%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM477+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:15:21 PM UTC 2026
% Result : Theorem 3.69s 1.48s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 16 unt; 2 def)
% Number of atoms : 134 ( 32 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 145 ( 62 ~; 59 |; 15 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 30 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(f27,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( X0 != sz00
=> sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(f35,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1494) ).
fof(f36,axiom,
( doDivides0(xm,xn)
& xn != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1494_04) ).
fof(f37,conjecture,
sdtlseqdt0(xm,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f38,negated_conjecture,
~ sdtlseqdt0(xm,xn),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f39,plain,
~ sdtlseqdt0(xm,xn),
inference(flattening,[],[f38]) ).
fof(f41,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f42,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f41]) ).
fof(f51,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f61,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f62,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f61]) ).
fof(f92,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f62]) ).
fof(f93,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X0,X3) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(rectify,[],[f92]) ).
fof(f94,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK0(X0,X1))
& sdtasdt0(X0,sK0(X0,X1)) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f93]) ).
fof(f98,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f35]) ).
fof(f99,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f35]) ).
fof(f100,plain,
sz00 != xn,
inference(cnf_transformation,[],[f36]) ).
fof(f101,plain,
doDivides0(xm,xn),
inference(cnf_transformation,[],[f36]) ).
fof(f102,plain,
~ sdtlseqdt0(xm,xn),
inference(cnf_transformation,[],[f39]) ).
fof(f103,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f114,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f51]) ).
fof(f124,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sdtasdt0(X0,sK0(X0,X1)) = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f125,plain,
! [X0,X1] :
( aNaturalNumber0(sK0(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f164,plain,
sz00 = sdtasdt0(xm,sz00),
inference(resolution,[],[f114,f99]) ).
fof(f286,plain,
( xn = sdtasdt0(xm,sK0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f124,f101]) ).
fof(f293,plain,
( xn = sdtasdt0(xm,sK0(xm,xn))
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f286,f99]) ).
fof(f298,plain,
xn = sdtasdt0(xm,sK0(xm,xn)),
inference(forward_subsumption_resolution,[],[f293,f98]) ).
fof(f319,plain,
( sdtlseqdt0(xm,xn)
| sz00 = sK0(xm,xn)
| ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f103,f298]) ).
fof(f322,plain,
( sz00 = sK0(xm,xn)
| ~ aNaturalNumber0(sK0(xm,xn))
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f319,f102]) ).
fof(f323,plain,
( sz00 = sK0(xm,xn)
| ~ aNaturalNumber0(sK0(xm,xn)) ),
inference(forward_subsumption_resolution,[],[f322,f99]) ).
fof(f325,definition,
( spl2_3
<=> aNaturalNumber0(sK0(xm,xn)) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f327,plain,
( ~ aNaturalNumber0(sK0(xm,xn))
| spl2_3 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f329,definition,
( spl2_4
<=> sz00 = sK0(xm,xn) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f331,plain,
( sz00 = sK0(xm,xn)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f332,plain,
( ~ spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f323,f329,f325]) ).
fof(f340,plain,
( ~ doDivides0(xm,xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| spl2_3 ),
inference(resolution,[],[f327,f125]) ).
fof(f341,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| spl2_3 ),
inference(forward_subsumption_resolution,[],[f340,f101]) ).
fof(f342,plain,
( ~ aNaturalNumber0(xn)
| spl2_3 ),
inference(forward_subsumption_resolution,[],[f341,f99]) ).
fof(f343,plain,
( $false
| spl2_3 ),
inference(forward_subsumption_resolution,[],[f342,f98]) ).
fof(f344,plain,
spl2_3,
inference(avatar_contradiction_clause,[],[f343]) ).
fof(f372,plain,
( xn = sdtasdt0(xm,sz00)
| ~ spl2_4 ),
inference(superposition,[],[f298,f331]) ).
fof(f374,plain,
( sz00 = xn
| ~ spl2_4 ),
inference(forward_demodulation,[],[f372,f164]) ).
fof(f375,plain,
( $false
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f374,f100]) ).
fof(f376,plain,
~ spl2_4,
inference(avatar_contradiction_clause,[],[f375]) ).
cnf(s2,plain,
( ~ spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f332]) ).
cnf(s3,plain,
spl2_3,
inference(sat_conversion,[],[f344]) ).
cnf(s4,plain,
~ spl2_4,
inference(sat_conversion,[],[f376]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s4,s3]) ).
fof(f377,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM477+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 20:05:37 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 3.69/1.48 % (3846296)Detected formulas, will run a generic FOF schedule.
