%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM849+1 : 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 : n016.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 12:17:15 PM UTC 2026
% Result : Theorem 3.48s 1.24s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 21 unt; 0 def)
% Number of atoms : 49 ( 48 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 7 |; 4 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 34 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( vmul(vmul(vd448,vd449),X0) = vmul(vd448,vmul(vd449,X0))
=> vmul(vmul(vd448,vd449),vsucc(X0)) = vmul(vd448,vmul(vd449,vsucc(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(ind(296), imp(296))') ).
fof(f2,negated_conjecture,
~ ! [X0] :
( vmul(vmul(vd448,vd449),X0) = vmul(vd448,vmul(vd449,X0))
=> vmul(vmul(vd448,vd449),vsucc(X0)) = vmul(vd448,vmul(vd449,vsucc(X0))) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,axiom,
! [X0] :
( vmul(vmul(vd448,vd449),X0) = vmul(vd448,vmul(vd449,X0))
=> vplus(vmul(vmul(vd448,vd449),X0),vmul(vd448,vd449)) = vplus(vmul(vd448,vmul(vd449,X0)),vmul(vd448,vd449)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(292), 1), 2)') ).
fof(f9,axiom,
! [X0,X1,X2] : vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
fof(f10,axiom,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof(f13,axiom,
! [X0,X1] :
( vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0)
& vmul(X0,v1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
fof(f48,axiom,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f52,axiom,
! [X0,X1] :
( vplus(X0,vsucc(X1)) = vsucc(vplus(X0,X1))
& vplus(X0,v1) = vsucc(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
fof(f58,plain,
? [X0] :
( vmul(vmul(vd448,vd449),vsucc(X0)) != vmul(vd448,vmul(vd449,vsucc(X0)))
& vmul(vmul(vd448,vd449),X0) = vmul(vd448,vmul(vd449,X0)) ),
inference(ennf_transformation,[],[f2]) ).
fof(f60,plain,
! [X0] :
( vplus(vmul(vmul(vd448,vd449),X0),vmul(vd448,vd449)) = vplus(vmul(vd448,vmul(vd449,X0)),vmul(vd448,vd449))
| vmul(vmul(vd448,vd449),X0) != vmul(vd448,vmul(vd449,X0)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f71,plain,
( vmul(vmul(vd448,vd449),vsucc(sK0)) != vmul(vd448,vmul(vd449,vsucc(sK0)))
& vmul(vmul(vd448,vd449),sK0) = vmul(vd448,vmul(vd449,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f58]) ).
fof(f73,plain,
vmul(vmul(vd448,vd449),sK0) = vmul(vd448,vmul(vd449,sK0)),
inference(cnf_transformation,[],[f71]) ).
fof(f74,plain,
vmul(vmul(vd448,vd449),vsucc(sK0)) != vmul(vd448,vmul(vd449,vsucc(sK0))),
inference(cnf_transformation,[],[f71]) ).
fof(f78,plain,
! [X0] :
( vplus(vmul(vd448,vmul(vd449,X0)),vmul(vd448,vd449)) = vplus(vmul(vmul(vd448,vd449),X0),vmul(vd448,vd449))
| vmul(vmul(vd448,vd449),X0) != vmul(vd448,vmul(vd449,X0)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f82,plain,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f83,plain,
! [X2,X0,X1] : vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f89,plain,
! [X0] : vsucc(X0) = vplus(X0,v1),
inference(cnf_transformation,[],[f52]) ).
fof(f93,plain,
! [X0,X1] : vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f96,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f48]) ).
fof(f105,plain,
vmul(vmul(vd448,vd449),vplus(sK0,v1)) != vmul(vd448,vmul(vd449,vplus(sK0,v1))),
inference(definition_unfolding,[],[f74,f89,f89]) ).
fof(f116,plain,
! [X0,X1] : vplus(vmul(X0,X1),X0) = vmul(X0,vplus(X1,v1)),
inference(definition_unfolding,[],[f93,f89]) ).
fof(f129,plain,
vmul(vd448,vmul(vd449,vplus(sK0,v1))) != vmul(vplus(sK0,v1),vmul(vd448,vd449)),
inference(superposition,[],[f105,f82]) ).
fof(f237,plain,
! [X0,X1] : vmul(X0,vplus(X1,v1)) = vplus(X0,vmul(X0,X1)),
inference(forward_demodulation,[],[f116,f96]) ).
fof(f534,plain,
! [X0] :
( vplus(vmul(vd448,vmul(vd449,X0)),vmul(vd448,vd449)) = vplus(vmul(vd448,vd449),vmul(vmul(vd448,vd449),X0))
| vmul(vmul(vd448,vd449),X0) != vmul(vd448,vmul(vd449,X0)) ),
inference(forward_demodulation,[],[f78,f96]) ).
fof(f535,plain,
! [X0] :
( vplus(vmul(vd448,vmul(vd449,X0)),vmul(vd448,vd449)) = vmul(vmul(vd448,vd449),vplus(X0,v1))
| vmul(vmul(vd448,vd449),X0) != vmul(vd448,vmul(vd449,X0)) ),
inference(forward_demodulation,[],[f534,f237]) ).
fof(f536,plain,
! [X0] :
( vmul(vmul(vd448,vd449),vplus(X0,v1)) = vplus(vmul(vd448,vd449),vmul(vd448,vmul(vd449,X0)))
| vmul(vmul(vd448,vd449),X0) != vmul(vd448,vmul(vd449,X0)) ),
inference(forward_demodulation,[],[f535,f96]) ).
