%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU307+1 : TPTP v9.0.0. Released v3.3.0.
% 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 : n020.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 08:53:35 PM UTC 2025
% Result : Theorem 7.66s 2.72s
% Output : CNFRefutation 7.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 14 ~; 11 |; 2 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 17 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 32 ( 32 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > element > v5_membered > v4_membered > v3_membered > v2_membered > v1_xreal_0 > v1_xcmplx_0 > v1_rat_1 > v1_membered > v1_int_1 > one_sorted_str > natural > empty > subset_intersection2 > set_intersection2 > #nlpp > the_carrier > powerset > cast_as_carrier_subset > empty_set > #skF_5 > #skF_2 > #skF_7 > #skF_6 > #skF_1 > #skF_4 > #skF_3
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(subset_intersection2,type,
subset_intersection2: ( $i * $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(the_carrier,type,
the_carrier: $i > $i ).
tff(v1_int_1,type,
v1_int_1: $i > $o ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff(one_sorted_str,type,
one_sorted_str: $i > $o ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff(v3_membered,type,
v3_membered: $i > $o ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(cast_as_carrier_subset,type,
cast_as_carrier_subset: $i > $i ).
tff(empty,type,
empty: $i > $o ).
tff(v1_xreal_0,type,
v1_xreal_0: $i > $o ).
tff(v5_membered,type,
v5_membered: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff(v2_membered,type,
v2_membered: $i > $o ).
tff(v1_membered,type,
v1_membered: $i > $o ).
tff(v1_xcmplx_0,type,
v1_xcmplx_0: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff(v1_rat_1,type,
v1_rat_1: $i > $o ).
tff(powerset,type,
powerset: $i > $i ).
tff(natural,type,
natural: $i > $o ).
tff(v4_membered,type,
v4_membered: $i > $o ).
tff(f_388,negated_conjecture,
~ ! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A)) = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_pre_topc) ).
tff(f_380,axiom,
! [A] :
( one_sorted_str(A)
=> ( cast_as_carrier_subset(A) = the_carrier(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pre_topc) ).
tff(f_376,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
tff(f_392,axiom,
! [A,B] :
( subset(A,B)
=> ( set_intersection2(A,B) = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
tff(f_332,axiom,
! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
tff(f_363,axiom,
! [A] :
( one_sorted_str(A)
=> element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
tff(f_359,axiom,
! [A,B,C] :
( ( element(B,powerset(A))
& element(C,powerset(A)) )
=> ( subset_intersection2(A,B,C) = set_intersection2(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
tff(f_340,axiom,
! [A,B,C] :
( ( element(B,powerset(A))
& element(C,powerset(A)) )
=> ( subset_intersection2(A,B,C) = subset_intersection2(A,C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
tff(c_234,plain,
one_sorted_str('#skF_6'),
inference(cnfTransformation,[status(thm)],[f_388]) ).
tff(c_429,plain,
! [A_141] :
( ( the_carrier(A_141) = cast_as_carrier_subset(A_141) )
| ~ one_sorted_str(A_141) ),
inference(cnfTransformation,[status(thm)],[f_380]) ).
tff(c_437,plain,
the_carrier('#skF_6') = cast_as_carrier_subset('#skF_6'),
inference(resolution,[status(thm)],[c_234,c_429]) ).
tff(c_230,plain,
subset_intersection2(the_carrier('#skF_6'),'#skF_7',cast_as_carrier_subset('#skF_6')) != '#skF_7',
inference(cnfTransformation,[status(thm)],[f_388]) ).
tff(c_442,plain,
subset_intersection2(cast_as_carrier_subset('#skF_6'),'#skF_7',cast_as_carrier_subset('#skF_6')) != '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_437,c_230]) ).
tff(c_232,plain,
element('#skF_7',powerset(the_carrier('#skF_6'))),
inference(cnfTransformation,[status(thm)],[f_388]) ).
tff(c_443,plain,
element('#skF_7',powerset(cast_as_carrier_subset('#skF_6'))),
inference(demodulation,[status(thm),theory(equality)],[c_437,c_232]) ).
tff(c_1639,plain,
! [A_255,B_256] :
( subset(A_255,B_256)
| ~ element(A_255,powerset(B_256)) ),
inference(cnfTransformation,[status(thm)],[f_376]) ).
tff(c_1658,plain,
subset('#skF_7',cast_as_carrier_subset('#skF_6')),
inference(resolution,[status(thm)],[c_443,c_1639]) ).
