%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM835+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 12:17:11 PM UTC 2026
% Result : Theorem 2.69s 6.35s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 18 unt; 5 def)
% Number of atoms : 113 ( 44 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 116 ( 50 ~; 46 |; 14 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 39 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X0] : vd165 = vplus(vd151,X0)
| ? [X1] : vd151 = vplus(vd165,X1)
| vd151 = vd165 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dis(case_distinction(conseq(110)))') ).
fof(f2,negated_conjecture,
~ ( ? [X0] : vd165 = vplus(vd151,X0)
| ? [X1] : vd151 = vplus(vd165,X1)
| vd151 = vd165 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f18,axiom,
! [X0,X1] :
( m(X1)
<=> ( X0 = X1
| ? [X2] : X0 = vplus(X1,X2)
| ? [X3] : X1 = vplus(X0,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(105), 0), 1)') ).
fof(f26,plain,
( ! [X0] : vd165 != vplus(vd151,X0)
& ! [X1] : vd151 != vplus(vd165,X1)
& vd165 != vd151 ),
inference(ennf_transformation,[],[f2]) ).
fof(f52,plain,
! [X0,X1] :
( ( m(X1)
| ( X0 != X1
& ! [X2] : vplus(X1,X2) != X0
& ! [X3] : vplus(X0,X3) != X1 ) )
& ( X0 = X1
| ? [X2] : X0 = vplus(X1,X2)
| ? [X3] : X1 = vplus(X0,X3)
| ~ m(X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f53,plain,
! [X0,X1] :
( ( m(X1)
| ( X0 != X1
& ! [X2] : vplus(X1,X2) != X0
& ! [X3] : vplus(X0,X3) != X1 ) )
& ( X0 = X1
| ? [X2] : X0 = vplus(X1,X2)
| ? [X3] : X1 = vplus(X0,X3)
| ~ m(X1) ) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( ( m(X1)
| ( X0 != X1
& ! [X2] : vplus(X1,X2) != X0
& ! [X3] : vplus(X0,X3) != X1 ) )
& ( X0 = X1
| ? [X4] : vplus(X1,X4) = X0
| ? [X5] : vplus(X0,X5) = X1
| ~ m(X1) ) ),
inference(rectify,[],[f53]) ).
fof(f55,plain,
! [X0,X1] :
( ( m(X1)
| ( X0 != X1
& ! [X2] : vplus(X1,X2) != X0
& ! [X3] : vplus(X0,X3) != X1 ) )
& ( X0 = X1
| vplus(X1,sK0(X0,X1)) = X0
| vplus(X0,sK1(X0,X1)) = X1
| ~ m(X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X4,sK0(X0,X1)),skolemize(X5,sK1(X0,X1))],[f54]) ).
fof(f56,plain,
vd165 != vd151,
inference(cnf_transformation,[],[f26]) ).
fof(f57,plain,
! [X1] : vd151 != vplus(vd165,X1),
inference(cnf_transformation,[],[f26]) ).
fof(f58,plain,
! [X0] : vd165 != vplus(vd151,X0),
inference(cnf_transformation,[],[f26]) ).
fof(f74,plain,
! [X0,X1] :
( X0 = X1
| vplus(X1,sK0(X0,X1)) = X0
| vplus(X0,sK1(X0,X1)) = X1
| ~ m(X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f77,plain,
! [X0,X1] :
( m(X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f55]) ).
fof(f105,plain,
! [X1] : m(X1),
inference(equality_resolution,[],[f77]) ).
fof(f108,definition,
! [X0,X1] :
( sQ2_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ2_eqProxy])],[equality_proxy_definition]) ).
fof(f109,plain,
! [X0] : ~ sQ2_eqProxy(vd165,vplus(vd151,X0)),
inference(equality_proxy_replacement,[],[f58,f108]) ).
fof(f110,plain,
! [X1] : ~ sQ2_eqProxy(vd151,vplus(vd165,X1)),
inference(equality_proxy_replacement,[],[f57,f108]) ).
fof(f111,plain,
~ sQ2_eqProxy(vd165,vd151),
inference(equality_proxy_replacement,[],[f56,f108]) ).
fof(f127,plain,
! [X0,X1] :
( sQ2_eqProxy(vplus(X0,sK1(X0,X1)),X1)
| sQ2_eqProxy(vplus(X1,sK0(X0,X1)),X0)
| sQ2_eqProxy(X0,X1)
| ~ m(X1) ),
inference(equality_proxy_replacement,[],[f74,f108,f108,f108]) ).
fof(f136,plain,
! [X0,X1] :
( sQ2_eqProxy(X1,X0)
| ~ sQ2_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f108]) ).
fof(f138,definition,
( spl3_1
<=> sQ2_eqProxy(vd165,vd151) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f178,definition,
( spl3_11
<=> ! [X0] : ~ sQ2_eqProxy(vd165,vplus(vd151,X0)) ),
introduced(definition,[new_symbols(definition,[spl3_11])],[avatar_definition]) ).
fof(f179,plain,
( ! [X0] : ~ sQ2_eqProxy(vd165,vplus(vd151,X0))
| ~ spl3_11 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f181,plain,
~ spl3_1,
inference(avatar_split_clause,[],[f111,f138]) ).
fof(f182,plain,
spl3_11,
inference(avatar_split_clause,[],[f109,f178]) ).
fof(f183,plain,
! [X0] : ~ sQ2_eqProxy(vplus(vd165,X0),vd151),
inference(resolution,[],[f136,f110]) ).
