%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM849+2 : 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 : n020.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 3.80s 1.52s
% Output : Refutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 17 unt; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 8 ~; 4 |; 2 &)
% ( 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 26 !; 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(f6,axiom,
! [X0] :
( vmul(vmul(vd448,vd449),X0) = vmul(vd448,vmul(vd449,X0))
=> vmul(vmul(vd448,vd449),vsucc(X0)) = vplus(vmul(vmul(vd448,vd449),X0),vmul(vd448,vd449)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(292), 1), 3)') ).
fof(f8,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(f9,axiom,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof(f10,axiom,
! [X0,X1] : vmul(vsucc(X0),X1) = vplus(vmul(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).
fof(f12,axiom,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f14,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(f15,plain,
! [X0] :
( vmul(vmul(vd448,vd449),vsucc(X0)) = vplus(vmul(vmul(vd448,vd449),X0),vmul(vd448,vd449))
| vmul(vmul(vd448,vd449),X0) != vmul(vd448,vmul(vd449,X0)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f19,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)],[f14]) ).
fof(f20,plain,
vmul(vmul(vd448,vd449),sK0) = vmul(vd448,vmul(vd449,sK0)),
inference(cnf_transformation,[],[f19]) ).
fof(f21,plain,
vmul(vmul(vd448,vd449),vsucc(sK0)) != vmul(vd448,vmul(vd449,vsucc(sK0))),
inference(cnf_transformation,[],[f19]) ).
fof(f22,plain,
! [X0] :
( vmul(vmul(vd448,vd449),vsucc(X0)) = vplus(vmul(vmul(vd448,vd449),X0),vmul(vd448,vd449))
| vmul(vmul(vd448,vd449),X0) != vmul(vd448,vmul(vd449,X0)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f27,plain,
! [X0,X1] : vmul(vsucc(X0),X1) = vplus(vmul(X0,X1),X1),
inference(cnf_transformation,[],[f10]) ).
fof(f28,plain,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
inference(cnf_transformation,[],[f12]) ).
fof(f29,plain,
! [X2,X0,X1] : vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f40,plain,
! [X0,X1] : vmul(vsucc(X0),X1) = vplus(X1,vmul(X0,X1)),
inference(forward_demodulation,[],[f27,f28]) ).
fof(f83,plain,
! [X0] :
( vmul(vmul(vd448,vd449),X0) != vmul(vd448,vmul(vd449,X0))
| vmul(vmul(vd448,vd449),vsucc(X0)) = vplus(vmul(vd448,vd449),vmul(vmul(vd448,vd449),X0)) ),
inference(forward_demodulation,[],[f22,f28]) ).
fof(f105,plain,
( vmul(vd448,vmul(vd449,sK0)) != vmul(vd448,vmul(vd449,sK0))
| vmul(vmul(vd448,vd449),vsucc(sK0)) = vplus(vmul(vd448,vd449),vmul(vd448,vmul(vd449,sK0))) ),
inference(superposition,[],[f83,f20]) ).
fof(f108,plain,
vmul(vmul(vd448,vd449),vsucc(sK0)) = vplus(vmul(vd448,vd449),vmul(vd448,vmul(vd449,sK0))),
inference(trivial_inequality_removal,[],[f105]) ).
fof(f111,plain,
vmul(vmul(vd448,vd449),vsucc(sK0)) = vmul(vd448,vplus(vd449,vmul(vd449,sK0))),
inference(forward_demodulation,[],[f108,f29]) ).
fof(f112,plain,
vmul(vmul(vd448,vd449),vsucc(sK0)) = vmul(vd448,vplus(vd449,vmul(sK0,vd449))),
inference(forward_demodulation,[],[f111,f26]) ).
fof(f113,plain,
vmul(vmul(vd448,vd449),vsucc(sK0)) = vmul(vd448,vmul(vsucc(sK0),vd449)),
inference(forward_demodulation,[],[f112,f40]) ).
