%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET677+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 : n002.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 5.88s 2.35s
% Output : CNFRefutation 6.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 77 ( 24 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 77 ( 31 ~; 26 |; 3 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 5 con; 0-3 aty)
% Number of variables : 41 ( 41 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > ilf_type > relation_like > empty > range > domain > relation_type > ordered_pair > cross_product > #nlpp > subset_type > range_of > power_set > member_type > identity_relation_of_type > identity_relation_of > domain_of > set_type > binary_relation_type > #skF_9 > #skF_11 > #skF_15 > #skF_1 > #skF_3 > #skF_14 > #skF_10 > #skF_8 > #skF_13 > #skF_4 > #skF_2 > #skF_12 > #skF_7 > #skF_5 > #skF_6
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(identity_relation_of_type,type,
identity_relation_of_type: $i > $i ).
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff(relation_type,type,
relation_type: ( $i * $i ) > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff(power_set,type,
power_set: $i > $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff(identity_relation_of,type,
identity_relation_of: $i > $i ).
tff(cross_product,type,
cross_product: ( $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(set_type,type,
set_type: $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(range,type,
range: ( $i * $i * $i ) > $i ).
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_13',type,
'#skF_13': $i > $i ).
tff(domain,type,
domain: ( $i * $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $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_12',type,
'#skF_12': $i > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff(f_378,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,identity_relation_of_type(B))
=> ( subset(identity_relation_of(B),C)
=> ( ( B = domain(B,B,C) )
& ( B = range(B,B,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_44) ).
tff(f_365,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p34) ).
tff(f_86,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/sandbox/benchmark/theBenchmark.p',p5) ).
tff(f_329,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( domain(B,C,D) = domain_of(D) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p30) ).
tff(f_41,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( subset(identity_relation_of(C),D)
=> ( ( C = domain(C,B,D) )
& subset(C,range(C,B,D)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
tff(f_56,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(identity_relation_of(C),D)
=> ( subset(C,domain(B,C,D))
& ( C = range(B,C,D) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
tff(c_134,plain,
ilf_type('#skF_15',identity_relation_of_type('#skF_14')),
inference(cnfTransformation,[status(thm)],[f_378]) ).
tff(c_128,plain,
! [B_181] : ilf_type(B_181,set_type),
inference(cnfTransformation,[status(thm)],[f_365]) ).
tff(c_20,plain,
! [C_25,B_23] :
( ilf_type(C_25,relation_type(B_23,B_23))
| ~ ilf_type(C_25,identity_relation_of_type(B_23))
| ~ ilf_type(C_25,set_type)
| ~ ilf_type(B_23,set_type) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_232,plain,
! [C_25,B_23] :
( ilf_type(C_25,relation_type(B_23,B_23))
| ~ ilf_type(C_25,identity_relation_of_type(B_23)) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_128,c_20]) ).
tff(c_120,plain,
! [B_153,C_157,D_159] :
( ( domain(B_153,C_157,D_159) = domain_of(D_159) )
| ~ ilf_type(D_159,relation_type(B_153,C_157))
| ~ ilf_type(C_157,set_type)
| ~ ilf_type(B_153,set_type) ),
inference(cnfTransformation,[status(thm)],[f_329]) ).
tff(c_709,plain,
! [B_292,C_293,D_294] :
( ( domain(B_292,C_293,D_294) = domain_of(D_294) )
| ~ ilf_type(D_294,relation_type(B_292,C_293)) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_128,c_120]) ).
tff(c_1048,plain,
! [B_361,C_362] :
( ( domain(B_361,B_361,C_362) = domain_of(C_362) )
| ~ ilf_type(C_362,identity_relation_of_type(B_361)) ),
inference(resolution,[status(thm)],[c_232,c_709]) ).
tff(c_1073,plain,
domain('#skF_14','#skF_14','#skF_15') = domain_of('#skF_15'),
inference(resolution,[status(thm)],[c_134,c_1048]) ).
