%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM344+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 : Tue Sep 29 12:18:22 PM UTC 2026
% Result : Theorem 0.64s 0.62s
% Output : Refutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 16 unt; 5 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 174 ( 90 ~; 70 |; 6 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 99 ( 0 sgn 95 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn0) ).
fof(f2,axiom,
rdn_translate(n1,rdn_pos(rdnn(n1))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn1) ).
fof(f129,axiom,
rdn_translate(nn1,rdn_neg(rdnn(n1))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdnn1) ).
fof(f282,axiom,
! [X0,X1,X2,X3] :
( ( rdn_translate(X0,rdn_neg(X2))
& rdn_translate(X1,rdn_pos(X3)) )
=> less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+1.ax',less_entry_point_neg_pos) ).
fof(f291,axiom,
! [X0,X1,X2] :
( ( rdn_translate(X0,rdn_pos(X2))
& rdn_translate(X1,rdn_neg(X2)) )
=> sum(X0,X1,n0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',sum_entry_point_posx_negx) ).
fof(f292,axiom,
! [X0,X1,X2,X3,X4] :
( ( rdn_translate(X0,rdn_neg(X3))
& rdn_translate(X1,rdn_pos(X4))
& sum(X1,X0,X2) )
=> sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',sum_entry_point_neg_pos) ).
fof(f402,conjecture,
? [X0,X1] :
( sum(X0,n1,X1)
& less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exist_bigger_plus_one) ).
fof(f403,negated_conjecture,
~ ? [X0,X1] :
( sum(X0,n1,X1)
& less(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f415,plain,
! [X0,X1,X2,X3] :
( less(X0,X1)
| ~ rdn_translate(X0,rdn_neg(X2))
| ~ rdn_translate(X1,rdn_pos(X3)) ),
inference(ennf_transformation,[],[f282]) ).
fof(f416,plain,
! [X0,X1,X2,X3] :
( less(X0,X1)
| ~ rdn_translate(X0,rdn_neg(X2))
| ~ rdn_translate(X1,rdn_pos(X3)) ),
inference(flattening,[],[f415]) ).
fof(f431,plain,
! [X0,X1,X2] :
( sum(X0,X1,n0)
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_translate(X1,rdn_neg(X2)) ),
inference(ennf_transformation,[],[f291]) ).
fof(f432,plain,
! [X0,X1,X2] :
( sum(X0,X1,n0)
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_translate(X1,rdn_neg(X2)) ),
inference(flattening,[],[f431]) ).
fof(f433,plain,
! [X0,X1,X2,X3,X4] :
( sum(X0,X1,X2)
| ~ rdn_translate(X0,rdn_neg(X3))
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ sum(X1,X0,X2) ),
inference(ennf_transformation,[],[f292]) ).
fof(f434,plain,
! [X0,X1,X2,X3,X4] :
( sum(X0,X1,X2)
| ~ rdn_translate(X0,rdn_neg(X3))
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ sum(X1,X0,X2) ),
inference(flattening,[],[f433]) ).
fof(f450,plain,
! [X0,X1] :
( ~ sum(X0,n1,X1)
| ~ less(X0,X1) ),
inference(ennf_transformation,[],[f403]) ).
fof(f451,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(cnf_transformation,[],[f1]) ).
fof(f452,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(cnf_transformation,[],[f2]) ).
fof(f579,plain,
rdn_translate(nn1,rdn_neg(rdnn(n1))),
inference(cnf_transformation,[],[f129]) ).
fof(f732,plain,
! [X2,X3,X0,X1] :
( less(X0,X1)
| ~ rdn_translate(X0,rdn_neg(X2))
| ~ rdn_translate(X1,rdn_pos(X3)) ),
inference(cnf_transformation,[],[f416]) ).
fof(f743,plain,
! [X2,X0,X1] :
( sum(X0,X1,n0)
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_translate(X1,rdn_neg(X2)) ),
inference(cnf_transformation,[],[f432]) ).
