%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO344+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 09:52:33 AM UTC 2026
% Result : Theorem 5.35s 11.76s
% Output : Refutation 5.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 18 unt; 0 def)
% Number of atoms : 213 ( 72 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 295 ( 124 ~; 117 |; 51 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 11 con; 0-0 aty)
% Number of variables : 71 ( 62 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ron(vd1409,X0)
& ron(vd1401,X0)
& rline(X0) )
=> X0 = vd1419 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(theu(the(409), 1), imp(the(409)))') ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ron(vd1409,X0)
& ron(vd1401,X0)
& rline(X0) )
=> X0 = vd1419 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
( ron(vd1409,vd1419)
& ron(vd1401,vd1419)
& rline(vd1419) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','and(pred(s2(plural(the(409))), 0), and(pred(s1(plural(the(409))), 0), pred(the(409), 0)))') ).
fof(f7,axiom,
vd1409 != vd1401,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(conjunct2(conjunct2(406))), 1413, 0)') ).
fof(f8,axiom,
rpoint(vd1409),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(406, 0)') ).
fof(f9,axiom,
( vd1406 = vd1407
& ron(vd1400,vd1406)
& ron(vd1399,vd1406)
& rline(vd1407)
& vd1400 != vd1401
& vd1399 != vd1401
& vd1399 != vd1400
& ? [X0] :
( vd1401 = X0
& rpoint(X0) )
& ? [X1] :
( vd1400 = X1
& rpoint(X1) )
& ? [X2] :
( vd1399 = X2
& rpoint(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','and(pred(conjunct2(405), 5), and(pred(s2(plural(conjunct2(405))), 0), and(pred(s1(plural(conjunct2(405))), 0), and(pred(conjunct2(405), 1), and(pred(conjunct1(405), 9), and(pred(conjunct1(405), 8), and(pred(conjunct1(405), 7), and(qe(s3(plural(405))), and(qe(s2(plural(405))), qe(s1(plural(405))))))))))))') ).
fof(f16,axiom,
! [X0,X1,X2,X3] :
( ( ron(X1,X3)
& ron(X1,X2)
& ron(X0,X3)
& ron(X0,X2)
& ? [X4] :
( X3 = X4
& rline(X4) )
& ? [X5] :
( X2 = X5
& rline(X5) )
& X0 != X1
& ? [X6] :
( X1 = X6
& rpoint(X6) )
& ? [X7] :
( X0 = X7
& rpoint(X7) ) )
=> X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(73), 0), imp(cond(axiom(73), 0)))') ).
fof(f131,plain,
? [X0] :
( vd1419 != X0
& ron(vd1409,X0)
& ron(vd1401,X0)
& rline(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f132,plain,
? [X0] :
( vd1419 != X0
& ron(vd1409,X0)
& ron(vd1401,X0)
& rline(X0) ),
inference(flattening,[],[f131]) ).
fof(f143,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ ron(X1,X3)
| ~ ron(X1,X2)
| ~ ron(X0,X3)
| ~ ron(X0,X2)
| ! [X4] :
( X3 != X4
| ~ rline(X4) )
| ! [X5] :
( X2 != X5
| ~ rline(X5) )
| X0 = X1
| ! [X6] :
( X1 != X6
| ~ rpoint(X6) )
| ! [X7] :
( X0 != X7
| ~ rpoint(X7) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f144,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ ron(X1,X3)
| ~ ron(X1,X2)
| ~ ron(X0,X3)
| ~ ron(X0,X2)
| ! [X4] :
( X3 != X4
| ~ rline(X4) )
| ! [X5] :
( X2 != X5
| ~ rline(X5) )
| X0 = X1
| ! [X6] :
( X1 != X6
| ~ rpoint(X6) )
| ! [X7] :
( X0 != X7
| ~ rpoint(X7) ) ),
inference(flattening,[],[f143]) ).
fof(f147,plain,
( vd1419 != sK0
& ron(vd1409,sK0)
& ron(vd1401,sK0)
& rline(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f132]) ).
fof(f148,plain,
( vd1406 = vd1407
& ron(vd1400,vd1406)
& ron(vd1399,vd1406)
& rline(vd1407)
& vd1400 != vd1401
& vd1399 != vd1401
& vd1399 != vd1400
& vd1401 = sK1
& rpoint(sK1)
& vd1400 = sK2
& rpoint(sK2)
& vd1399 = sK3
& rpoint(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f9]) ).
