%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV608+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:58:25 PM UTC 2026
% Result : Theorem 3.72s 1.43s
% Output : Refutation 4.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 7 unt; 0 def)
% Number of atoms : 66 ( 13 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 74 ( 28 ~; 22 |; 12 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 27 ( 21 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1538,axiom,
! [X0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X0)
=> ! [X1] :
( cColor_2egraph___24t(X1)
=> ! [X2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X2)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(X0),X1)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X2)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X2,X1)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Color.select_terminates') ).
fof(f2868,conjecture,
! [X0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X0)
=> ! [X1] :
( cColor_2egraph___24t(X1)
=> ! [X2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X2)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(X0),X1)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X2)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X2,X1)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
fof(f2869,negated_conjecture,
~ ! [X0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X0)
=> ! [X1] :
( cColor_2egraph___24t(X1)
=> ! [X2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X2)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(X0),X1)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X2)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X2,X1)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,X1)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2868]) ).
fof(f2872,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X2,X1)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,X1))
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(X0),X1)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X2)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X2) )
& cColor_2egraph___24t(X1) )
& cCoq_2eInit_2eDatatypes_2enat___24t(X0) ),
inference(ennf_transformation,[],[f2869]) ).
fof(f2873,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X2,X1)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,X1))
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(X0),X1)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X2)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X2) )
& cColor_2egraph___24t(X1) )
& cCoq_2eInit_2eDatatypes_2enat___24t(X0) ),
inference(flattening,[],[f2872]) ).
fof(f2920,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X2,X1)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,X1))
| cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X2) != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(X0),X1))
| ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X2) )
| ~ cColor_2egraph___24t(X1) )
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X0) ),
inference(ennf_transformation,[],[f1538]) ).
fof(f2921,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X2,X1)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,X1))
| cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X2) != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(X0),X1))
| ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X2) )
| ~ cColor_2egraph___24t(X1) )
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X0) ),
inference(flattening,[],[f2920]) ).
fof(f2922,plain,
( ~ cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(sK2,sK1)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,sK1))
& cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,sK2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(sK0),sK1))
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(sK2)
& cColor_2egraph___24t(sK1)
& cCoq_2eInit_2eDatatypes_2enat___24t(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f2873]) ).
fof(f2927,plain,
cCoq_2eInit_2eDatatypes_2enat___24t(sK0),
inference(cnf_transformation,[],[f2922]) ).
fof(f2928,plain,
cColor_2egraph___24t(sK1),
inference(cnf_transformation,[],[f2922]) ).
fof(f2929,plain,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(sK2),
inference(cnf_transformation,[],[f2922]) ).
fof(f2930,plain,
cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,sK2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(sK0),sK1)),
inference(cnf_transformation,[],[f2922]) ).
fof(f2931,plain,
~ cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(sK2,sK1)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,sK1)),
inference(cnf_transformation,[],[f2922]) ).
fof(f2963,plain,
! [X2,X0,X1] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X2) != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(X0),X1))
| cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X2,X1)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,X1))
| ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X2)
| ~ cColor_2egraph___24t(X1)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X0) ),
inference(cnf_transformation,[],[f2921]) ).
fof(f2984,plain,
! [X0] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,sK2) != cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X0)
| cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X0,sK1)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,sK1))
| ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X0)
| ~ cColor_2egraph___24t(sK1)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(sK0) ),
inference(superposition,[],[f2963,f2930]) ).
fof(f2985,plain,
! [X0] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,sK2) != cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X0)
| cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X0,sK1)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,sK1))
| ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X0)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(sK0) ),
inference(forward_subsumption_resolution,[],[f2984,f2928]) ).
fof(f2986,plain,
! [X0] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,sK2) != cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X0)
| cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X0,sK1)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,sK1))
| ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X0) ),
inference(forward_subsumption_resolution,[],[f2985,f2927]) ).
fof(f3015,plain,
( cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(sK2,sK1)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,sK1))
| ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(sK2) ),
inference(equality_resolution,[],[f2986]) ).
fof(f3016,plain,
~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(sK2),
inference(forward_subsumption_resolution,[],[f3015,f2931]) ).
fof(f3017,plain,
$false,
inference(forward_subsumption_resolution,[],[f3016,f2929]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV608+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n007.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 06:39:25 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 3.72/1.43 % (2192439)Detected formulas, will run a generic FOF schedule.
