%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : TOP022+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Sun Sep 27 09:52:38 AM UTC 2026
% Result : Theorem 12.97s 2.34s
% Output : CNFRefutation 12.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 6 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 40 ( 17 ~; 12 |; 5 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 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 : 34 ( 2 sgn 15 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(isomorphic_groups_defn,axiom,
! [X0,X1] :
( 'isomorphic$ugroups'(X0,X1)
<=> ? [X2] : 'a$ugroup$uisomorphism$ufrom$uto'(X2,X0,X1) ) ).
fof(path_connected_defn,axiom,
! [X0,X1,X2] :
( 'path$uconnected'(X0)
<=> ( ( 'a$umember$uof'(X2,X0)
& 'a$umember$uof'(X1,X0) )
=> ? [X3] : 'a$upath$ufrom$uto$uin'(X3,X1,X2,X0) ) ) ).
fof(m_8_2_1,axiom,
! [X0,X1,X2,X3] :
( 'a$upath$ufrom$uto$uin'(X0,X1,X2,X3)
=> 'a$ugroup$uisomorphism$ufrom$uto'('alpha$uhat'(X0),'first$uhomotop$ugrp'(X3,X1),'first$uhomotop$ugrp'(X3,X2)) ) ).
fof(m_8_2_2,conjecture,
! [X0,X1,X2] :
( ( 'a$umember$uof'(X2,X0)
& 'a$umember$uof'(X1,X0)
& 'path$uconnected'(X0) )
=> 'isomorphic$ugroups'('first$uhomotop$ugrp'(X0,X1),'first$uhomotop$ugrp'(X0,X2)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( 'a$umember$uof'(X2,X0)
& 'a$umember$uof'(X1,X0)
& 'path$uconnected'(X0) )
=> 'isomorphic$ugroups'('first$uhomotop$ugrp'(X0,X1),'first$uhomotop$ugrp'(X0,X2)) ),
inference(negate_conjecture,[status(cth)],[m_8_2_2]) ).
cnf(c1,plain,
( ~ 'a$ugroup$uisomorphism$ufrom$uto'(X2,X0,X1)
| 'isomorphic$ugroups'(X0,X1) ),
inference(clausification,[status(esa)],[isomorphic_groups_defn]) ).
cnf(c2,plain,
( 'a$upath$ufrom$uto$uin'(sK7(X0,X1,X2),X1,X2,X0)
| ~ 'a$umember$uof'(X2,X0)
| ~ 'a$umember$uof'(X1,X0)
| ~ 'path$uconnected'(X0) ),
inference(clausification,[status(esa)],[path_connected_defn]) ).
cnf(c6,plain,
( 'a$ugroup$uisomorphism$ufrom$uto'('alpha$uhat'(X0),'first$uhomotop$ugrp'(X3,X1),'first$uhomotop$ugrp'(X3,X2))
| ~ 'a$upath$ufrom$uto$uin'(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[m_8_2_1]) ).
cnf(c7,plain,
'path$uconnected'(sK13),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c8,plain,
'a$umember$uof'(sK14,sK13),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c9,plain,
'a$umember$uof'(sK15,sK13),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c10,plain,
~ 'isomorphic$ugroups'('first$uhomotop$ugrp'(sK13,sK14),'first$uhomotop$ugrp'(sK13,sK15)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'isomorphic$ugroups'('first$uhomotop$ugrp'(X3,X1),'first$uhomotop$ugrp'(X3,X2))
| ~ 'a$upath$ufrom$uto$uin'(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c6,c1]) ).
cnf(d1,plain,
( ~ 'path$uconnected'(X0)
| ~ 'a$umember$uof'(X2,X0)
| ~ 'a$umember$uof'(X1,X0)
| 'isomorphic$ugroups'('first$uhomotop$ugrp'(X0,X1),'first$uhomotop$ugrp'(X0,X2)) ),
inference(resolution,[status(thm)],[d0,c2]) ).
cnf(d2,plain,
( ~ 'path$uconnected'(sK13)
| ~ 'a$umember$uof'(sK14,sK13)
| ~ 'a$umember$uof'(sK15,sK13) ),
inference(resolution,[status(thm)],[d1,c10]) ).
cnf(d3,plain,
( ~ 'a$umember$uof'(sK15,sK13)
| ~ 'a$umember$uof'(sK14,sK13) ),
inference(resolution,[status(thm)],[c7,d2]) ).
cnf(d4,plain,
~ 'a$umember$uof'(sK15,sK13),
inference(resolution,[status(thm)],[c8,d3]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c9,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : TOP022+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n020.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 20:33:19 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.97/2.34 % SZS status Theorem for theBenchmark.p
% 12.97/2.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------