%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM845+2 : 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 : n008.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 12:17:14 PM UTC 2026
% Result : Theorem 1.14s 1.04s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 65 ( 35 unt; 2 def)
% Number of atoms : 95 ( 74 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 58 ( 28 ~; 20 |; 2 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 27 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( vmul(vsucc(vd411),X0) = vplus(vmul(vd411,X0),X0)
=> vmul(vsucc(vd411),vsucc(X0)) = vplus(vmul(vd411,vsucc(X0)),vsucc(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(ind(267), imp(267))') ).
fof(f2,negated_conjecture,
~ ! [X0] :
( vmul(vsucc(vd411),X0) = vplus(vmul(vd411,X0),X0)
=> vmul(vsucc(vd411),vsucc(X0)) = vplus(vmul(vd411,vsucc(X0)),vsucc(X0)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
! [X0] :
( vmul(vsucc(vd411),X0) = vplus(vmul(vd411,X0),X0)
=> vplus(vplus(vmul(vd411,X0),vd411),vsucc(X0)) = vplus(vmul(vd411,vsucc(X0)),vsucc(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 0)') ).
fof(f5,axiom,
! [X0] :
( vmul(vsucc(vd411),X0) = vplus(vmul(vd411,X0),X0)
=> vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) = vplus(vmul(vd411,X0),vplus(vd411,vsucc(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 2)') ).
fof(f6,axiom,
! [X0] :
( vmul(vsucc(vd411),X0) = vplus(vmul(vd411,X0),X0)
=> vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0)) = vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 3)') ).
fof(f7,axiom,
! [X0] :
( vmul(vsucc(vd411),X0) = vplus(vmul(vd411,X0),X0)
=> vplus(vmul(vd411,X0),vplus(X0,vsucc(vd411))) = vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 4)') ).
fof(f10,axiom,
! [X0] :
( vmul(vsucc(vd411),X0) = vplus(vmul(vd411,X0),X0)
=> vmul(vsucc(vd411),vsucc(X0)) = vplus(vmul(vsucc(vd411),X0),vsucc(vd411)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 7)') ).
fof(f13,axiom,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f15,axiom,
! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof(f17,plain,
? [X0] :
( vmul(vsucc(vd411),vsucc(X0)) != vplus(vmul(vd411,vsucc(X0)),vsucc(X0))
& vmul(vsucc(vd411),X0) = vplus(vmul(vd411,X0),X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f18,plain,
! [X0] :
( vmul(vsucc(vd411),vsucc(X0)) = vplus(vmul(vsucc(vd411),X0),vsucc(vd411))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f21,plain,
! [X0] :
( vplus(vmul(vd411,X0),vplus(X0,vsucc(vd411))) = vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f22,plain,
! [X0] :
( vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0)) = vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f23,plain,
! [X0] :
( vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) = vplus(vmul(vd411,X0),vplus(vd411,vsucc(X0)))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f25,plain,
! [X0] :
( vplus(vplus(vmul(vd411,X0),vd411),vsucc(X0)) = vplus(vmul(vd411,vsucc(X0)),vsucc(X0))
| vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f26,plain,
( vmul(vsucc(vd411),vsucc(sK0)) != vplus(vmul(vd411,vsucc(sK0)),vsucc(sK0))
& vmul(vsucc(vd411),sK0) = vplus(vmul(vd411,sK0),sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f17]) ).
fof(f27,plain,
vmul(vsucc(vd411),sK0) = vplus(vmul(vd411,sK0),sK0),
inference(cnf_transformation,[],[f26]) ).
fof(f28,plain,
vmul(vsucc(vd411),vsucc(sK0)) != vplus(vmul(vd411,vsucc(sK0)),vsucc(sK0)),
inference(cnf_transformation,[],[f26]) ).
fof(f29,plain,
! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
inference(cnf_transformation,[],[f13]) ).