fof(f114,plain,
vmul(vmul(vd448,vd449),vsucc(sK0)) = vmul(vd448,vmul(vd449,vsucc(sK0))),
inference(forward_demodulation,[],[f113,f26]) ).
fof(f115,plain,
$false,
inference(forward_subsumption_resolution,[],[f114,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM849+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.37 % Computer : n020.cluster.edu
% 0.04/0.37 % Model : x86_64 x86_64
% 0.04/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.37 % Memory : 8046.5625MB
% 0.04/0.37 % OS : Linux 6.8.0-71-generic
% 0.04/0.37 % CPULimit : 300
% 0.04/0.37 % WCLimit : 300
% 0.04/0.37 % DateTime : Sun Sep 27 21:31:19 UTC 2026
% 0.04/0.38 % CPUTime :
% 0.04/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.41 Running first-order theorem proving
% 0.04/0.41 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
% 3.80/1.52 % (3773650)Detected formulas, will run a generic FOF schedule.
% 3.80/1.52 % (3773661)dis-21_1_sil=8000:lcm=predicate:random_seed=2832846111: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)
% 3.80/1.52 % (3773661)Refutation not found, incomplete strategy
% 3.80/1.52 % (3773661)------------------------------
% 3.80/1.52 % (3773661)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.52 % (3773661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.52 % (3773661)CaDiCaL version: 2.1.3
% 3.80/1.52 % (3773661)Termination reason: Refutation not found, incomplete strategy
% 3.80/1.52 % (3773661)Time elapsed: 0.001 s
% 3.80/1.52 % (3773661)Peak memory usage: 88 MB
% 3.80/1.52 % (3773661)Instructions burned: 1 (million)
% 3.80/1.52 % (3773659)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1672015365:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.80/1.52 % (3773656)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=959847039:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.80/1.52 % (3773655)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=3373749010:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.80/1.52 % (3773660)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4167723288:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.80/1.52 % (3773657)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=3591804397:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.80/1.52 % (3773658)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3473903277:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.80/1.52 % (3773658)Refutation not found, incomplete strategy
% 3.80/1.52 % (3773658)------------------------------
% 3.80/1.52 % (3773658)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.52 % (3773658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.52 % (3773658)CaDiCaL version: 2.1.3
% 3.80/1.52 % (3773658)Termination reason: Refutation not found, incomplete strategy
% 3.80/1.52 % (3773658)Time elapsed: 0.002 s
% 3.80/1.52 % (3773658)Peak memory usage: 88 MB
% 3.80/1.52 % (3773658)Instructions burned: 1 (million)
% 3.80/1.52 % (3773659)First to succeed.
% 3.80/1.52 % (3773659)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3773650"
% 3.80/1.52 % (3773660)Also succeeded, but the first one will report.
% 3.80/1.52 % (3773661)------------------------------
% 3.80/1.52 % (3773661)------------------------------
% 3.80/1.52 % (3773669)lrs+10_1_sil=8000:sp=occurrence:random_seed=3923419521:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.80/1.52 % (3773669)Also succeeded, but the first one will report.
% 3.80/1.52 % (3773658)------------------------------
% 3.80/1.52 % (3773658)------------------------------
% 3.80/1.52 % (3773659)Refutation found. Thanks to Tanya!
% 3.80/1.52 % SZS status Theorem for theBenchmark
% 3.80/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 3.80/1.52 % (3773659)------------------------------
% 3.80/1.52 % (3773659)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.52 % (3773659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.52 % (3773659)CaDiCaL version: 2.1.3
% 3.80/1.52 % (3773659)Termination reason: Refutation
% 3.80/1.52 % (3773659)Time elapsed: 0.005 s
% 3.80/1.52 % (3773659)Peak memory usage: 88 MB
% 3.80/1.52 % (3773659)Instructions burned: 6 (million)
% 3.80/1.52 % (3773659)------------------------------
% 3.80/1.52 % (3773659)------------------------------
% 3.80/1.52 % (3773650)Success in time 0.445 s
% 3.80/1.52 % Vampire exiting
%------------------------------------------------------------------------------