fof(f156,plain,
rline(sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f157,plain,
ron(vd1401,sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f158,plain,
ron(vd1409,sK0),
inference(cnf_transformation,[],[f147]) ).
fof(f159,plain,
vd1419 != sK0,
inference(cnf_transformation,[],[f147]) ).
fof(f163,plain,
rpoint(vd1409),
inference(cnf_transformation,[],[f8]) ).
fof(f164,plain,
vd1409 != vd1401,
inference(cnf_transformation,[],[f7]) ).
fof(f165,plain,
rline(vd1419),
inference(cnf_transformation,[],[f3]) ).
fof(f166,plain,
ron(vd1401,vd1419),
inference(cnf_transformation,[],[f3]) ).
fof(f167,plain,
ron(vd1409,vd1419),
inference(cnf_transformation,[],[f3]) ).
fof(f172,plain,
rpoint(sK1),
inference(cnf_transformation,[],[f148]) ).
fof(f173,plain,
vd1401 = sK1,
inference(cnf_transformation,[],[f148]) ).
fof(f198,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( X2 = X3
| ~ ron(X1,X3)
| ~ ron(X1,X2)
| ~ ron(X0,X3)
| ~ ron(X0,X2)
| X3 != X4
| ~ rline(X4)
| X2 != X5
| ~ rline(X5)
| X0 = X1
| X1 != X6
| ~ rpoint(X6)
| X0 != X7
| ~ rpoint(X7) ),
inference(cnf_transformation,[],[f144]) ).
fof(f202,plain,
ron(sK1,sK0),
inference(definition_unfolding,[],[f157,f173]) ).
fof(f206,plain,
vd1409 != sK1,
inference(definition_unfolding,[],[f164,f173]) ).
fof(f207,plain,
ron(sK1,vd1419),
inference(definition_unfolding,[],[f166,f173]) ).
fof(f252,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( X2 = X4
| ~ ron(X1,X4)
| ~ ron(X1,X2)
| ~ ron(X0,X4)
| ~ ron(X0,X2)
| ~ rline(X4)
| X2 != X5
| ~ rline(X5)
| X0 = X1
| X1 != X6
| ~ rpoint(X6)
| X0 != X7
| ~ rpoint(X7) ),
inference(equality_resolution,[],[f198]) ).
fof(f253,plain,
! [X0,X1,X6,X7,X4,X5] :
( X4 = X5
| ~ ron(X1,X4)
| ~ ron(X1,X5)
| ~ ron(X0,X4)
| ~ ron(X0,X5)
| ~ rline(X4)
| ~ rline(X5)
| X0 = X1
| X1 != X6
| ~ rpoint(X6)
| X0 != X7
| ~ rpoint(X7) ),
inference(equality_resolution,[],[f252]) ).
fof(f254,plain,
! [X0,X6,X7,X4,X5] :
( X4 = X5
| ~ ron(X6,X4)
| ~ ron(X6,X5)
| ~ ron(X0,X4)
| ~ ron(X0,X5)
| ~ rline(X4)
| ~ rline(X5)
| X0 = X6
| ~ rpoint(X6)
| X0 != X7
| ~ rpoint(X7) ),
inference(equality_resolution,[],[f253]) ).
fof(f255,plain,
! [X6,X7,X4,X5] :
( ~ rline(X4)
| ~ ron(X6,X4)
| ~ ron(X6,X5)
| ~ ron(X7,X4)
| ~ ron(X7,X5)
| X4 = X5
| ~ rline(X5)
| X6 = X7
| ~ rpoint(X6)
| ~ rpoint(X7) ),
inference(equality_resolution,[],[f254]) ).
fof(f300,plain,
! [X2,X0,X1] :
( ~ rline(X1)
| ~ ron(X0,X1)
| ~ ron(X2,sK0)
| ~ ron(X2,X1)
| sK0 = X1
| ~ ron(X0,sK0)
| X0 = X2
| ~ rpoint(X0)
| ~ rpoint(X2) ),
inference(resolution,[],[f255,f156]) ).
fof(f302,plain,
! [X0,X1] :
( ~ ron(X0,vd1419)
| ~ ron(X1,sK0)
| ~ ron(X1,vd1419)
| vd1419 = sK0
| ~ ron(X0,sK0)
| X0 = X1
| ~ rpoint(X0)
| ~ rpoint(X1) ),
inference(resolution,[],[f300,f165]) ).
