%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV629+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 : n005.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 12:58:27 PM UTC 2026
% Result : Theorem 5.76s 2.28s
% Output : Refutation 5.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 10 unt; 0 def)
% Number of atoms : 76 ( 2 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 76 ( 28 ~; 26 |; 12 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 64 ( 61 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f181,axiom,
! [X0,X1] :
( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(X0,X1)
<=> ! [X2] :
( t(X2,X0)
=> p(happ(happ(X1,X2),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_def_Coq.Relations.Relation_Definitions.reflexive') ).
fof(f290,axiom,
! [X0,X1,X2] :
( cHahnSets_2eset__subset___24a3(X0,X1,X2)
<=> ! [X3] :
( t(X3,X0)
=> ( p(happ(X1,X3))
=> p(happ(X2,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_def_HahnSets.set_subset') ).
fof(f2077,axiom,
! [X0] : happ(cHahnSets_2eset__subset,X0) = cHahnSets_2eset__subset___24a1(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$adef_HahnSets.set_subset_$a1') ).
fof(f2469,axiom,
! [X0,X1,X2] :
( p(happ(happ(happ(cHahnSets_2eset__subset,X0),X1),X2))
<=> cHahnSets_2eset__subset___24a3(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$adef_HahnSets.set_subset_$a3') ).
fof(f2963,conjecture,
cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(c_24__type__35378,cHahnSets_2eset__subset___24a1(cA)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
fof(f2964,negated_conjecture,
~ cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(c_24__type__35378,cHahnSets_2eset__subset___24a1(cA)),
inference(negated_conjecture,[status(cth)],[f2963]) ).
fof(f2965,plain,
~ cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(c_24__type__35378,cHahnSets_2eset__subset___24a1(cA)),
inference(flattening,[],[f2964]) ).
fof(f2968,plain,
! [X0,X1] :
( ! [X2] :
( t(X2,X0)
=> p(happ(happ(X1,X2),X2)) )
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f181]) ).
fof(f2969,plain,
! [X0,X1] :
( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(X0,X1)
| ? [X2] :
( ~ p(happ(happ(X1,X2),X2))
& t(X2,X0) ) ),
inference(ennf_transformation,[],[f2968]) ).
fof(f2970,plain,
! [X0,X1,X2] :
( cHahnSets_2eset__subset___24a3(X0,X1,X2)
<=> ! [X3] :
( p(happ(X2,X3))
| ~ p(happ(X1,X3))
| ~ t(X3,X0) ) ),
inference(ennf_transformation,[],[f290]) ).
fof(f2971,plain,
! [X0,X1,X2] :
( cHahnSets_2eset__subset___24a3(X0,X1,X2)
<=> ! [X3] :
( p(happ(X2,X3))
| ~ p(happ(X1,X3))
| ~ t(X3,X0) ) ),
inference(flattening,[],[f2970]) ).
fof(f3000,plain,
! [X0,X1] :
( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(X0,X1)
| ( ~ p(happ(happ(X1,sK0(X0,X1)),sK0(X0,X1)))
& t(sK0(X0,X1),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f2969]) ).
fof(f3001,plain,
! [X0,X1,X2] :
( ( p(happ(happ(happ(cHahnSets_2eset__subset,X0),X1),X2))
| ~ cHahnSets_2eset__subset___24a3(X0,X1,X2) )
& ( cHahnSets_2eset__subset___24a3(X0,X1,X2)
| ~ p(happ(happ(happ(cHahnSets_2eset__subset,X0),X1),X2)) ) ),
inference(nnf_transformation,[],[f2469]) ).
fof(f3002,plain,
! [X0,X1,X2] :
( ( cHahnSets_2eset__subset___24a3(X0,X1,X2)
| ? [X3] :
( ~ p(happ(X2,X3))
& p(happ(X1,X3))
& t(X3,X0) ) )
& ( ! [X3] :
( p(happ(X2,X3))
| ~ p(happ(X1,X3))
| ~ t(X3,X0) )
| ~ cHahnSets_2eset__subset___24a3(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f2971]) ).
fof(f3003,plain,
! [X0,X1,X2] :
( ( cHahnSets_2eset__subset___24a3(X0,X1,X2)
| ? [X3] :
( ~ p(happ(X2,X3))
& p(happ(X1,X3))
& t(X3,X0) ) )
& ( ! [X4] :
( p(happ(X2,X4))
| ~ p(happ(X1,X4))
| ~ t(X4,X0) )
| ~ cHahnSets_2eset__subset___24a3(X0,X1,X2) ) ),
inference(rectify,[],[f3002]) ).