tff(c_130,plain,
( ( range('#skF_14','#skF_14','#skF_15') != '#skF_14' )
| ( domain('#skF_14','#skF_14','#skF_15') != '#skF_14' ) ),
inference(cnfTransformation,[status(thm)],[f_378]) ).
tff(c_257,plain,
domain('#skF_14','#skF_14','#skF_15') != '#skF_14',
inference(splitLeft,[status(thm)],[c_130]) ).
tff(c_1074,plain,
domain_of('#skF_15') != '#skF_14',
inference(demodulation,[status(thm),theory(equality)],[c_1073,c_257]) ).
tff(c_132,plain,
subset(identity_relation_of('#skF_14'),'#skF_15'),
inference(cnfTransformation,[status(thm)],[f_378]) ).
tff(c_4,plain,
! [C_5,B_1,D_7] :
( ( domain(C_5,B_1,D_7) = C_5 )
| ~ subset(identity_relation_of(C_5),D_7)
| ~ ilf_type(D_7,relation_type(C_5,B_1))
| ~ ilf_type(C_5,set_type)
| ~ ilf_type(B_1,set_type) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_1157,plain,
! [C_369,B_370,D_371] :
( ( domain(C_369,B_370,D_371) = C_369 )
| ~ subset(identity_relation_of(C_369),D_371)
| ~ ilf_type(D_371,relation_type(C_369,B_370)) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_128,c_4]) ).
tff(c_1213,plain,
! [B_377] :
( ( domain('#skF_14',B_377,'#skF_15') = '#skF_14' )
| ~ ilf_type('#skF_15',relation_type('#skF_14',B_377)) ),
inference(resolution,[status(thm)],[c_132,c_1157]) ).
tff(c_1224,plain,
( ( domain('#skF_14','#skF_14','#skF_15') = '#skF_14' )
| ~ ilf_type('#skF_15',identity_relation_of_type('#skF_14')) ),
inference(resolution,[status(thm)],[c_232,c_1213]) ).
tff(c_1229,plain,
domain_of('#skF_15') = '#skF_14',
inference(demodulation,[status(thm),theory(equality)],[c_134,c_1073,c_1224]) ).
tff(c_1231,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1074,c_1229]) ).
tff(c_1232,plain,
range('#skF_14','#skF_14','#skF_15') != '#skF_14',
inference(splitRight,[status(thm)],[c_130]) ).
tff(c_6,plain,
! [B_8,C_12,D_14] :
( ( range(B_8,C_12,D_14) = C_12 )
| ~ subset(identity_relation_of(C_12),D_14)
| ~ 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_56]) ).
tff(c_2060,plain,
! [B_555,C_556,D_557] :
( ( range(B_555,C_556,D_557) = C_556 )
| ~ subset(identity_relation_of(C_556),D_557)
| ~ ilf_type(D_557,relation_type(B_555,C_556)) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_128,c_6]) ).
tff(c_2114,plain,
! [B_564] :
( ( range(B_564,'#skF_14','#skF_15') = '#skF_14' )
| ~ ilf_type('#skF_15',relation_type(B_564,'#skF_14')) ),
inference(resolution,[status(thm)],[c_132,c_2060]) ).
tff(c_2122,plain,
( ( range('#skF_14','#skF_14','#skF_15') = '#skF_14' )
| ~ ilf_type('#skF_15',identity_relation_of_type('#skF_14')) ),
inference(resolution,[status(thm)],[c_232,c_2114]) ).
tff(c_2126,plain,
range('#skF_14','#skF_14','#skF_15') = '#skF_14',
inference(demodulation,[status(thm),theory(equality)],[c_134,c_2122]) ).
tff(c_2128,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1232,c_2126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET677+3 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.13 % 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
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 8 21:24:32 EDT 2025
% 0.12/0.34 % CPUTime :
% 5.88/2.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.88/2.35
% 5.88/2.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------