fof(f324,plain,
! [X0,X1] :
( ~ ron(X0,vd1419)
| ~ ron(X1,sK0)
| ~ ron(X1,vd1419)
| ~ ron(X0,sK0)
| X0 = X1
| ~ rpoint(X0)
| ~ rpoint(X1) ),
inference(forward_subsumption_resolution,[],[f302,f159]) ).
fof(f386,plain,
! [X0] :
( ~ ron(X0,sK0)
| ~ ron(X0,vd1419)
| ~ ron(sK1,sK0)
| sK1 = X0
| ~ rpoint(sK1)
| ~ rpoint(X0) ),
inference(resolution,[],[f324,f207]) ).
fof(f395,plain,
! [X0] :
( ~ ron(X0,sK0)
| ~ ron(X0,vd1419)
| sK1 = X0
| ~ rpoint(sK1)
| ~ rpoint(X0) ),
inference(forward_subsumption_resolution,[],[f386,f202]) ).
fof(f401,plain,
! [X0] :
( ~ ron(X0,sK0)
| ~ ron(X0,vd1419)
| sK1 = X0
| ~ rpoint(X0) ),
inference(forward_subsumption_resolution,[],[f395,f172]) ).
fof(f615,plain,
( ~ ron(vd1409,vd1419)
| vd1409 = sK1
| ~ rpoint(vd1409) ),
inference(resolution,[],[f401,f158]) ).
fof(f625,plain,
( vd1409 = sK1
| ~ rpoint(vd1409) ),
inference(forward_subsumption_resolution,[],[f615,f167]) ).
fof(f631,plain,
~ rpoint(vd1409),
inference(forward_subsumption_resolution,[],[f625,f206]) ).
fof(f641,plain,
$false,
inference(forward_subsumption_resolution,[],[f631,f163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO344+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/10.41 % Computer : n002.cluster.edu
% 0.13/10.41 % Model : x86_64 x86_64
% 0.13/10.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.41 % Memory : 8046.5625MB
% 0.13/10.41 % OS : Linux 6.8.0-71-generic
% 0.13/10.41 % CPULimit : 300
% 0.13/10.41 % WCLimit : 300
% 0.13/10.41 % DateTime : Sun Sep 27 08:11:02 UTC 2026
% 0.13/10.42 % CPUTime :
% 0.13/10.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/10.45 Running first-order theorem proving
% 0.13/10.45 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.96/11.57 % (3223658)Detected formulas, will run a generic FOF schedule.
% 3.96/11.57 % (3223669)dis-21_1_sil=8000:lcm=predicate:random_seed=1552911096: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)
% 3.96/11.57 % (3223665)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=1120520624:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.96/11.57 % (3223666)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4253044991:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.96/11.57 % (3223667)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4045683193:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.96/11.57 % (3223664)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=2095553747:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.96/11.57 % (3223663)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=480080861:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.96/11.57 % (3223668)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4284600923:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.96/11.57 % (3223669)Instruction limit reached!
% 3.96/11.57 % (3223669)------------------------------
% 3.96/11.57 % (3223669)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/11.57 % (3223669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/11.57 % (3223669)CaDiCaL version: 2.1.3
% 3.96/11.57 % (3223669)Termination reason: Instruction limit
% 3.96/11.57 % (3223669)Termination phase: Saturation
% 3.96/11.57 % (3223669)Time elapsed: 0.037 s
% 3.96/11.57 % (3223669)Peak memory usage: 90 MB
% 3.96/11.57 % (3223669)Instructions burned: 133 (million)
% 3.96/11.57 % (3223666)Instruction limit reached!
% 3.96/11.57 % (3223666)------------------------------
% 3.96/11.57 % (3223666)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/11.57 % (3223666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/11.57 % (3223666)CaDiCaL version: 2.1.3
% 3.96/11.57 % (3223666)Termination reason: Instruction limit
% 3.96/11.57 % (3223666)Termination phase: Saturation
% 3.96/11.57 % (3223666)Time elapsed: 0.060 s
% 3.96/11.57 % (3223666)Peak memory usage: 89 MB
% 3.96/11.57 % (3223666)Instructions burned: 110 (million)
% 3.96/11.57 % (3223667)Instruction limit reached!