fof(f744,plain,
! [X2,X3,X0,X1,X4] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2)
| ~ rdn_translate(X0,rdn_neg(X3))
| ~ rdn_translate(X1,rdn_pos(X4)) ),
inference(cnf_transformation,[],[f434]) ).
fof(f855,plain,
! [X0,X1] :
( ~ less(X0,X1)
| ~ sum(X0,n1,X1) ),
inference(cnf_transformation,[],[f450]) ).
fof(f873,plain,
! [X2,X3,X0,X1] :
( ~ sum(X0,n1,X2)
| ~ rdn_translate(X2,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_neg(X1)) ),
inference(resolution,[],[f732,f855]) ).
fof(f1170,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(n1,X0,X1)
| ~ rdn_translate(X0,rdn_neg(X2))
| ~ rdn_translate(n1,rdn_pos(X3))
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_neg(X5)) ),
inference(resolution,[],[f744,f873]) ).
fof(f1181,definition,
( spl0_1
<=> ! [X3] : ~ rdn_translate(n1,rdn_pos(X3)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f1182,plain,
( ! [X3] : ~ rdn_translate(n1,rdn_pos(X3))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f1181]) ).
fof(f1189,definition,
( spl0_3
<=> ! [X2,X4,X0,X5,X1] :
( ~ sum(n1,X0,X1)
| ~ rdn_translate(X0,rdn_neg(X5))
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_neg(X2)) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f1190,plain,
( ! [X2,X0,X1,X4,X5] :
( ~ sum(n1,X0,X1)
| ~ rdn_translate(X0,rdn_neg(X5))
| ~ rdn_translate(X1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_neg(X2)) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f1189]) ).
fof(f1191,plain,
( spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f1170,f1189,f1181]) ).
fof(f1203,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f1182,f452]) ).
fof(f1204,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f1203]) ).
fof(f1205,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ rdn_translate(X0,rdn_neg(X1))
| ~ rdn_translate(n0,rdn_pos(X2))
| ~ rdn_translate(X0,rdn_neg(X3))
| ~ rdn_translate(n1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_neg(X4)) )
| ~ spl0_3 ),
inference(resolution,[],[f1190,f743]) ).
fof(f1208,definition,
( spl0_6
<=> ! [X2] : ~ rdn_translate(n0,rdn_pos(X2)) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f1209,plain,
( ! [X2] : ~ rdn_translate(n0,rdn_pos(X2))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f1208]) ).
fof(f1211,definition,
( spl0_7
<=> ! [X4,X0,X3,X1] :
( ~ rdn_translate(X0,rdn_neg(X1))
| ~ rdn_translate(X0,rdn_neg(X4))
| ~ rdn_translate(n1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_neg(X3)) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f1212,plain,
( ! [X3,X0,X1,X4] :
( ~ rdn_translate(X0,rdn_neg(X1))
| ~ rdn_translate(X0,rdn_neg(X4))
| ~ rdn_translate(n1,rdn_pos(X4))
| ~ rdn_translate(X0,rdn_neg(X3)) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f1211]) ).
fof(f1213,plain,
( spl0_6
| spl0_7
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f1205,f1189,f1211,f1208]) ).
fof(f1342,plain,
( ! [X0,X1] :
( ~ rdn_translate(nn1,rdn_neg(X0))
| ~ rdn_translate(n1,rdn_pos(rdnn(n1)))
| ~ rdn_translate(nn1,rdn_neg(X1)) )
| ~ spl0_7 ),
inference(resolution,[],[f1212,f579]) ).
fof(f2492,definition,
( spl0_263
<=> ! [X0] : ~ rdn_translate(nn1,rdn_neg(X0)) ),
introduced(definition,[new_symbols(definition,[spl0_263])],[avatar_definition]) ).
