%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM846+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 12:17:14 PM UTC 2026
% Result : Theorem 2.66s 1.35s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 24 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 8 ( 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(286, 441, 2)') ).
fof(f2,negated_conjecture,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,axiom,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd436,vd437),vmul(vd436,vd439)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(285, 440, 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(f15,axiom,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f23,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(flattening,[],[f2]) ).
fof(f25,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
inference(cnf_transformation,[],[f23]) ).
fof(f29,plain,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd436,vd437),vmul(vd436,vd439)),
inference(cnf_transformation,[],[f5]) ).
fof(f33,plain,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
inference(cnf_transformation,[],[f15]) ).
fof(f37,plain,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f85,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vplus(vmul(vd436,vd437),vmul(vd439,vd436)),vd436),
inference(superposition,[],[f25,f37]) ).
fof(f88,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vd436,vplus(vmul(vd436,vd437),vmul(vd439,vd436))),
inference(forward_demodulation,[],[f85,f33]) ).
fof(f96,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vd436,vplus(vmul(vd439,vd436),vmul(vd436,vd437))),
inference(forward_demodulation,[],[f88,f33]) ).
fof(f102,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) != vplus(vd436,vplus(vmul(vd439,vd436),vmul(vd437,vd436))),
inference(forward_demodulation,[],[f96,f37]) ).
fof(f108,plain,
vplus(vd436,vmul(vd436,vplus(vd437,vd439))) != vplus(vd436,vplus(vmul(vd439,vd436),vmul(vd437,vd436))),
inference(forward_demodulation,[],[f102,f33]) ).
fof(f112,plain,
vplus(vd436,vmul(vd436,vplus(vd439,vd437))) != vplus(vd436,vplus(vmul(vd439,vd436),vmul(vd437,vd436))),
inference(forward_demodulation,[],[f108,f33]) ).
fof(f231,plain,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd436,vd439),vmul(vd436,vd437)),
inference(forward_demodulation,[],[f29,f33]) ).
fof(f232,plain,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd436,vd439),vmul(vd437,vd436)),
inference(forward_demodulation,[],[f231,f37]) ).
fof(f233,plain,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd437,vd436),vmul(vd436,vd439)),
inference(forward_demodulation,[],[f232,f33]) ).
fof(f234,plain,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd437,vd436),vmul(vd439,vd436)),
inference(forward_demodulation,[],[f233,f37]) ).
fof(f235,plain,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd439,vd436),vmul(vd437,vd436)),
inference(forward_demodulation,[],[f234,f33]) ).
fof(f236,plain,
vmul(vd436,vplus(vd439,vd437)) = vplus(vmul(vd439,vd436),vmul(vd437,vd436)),
inference(forward_demodulation,[],[f235,f33]) ).
fof(f251,plain,
vplus(vd436,vmul(vd436,vplus(vd439,vd437))) != vplus(vd436,vmul(vd436,vplus(vd439,vd437))),
inference(superposition,[],[f112,f236]) ).
fof(f253,plain,
$false,
inference(trivial_inequality_removal,[],[f251]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM846+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n020.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 21:31:04 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.66/1.35 % (3773236)Detected formulas, will run a generic FOF schedule.
% 2.66/1.35 % (3773245)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3295966408:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.66/1.35 % (3773245)First to succeed.
% 2.66/1.35 % (3773245)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3773236"
% 2.66/1.35 % (3773247)dis-21_1_sil=8000:lcm=predicate:random_seed=134560916: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)
% 2.66/1.35 % (3773241)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=473803910:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.66/1.35 % (3773246)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2281526144:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.66/1.35 % (3773242)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=1887610345:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.66/1.35 % (3773244)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1015394728:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.66/1.35 % (3773243)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=4246507820:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.66/1.35 % (3773244)Refutation not found, incomplete strategy
% 2.66/1.35 % (3773244)------------------------------
% 2.66/1.35 % (3773244)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.35 % (3773244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.35 % (3773244)CaDiCaL version: 2.1.3
% 2.66/1.35 % (3773244)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.35 % (3773244)Time elapsed: 0.002 s
% 2.66/1.35 % (3773244)Peak memory usage: 88 MB
% 2.66/1.35 % (3773244)Instructions burned: 1 (million)
% 2.66/1.35 % (3773247)Refutation not found, incomplete strategy
% 2.66/1.35 % (3773247)------------------------------
% 2.66/1.35 % (3773247)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.35 % (3773247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.35 % (3773247)CaDiCaL version: 2.1.3
% 2.66/1.35 % (3773247)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.35 % (3773247)Time elapsed: 0.002 s
% 2.66/1.35 % (3773247)Peak memory usage: 88 MB
% 2.66/1.35 % (3773247)Instructions burned: 1 (million)
% 2.66/1.35 % (3773246)Also succeeded, but the first one will report.
% 2.66/1.35 % (3773245)Refutation found. Thanks to Tanya!
% 2.66/1.35 % SZS status Theorem for theBenchmark
% 2.66/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.66/1.35 % (3773245)------------------------------
% 2.66/1.35 % (3773245)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.35 % (3773245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.35 % (3773245)CaDiCaL version: 2.1.3
% 2.66/1.35 % (3773245)Termination reason: Refutation
% 2.66/1.35 % (3773245)Time elapsed: 0.004 s
% 2.66/1.35 % (3773245)Peak memory usage: 88 MB
% 2.66/1.35 % (3773245)Instructions burned: 10 (million)
% 2.66/1.35 % (3773245)------------------------------
% 2.66/1.35 % (3773245)------------------------------
% 2.66/1.35 % (3773236)Success in time 0.292 s
% 2.66/1.35 % Vampire exiting
%------------------------------------------------------------------------------