% 3.96/11.57 % (3223667)------------------------------
% 3.96/11.57 % (3223667)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/11.57 % (3223667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/11.57 % (3223667)CaDiCaL version: 2.1.3
% 3.96/11.57 % (3223667)Termination reason: Instruction limit
% 3.96/11.57 % (3223667)Termination phase: Saturation
% 3.96/11.57 % (3223667)Time elapsed: 0.065 s
% 3.96/11.57 % (3223667)Peak memory usage: 88 MB
% 3.96/11.57 % (3223667)Instructions burned: 119 (million)
% 3.96/11.57 % (3223668)Instruction limit reached!
% 3.96/11.57 % (3223668)------------------------------
% 3.96/11.57 % (3223668)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/11.57 % (3223668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/11.57 % (3223668)CaDiCaL version: 2.1.3
% 3.96/11.57 % (3223668)Termination reason: Instruction limit
% 3.96/11.57 % (3223668)Termination phase: Saturation
% 3.96/11.57 % (3223668)Time elapsed: 0.083 s
% 3.96/11.57 % (3223668)Peak memory usage: 90 MB
% 3.96/11.57 % (3223668)Instructions burned: 140 (million)
% 3.96/11.57 % (3223677)lrs+10_1_sil=8000:sp=occurrence:random_seed=1464242690:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.96/11.57 % (3223678)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3377655580:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.96/11.57 % (3223679)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2923903005:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.96/11.57 % (3223677)Instruction limit reached!
% 3.96/11.57 % (3223677)------------------------------
% 3.96/11.57 % (3223677)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/11.57 % (3223677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/11.76 % (3223677)CaDiCaL version: 2.1.3
% 5.35/11.76 % (3223677)Termination reason: Instruction limit
% 5.35/11.76 % (3223677)Termination phase: Saturation
% 5.35/11.76 % (3223677)Time elapsed: 0.081 s
% 5.35/11.76 % (3223677)Peak memory usage: 91 MB
% 5.35/11.76 % (3223677)Instructions burned: 288 (million)
% 5.35/11.76 % (3223679)First to succeed.
% 5.35/11.76 % (3223679)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3223658"
% 5.35/11.76 % (3223680)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1116402139:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.35/11.76 % (3223678)Instruction limit reached!
% 5.35/11.76 % (3223678)------------------------------
% 5.35/11.76 % (3223678)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.35/11.76 % (3223678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/11.76 % (3223678)CaDiCaL version: 2.1.3
% 5.35/11.76 % (3223678)Termination reason: Instruction limit
% 5.35/11.76 % (3223678)Termination phase: Saturation
% 5.35/11.76 % (3223678)Time elapsed: 0.073 s
% 5.35/11.76 % (3223678)Peak memory usage: 89 MB
% 5.35/11.76 % (3223678)Instructions burned: 159 (million)
% 5.35/11.76 % (3223684)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1241435743:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 5.35/11.76 % (3223684)Also succeeded, but the first one will report.
% 5.35/11.76 % (3223680)Instruction limit reached!
% 5.35/11.76 % (3223680)------------------------------
% 5.35/11.76 % (3223680)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.35/11.76 % (3223680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/11.76 % (3223680)CaDiCaL version: 2.1.3
% 5.35/11.76 % (3223680)Termination reason: Instruction limit
% 5.35/11.76 % (3223680)Termination phase: Saturation
% 5.35/11.76 % (3223680)Time elapsed: 0.114 s
% 5.35/11.76 % (3223680)Peak memory usage: 90 MB
% 5.35/11.76 % (3223680)Instructions burned: 249 (million)
% 5.35/11.76 % (3223686)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1191431451:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 5.35/11.76 % (3223679)Refutation found. Thanks to Tanya!
% 5.35/11.76 % SZS status Theorem for theBenchmark
% 5.35/11.76 % SZS output start Proof for theBenchmark
% See solution above
% 5.35/11.76 % (3223679)------------------------------
% 5.35/11.76 % (3223679)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.35/11.76 % (3223679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.35/11.76 % (3223679)CaDiCaL version: 2.1.3
% 5.35/11.76 % (3223679)Termination reason: Refutation
% 5.35/11.76 % (3223679)Time elapsed: 0.016 s
% 5.35/11.76 % (3223679)Peak memory usage: 89 MB
% 5.35/11.76 % (3223679)Instructions burned: 23 (million)
% 5.35/11.76 % (3223679)------------------------------
% 5.35/11.76 % (3223679)------------------------------
% 5.35/11.76 % (3223658)Success in time 0.673 s
% 5.35/11.76 % Vampire exiting
%------------------------------------------------------------------------------