% 3.69/1.48 % (3846305)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2549424856:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.69/1.48 % (3846305)Instruction limit reached!
% 3.69/1.48 % (3846305)------------------------------
% 3.69/1.48 % (3846305)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.48 % (3846305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.48 % (3846305)CaDiCaL version: 2.1.3
% 3.69/1.48 % (3846305)Termination reason: Instruction limit
% 3.69/1.48 % (3846305)Termination phase: Saturation
% 3.69/1.48 % (3846305)Time elapsed: 0.039 s
% 3.69/1.48 % (3846305)Peak memory usage: 89 MB
% 3.69/1.48 % (3846305)Instructions burned: 120 (million)
% 3.69/1.48 % (3846303)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=4086484941:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.69/1.48 % (3846301)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=3734165710:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.69/1.48 % (3846302)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=384841338:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.69/1.48 % (3846304)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3883758849:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.69/1.48 % (3846307)dis-21_1_sil=8000:lcm=predicate:random_seed=2716391136: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)
% 3.69/1.48 % (3846306)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2016208074:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.69/1.48 % (3846304)Instruction limit reached!
% 3.69/1.48 % (3846304)------------------------------
% 3.69/1.48 % (3846304)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.48 % (3846304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.48 % (3846304)CaDiCaL version: 2.1.3
% 3.69/1.48 % (3846304)Termination reason: Instruction limit
% 3.69/1.48 % (3846304)Termination phase: Saturation
% 3.69/1.48 % (3846304)Time elapsed: 0.042 s
% 3.69/1.48 % (3846304)Peak memory usage: 88 MB
% 3.69/1.48 % (3846304)Instructions burned: 109 (million)
% 3.69/1.48 % (3846307)Instruction limit reached!
% 3.69/1.48 % (3846307)------------------------------
% 3.69/1.48 % (3846307)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.48 % (3846307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.48 % (3846307)CaDiCaL version: 2.1.3
% 3.69/1.48 % (3846307)Termination reason: Instruction limit
% 3.69/1.48 % (3846307)Termination phase: Saturation
% 3.69/1.48 % (3846307)Time elapsed: 0.078 s
% 3.69/1.48 % (3846307)Peak memory usage: 91 MB
% 3.69/1.48 % (3846307)Instructions burned: 129 (million)
% 3.69/1.48 % (3846306)Instruction limit reached!
% 3.69/1.48 % (3846306)------------------------------
% 3.69/1.48 % (3846306)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.48 % (3846306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.48 % (3846306)CaDiCaL version: 2.1.3
% 3.69/1.48 % (3846306)Termination reason: Instruction limit
% 3.69/1.48 % (3846306)Termination phase: Saturation
% 3.69/1.48 % (3846306)Time elapsed: 0.091 s
% 3.69/1.48 % (3846306)Peak memory usage: 90 MB
% 3.69/1.48 % (3846306)Instructions burned: 139 (million)
% 3.69/1.48 % (3846313)lrs+10_1_sil=8000:sp=occurrence:random_seed=4206322426:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.69/1.48 % (3846313)First to succeed.
% 3.69/1.48 % (3846313)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3846296"
% 3.69/1.48 % (3846316)lrs+10_1_sil=32000:urr=on:br=off:random_seed=210652880:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.69/1.48 % (3846317)lrs+1011_1_sil=32000:sp=occurrence:random_seed=179267471:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.69/1.48 % (3846318)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2227429596:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 3.69/1.48 % (3846313)Refutation found. Thanks to Tanya!
% 3.69/1.48 % SZS status Theorem for theBenchmark
% 3.69/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.48 % (3846313)------------------------------
% 3.69/1.48 % (3846313)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.48 % (3846313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.48 % (3846313)CaDiCaL version: 2.1.3
% 3.69/1.48 % (3846313)Termination reason: Refutation
% 3.69/1.48 % (3846313)Time elapsed: 0.005 s
% 3.69/1.48 % (3846313)Peak memory usage: 90 MB
% 3.69/1.48 % (3846313)Instructions burned: 12 (million)
% 3.69/1.48 % (3846313)------------------------------
% 3.69/1.48 % (3846313)------------------------------
% 3.69/1.48 % (3846296)Success in time 0.446 s
% 3.69/1.48 % Vampire exiting
%------------------------------------------------------------------------------