%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : TOP022+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Apr 9 10:52:24 PM UTC 2025
% Result : Theorem 2.51s 1.60s
% Output : CNFRefutation 2.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 33 ( 14 ~; 11 |; 3 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 31 ( 29 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ a_path_from_to_in > a_group_isomorphism_from_to > isomorphic_groups > a_member_of > path_connected > first_homotop_grp > #nlpp > alpha_hat > #skF_5 > #skF_3 > #skF_2 > #skF_4 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a_group_isomorphism_from_to,type,
a_group_isomorphism_from_to: ( $i * $i * $i ) > $o ).
tff(path_connected,type,
path_connected: $i > $o ).
tff(first_homotop_grp,type,
first_homotop_grp: ( $i * $i ) > $i ).
tff(a_member_of,type,
a_member_of: ( $i * $i ) > $o ).
tff(isomorphic_groups,type,
isomorphic_groups: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff(a_path_from_to_in,type,
a_path_from_to_in: ( $i * $i * $i * $i ) > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(alpha_hat,type,
alpha_hat: $i > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_55,negated_conjecture,
~ ! [X,X0,X1] :
( ( path_connected(X)
& a_member_of(X0,X)
& a_member_of(X1,X) )
=> isomorphic_groups(first_homotop_grp(X,X0),first_homotop_grp(X,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_8_2_2) ).
tff(f_41,axiom,
! [X,X0,X1] :
( path_connected(X)
<=> ( ( a_member_of(X0,X)
& a_member_of(X1,X) )
=> ? [P] : a_path_from_to_in(P,X0,X1,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_connected_defn) ).
tff(f_46,axiom,
! [A,X0,X1,X] :
( a_path_from_to_in(A,X0,X1,X)
=> a_group_isomorphism_from_to(alpha_hat(A),first_homotop_grp(X,X0),first_homotop_grp(X,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_8_2_1) ).
tff(f_31,axiom,
! [A,B] :
( isomorphic_groups(A,B)
<=> ? [F] : a_group_isomorphism_from_to(F,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isomorphic_groups_defn) ).
tff(c_22,plain,
path_connected('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_20,plain,
a_member_of('#skF_4','#skF_3'),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_18,plain,
a_member_of('#skF_5','#skF_3'),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_6,plain,
! [X_6,X0_7,X1_8] :
( a_path_from_to_in('#skF_2'(X_6,X0_7,X1_8),X0_7,X1_8,X_6)
| ~ a_member_of(X1_8,X_6)
| ~ a_member_of(X0_7,X_6)
| ~ path_connected(X_6) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_31,plain,
! [A_27,X_28,X0_29,X1_30] :
( a_group_isomorphism_from_to(alpha_hat(A_27),first_homotop_grp(X_28,X0_29),first_homotop_grp(X_28,X1_30))
| ~ a_path_from_to_in(A_27,X0_29,X1_30,X_28) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_4,plain,
! [A_1,B_2,F_5] :
( isomorphic_groups(A_1,B_2)
| ~ a_group_isomorphism_from_to(F_5,A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_41,plain,
! [X_34,X0_35,X1_36,A_37] :
( isomorphic_groups(first_homotop_grp(X_34,X0_35),first_homotop_grp(X_34,X1_36))
| ~ a_path_from_to_in(A_37,X0_35,X1_36,X_34) ),
inference(resolution,[status(thm)],[c_31,c_4]) ).
tff(c_45,plain,
! [X_38,X0_39,X1_40] :
( isomorphic_groups(first_homotop_grp(X_38,X0_39),first_homotop_grp(X_38,X1_40))
| ~ a_member_of(X1_40,X_38)
| ~ a_member_of(X0_39,X_38)
| ~ path_connected(X_38) ),
inference(resolution,[status(thm)],[c_6,c_41]) ).
tff(c_16,plain,
~ isomorphic_groups(first_homotop_grp('#skF_3','#skF_4'),first_homotop_grp('#skF_3','#skF_5')),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_48,plain,
( ~ a_member_of('#skF_5','#skF_3')
| ~ a_member_of('#skF_4','#skF_3')
| ~ path_connected('#skF_3') ),
inference(resolution,[status(thm)],[c_45,c_16]) ).
tff(c_52,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_22,c_20,c_18,c_48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : TOP022+1 : TPTP v9.0.0. Released v3.1.0.
% 0.12/0.12 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.32 % Computer : n022.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Apr 9 10:31:21 EDT 2025
% 0.12/0.32 % CPUTime :
% 2.51/1.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.51/1.60
% 2.51/1.60 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------