%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET676+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n032.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 08:39:03 PM UTC 2025
% Result : Theorem 3.47s 1.63s
% Output : CNFRefutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 20 ( 8 ~; 6 |; 0 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 2 con; 0-3 aty)
% Number of variables : 16 ( 16 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ member > ilf_type > relation_like > empty > relation_type > ordered_pair > cross_product > #nlpp > subset_type > power_set > member_type > identity_relation_of_type > set_type > #skF_7 > #skF_5 > #skF_6 > #skF_1 > #skF_8 > #skF_10 > #skF_2 > #skF_3 > #skF_11 > #skF_9 > #skF_12 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(identity_relation_of_type,type,
identity_relation_of_type: $i > $i ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(relation_type,type,
relation_type: ( $i * $i ) > $i ).
tff(power_set,type,
power_set: $i > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff(cross_product,type,
cross_product: ( $i * $i ) > $i ).
tff(set_type,type,
set_type: $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(ilf_type,type,
ilf_type: ( $i * $i ) > $o ).
tff(member_type,type,
member_type: $i > $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff(subset_type,type,
subset_type: $i > $i ).
tff(relation_like,type,
relation_like: $i > $o ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_224,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).
tff(f_33,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(cross_product(B,C),relation_type(B,C)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
tff(f_74,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,identity_relation_of_type(B))
<=> ilf_type(C,relation_type(B,B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
tff(f_230,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ilf_type(cross_product(B,B),identity_relation_of_type(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_41) ).
tff(c_78,plain,
! [B_144] : ilf_type(B_144,set_type),
inference(cnfTransformation,[status(thm)],[f_224]) ).
tff(c_2,plain,
! [B_1,C_3] :
( ilf_type(cross_product(B_1,C_3),relation_type(B_1,C_3))
| ~ ilf_type(C_3,set_type)
| ~ ilf_type(B_1,set_type) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_159,plain,
! [B_1,C_3] : ilf_type(cross_product(B_1,C_3),relation_type(B_1,C_3)),
inference(demodulation,[status(thm),theory(equality)],[c_78,c_78,c_2]) ).
tff(c_18,plain,
! [C_62,B_60] :
( ilf_type(C_62,identity_relation_of_type(B_60))
| ~ ilf_type(C_62,relation_type(B_60,B_60))
| ~ ilf_type(C_62,set_type)
| ~ ilf_type(B_60,set_type) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_187,plain,
! [C_167,B_168] :
( ilf_type(C_167,identity_relation_of_type(B_168))
| ~ ilf_type(C_167,relation_type(B_168,B_168)) ),
inference(demodulation,[status(thm),theory(equality)],[c_78,c_78,c_18]) ).
tff(c_197,plain,
! [C_3] : ilf_type(cross_product(C_3,C_3),identity_relation_of_type(C_3)),
inference(resolution,[status(thm)],[c_159,c_187]) ).
tff(c_80,plain,
~ ilf_type(cross_product('#skF_12','#skF_12'),identity_relation_of_type('#skF_12')),
inference(cnfTransformation,[status(thm)],[f_230]) ).
tff(c_201,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_197,c_80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : SET676+3 : TPTP v9.0.0. Released v2.2.0.
% 0.04/0.08 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.08/0.27 % Computer : n032.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Tue Apr 8 21:24:16 EDT 2025
% 0.08/0.27 % CPUTime :
% 3.47/1.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.47/1.63
% 3.47/1.63 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------