fof(f2493,plain,
( ! [X0] : ~ rdn_translate(nn1,rdn_neg(X0))
| ~ spl0_263 ),
inference(avatar_component_clause,[],[f2492]) ).
fof(f3130,plain,
( ! [X0,X1] :
( ~ rdn_translate(nn1,rdn_neg(X0))
| ~ rdn_translate(nn1,rdn_neg(X1)) )
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f1342,f452]) ).
fof(f3259,plain,
( spl0_263
| spl0_263
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f3130,f1211,f2492,f2492]) ).
fof(f3260,plain,
( $false
| ~ spl0_263 ),
inference(resolution,[],[f2493,f579]) ).
fof(f3261,plain,
~ spl0_263,
inference(avatar_contradiction_clause,[],[f3260]) ).
fof(f3266,plain,
( $false
| ~ spl0_6 ),
inference(resolution,[],[f1209,f451]) ).
fof(f3267,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f3266]) ).
cnf(s3,plain,
( spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f1191]) ).
cnf(s6,plain,
~ spl0_1,
inference(sat_conversion,[],[f1204]) ).
cnf(s7,plain,
( ~ spl0_3
| spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f1213]) ).
cnf(s518,plain,
( spl0_263
| ~ spl0_7
| spl0_263 ),
inference(sat_conversion,[],[f3259]) ).
cnf(s519,plain,
( ~ spl0_7
| spl0_263 ),
inference(rat,[],[s518]) ).
cnf(s520,plain,
~ spl0_263,
inference(sat_conversion,[],[f3261]) ).
cnf(s521,plain,
~ spl0_6,
inference(sat_conversion,[],[f3267]) ).
cnf(s522,plain,
~ spl0_7,
inference(rat,[],[s519,s520]) ).
cnf(s523,plain,
~ spl0_3,
inference(rat,[],[s7,s522,s521]) ).
cnf(s526,plain,
$false,
inference(rat,[],[s3,s523,s6]) ).
fof(f3268,plain,
$false,
inference(avatar_sat_refutation,[],[s526]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM344+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.41 % Computer : n016.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sun Sep 27 19:40:17 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.21/0.47 Running first-order model finding
% 0.21/0.48 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.64/0.62 % (2949369)Will run a generic schedule for satisfiability detection.
% 0.64/0.62 % (2949374)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=275735336_2999 on theBenchmark for (2999ds/0Mi)
% 0.64/0.62 % (2949376)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1938095414:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.64/0.62 % (2949375)% WARNING: option uhcvi not known.
% 0.64/0.62 % (2949380)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=440638280:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.64/0.62 % (2949377)dis+10_1_sil=32000:sp=arity:random_seed=1826673170:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.64/0.62 % (2949378)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2872867998:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.64/0.62 % (2949375)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4057324866:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.64/0.62 % (2949379)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3651586691:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.64/0.62 % TRYING [1]
% 0.64/0.62 % TRYING [2]
% 0.64/0.62 % TRYING [3]
% 0.64/0.62 % (2949378) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2949369-2949378"...
% 0.64/0.62 % (2949378)...printing done.
% 0.64/0.62 % (2949378)Refutation found. Thanks to Tanya!
% 0.64/0.62 % SZS status Theorem for theBenchmark
% 0.64/0.62 % SZS output start Proof for theBenchmark
% See solution above
% 0.64/0.62 % (2949378)------------------------------
% 0.64/0.62 % (2949378)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.62 % (2949378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.62 % (2949378)CaDiCaL version: 2.1.3
% 0.64/0.62 % (2949378)Termination reason: Refutation
% 0.64/0.62 % (2949378)Time elapsed: 0.077 s
% 0.64/0.62 % (2949378)Peak memory usage: 14 MB
% 0.64/0.62 % (2949378)Instructions burned: 85 (million)
% 0.64/0.62 % (2949369)Success in time 0.129 s
% 0.64/0.62 % Vampire exiting
%------------------------------------------------------------------------------