%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM840+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:17:13 PM UTC 2026
% Result : Theorem 3.54s 1.48s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 13 unt; 2 def)
% Number of atoms : 76 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 65 ( 30 ~; 29 |; 1 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
less(vd328,vd329),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq(conjunct2(conjunct2(204))), 336, 0)') ).
fof(f2,negated_conjecture,
~ less(vd328,vd329),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
less(vplus(vd328,vd330),vplus(vd329,vd330)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(antec(conjunct2(conjunct2(204))), 335, 0)') ).
fof(f6,axiom,
! [X0,X1,X2] :
( less(X0,X1)
=> less(vplus(X0,X2),vplus(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 0)') ).
fof(f12,axiom,
! [X0,X1,X2] :
( ( less(X1,X2)
& less(X0,X1) )
=> less(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(168, 0), 0)') ).
fof(f18,axiom,
! [X0,X1] :
( greater(X0,X1)
=> less(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
fof(f19,axiom,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| less(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof(f20,axiom,
! [X0,X1] :
( X0 != X1
| ~ less(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
fof(f41,plain,
~ less(vd328,vd329),
inference(flattening,[],[f2]) ).
fof(f44,plain,
! [X0,X1,X2] :
( less(vplus(X0,X2),vplus(X1,X2))
| ~ less(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f50,plain,
! [X0,X1,X2] :
( less(X0,X2)
| ~ less(X1,X2)
| ~ less(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f51,plain,
! [X0,X1,X2] :
( less(X0,X2)
| ~ less(X1,X2)
| ~ less(X0,X1) ),
inference(flattening,[],[f50]) ).
fof(f55,plain,
! [X0,X1] :
( less(X1,X0)
| ~ greater(X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f74,plain,
~ less(vd328,vd329),
inference(cnf_transformation,[],[f41]) ).
fof(f75,plain,
less(vplus(vd328,vd330),vplus(vd329,vd330)),
inference(cnf_transformation,[],[f3]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ less(X0,X1)
| less(vplus(X0,X2),vplus(X1,X2)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f85,plain,
! [X2,X0,X1] :
( ~ less(X1,X2)
| less(X0,X2)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f95,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| less(X1,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f96,plain,
! [X0,X1] :
( greater(X0,X1)
| X0 = X1
| less(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f97,plain,
! [X0,X1] :
( X0 != X1
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f124,plain,
! [X1] : ~ less(X1,X1),
inference(equality_resolution,[],[f97]) ).
fof(f145,definition,
( spl4_4
<=> vd328 = vd329 ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f147,plain,
( vd328 = vd329
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f160,plain,
! [X0] :
( ~ less(X0,vplus(vd328,vd330))
| less(X0,vplus(vd329,vd330)) ),
inference(resolution,[],[f85,f75]) ).
fof(f168,plain,
! [X0,X1] :
( less(X0,X1)
| X0 = X1
| less(X1,X0) ),
inference(resolution,[],[f96,f95]) ).
fof(f299,plain,
( vd328 = vd329
| less(vd329,vd328) ),
inference(resolution,[],[f168,f74]) ).
fof(f305,definition,
( spl4_5
<=> less(vd329,vd328) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f307,plain,
( less(vd329,vd328)
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f308,plain,
( spl4_5
| spl4_4 ),
inference(avatar_split_clause,[],[f299,f145,f305]) ).
fof(f312,plain,
( less(vplus(vd328,vd330),vplus(vd328,vd330))
| ~ spl4_4 ),
inference(superposition,[],[f75,f147]) ).
fof(f316,plain,
( $false
| ~ spl4_4 ),
inference(forward_subsumption_resolution,[],[f312,f124]) ).
fof(f317,plain,
~ spl4_4,
inference(avatar_contradiction_clause,[],[f316]) ).
fof(f321,plain,
( ! [X0] : less(vplus(vd329,X0),vplus(vd328,X0))
| ~ spl4_5 ),
inference(resolution,[],[f307,f78]) ).
fof(f733,plain,
( less(vplus(vd329,vd330),vplus(vd329,vd330))
| ~ spl4_5 ),
inference(resolution,[],[f321,f160]) ).
fof(f757,plain,
( $false
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f733,f124]) ).
fof(f758,plain,
~ spl4_5,
inference(avatar_contradiction_clause,[],[f757]) ).
cnf(s3,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f308]) ).
cnf(s5,plain,
~ spl4_4,
inference(sat_conversion,[],[f317]) ).
cnf(s8,plain,
~ spl4_5,
inference(sat_conversion,[],[f758]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s3,s8,s5]) ).
fof(f760,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM840+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n004.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 21:29:37 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.54/1.48 % (3897670)Detected formulas, will run a generic FOF schedule.
