%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : TOP022+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 02:33:52 PM UTC 2026
% Result : Theorem 3.46s 1.25s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 6 unt; 0 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 115 ( 44 ~; 36 |; 26 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 76 ( 62 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( isomorphic_groups(X0,X1)
<=> ? [X2] : a_group_isomorphism_from_to(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isomorphic_groups_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( path_connected(X0)
<=> ( ( a_member_of(X1,X0)
& a_member_of(X2,X0) )
=> ? [X3] : a_path_from_to_in(X3,X1,X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_connected_defn) ).
fof(f3,axiom,
! [X0,X1,X2,X3] :
( a_path_from_to_in(X0,X1,X2,X3)
=> a_group_isomorphism_from_to(alpha_hat(X0),first_homotop_grp(X3,X1),first_homotop_grp(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_8_2_1) ).
fof(f4,conjecture,
! [X0,X1,X2] :
( ( path_connected(X0)
& a_member_of(X1,X0)
& a_member_of(X2,X0) )
=> isomorphic_groups(first_homotop_grp(X0,X1),first_homotop_grp(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_8_2_2) ).
fof(f5,negated_conjecture,
~ ! [X0,X1,X2] :
( ( path_connected(X0)
& a_member_of(X1,X0)
& a_member_of(X2,X0) )
=> isomorphic_groups(first_homotop_grp(X0,X1),first_homotop_grp(X0,X2)) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X0,X1] :
( ? [X2] : a_group_isomorphism_from_to(X2,X0,X1)
=> isomorphic_groups(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f7,plain,
! [X0,X1] :
( isomorphic_groups(X0,X1)
| ! [X2] : ~ a_group_isomorphism_from_to(X2,X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f8,plain,
! [X0,X1,X2] :
( path_connected(X0)
<=> ( ? [X3] : a_path_from_to_in(X3,X1,X2,X0)
| ~ a_member_of(X1,X0)
| ~ a_member_of(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
! [X0,X1,X2] :
( path_connected(X0)
<=> ( ? [X3] : a_path_from_to_in(X3,X1,X2,X0)
| ~ a_member_of(X1,X0)
| ~ a_member_of(X2,X0) ) ),
inference(flattening,[],[f8]) ).
fof(f10,plain,
! [X0,X1,X2,X3] :
( a_group_isomorphism_from_to(alpha_hat(X0),first_homotop_grp(X3,X1),first_homotop_grp(X3,X2))
| ~ a_path_from_to_in(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f3]) ).
fof(f11,plain,
? [X0,X1,X2] :
( ~ isomorphic_groups(first_homotop_grp(X0,X1),first_homotop_grp(X0,X2))
& path_connected(X0)
& a_member_of(X1,X0)
& a_member_of(X2,X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f12,plain,
? [X0,X1,X2] :
( ~ isomorphic_groups(first_homotop_grp(X0,X1),first_homotop_grp(X0,X2))
& path_connected(X0)
& a_member_of(X1,X0)
& a_member_of(X2,X0) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( path_connected(X0)
| ( ! [X3] : ~ a_path_from_to_in(X3,X1,X2,X0)
& a_member_of(X1,X0)
& a_member_of(X2,X0) ) )
& ( ? [X3] : a_path_from_to_in(X3,X1,X2,X0)
| ~ a_member_of(X1,X0)
| ~ a_member_of(X2,X0)
| ~ path_connected(X0) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( path_connected(X0)
| ( ! [X3] : ~ a_path_from_to_in(X3,X1,X2,X0)
& a_member_of(X1,X0)
& a_member_of(X2,X0) ) )
& ( ? [X3] : a_path_from_to_in(X3,X1,X2,X0)
| ~ a_member_of(X1,X0)
| ~ a_member_of(X2,X0)
| ~ path_connected(X0) ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( path_connected(X0)
| ( ! [X3] : ~ a_path_from_to_in(X3,X1,X2,X0)
& a_member_of(X1,X0)
& a_member_of(X2,X0) ) )
& ( ? [X4] : a_path_from_to_in(X4,X1,X2,X0)
| ~ a_member_of(X1,X0)
| ~ a_member_of(X2,X0)
| ~ path_connected(X0) ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( path_connected(X0)
| ( ! [X3] : ~ a_path_from_to_in(X3,X1,X2,X0)
& a_member_of(X1,X0)
& a_member_of(X2,X0) ) )
& ( a_path_from_to_in(sK0(X0,X1,X2),X1,X2,X0)
| ~ a_member_of(X1,X0)
| ~ a_member_of(X2,X0)
| ~ path_connected(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X4,sK0(X0,X1,X2))],[f15]) ).
fof(f17,plain,
( ~ isomorphic_groups(first_homotop_grp(sK1,sK2),first_homotop_grp(sK1,sK3))
& path_connected(sK1)
& a_member_of(sK2,sK1)
& a_member_of(sK3,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f12]) ).