fof(f3004,plain,
! [X0,X1,X2] :
( ( cHahnSets_2eset__subset___24a3(X0,X1,X2)
| ( ~ p(happ(X2,sK1(X0,X1,X2)))
& p(happ(X1,sK1(X0,X1,X2)))
& t(sK1(X0,X1,X2),X0) ) )
& ( ! [X4] :
( p(happ(X2,X4))
| ~ p(happ(X1,X4))
| ~ t(X4,X0) )
| ~ cHahnSets_2eset__subset___24a3(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f3003]) ).
fof(f3012,plain,
~ cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(c_24__type__35378,cHahnSets_2eset__subset___24a1(cA)),
inference(cnf_transformation,[],[f2965]) ).
fof(f3014,plain,
! [X0,X1] :
( ~ p(happ(happ(X1,sK0(X0,X1)),sK0(X0,X1)))
| cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(X0,X1) ),
inference(cnf_transformation,[],[f3000]) ).
fof(f3016,plain,
! [X0] : happ(cHahnSets_2eset__subset,X0) = cHahnSets_2eset__subset___24a1(X0),
inference(cnf_transformation,[],[f2077]) ).
fof(f3018,plain,
! [X2,X0,X1] :
( p(happ(happ(happ(cHahnSets_2eset__subset,X0),X1),X2))
| ~ cHahnSets_2eset__subset___24a3(X0,X1,X2) ),
inference(cnf_transformation,[],[f3001]) ).
fof(f3022,plain,
! [X2,X0,X1] :
( p(happ(X1,sK1(X0,X1,X2)))
| cHahnSets_2eset__subset___24a3(X0,X1,X2) ),
inference(cnf_transformation,[],[f3004]) ).
fof(f3023,plain,
! [X2,X0,X1] :
( ~ p(happ(X2,sK1(X0,X1,X2)))
| cHahnSets_2eset__subset___24a3(X0,X1,X2) ),
inference(cnf_transformation,[],[f3004]) ).
fof(f3052,plain,
~ cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(c_24__type__35378,happ(cHahnSets_2eset__subset,cA)),
inference(definition_unfolding,[],[f3012,f3016]) ).
fof(f3054,plain,
! [X0,X1] :
( cHahnSets_2eset__subset___24a3(X0,X1,X1)
| cHahnSets_2eset__subset___24a3(X0,X1,X1) ),
inference(resolution,[],[f3023,f3022]) ).
fof(f3055,plain,
! [X0,X1] : cHahnSets_2eset__subset___24a3(X0,X1,X1),
inference(duplicate_literal_removal,[],[f3054]) ).
fof(f3059,plain,
! [X0,X1] :
( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(X0,happ(cHahnSets_2eset__subset,X1))
| ~ cHahnSets_2eset__subset___24a3(X1,sK0(X0,happ(cHahnSets_2eset__subset,X1)),sK0(X0,happ(cHahnSets_2eset__subset,X1))) ),
inference(resolution,[],[f3014,f3018]) ).
fof(f3060,plain,
! [X0,X1] : cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(X0,happ(cHahnSets_2eset__subset,X1)),
inference(forward_subsumption_resolution,[],[f3059,f3055]) ).
fof(f3064,plain,
$false,
inference(resolution,[],[f3060,f3052]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV629+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.43 % Computer : n005.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 28 06:44:32 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.49 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
% 5.76/2.28 % (600790)Detected formulas, will run a generic FOF schedule.