fof(f31,plain,
! [X0] :
( vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0)
| vmul(vsucc(vd411),vsucc(X0)) = vplus(vmul(vsucc(vd411),X0),vsucc(vd411)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
! [X0] :
( vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0)
| vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0)) = vplus(vmul(vd411,X0),vplus(X0,vsucc(vd411))) ),
inference(cnf_transformation,[],[f21]) ).
fof(f35,plain,
! [X0] :
( vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0)
| vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) = vplus(vmul(vd411,X0),vplus(vsucc(vd411),X0)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
! [X0] :
( vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0)
| vplus(vmul(vd411,X0),vplus(vd411,vsucc(X0))) = vplus(vmul(vd411,X0),vsucc(vplus(vd411,X0))) ),
inference(cnf_transformation,[],[f23]) ).
fof(f38,plain,
! [X0] :
( vmul(vsucc(vd411),X0) != vplus(vmul(vd411,X0),X0)
| vplus(vmul(vd411,vsucc(X0)),vsucc(X0)) = vplus(vplus(vmul(vd411,X0),vd411),vsucc(X0)) ),
inference(cnf_transformation,[],[f25]) ).
fof(f39,definition,
~ sP1(vmul(vsucc(vd411),vsucc(sK0))),
introduced(definition,[new_symbols(definition,[sP1])],[inequality_splitting_name_introduction]) ).
fof(f40,plain,
sP1(vplus(vmul(vd411,vsucc(sK0)),vsucc(sK0))),
inference(inequality_splitting,[],[f28,f39]) ).
fof(f41,plain,
vmul(vsucc(vd411),sK0) = vplus(sK0,vmul(vd411,sK0)),
inference(forward_demodulation,[],[f27,f30]) ).
fof(f42,plain,
sP1(vplus(vsucc(sK0),vmul(vd411,vsucc(sK0)))),
inference(forward_demodulation,[],[f40,f30]) ).
fof(f43,plain,
( vplus(vmul(vd411,sK0),sK0) != vplus(sK0,vmul(vd411,sK0))
| vmul(vsucc(vd411),vsucc(sK0)) = vplus(vplus(sK0,vmul(vd411,sK0)),vsucc(vd411)) ),
inference(superposition,[],[f31,f41]) ).
fof(f46,plain,
( vplus(vmul(vd411,sK0),sK0) != vplus(sK0,vmul(vd411,sK0))
| vplus(vmul(vd411,sK0),vplus(sK0,vsucc(vd411))) = vplus(vmul(vd411,sK0),vplus(vsucc(vd411),sK0)) ),
inference(superposition,[],[f34,f41]) ).
fof(f47,plain,
( vplus(vmul(vd411,sK0),sK0) != vplus(sK0,vmul(vd411,sK0))
| vplus(vmul(vd411,sK0),vplus(vsucc(vd411),sK0)) = vplus(vmul(vd411,sK0),vsucc(vplus(vd411,sK0))) ),
inference(superposition,[],[f35,f41]) ).
fof(f48,plain,
( vplus(vmul(vd411,sK0),sK0) != vplus(sK0,vmul(vd411,sK0))
| vplus(vmul(vd411,sK0),vsucc(vplus(vd411,sK0))) = vplus(vmul(vd411,sK0),vplus(vd411,vsucc(sK0))) ),
inference(superposition,[],[f36,f41]) ).
fof(f50,plain,
( vplus(vmul(vd411,sK0),sK0) != vplus(sK0,vmul(vd411,sK0))
| vplus(vmul(vd411,vsucc(sK0)),vsucc(sK0)) = vplus(vplus(vmul(vd411,sK0),vd411),vsucc(sK0)) ),
inference(superposition,[],[f38,f41]) ).
fof(f51,plain,
vplus(vmul(vd411,vsucc(sK0)),vsucc(sK0)) = vplus(vplus(vmul(vd411,sK0),vd411),vsucc(sK0)),
inference(forward_subsumption_resolution,[],[f50,f30]) ).
fof(f52,plain,
vplus(vmul(vd411,sK0),vsucc(vplus(vd411,sK0))) = vplus(vmul(vd411,sK0),vplus(vd411,vsucc(sK0))),
inference(forward_subsumption_resolution,[],[f48,f30]) ).
