%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM457+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 : n011.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 12:15:16 PM UTC 2026
% Result : Theorem 3.46s 1.47s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 53 ( 18 unt; 5 def)
% Number of atoms : 134 ( 57 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 147 ( 66 ~; 61 |; 10 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 != sz00
=> ! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X0,X1) = sdtasdt0(X0,X2)
| sdtasdt0(X1,X0) = sdtasdt0(X2,X0) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(f17,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__624) ).
fof(f18,conjecture,
( sdtasdt0(xm,xn) = sz00
=> ( xm = sz00
| xn = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f19,negated_conjecture,
~ ( sdtasdt0(xm,xn) = sz00
=> ( xm = sz00
| xn = sz00 ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f21,plain,
( sz00 != xm
& sz00 != xn
& sdtasdt0(xm,xn) = sz00 ),
inference(ennf_transformation,[],[f19]) ).
fof(f22,plain,
( sz00 != xm
& sz00 != xn
& sdtasdt0(xm,xn) = sz00 ),
inference(flattening,[],[f21]) ).
fof(f25,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f26,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f35,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f17]) ).
fof(f36,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f17]) ).
fof(f37,plain,
sz00 = sdtasdt0(xm,xn),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
sz00 != xn,
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
sz00 != xm,
inference(cnf_transformation,[],[f22]) ).
fof(f43,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f45,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f48,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f52,definition,
~ sP0(sz00),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f53,plain,
sP0(xm),
inference(inequality_splitting,[],[f39,f52]) ).
fof(f54,definition,
~ sP1(sz00),
introduced(definition,[new_symbols(definition,[sP1])],[inequality_splitting_name_introduction]) ).
fof(f55,plain,
sP1(xn),
inference(inequality_splitting,[],[f38,f54]) ).
fof(f62,plain,
! [X0] :
( sz00 != sdtasdt0(xm,X0)
| xn = X0
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| sz00 = xm
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f43,f37]) ).
fof(f68,plain,
! [X0] :
( sz00 != sdtasdt0(xm,X0)
| xn = X0
| ~ aNaturalNumber0(X0)
| sz00 = xm
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f62,f35]) ).
fof(f73,plain,
! [X0] :
( sz00 != sdtasdt0(xm,X0)
| xn = X0
| ~ aNaturalNumber0(X0)
| sz00 = xm ),
inference(forward_subsumption_resolution,[],[f68,f36]) ).
fof(f77,definition,
( spl4_1
<=> sz00 = xm ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f79,plain,
( sz00 = xm
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f81,definition,
( spl4_2
<=> ! [X0] :
( sz00 != sdtasdt0(xm,X0)
| ~ aNaturalNumber0(X0)
| xn = X0 ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f82,plain,
( ! [X0] :
( sz00 != sdtasdt0(xm,X0)
| ~ aNaturalNumber0(X0)
| xn = X0 )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f73,f81,f77]) ).
fof(f86,definition,
( spl4_3
<=> sz00 = xn ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f87,plain,
( sz00 != xn
| spl4_3 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f88,plain,
( sz00 = xn
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f96,plain,
( sP1(sz00)
| ~ spl4_3 ),
inference(superposition,[],[f55,f88]) ).
fof(f97,plain,
( $false
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f96,f54]) ).
fof(f98,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[],[f97]) ).
fof(f99,plain,
( sz00 != sz00
| ~ aNaturalNumber0(sz00)
| sz00 = xn
| ~ aNaturalNumber0(xm)
| ~ spl4_2 ),
inference(superposition,[],[f82,f45]) ).
fof(f104,plain,
( ~ aNaturalNumber0(sz00)
| sz00 = xn
| ~ aNaturalNumber0(xm)
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f99]) ).
fof(f107,plain,
( sz00 = xn
| ~ aNaturalNumber0(xm)
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f104,f48]) ).
fof(f108,plain,
( ~ aNaturalNumber0(xm)
| ~ spl4_2
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f107,f87]) ).
fof(f109,plain,
( $false
| ~ spl4_2
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f108,f36]) ).
fof(f110,plain,
( ~ spl4_2
| spl4_3 ),
inference(avatar_contradiction_clause,[],[f109]) ).
fof(f113,plain,
( sP0(sz00)
| ~ spl4_1 ),
inference(superposition,[],[f53,f79]) ).
fof(f114,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f113,f52]) ).
fof(f115,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f114]) ).
cnf(s2,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f84]) ).
cnf(s5,plain,
~ spl4_3,
inference(sat_conversion,[],[f98]) ).
cnf(s6,plain,
( ~ spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f110]) ).
cnf(s7,plain,
~ spl4_1,
inference(sat_conversion,[],[f115]) ).
cnf(s8,plain,
~ spl4_2,
inference(rat,[],[s6,s5]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s2,s8,s7]) ).
fof(f116,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM457+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n011.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 20:00:16 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.44 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
% 3.46/1.47 % (2721128)Detected formulas, will run a generic FOF schedule.
% 3.46/1.47 % (2721135)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=2744990501:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.46/1.47 % (2721134)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=2140883056:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.46/1.47 % (2721139)dis-21_1_sil=8000:lcm=predicate:random_seed=2216640523: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)
% 3.46/1.47 % (2721136)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3386961886:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.46/1.47 % (2721137)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3091395311:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.46/1.47 % (2721133)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=3010755007:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.46/1.47 % (2721138)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2695808771:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.46/1.47 % (2721136)First to succeed.
% 3.46/1.47 % (2721139)Refutation not found, incomplete strategy
% 3.46/1.47 % (2721139)------------------------------
% 3.46/1.47 % (2721139)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.47 % (2721139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.47 % (2721139)CaDiCaL version: 2.1.3
% 3.46/1.47 % (2721139)Termination reason: Refutation not found, incomplete strategy
% 3.46/1.47 % (2721139)Time elapsed: 0.003 s
% 3.46/1.47 % (2721139)Peak memory usage: 88 MB
% 3.46/1.47 % (2721139)Instructions burned: 3 (million)
% 3.46/1.47 % (2721136)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2721128"
% 3.46/1.47 % (2721137)Also succeeded, but the first one will report.
% 3.46/1.47 % (2721138)Also succeeded, but the first one will report.
% 3.46/1.47 % (2721139)------------------------------
% 3.46/1.47 % (2721139)------------------------------
% 3.46/1.47 % (2721136)Refutation found. Thanks to Tanya!
% 3.46/1.47 % SZS status Theorem for theBenchmark
% 3.46/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.47 % (2721136)------------------------------
% 3.46/1.47 % (2721136)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.47 % (2721136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.47 % (2721136)CaDiCaL version: 2.1.3
% 3.46/1.47 % (2721136)Termination reason: Refutation
% 3.46/1.47 % (2721136)Time elapsed: 0.004 s
% 3.46/1.47 % (2721136)Peak memory usage: 89 MB
% 3.46/1.47 % (2721136)Instructions burned: 3 (million)
% 3.46/1.47 % (2721136)------------------------------
% 3.46/1.47 % (2721136)------------------------------
% 3.46/1.47 % (2721128)Success in time 0.407 s
% 3.46/1.47 % Vampire exiting
%------------------------------------------------------------------------------