fof(f537,plain,
! [X0] :
( vmul(vmul(vd448,vd449),X0) != vmul(vd448,vmul(vd449,X0))
| vmul(vmul(vd448,vd449),vplus(X0,v1)) = vmul(vd448,vplus(vd449,vmul(vd449,X0))) ),
inference(forward_demodulation,[],[f536,f83]) ).
fof(f538,plain,
( vmul(vd448,vmul(vd449,sK0)) != vmul(vd448,vmul(vd449,sK0))
| vmul(vmul(vd448,vd449),vplus(sK0,v1)) = vmul(vd448,vplus(vd449,vmul(vd449,sK0))) ),
inference(superposition,[],[f537,f73]) ).
fof(f542,plain,
vmul(vmul(vd448,vd449),vplus(sK0,v1)) = vmul(vd448,vplus(vd449,vmul(vd449,sK0))),
inference(trivial_inequality_removal,[],[f538]) ).
fof(f545,plain,
vmul(vmul(vd448,vd449),vplus(sK0,v1)) = vmul(vd448,vplus(vd449,vmul(sK0,vd449))),
inference(forward_demodulation,[],[f542,f82]) ).
fof(f547,plain,
vmul(vplus(sK0,v1),vmul(vd448,vd449)) = vmul(vd448,vplus(vd449,vmul(sK0,vd449))),
inference(forward_demodulation,[],[f545,f82]) ).
fof(f552,plain,
vmul(vd448,vmul(vd449,vplus(sK0,v1))) != vmul(vd448,vplus(vd449,vmul(sK0,vd449))),
inference(superposition,[],[f129,f547]) ).
fof(f559,plain,
vmul(vd448,vplus(vd449,vmul(vd449,sK0))) != vmul(vd448,vplus(vd449,vmul(sK0,vd449))),
inference(forward_demodulation,[],[f552,f237]) ).
fof(f562,plain,
vmul(vd448,vplus(vd449,vmul(sK0,vd449))) != vmul(vd448,vplus(vd449,vmul(sK0,vd449))),
inference(forward_demodulation,[],[f559,f82]) ).
fof(f563,plain,
$false,
inference(trivial_inequality_removal,[],[f562]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM849+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n016.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 21:35:32 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.41 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
% 3.48/1.24 % (3010645)Detected formulas, will run a generic FOF schedule.
% 3.48/1.24 % (3010656)dis-21_1_sil=8000:lcm=predicate:random_seed=3916883812: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)
% 3.48/1.24 % (3010654)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2088567427:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.48/1.24 % (3010653)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2314555880:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.48/1.24 % (3010651)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=894060786:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.48/1.24 % (3010652)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=3452330506:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.48/1.24 % (3010650)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=1392244989:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.48/1.24 % (3010655)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=108002789:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.48/1.24 % (3010656)Instruction limit reached!
% 3.48/1.24 % (3010656)------------------------------
% 3.48/1.24 % (3010656)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.24 % (3010656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.24 % (3010656)CaDiCaL version: 2.1.3
% 3.48/1.24 % (3010656)Termination reason: Instruction limit
% 3.48/1.24 % (3010656)Termination phase: Saturation
% 3.48/1.24 % (3010656)Time elapsed: 0.042 s
% 3.48/1.24 % (3010656)Peak memory usage: 89 MB
% 3.48/1.24 % (3010656)Instructions burned: 131 (million)
% 3.48/1.24 % (3010653)Refutation not found, incomplete strategy
% 3.48/1.24 % (3010653)------------------------------
% 3.48/1.24 % (3010653)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.24 % (3010653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.24 % (3010653)CaDiCaL version: 2.1.3
% 3.48/1.24 % (3010653)Termination reason: Refutation not found, incomplete strategy
% 3.48/1.24 % (3010653)Time elapsed: 0.002 s
% 3.48/1.24 % (3010653)Peak memory usage: 88 MB
% 3.48/1.24 % (3010653)Instructions burned: 1 (million)
% 3.48/1.24 % (3010654)First to succeed.
% 3.48/1.24 % (3010654)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3010645"
% 3.48/1.24 % (3010655)Also succeeded, but the first one will report.
% 3.48/1.24 % (3010664)lrs+10_1_sil=8000:sp=occurrence:random_seed=1132520231:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.48/1.24 % (3010664)Also succeeded, but the first one will report.
% 3.48/1.24 % (3010653)------------------------------
% 3.48/1.24 % (3010653)------------------------------
% 3.48/1.24 % (3010654)Refutation found. Thanks to Tanya!
% 3.48/1.24 % SZS status Theorem for theBenchmark
% 3.48/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.24 % (3010654)------------------------------
% 3.48/1.24 % (3010654)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.24 % (3010654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.24 % (3010654)CaDiCaL version: 2.1.3
% 3.48/1.24 % (3010654)Termination reason: Refutation
% 3.48/1.24 % (3010654)Time elapsed: 0.014 s
% 3.48/1.24 % (3010654)Peak memory usage: 88 MB
% 3.48/1.24 % (3010654)Instructions burned: 23 (million)
% 3.48/1.24 % (3010654)------------------------------
% 3.48/1.24 % (3010654)------------------------------
% 3.48/1.24 % (3010645)Success in time 0.439 s
% 3.48/1.24 % Vampire exiting
%------------------------------------------------------------------------------