fof(f53,plain,
vplus(vmul(vd411,sK0),vplus(vsucc(vd411),sK0)) = vplus(vmul(vd411,sK0),vsucc(vplus(vd411,sK0))),
inference(forward_subsumption_resolution,[],[f47,f30]) ).
fof(f54,plain,
vplus(vmul(vd411,sK0),vplus(sK0,vsucc(vd411))) = vplus(vmul(vd411,sK0),vplus(vsucc(vd411),sK0)),
inference(forward_subsumption_resolution,[],[f46,f30]) ).
fof(f56,plain,
vmul(vsucc(vd411),vsucc(sK0)) = vplus(vplus(sK0,vmul(vd411,sK0)),vsucc(vd411)),
inference(forward_subsumption_resolution,[],[f43,f30]) ).
fof(f57,plain,
vplus(vmul(vd411,vsucc(sK0)),vsucc(sK0)) = vplus(vmul(vd411,sK0),vplus(vd411,vsucc(sK0))),
inference(forward_demodulation,[],[f51,f29]) ).
fof(f58,plain,
vplus(vmul(vd411,sK0),vsucc(vplus(vd411,sK0))) = vplus(vplus(vsucc(vd411),sK0),vmul(vd411,sK0)),
inference(forward_demodulation,[],[f53,f30]) ).
fof(f59,plain,
vplus(vmul(vd411,sK0),vplus(sK0,vsucc(vd411))) = vplus(vplus(vsucc(vd411),sK0),vmul(vd411,sK0)),
inference(forward_demodulation,[],[f54,f30]) ).
fof(f61,plain,
vmul(vsucc(vd411),vsucc(sK0)) = vplus(sK0,vplus(vmul(vd411,sK0),vsucc(vd411))),
inference(forward_demodulation,[],[f56,f29]) ).
fof(f62,plain,
vplus(vsucc(sK0),vmul(vd411,vsucc(sK0))) = vplus(vmul(vd411,sK0),vplus(vd411,vsucc(sK0))),
inference(forward_demodulation,[],[f57,f30]) ).
fof(f63,plain,
vplus(vmul(vd411,sK0),vsucc(vplus(vd411,sK0))) = vplus(vsucc(vd411),vplus(sK0,vmul(vd411,sK0))),
inference(forward_demodulation,[],[f58,f29]) ).
fof(f64,plain,
vplus(vmul(vd411,sK0),vplus(sK0,vsucc(vd411))) = vplus(vsucc(vd411),vplus(sK0,vmul(vd411,sK0))),
inference(forward_demodulation,[],[f59,f29]) ).
fof(f66,plain,
vmul(vsucc(vd411),vsucc(sK0)) = vplus(sK0,vplus(vsucc(vd411),vmul(vd411,sK0))),
inference(forward_demodulation,[],[f61,f30]) ).
fof(f67,plain,
vplus(vsucc(vd411),vplus(sK0,vmul(vd411,sK0))) = vplus(vplus(sK0,vsucc(vd411)),vmul(vd411,sK0)),
inference(forward_demodulation,[],[f64,f30]) ).
fof(f69,plain,
vplus(vsucc(vd411),vplus(sK0,vmul(vd411,sK0))) = vplus(sK0,vplus(vsucc(vd411),vmul(vd411,sK0))),
inference(forward_demodulation,[],[f67,f29]) ).
fof(f73,plain,
~ sP1(vplus(sK0,vplus(vsucc(vd411),vmul(vd411,sK0)))),
inference(superposition,[],[f39,f66]) ).
fof(f88,plain,
~ sP1(vplus(vsucc(vd411),vplus(sK0,vmul(vd411,sK0)))),
inference(forward_demodulation,[],[f73,f69]) ).