% 5.76/2.28 % (600795)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=597845912:i=141193_2998 on theBenchmark for (2998ds/141193Mi)
% 5.76/2.28 % (600801)dis-21_1_sil=8000:lcm=predicate:random_seed=2567033836: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)
% 5.76/2.28 % (600796)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=585344543:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2998 on theBenchmark for (2998ds/134677Mi)
% 5.76/2.28 % (600800)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=408641440:s2a=on:i=139:gtg=position_2998 on theBenchmark for (2998ds/139Mi)
% 5.76/2.28 % (600799)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2940897585:i=119:av=off:ss=axioms_2998 on theBenchmark for (2998ds/119Mi)
% 5.76/2.28 % (600798)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2267953809:i=109:sd=1:ins=1:gsp=on:ss=axioms_2998 on theBenchmark for (2998ds/109Mi)
% 5.76/2.28 % (600797)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=1627574888:i=141695:sd=1:nm=32:gsp=on:ss=included_2998 on theBenchmark for (2998ds/141695Mi)
% 5.76/2.28 % (600798)Refutation not found, incomplete strategy
% 5.76/2.28 % (600798)------------------------------
% 5.76/2.28 % (600798)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.76/2.28 % (600798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.76/2.28 % (600798)CaDiCaL version: 2.1.3
% 5.76/2.28 % (600798)Termination reason: Refutation not found, incomplete strategy
% 5.76/2.28 % (600798)Time elapsed: 0.021 s
% 5.76/2.28 % (600798)Peak memory usage: 91 MB
% 5.76/2.28 % (600798)Instructions burned: 29 (million)
% 5.76/2.28 % (600799)First to succeed.
% 5.76/2.28 % (600799)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-600790"
% 5.76/2.28 % (600801)Instruction limit reached!
% 5.76/2.28 % (600801)------------------------------
% 5.76/2.28 % (600801)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.76/2.28 % (600801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.76/2.28 % (600801)CaDiCaL version: 2.1.3
% 5.76/2.28 % (600801)Termination reason: Instruction limit
% 5.76/2.28 % (600801)Termination phase: Preprocessing 3
% 5.76/2.28 % (600801)Time elapsed: 0.085 s
% 5.76/2.28 % (600801)Peak memory usage: 94 MB
% 5.76/2.28 % (600801)Instructions burned: 131 (million)
% 5.76/2.28 % (600800)Instruction limit reached!
% 5.76/2.28 % (600800)------------------------------
% 5.76/2.28 % (600800)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.76/2.28 % (600800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.76/2.28 % (600800)CaDiCaL version: 2.1.3
% 5.76/2.28 % (600800)Termination reason: Instruction limit
% 5.76/2.28 % (600800)Termination phase: Preprocessing 3
% 5.76/2.28 % (600800)Time elapsed: 0.122 s
% 5.76/2.28 % (600800)Peak memory usage: 93 MB
% 5.76/2.28 % (600800)Instructions burned: 139 (million)
% 5.76/2.28 % (600809)lrs+10_1_sil=8000:sp=occurrence:random_seed=2850370770:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 5.76/2.28 % (600810)lrs+10_1_sil=32000:urr=on:br=off:random_seed=727040807:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2994 on theBenchmark for (2994ds/157Mi)
% 5.76/2.28 % (600809)Also succeeded, but the first one will report.
% 5.76/2.28 % (600810)Refutation not found, incomplete strategy
% 5.76/2.28 % (600810)------------------------------
% 5.76/2.28 % (600810)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.76/2.28 % (600810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.76/2.28 % (600810)CaDiCaL version: 2.1.3
% 5.76/2.28 % (600810)Termination reason: Refutation not found, incomplete strategy
% 5.76/2.28 % (600810)Time elapsed: 0.048 s
% 5.76/2.28 % (600810)Peak memory usage: 92 MB
% 5.76/2.28 % (600810)Instructions burned: 64 (million)
% 5.76/2.28 % (600798)------------------------------
% 5.76/2.28 % (600798)------------------------------
% 5.76/2.28 % (600799)Refutation found. Thanks to Tanya!
% 5.76/2.28 % SZS status Theorem for theBenchmark
% 5.76/2.28 % SZS output start Proof for theBenchmark
% See solution above
% 5.76/2.28 % (600799)------------------------------
% 5.76/2.28 % (600799)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.76/2.28 % (600799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.76/2.28 % (600799)CaDiCaL version: 2.1.3
% 5.76/2.28 % (600799)Termination reason: Refutation
% 5.76/2.28 % (600799)Time elapsed: 0.025 s
% 5.76/2.28 % (600799)Peak memory usage: 92 MB
% 5.76/2.28 % (600799)Instructions burned: 33 (million)
% 5.76/2.28 % (600799)------------------------------
% 5.76/2.28 % (600799)------------------------------
% 5.76/2.28 % (600790)Success in time 0.839 s
% 5.76/2.28 % Vampire exiting
%------------------------------------------------------------------------------