% 3.54/1.48 % (3897676)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=1719662792:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.54/1.48 % (3897679)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2487990910:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.54/1.48 % (3897678)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4177621588:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.54/1.48 % (3897675)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=3399818926:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.54/1.48 % (3897681)dis-21_1_sil=8000:lcm=predicate:random_seed=625115790: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)
% 3.54/1.48 % (3897677)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=3765394022:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.54/1.48 % (3897680)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1437791364:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.54/1.48 % (3897678)Refutation not found, incomplete strategy
% 3.54/1.48 % (3897678)------------------------------
% 3.54/1.48 % (3897678)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.48 % (3897678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.48 % (3897678)CaDiCaL version: 2.1.3
% 3.54/1.48 % (3897678)Termination reason: Refutation not found, incomplete strategy
% 3.54/1.48 % (3897678)Time elapsed: 0.001 s
% 3.54/1.48 % (3897678)Peak memory usage: 88 MB
% 3.54/1.48 % (3897680)First to succeed.
% 3.54/1.48 % (3897680)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3897670"
% 3.54/1.48 % (3897679)Instruction limit reached!
% 3.54/1.48 % (3897679)------------------------------
% 3.54/1.48 % (3897679)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.48 % (3897679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.48 % (3897679)CaDiCaL version: 2.1.3
% 3.54/1.48 % (3897679)Termination reason: Instruction limit
% 3.54/1.48 % (3897679)Termination phase: Saturation
% 3.54/1.48 % (3897679)Time elapsed: 0.070 s
% 3.54/1.48 % (3897679)Peak memory usage: 89 MB
% 3.54/1.48 % (3897679)Instructions burned: 120 (million)
% 3.54/1.48 % (3897681)Instruction limit reached!
% 3.54/1.48 % (3897681)------------------------------
% 3.54/1.48 % (3897681)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.48 % (3897681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.48 % (3897681)CaDiCaL version: 2.1.3
% 3.54/1.48 % (3897681)Termination reason: Instruction limit
% 3.54/1.48 % (3897681)Termination phase: Saturation
% 3.54/1.48 % (3897681)Time elapsed: 0.080 s
% 3.54/1.48 % (3897681)Peak memory usage: 88 MB
% 3.54/1.48 % (3897681)Instructions burned: 129 (million)
% 3.54/1.48 % (3897690)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3705126599:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.54/1.48 % (3897689)lrs+10_1_sil=8000:sp=occurrence:random_seed=3028012880:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.54/1.48 % (3897689)Also succeeded, but the first one will report.
% 3.54/1.48 % (3897678)------------------------------
% 3.54/1.48 % (3897678)------------------------------
% 3.54/1.48 % (3897680)Refutation found. Thanks to Tanya!
% 3.54/1.48 % SZS status Theorem for theBenchmark
% 3.54/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.54/1.48 % (3897680)------------------------------
% 3.54/1.48 % (3897680)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.54/1.48 % (3897680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/1.48 % (3897680)CaDiCaL version: 2.1.3
% 3.54/1.48 % (3897680)Termination reason: Refutation
% 3.54/1.48 % (3897680)Time elapsed: 0.019 s
% 3.54/1.48 % (3897680)Peak memory usage: 90 MB
% 3.54/1.48 % (3897680)Instructions burned: 23 (million)
% 3.54/1.48 % (3897680)------------------------------
% 3.54/1.48 % (3897680)------------------------------
% 3.54/1.48 % (3897670)Success in time 0.418 s
% 3.54/1.48 % Vampire exiting
%------------------------------------------------------------------------------