tff(c_236,plain,
! [A_104,B_105] :
( ( set_intersection2(A_104,B_105) = A_104 )
| ~ subset(A_104,B_105) ),
inference(cnfTransformation,[status(thm)],[f_392]) ).
tff(c_1670,plain,
set_intersection2('#skF_7',cast_as_carrier_subset('#skF_6')) = '#skF_7',
inference(resolution,[status(thm)],[c_1658,c_236]) ).
tff(c_192,plain,
! [B_79,A_78] : ( set_intersection2(B_79,A_78) = set_intersection2(A_78,B_79) ),
inference(cnfTransformation,[status(thm)],[f_332]) ).
tff(c_2125,plain,
! [A_297] :
( element(cast_as_carrier_subset(A_297),powerset(the_carrier(A_297)))
| ~ one_sorted_str(A_297) ),
inference(cnfTransformation,[status(thm)],[f_363]) ).
tff(c_2197,plain,
( element(cast_as_carrier_subset('#skF_6'),powerset(cast_as_carrier_subset('#skF_6')))
| ~ one_sorted_str('#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_437,c_2125]) ).
tff(c_2225,plain,
element(cast_as_carrier_subset('#skF_6'),powerset(cast_as_carrier_subset('#skF_6'))),
inference(demodulation,[status(thm),theory(equality)],[c_234,c_2197]) ).
tff(c_3725,plain,
! [A_393,B_394,C_395] :
( ( subset_intersection2(A_393,B_394,C_395) = set_intersection2(B_394,C_395) )
| ~ element(C_395,powerset(A_393))
| ~ element(B_394,powerset(A_393)) ),
inference(cnfTransformation,[status(thm)],[f_359]) ).
tff(c_3803,plain,
! [B_399] :
( ( subset_intersection2(cast_as_carrier_subset('#skF_6'),B_399,'#skF_7') = set_intersection2(B_399,'#skF_7') )
| ~ element(B_399,powerset(cast_as_carrier_subset('#skF_6'))) ),
inference(resolution,[status(thm)],[c_443,c_3725]) ).
tff(c_3810,plain,
subset_intersection2(cast_as_carrier_subset('#skF_6'),cast_as_carrier_subset('#skF_6'),'#skF_7') = set_intersection2(cast_as_carrier_subset('#skF_6'),'#skF_7'),
inference(resolution,[status(thm)],[c_2225,c_3803]) ).
tff(c_3833,plain,
subset_intersection2(cast_as_carrier_subset('#skF_6'),cast_as_carrier_subset('#skF_6'),'#skF_7') = '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_1670,c_192,c_3810]) ).
tff(c_3862,plain,
! [A_400,C_401,B_402] :
( ( subset_intersection2(A_400,C_401,B_402) = subset_intersection2(A_400,B_402,C_401) )
| ~ element(C_401,powerset(A_400))
| ~ element(B_402,powerset(A_400)) ),
inference(cnfTransformation,[status(thm)],[f_340]) ).
tff(c_3902,plain,
! [B_404] :
( ( subset_intersection2(cast_as_carrier_subset('#skF_6'),B_404,'#skF_7') = subset_intersection2(cast_as_carrier_subset('#skF_6'),'#skF_7',B_404) )
| ~ element(B_404,powerset(cast_as_carrier_subset('#skF_6'))) ),
inference(resolution,[status(thm)],[c_443,c_3862]) ).
tff(c_3909,plain,
subset_intersection2(cast_as_carrier_subset('#skF_6'),cast_as_carrier_subset('#skF_6'),'#skF_7') = subset_intersection2(cast_as_carrier_subset('#skF_6'),'#skF_7',cast_as_carrier_subset('#skF_6')),
inference(resolution,[status(thm)],[c_2225,c_3902]) ).
tff(c_3931,plain,
subset_intersection2(cast_as_carrier_subset('#skF_6'),'#skF_7',cast_as_carrier_subset('#skF_6')) = '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_3833,c_3909]) ).
tff(c_3933,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_442,c_3931]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU307+1 : TPTP v9.0.0. Released v3.3.0.
% 0.12/0.13 % 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
% 0.12/0.34 % Computer : n020.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 22:44:19 EDT 2025
% 0.12/0.34 % CPUTime :
% 7.66/2.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.66/2.73
% 7.66/2.73 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------