%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM852+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 : 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 12:17:16 PM UTC 2026
% Result : Theorem 4.13s 1.53s
% Output : Refutation 4.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 20 unt; 0 def)
% Number of atoms : 44 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 33 ( 18 ~; 10 |; 3 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 45 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
greater(vmul(vd481,vd469),vmul(vd480,vd469)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)') ).
fof(f2,negated_conjecture,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
greater(vd481,vd480),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq(304)), 483, 0)') ).
fof(f11,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(f12,axiom,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof(f24,axiom,
! [X0,X1,X2] :
( greater(vplus(X0,X2),vplus(X1,X2))
=> greater(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 2)') ).
fof(f28,axiom,
! [X0,X1] : greater(vplus(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
fof(f43,axiom,
! [X0,X1] :
( greater(X1,X0)
<=> ? [X2] : X1 = vplus(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof(f60,plain,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(flattening,[],[f2]) ).
fof(f75,plain,
! [X0,X1,X2] :
( greater(X0,X1)
| ~ greater(vplus(X0,X2),vplus(X1,X2)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f102,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X2] : X1 = vplus(X0,X2)
| ~ greater(X1,X0) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f103,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X3] : vplus(X0,X3) = X1
| ~ greater(X1,X0) ) ),
inference(rectify,[],[f102]) ).
fof(f104,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( vplus(X0,sK1(X0,X1)) = X1
| ~ greater(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f103]) ).
fof(f106,plain,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(cnf_transformation,[],[f60]) ).
fof(f107,plain,
greater(vd481,vd480),
inference(cnf_transformation,[],[f3]) ).
fof(f115,plain,
! [X2,X0,X1] : vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)),
inference(cnf_transformation,[],[f11]) ).
fof(f116,plain,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[],[f12]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ greater(vplus(X0,X2),vplus(X1,X2))
| greater(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f134,plain,
! [X0,X1] : greater(vplus(X0,X1),X0),
inference(cnf_transformation,[],[f28]) ).
fof(f155,plain,
! [X0,X1] :
( ~ greater(X1,X0)
| vplus(X0,sK1(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f104]) ).
fof(f202,plain,
~ greater(vmul(vd481,vd469),vmul(vd469,vd480)),
inference(superposition,[],[f106,f116]) ).
fof(f204,plain,
~ greater(vmul(vd469,vd481),vmul(vd469,vd480)),
inference(forward_demodulation,[],[f202,f116]) ).
fof(f256,plain,
vd481 = vplus(vd480,sK1(vd480,vd481)),
inference(resolution,[],[f155,f107]) ).
fof(f287,plain,
! [X2,X3,X0,X1] :
( greater(X3,vmul(X0,X1))
| ~ greater(vplus(X3,vmul(X0,X2)),vmul(X0,vplus(X1,X2))) ),
inference(superposition,[],[f130,f115]) ).
fof(f289,plain,
! [X2,X0,X1] : greater(vmul(X0,vplus(X1,X2)),vmul(X0,X1)),
inference(superposition,[],[f134,f115]) ).
fof(f3111,plain,
! [X0] : ~ greater(vplus(vmul(vd469,vd481),vmul(vd469,X0)),vmul(vd469,vplus(vd480,X0))),
inference(resolution,[],[f287,f204]) ).
fof(f3138,plain,
! [X0] : ~ greater(vmul(vd469,vplus(vd481,X0)),vmul(vd469,vplus(vd480,X0))),
inference(forward_demodulation,[],[f3111,f115]) ).
fof(f3158,plain,
~ greater(vmul(vd469,vplus(vd481,sK1(vd480,vd481))),vmul(vd469,vd481)),
inference(superposition,[],[f3138,f256]) ).
fof(f3170,plain,
$false,
inference(forward_subsumption_resolution,[],[f3158,f289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM852+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n020.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 21:31:34 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 4.13/1.53 % (3774066)Detected formulas, will run a generic FOF schedule.
% 4.13/1.53 % (3774071)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=747238887:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.13/1.53 % (3774074)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1524181234:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.13/1.53 % (3774073)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=1536094611:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.13/1.53 % (3774072)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=1078334420:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.13/1.53 % (3774076)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4218509241:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.13/1.53 % (3774075)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1876238703:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.13/1.53 % (3774074)Refutation not found, incomplete strategy
% 4.13/1.53 % (3774074)------------------------------
% 4.13/1.53 % (3774074)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.53 % (3774074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.53 % (3774074)CaDiCaL version: 2.1.3
% 4.13/1.53 % (3774074)Termination reason: Refutation not found, incomplete strategy
% 4.13/1.53 % (3774074)Time elapsed: 0.002 s
% 4.13/1.53 % (3774074)Peak memory usage: 88 MB
% 4.13/1.53 % (3774077)dis-21_1_sil=8000:lcm=predicate:random_seed=4051284565: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)
% 4.13/1.53 % (3774076)First to succeed.
% 4.13/1.53 % (3774076)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3774066"
% 4.13/1.53 % (3774075)Instruction limit reached!
% 4.13/1.53 % (3774075)------------------------------
% 4.13/1.53 % (3774075)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.53 % (3774075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.53 % (3774075)CaDiCaL version: 2.1.3
% 4.13/1.53 % (3774075)Termination reason: Instruction limit
% 4.13/1.53 % (3774075)Termination phase: Saturation
% 4.13/1.53 % (3774075)Time elapsed: 0.073 s
% 4.13/1.53 % (3774075)Peak memory usage: 89 MB
% 4.13/1.53 % (3774075)Instructions burned: 120 (million)
% 4.13/1.53 % (3774077)Instruction limit reached!
% 4.13/1.53 % (3774077)------------------------------
% 4.13/1.53 % (3774077)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.53 % (3774077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.53 % (3774077)CaDiCaL version: 2.1.3
% 4.13/1.53 % (3774077)Termination reason: Instruction limit
% 4.13/1.53 % (3774077)Termination phase: Saturation
% 4.13/1.53 % (3774077)Time elapsed: 0.081 s
% 4.13/1.53 % (3774077)Peak memory usage: 89 MB
% 4.13/1.53 % (3774077)Instructions burned: 129 (million)
% 4.13/1.53 % (3774085)lrs+10_1_sil=8000:sp=occurrence:random_seed=525157397:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.13/1.53 % (3774074)------------------------------
% 4.13/1.53 % (3774074)------------------------------
% 4.13/1.53 % (3774086)lrs+10_1_sil=32000:urr=on:br=off:random_seed=408624872:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.13/1.53 % (3774086)Also succeeded, but the first one will report.
% 4.13/1.53 % (3774085)Also succeeded, but the first one will report.
% 4.13/1.53 % (3774076)Refutation found. Thanks to Tanya!
% 4.13/1.53 % SZS status Theorem for theBenchmark
% 4.13/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 4.13/1.53 % (3774076)------------------------------
% 4.13/1.53 % (3774076)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.53 % (3774076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.53 % (3774076)CaDiCaL version: 2.1.3
% 4.13/1.53 % (3774076)Termination reason: Refutation
% 4.13/1.53 % (3774076)Time elapsed: 0.069 s
% 4.13/1.53 % (3774076)Peak memory usage: 90 MB
% 4.13/1.53 % (3774076)Instructions burned: 107 (million)
% 4.13/1.53 % (3774076)------------------------------
% 4.13/1.53 % (3774076)------------------------------
% 4.13/1.53 % (3774066)Success in time 0.5 s
% 4.13/1.53 % Vampire exiting
%------------------------------------------------------------------------------