% 3.72/1.43 % (2192463)dis-21_1_sil=8000:lcm=predicate:random_seed=758810017:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2998 on theBenchmark for (2998ds/129Mi)
% 3.72/1.43 % (2192463)Instruction limit reached!
% 3.72/1.43 % (2192463)------------------------------
% 3.72/1.43 % (2192463)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.43 % (2192463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.43 % (2192463)CaDiCaL version: 2.1.3
% 3.72/1.43 % (2192463)Termination reason: Instruction limit
% 3.72/1.43 % (2192463)Termination phase: Preprocessing 3
% 3.72/1.43 % (2192463)Time elapsed: 0.051 s
% 3.72/1.43 % (2192463)Peak memory usage: 93 MB
% 3.72/1.43 % (2192463)Instructions burned: 130 (million)
% 3.72/1.43 % (2192457)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=4146008023:i=141193_2998 on theBenchmark for (2998ds/141193Mi)
% 3.72/1.43 % (2192462)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2293214555:s2a=on:i=139:gtg=position_2998 on theBenchmark for (2998ds/139Mi)
% 3.72/1.43 % (2192459)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=2818601416:i=141695:sd=1:nm=32:gsp=on:ss=included_2998 on theBenchmark for (2998ds/141695Mi)
% 3.72/1.43 % (2192460)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4010125187:i=109:sd=1:ins=1:gsp=on:ss=axioms_2998 on theBenchmark for (2998ds/109Mi)
% 3.72/1.43 % (2192461)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3848906052:i=119:av=off:ss=axioms_2998 on theBenchmark for (2998ds/119Mi)
% 3.72/1.43 % (2192458)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=2694412047:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2998 on theBenchmark for (2998ds/134677Mi)
% 3.72/1.43 % (2192460)First to succeed.
% 3.72/1.43 % (2192461)Also succeeded, but the first one will report.
% 3.72/1.43 % (2192460)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2192439"
% 3.72/1.43 % (2192462)Instruction limit reached!
% 3.72/1.43 % (2192462)------------------------------
% 3.72/1.43 % (2192462)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.43 % (2192462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.43 % (2192462)CaDiCaL version: 2.1.3
% 3.72/1.43 % (2192462)Termination reason: Instruction limit
% 3.72/1.43 % (2192462)Termination phase: Preprocessing 1
% 3.72/1.43 % (2192462)Time elapsed: 0.099 s
% 3.72/1.43 % (2192462)Peak memory usage: 90 MB
% 3.72/1.43 % (2192462)Instructions burned: 140 (million)
% 3.72/1.43 % (2192483)lrs+10_1_sil=8000:sp=occurrence:random_seed=3154384508:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 3.72/1.43 % (2192483)Also succeeded, but the first one will report.
% 3.72/1.43 % (2192493)lrs+10_1_sil=32000:urr=on:br=off:random_seed=233431311:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 3.72/1.43 % (2192460)Refutation found. Thanks to Tanya!
% 3.72/1.43 % SZS status Theorem for theBenchmark
% 3.72/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 4.99/1.65 % (2192460)------------------------------
% 4.99/1.65 % (2192460)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.99/1.65 % (2192460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.99/1.65 % (2192460)CaDiCaL version: 2.1.3
% 4.99/1.65 % (2192460)Termination reason: Refutation
% 4.99/1.65 % (2192460)Time elapsed: 0.033 s
% 4.99/1.65 % (2192460)Peak memory usage: 94 MB
% 4.99/1.65 % (2192460)Instructions burned: 42 (million)
% 4.99/1.65 % (2192460)------------------------------
% 4.99/1.65 % (2192460)------------------------------
% 4.99/1.65 % (2192439)Success in time 0.779 s
% 4.99/1.65 % Vampire exiting
%------------------------------------------------------------------------------