDiCaL version: 2.1.3
% 0.19/0.26 % (1138317)Termination reason: Refutation
% 0.19/0.27 % (1138317)Time elapsed: 0.002 s
% 0.19/0.27 % (1138317)Peak memory usage: 12 MB
% 0.19/0.27 % (1138317)Instructions burned: 3 (million)
% 0.19/0.27 % (1138310)Success in time 0.033 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------