fof(f185,plain,
( ! [X0] : ~ sQ2_eqProxy(vplus(vd151,X0),vd165)
| ~ spl3_11 ),
inference(resolution,[],[f136,f179]) ).
fof(f192,plain,
( sQ2_eqProxy(vplus(vd151,sK0(vd165,vd151)),vd165)
| sQ2_eqProxy(vd165,vd151)
| ~ m(vd151) ),
inference(resolution,[],[f127,f183]) ).
fof(f194,definition,
( spl3_12
<=> m(vd151) ),
introduced(definition,[new_symbols(definition,[spl3_12])],[avatar_definition]) ).
fof(f195,plain,
( ~ m(vd151)
| spl3_12 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f198,definition,
( spl3_13
<=> sQ2_eqProxy(vplus(vd151,sK0(vd165,vd151)),vd165) ),
introduced(definition,[new_symbols(definition,[spl3_13])],[avatar_definition]) ).
fof(f199,plain,
( sQ2_eqProxy(vplus(vd151,sK0(vd165,vd151)),vd165)
| ~ spl3_13 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f200,plain,
( ~ spl3_12
| spl3_1
| spl3_13 ),
inference(avatar_split_clause,[],[f192,f198,f138,f194]) ).
fof(f211,plain,
( $false
| spl3_12 ),
inference(resolution,[],[f195,f105]) ).
fof(f212,plain,
spl3_12,
inference(avatar_contradiction_clause,[],[f211]) ).
fof(f213,plain,
( $false
| ~ spl3_11
| ~ spl3_13 ),
inference(resolution,[],[f199,f185]) ).
fof(f214,plain,
( ~ spl3_11
| ~ spl3_13 ),
inference(avatar_contradiction_clause,[],[f213]) ).
cnf(s12,plain,
~ spl3_1,
inference(sat_conversion,[],[f181]) ).
cnf(s13,plain,
spl3_11,
inference(sat_conversion,[],[f182]) ).
cnf(s14,plain,
( spl3_1
| ~ spl3_12
| spl3_13 ),
inference(sat_conversion,[],[f200]) ).
cnf(s16,plain,
spl3_12,
inference(sat_conversion,[],[f212]) ).
cnf(s17,plain,
( ~ spl3_11
| ~ spl3_13 ),
inference(sat_conversion,[],[f214]) ).
cnf(s18,plain,
( spl3_1
| spl3_13 ),
inference(rat,[],[s14,s16]) ).
cnf(s19,plain,
~ spl3_13,
inference(rat,[],[s17,s13]) ).
cnf(s20,plain,
spl3_1,
inference(rat,[],[s18,s19]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s12,s20]) ).
fof(f215,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM835+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/5.38 % Computer : n017.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sun Sep 27 21:24:41 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.69/6.35 % (2952242)Detected formulas, will run a generic FOF schedule.
% 2.69/6.35 % (2952253)dis-21_1_sil=8000:lcm=predicate:random_seed=2388455969:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.69/6.35 % (2952253)First to succeed.
% 2.69/6.35 % (2952253)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2952242"
% 2.69/6.35 % (2952249)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1968011534:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/6.35 % (2952250)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2281339088:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/6.35 % (2952251)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=539879831:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/6.35 % (2952248)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=935767134:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/6.35 % (2952247)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1397772849:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/6.35 % (2952252)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2267340169:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/6.35 % (2952252)Also succeeded, but the first one will report.
% 2.69/6.35 % (2952251)Instruction limit reached!
% 2.69/6.35 % (2952251)------------------------------
% 2.69/6.35 % (2952251)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/6.35 % (2952251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/6.35 % (2952251)CaDiCaL version: 2.1.3
% 2.69/6.35 % (2952251)Termination reason: Instruction limit
% 2.69/6.35 % (2952251)Termination phase: Saturation
% 2.69/6.35 % (2952251)Time elapsed: 0.057 s
% 2.69/6.35 % (2952251)Peak memory usage: 88 MB
% 2.69/6.35 % (2952251)Instructions burned: 120 (million)
% 2.69/6.35 % (2952250)Instruction limit reached!
% 2.69/6.35 % (2952250)------------------------------
% 2.69/6.35 % (2952250)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/6.35 % (2952250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/6.35 % (2952250)CaDiCaL version: 2.1.3
% 2.69/6.35 % (2952250)Termination reason: Instruction limit
% 2.69/6.35 % (2952250)Termination phase: Saturation
% 2.69/6.35 % (2952250)Time elapsed: 0.067 s
% 2.69/6.35 % (2952250)Peak memory usage: 89 MB
% 2.69/6.35 % (2952250)Instructions burned: 110 (million)
% 2.69/6.35 % (2952253)Refutation found. Thanks to Tanya!
% 2.69/6.35 % SZS status Theorem for theBenchmark
% 2.69/6.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/6.35 % (2952253)------------------------------
% 2.69/6.35 % (2952253)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/6.35 % (2952253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/6.35 % (2952253)CaDiCaL version: 2.1.3
% 2.69/6.35 % (2952253)Termination reason: Refutation
% 2.69/6.35 % (2952253)Time elapsed: 0.002 s
% 2.69/6.35 % (2952253)Peak memory usage: 89 MB
% 2.69/6.35 % (2952253)Instructions burned: 3 (million)
% 2.69/6.35 % (2952253)------------------------------
% 2.69/6.35 % (2952253)------------------------------
% 2.69/6.35 % (2952242)Success in time 0.298 s
% 2.69/6.35 % Vampire exiting
%------------------------------------------------------------------------------