fof(f18,plain,
! [X2,X0,X1] :
( ~ a_group_isomorphism_from_to(X2,X0,X1)
| isomorphic_groups(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f19,plain,
! [X2,X0,X1] :
( a_path_from_to_in(sK0(X0,X1,X2),X1,X2,X0)
| ~ a_member_of(X1,X0)
| ~ a_member_of(X2,X0)
| ~ path_connected(X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f23,plain,
! [X2,X3,X0,X1] :
( ~ a_path_from_to_in(X0,X1,X2,X3)
| a_group_isomorphism_from_to(alpha_hat(X0),first_homotop_grp(X3,X1),first_homotop_grp(X3,X2)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f24,plain,
a_member_of(sK3,sK1),
inference(cnf_transformation,[],[f17]) ).
fof(f25,plain,
a_member_of(sK2,sK1),
inference(cnf_transformation,[],[f17]) ).
fof(f26,plain,
path_connected(sK1),
inference(cnf_transformation,[],[f17]) ).
fof(f27,plain,
~ isomorphic_groups(first_homotop_grp(sK1,sK2),first_homotop_grp(sK1,sK3)),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
! [X2,X0,X1] :
( a_group_isomorphism_from_to(alpha_hat(sK0(X1,X0,X2)),first_homotop_grp(X1,X0),first_homotop_grp(X1,X2))
| ~ a_member_of(X2,X1)
| ~ path_connected(X1)
| ~ a_member_of(X0,X1) ),
inference(resolution,[],[f19,f23]) ).
fof(f29,plain,
! [X2,X0,X1] :
( isomorphic_groups(first_homotop_grp(X1,X2),first_homotop_grp(X1,X0))
| ~ path_connected(X1)
| ~ a_member_of(X2,X1)
| ~ a_member_of(X0,X1) ),
inference(resolution,[],[f28,f18]) ).
fof(f30,plain,
( ~ path_connected(sK1)
| ~ a_member_of(sK2,sK1)
| ~ a_member_of(sK3,sK1) ),
inference(resolution,[],[f29,f27]) ).
fof(f31,plain,
( ~ a_member_of(sK2,sK1)
| ~ a_member_of(sK3,sK1) ),
inference(forward_subsumption_resolution,[],[f30,f26]) ).
fof(f32,plain,
~ a_member_of(sK3,sK1),
inference(forward_subsumption_resolution,[],[f31,f25]) ).
fof(f33,plain,
$false,
inference(forward_subsumption_resolution,[],[f32,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : TOP022+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n004.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 18:48:37 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 3.46/1.25 % (647913)Detected formulas, will run a generic FOF schedule.
% 3.46/1.25 % (647918)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=3486669282:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.46/1.25 % (647920)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=2924989052:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.46/1.25 % (647923)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3793689572:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.46/1.25 % (647923)First to succeed.
% 3.46/1.25 % (647923)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-647913"
% 3.46/1.25 % (647922)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=86814092:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.46/1.25 % (647921)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3643563860:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.46/1.25 % (647924)dis-21_1_sil=8000:lcm=predicate:random_seed=2213875564: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)
% 3.46/1.25 % (647919)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=2033709123:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.46/1.25 % (647921)Refutation not found, incomplete strategy
% 3.46/1.25 % (647921)------------------------------
% 3.46/1.25 % (647921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.25 % (647921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.25 % (647921)CaDiCaL version: 2.1.3
% 3.46/1.25 % (647921)Termination reason: Refutation not found, incomplete strategy
% 3.46/1.25 % (647921)Time elapsed: 0.001 s
% 3.46/1.25 % (647921)Peak memory usage: 87 MB
% 3.46/1.25 % (647922)Refutation not found, incomplete strategy
% 3.46/1.25 % (647922)------------------------------
% 3.46/1.25 % (647922)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.25 % (647922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.25 % (647922)CaDiCaL version: 2.1.3
% 3.46/1.25 % (647922)Termination reason: Refutation not found, incomplete strategy
% 3.46/1.25 % (647922)Time elapsed: 0.001 s
% 3.46/1.25 % (647922)Peak memory usage: 87 MB
% 3.46/1.25 % (647924)Also succeeded, but the first one will report.
% 3.46/1.25 % (647923)Refutation found. Thanks to Tanya!
% 3.46/1.25 % SZS status Theorem for theBenchmark
% 3.46/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.25 % (647923)------------------------------
% 3.46/1.25 % (647923)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.25 % (647923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.25 % (647923)CaDiCaL version: 2.1.3
% 3.46/1.25 % (647923)Termination reason: Refutation
% 3.46/1.25 % (647923)Time elapsed: 0.003 s
% 3.46/1.25 % (647923)Peak memory usage: 88 MB
% 3.46/1.25 % (647923)Instructions burned: 1 (million)
% 3.46/1.25 % (647923)------------------------------
% 3.46/1.25 % (647923)------------------------------
% 3.46/1.25 % (647913)Success in time 0.402 s
% 3.46/1.25 % Vampire exiting
%------------------------------------------------------------------------------