%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET653+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/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 : n031.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 08:39:00 PM UTC 2025
% Result : Theorem 5.67s 2.37s
% Output : CNFRefutation 5.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 62 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 65 ( 24 ~; 22 |; 2 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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; 0-2 aty)
% Number of functors : 23 ( 23 usr; 6 con; 0-2 aty)
% Number of variables : 40 ( 40 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > ilf_type > relation_like > empty > relation_type > ordered_pair > cross_product > #nlpp > subset_type > range_of > power_set > member_type > domain_of > set_type > binary_relation_type > #skF_9 > #skF_5 > #skF_11 > #skF_10 > #skF_13 > #skF_8 > #skF_3 > #skF_2 > #skF_7 > #skF_1 > #skF_6 > #skF_12 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_9',type,
'#skF_9': $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_11',type,
'#skF_11': $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(cross_product,type,
cross_product: ( $i * $i ) > $i ).
tff(set_type,type,
set_type: $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_8',type,
'#skF_8': ( $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(range_of,type,
range_of: $i > $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff(domain_of,type,
domain_of: $i > $i ).
tff(subset_type,type,
subset_type: $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(binary_relation_type,type,
binary_relation_type: $i ).
tff(relation_like,type,
relation_like: $i > $o ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_269,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,D))
=> ( subset(B,C)
=> ilf_type(E,relation_type(C,D)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_15) ).
tff(f_252,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
tff(f_54,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(domain_of(D),B)
& subset(range_of(D),C) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
tff(f_41,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( ( subset(B,C)
& subset(C,D) )
=> subset(B,D) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
tff(f_70,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,D))
=> ( subset(domain_of(E),C)
=> ilf_type(E,relation_type(C,D)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
tff(c_82,plain,
~ ilf_type('#skF_13',relation_type('#skF_11','#skF_12')),
inference(cnfTransformation,[status(thm)],[f_269]) ).
tff(c_86,plain,
ilf_type('#skF_13',relation_type('#skF_10','#skF_12')),
inference(cnfTransformation,[status(thm)],[f_269]) ).
tff(c_80,plain,
! [B_125] : ilf_type(B_125,set_type),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_6,plain,
! [D_14,B_8,C_12] :
( subset(domain_of(D_14),B_8)
| ~ ilf_type(D_14,relation_type(B_8,C_12))
| ~ ilf_type(C_12,set_type)
| ~ ilf_type(B_8,set_type) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_389,plain,
! [D_198,B_199,C_200] :
( subset(domain_of(D_198),B_199)
| ~ ilf_type(D_198,relation_type(B_199,C_200)) ),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_80,c_6]) ).
tff(c_395,plain,
subset(domain_of('#skF_13'),'#skF_10'),
inference(resolution,[status(thm)],[c_86,c_389]) ).
tff(c_84,plain,
subset('#skF_10','#skF_11'),
inference(cnfTransformation,[status(thm)],[f_269]) ).
tff(c_2,plain,
! [B_1,D_7,C_5] :
( subset(B_1,D_7)
| ~ subset(C_5,D_7)
| ~ subset(B_1,C_5)
| ~ ilf_type(D_7,set_type)
| ~ ilf_type(C_5,set_type)
| ~ ilf_type(B_1,set_type) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_211,plain,
! [B_163,D_164,C_165] :
( subset(B_163,D_164)
| ~ subset(C_165,D_164)
| ~ subset(B_163,C_165) ),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_80,c_80,c_2]) ).
tff(c_220,plain,
! [B_163] :
( subset(B_163,'#skF_11')
| ~ subset(B_163,'#skF_10') ),
inference(resolution,[status(thm)],[c_84,c_211]) ).
tff(c_8,plain,
! [E_29,C_23,D_27,B_15] :
( ilf_type(E_29,relation_type(C_23,D_27))
| ~ subset(domain_of(E_29),C_23)
| ~ ilf_type(E_29,relation_type(B_15,D_27))
| ~ ilf_type(D_27,set_type)
| ~ ilf_type(C_23,set_type)
| ~ ilf_type(B_15,set_type) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_1191,plain,
! [E_292,C_293,D_294,B_295] :
( ilf_type(E_292,relation_type(C_293,D_294))
| ~ subset(domain_of(E_292),C_293)
| ~ ilf_type(E_292,relation_type(B_295,D_294)) ),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_80,c_80,c_8]) ).
tff(c_1646,plain,
! [E_319,D_320,B_321] :
( ilf_type(E_319,relation_type('#skF_11',D_320))
| ~ ilf_type(E_319,relation_type(B_321,D_320))
| ~ subset(domain_of(E_319),'#skF_10') ),
inference(resolution,[status(thm)],[c_220,c_1191]) ).
tff(c_1656,plain,
( ilf_type('#skF_13',relation_type('#skF_11','#skF_12'))
| ~ subset(domain_of('#skF_13'),'#skF_10') ),
inference(resolution,[status(thm)],[c_86,c_1646]) ).
tff(c_1663,plain,
ilf_type('#skF_13',relation_type('#skF_11','#skF_12')),
inference(demodulation,[status(thm),theory(equality)],[c_395,c_1656]) ).
tff(c_1665,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_82,c_1663]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : SET653+3 : TPTP v9.0.0. Released v2.2.0.
% 0.04/0.10 % 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
% 0.09/0.29 % Computer : n031.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Tue Apr 8 21:22:52 EDT 2025
% 0.09/0.29 % CPUTime :
% 5.67/2.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.95/2.38
% 5.95/2.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------