fof(f107,definition,
( spl2_2
<=> vplus(vmul(vd411,sK0),vplus(vd411,vsucc(sK0))) = vplus(vsucc(vd411),vplus(sK0,vmul(vd411,sK0))) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f108,plain,
( vplus(vmul(vd411,sK0),vplus(vd411,vsucc(sK0))) = vplus(vsucc(vd411),vplus(sK0,vmul(vd411,sK0)))
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f109,plain,
( vplus(vmul(vd411,sK0),vplus(vd411,vsucc(sK0))) != vplus(vsucc(vd411),vplus(sK0,vmul(vd411,sK0)))
| spl2_2 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f154,plain,
sP1(vplus(vmul(vd411,sK0),vplus(vd411,vsucc(sK0)))),
inference(superposition,[],[f42,f62]) ).
fof(f161,plain,
vplus(vmul(vd411,sK0),vplus(vd411,vsucc(sK0))) = vplus(vsucc(vd411),vplus(sK0,vmul(vd411,sK0))),
inference(superposition,[],[f63,f52]) ).
fof(f167,plain,
( $false
| spl2_2 ),
inference(forward_subsumption_resolution,[],[f161,f109]) ).
fof(f168,plain,
spl2_2,
inference(avatar_contradiction_clause,[],[f167]) ).
fof(f176,plain,
( sP1(vplus(vsucc(vd411),vplus(sK0,vmul(vd411,sK0))))
| ~ spl2_2 ),
inference(superposition,[],[f154,f108]) ).
fof(f179,plain,
( $false
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f176,f88]) ).
fof(f180,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f179]) ).
cnf(s8,plain,
spl2_2,
inference(sat_conversion,[],[f168]) ).
cnf(s9,plain,
~ spl2_2,
inference(sat_conversion,[],[f180]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s8,s9]) ).
fof(f183,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM845+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n008.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 21:31:09 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 1.14/1.04 % (1619281)Detected formulas, will run a generic FOF schedule.
% 1.14/1.04 % (1619291)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3349976809:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.14/1.04 % (1619288)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=2406590301:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.14/1.04 % (1619289)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2601569371:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.14/1.04 % (1619290)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3923899670:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.14/1.04 % (1619287)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=1098377057:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.14/1.04 % (1619292)dis-21_1_sil=8000:lcm=predicate:random_seed=2401612937: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)
% 1.14/1.04 % (1619286)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=2940957298:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.14/1.04 % (1619292)Refutation not found, incomplete strategy
% 1.14/1.04 % (1619292)------------------------------
% 1.14/1.04 % (1619292)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.14/1.04 % (1619292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.14/1.04 % (1619292)CaDiCaL version: 2.1.3
% 1.14/1.04 % (1619292)Termination reason: Refutation not found, incomplete strategy
% 1.14/1.04 % (1619292)Time elapsed: 0.002 s
% 1.14/1.04 % (1619292)Peak memory usage: 88 MB
% 1.14/1.04 % (1619292)Instructions burned: 2 (million)
% 1.14/1.04 % (1619289)First to succeed.
% 1.14/1.04 % (1619289)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1619281"
% 1.14/1.04 % (1619290)Also succeeded, but the first one will report.
% 1.14/1.04 % (1619291)Also succeeded, but the first one will report.
% 1.14/1.04 % (1619292)------------------------------
% 1.14/1.04 % (1619292)------------------------------
% 1.14/1.04 % (1619289)Refutation found. Thanks to Tanya!
% 1.14/1.04 % SZS status Theorem for theBenchmark
% 1.14/1.04 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.14 % (1619289)------------------------------
% 0.17/1.14 % (1619289)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.14 % (1619289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.14 % (1619289)CaDiCaL version: 2.1.3
% 0.17/1.14 % (1619289)Termination reason: Refutation
% 0.17/1.14 % (1619289)Time elapsed: 0.006 s
% 0.17/1.14 % (1619289)Peak memory usage: 89 MB
% 0.17/1.14 % (1619289)Instructions burned: 9 (million)
% 0.17/1.14 % (1619289)------------------------------
% 0.17/1.14 % (1619289)------------------------------
% 0.17/1.14 % (1619281)Success in time 0.425 s
% 0.17/1.14 % Vampire exiting
%------------------------------------------------------------------------------