%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET997+1 : TPTP v9.0.0. Released v3.2.0.
% 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 : n016.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 08:39:44 PM UTC 2025
% Result : Theorem 5.28s 2.33s
% Output : CNFRefutation 5.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 44 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 45 ( 18 ~; 15 |; 5 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-3 aty)
% Number of variables : 23 ( 22 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > relation_empty_yielding > relation > function > empty > apply > #nlpp > relation_rng > relation_dom > powerset > empty_set > #skF_9 > #skF_11 > #skF_15 > #skF_7 > #skF_3 > #skF_10 > #skF_16 > #skF_14 > #skF_13 > #skF_5 > #skF_8 > #skF_17 > #skF_2 > #skF_12 > #skF_1 > #skF_6 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(function,type,
function: $i > $o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff('#skF_16',type,
'#skF_16': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff(relation_dom,type,
relation_dom: $i > $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_17',type,
'#skF_17': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(relation_rng,type,
relation_rng: $i > $i ).
tff('#skF_12',type,
'#skF_12': $i > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_159,negated_conjecture,
~ ! [A,B] :
( ( relation(B)
& function(B) )
=> ( ! [C] :
~ ( in(C,A)
& ! [D] :
~ ( in(D,relation_dom(B))
& ( C = apply(B,D) ) ) )
=> subset(A,relation_rng(B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funct_1) ).
tff(f_46,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
tff(f_61,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ! [B] :
( ( B = relation_rng(A) )
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,relation_dom(A))
& ( C = apply(A,D) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
tff(c_90,plain,
~ subset('#skF_15',relation_rng('#skF_16')),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_12,plain,
! [A_5,B_6] :
( in('#skF_1'(A_5,B_6),A_5)
| subset(A_5,B_6) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_98,plain,
! [C_66] :
( in('#skF_17'(C_66),relation_dom('#skF_16'))
| ~ in(C_66,'#skF_15') ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_94,plain,
relation('#skF_16'),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_92,plain,
function('#skF_16'),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_96,plain,
! [C_66] :
( ( apply('#skF_16','#skF_17'(C_66)) = C_66 )
| ~ in(C_66,'#skF_15') ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_796,plain,
! [A_188,D_189] :
( in(apply(A_188,D_189),relation_rng(A_188))
| ~ in(D_189,relation_dom(A_188))
| ~ function(A_188)
| ~ relation(A_188) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_825,plain,
! [C_66] :
( in(C_66,relation_rng('#skF_16'))
| ~ in('#skF_17'(C_66),relation_dom('#skF_16'))
| ~ function('#skF_16')
| ~ relation('#skF_16')
| ~ in(C_66,'#skF_15') ),
inference(superposition,[status(thm),theory(equality)],[c_96,c_796]) ).
tff(c_1000,plain,
! [C_215] :
( in(C_215,relation_rng('#skF_16'))
| ~ in('#skF_17'(C_215),relation_dom('#skF_16'))
| ~ in(C_215,'#skF_15') ),
inference(demodulation,[status(thm),theory(equality)],[c_94,c_92,c_825]) ).
tff(c_1011,plain,
! [C_216] :
( in(C_216,relation_rng('#skF_16'))
| ~ in(C_216,'#skF_15') ),
inference(resolution,[status(thm)],[c_98,c_1000]) ).
tff(c_10,plain,
! [A_5,B_6] :
( ~ in('#skF_1'(A_5,B_6),B_6)
| subset(A_5,B_6) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_1233,plain,
! [A_235] :
( subset(A_235,relation_rng('#skF_16'))
| ~ in('#skF_1'(A_235,relation_rng('#skF_16')),'#skF_15') ),
inference(resolution,[status(thm)],[c_1011,c_10]) ).
tff(c_1237,plain,
subset('#skF_15',relation_rng('#skF_16')),
inference(resolution,[status(thm)],[c_12,c_1233]) ).
tff(c_1244,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_90,c_90,c_1237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET997+1 : TPTP v9.0.0. Released v3.2.0.
% 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
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Apr 8 21:54:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 5.28/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.28/2.33
% 5.28/2.33 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------