%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM847+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 : n002.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 2.68s 1.34s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 9 unt; 1 def)
% Number of atoms : 11 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 4 ~; 0 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 11 ( 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(286, 441, 3)') ).
fof(f2,negated_conjecture,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f51,axiom,
! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof(f58,plain,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(flattening,[],[f2]) ).
fof(f99,plain,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(cnf_transformation,[],[f58]) ).
fof(f157,plain,
! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f51]) ).
fof(f189,definition,
! [X0,X1] :
( sQ4_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ4_eqProxy])],[equality_proxy_definition]) ).
fof(f190,plain,
~ sQ4_eqProxy(vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))),
inference(equality_proxy_replacement,[],[f99,f189]) ).
fof(f218,plain,
! [X2,X0,X1] : sQ4_eqProxy(vplus(vplus(X0,X1),X2),vplus(X0,vplus(X1,X2))),
inference(equality_proxy_replacement,[],[f157,f189]) ).
fof(f2381,plain,
$false,
inference(resolution,[],[f218,f190]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM847+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 21:32:52 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.68/1.34 % (3907236)Detected formulas, will run a generic FOF schedule.
% 2.68/1.34 % (3907247)dis-21_1_sil=8000:lcm=predicate:random_seed=2772190658: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)
% 2.68/1.34 % (3907247)First to succeed.
% 2.68/1.34 % (3907247)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3907236"
% 2.68/1.34 % (3907245)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=179031723:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.34 % (3907245)Also succeeded, but the first one will report.
% 2.68/1.34 % (3907241)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=4181735334:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.34 % (3907242)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=715539283:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.34 % (3907244)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3166405384:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.34 % (3907243)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=2088289622:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.34 % (3907244)Also succeeded, but the first one will report.
% 2.68/1.34 % (3907246)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1440528298:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.34 % (3907246)Also succeeded, but the first one will report.
% 2.68/1.34 % (3907247)Refutation found. Thanks to Tanya!
% 2.68/1.34 % SZS status Theorem for theBenchmark
% 2.68/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.34 % (3907247)------------------------------
% 2.68/1.34 % (3907247)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.34 % (3907247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.34 % (3907247)CaDiCaL version: 2.1.3
% 2.68/1.34 % (3907247)Termination reason: Refutation
% 2.68/1.34 % (3907247)Time elapsed: 0.024 s
% 2.68/1.34 % (3907247)Peak memory usage: 89 MB
% 2.68/1.34 % (3907247)Instructions burned: 70 (million)
% 2.68/1.34 % (3907247)------------------------------
% 2.68/1.34 % (3907247)------------------------------
% 2.68/1.34 % (3907236)Success in time 0.297 s
% 2.68/1.34 % Vampire exiting
%------------------------------------------------------------------------------