%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU309+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 : n012.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 08:53:36 PM UTC 2025
% Result : Theorem 33.39s 17.72s
% Output : CNFRefutation 33.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 52 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 95 ( 34 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 76 ( 33 ~; 28 |; 4 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 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 : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 61 ( 61 !; 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 > subset_difference > set_intersection2 > set_difference > #nlpp > the_carrier > powerset > cast_as_carrier_subset > empty_set > #skF_5 > #skF_2 > #skF_4 > #skF_7 > #skF_6 > #skF_3 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(subset_intersection2,type,
subset_intersection2: ( $i * $i * $i ) > $i ).
tff(subset_difference,type,
subset_difference: ( $i * $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff('#skF_4',type,
'#skF_4': $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_3',type,
'#skF_3': $i ).
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(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_405,negated_conjecture,
~ ! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( subset_difference(the_carrier(A),cast_as_carrier_subset(A),subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)) = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_pre_topc) ).
tff(f_181,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_186,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_384,axiom,
! [A,B,C] :
( ( element(B,powerset(A))
& element(C,powerset(A)) )
=> ( subset_difference(A,B,C) = set_difference(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
tff(f_198,axiom,
! [A,B,C] :
( ( element(B,powerset(A))
& element(C,powerset(A)) )
=> element(subset_difference(A,B,C),powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
tff(f_419,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
tff(f_393,axiom,
! [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_177,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(f_171,axiom,
! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
tff(f_386,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
tff(f_378,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_421,axiom,
! [A,B] : ( set_difference(A,set_difference(A,B)) = set_intersection2(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
tff(c_254,plain,
one_sorted_str('#skF_6'),
inference(cnfTransformation,[status(thm)],[f_405]) ).
tff(c_435,plain,
! [A_152] :
( ( the_carrier(A_152) = cast_as_carrier_subset(A_152) )
| ~ one_sorted_str(A_152) ),
inference(cnfTransformation,[status(thm)],[f_181]) ).
tff(c_443,plain,
the_carrier('#skF_6') = cast_as_carrier_subset('#skF_6'),
inference(resolution,[status(thm)],[c_254,c_435]) ).
tff(c_2142,plain,
! [A_333] :
( element(cast_as_carrier_subset(A_333),powerset(the_carrier(A_333)))
| ~ one_sorted_str(A_333) ),
inference(cnfTransformation,[status(thm)],[f_186]) ).
tff(c_2208,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_443,c_2142]) ).
tff(c_2234,plain,
element(cast_as_carrier_subset('#skF_6'),powerset(cast_as_carrier_subset('#skF_6'))),
inference(demodulation,[status(thm),theory(equality)],[c_254,c_2208]) ).
tff(c_252,plain,
element('#skF_7',powerset(the_carrier('#skF_6'))),
inference(cnfTransformation,[status(thm)],[f_405]) ).
tff(c_449,plain,
element('#skF_7',powerset(cast_as_carrier_subset('#skF_6'))),
inference(demodulation,[status(thm),theory(equality)],[c_443,c_252]) ).
tff(c_4220,plain,
! [A_458,B_459,C_460] :
( ( subset_difference(A_458,B_459,C_460) = set_difference(B_459,C_460) )
| ~ element(C_460,powerset(A_458))
| ~ element(B_459,powerset(A_458)) ),
inference(cnfTransformation,[status(thm)],[f_384]) ).
tff(c_4284,plain,
! [B_463] :
( ( subset_difference(cast_as_carrier_subset('#skF_6'),B_463,'#skF_7') = set_difference(B_463,'#skF_7') )
| ~ element(B_463,powerset(cast_as_carrier_subset('#skF_6'))) ),
inference(resolution,[status(thm)],[c_449,c_4220]) ).
tff(c_4312,plain,
subset_difference(cast_as_carrier_subset('#skF_6'),cast_as_carrier_subset('#skF_6'),'#skF_7') = set_difference(cast_as_carrier_subset('#skF_6'),'#skF_7'),
inference(resolution,[status(thm)],[c_2234,c_4284]) ).
tff(c_100,plain,
! [A_48,B_49,C_50] :
( element(subset_difference(A_48,B_49,C_50),powerset(A_48))
| ~ element(C_50,powerset(A_48))
| ~ element(B_49,powerset(A_48)) ),
inference(cnfTransformation,[status(thm)],[f_198]) ).
tff(c_4534,plain,
( element(set_difference(cast_as_carrier_subset('#skF_6'),'#skF_7'),powerset(cast_as_carrier_subset('#skF_6')))
| ~ element('#skF_7',powerset(cast_as_carrier_subset('#skF_6')))
| ~ element(cast_as_carrier_subset('#skF_6'),powerset(cast_as_carrier_subset('#skF_6'))) ),
inference(superposition,[status(thm),theory(equality)],[c_4312,c_100]) ).
tff(c_4538,plain,
element(set_difference(cast_as_carrier_subset('#skF_6'),'#skF_7'),powerset(cast_as_carrier_subset('#skF_6'))),
inference(demodulation,[status(thm),theory(equality)],[c_2234,c_449,c_4534]) ).
tff(c_262,plain,
! [A_111,B_112] :
( subset(A_111,B_112)
| ~ element(A_111,powerset(B_112)) ),
inference(cnfTransformation,[status(thm)],[f_419]) ).
tff(c_4810,plain,
subset(set_difference(cast_as_carrier_subset('#skF_6'),'#skF_7'),cast_as_carrier_subset('#skF_6')),
inference(resolution,[status(thm)],[c_4538,c_262]) ).
tff(c_3789,plain,
! [A_436,B_437] :
( ( subset_intersection2(the_carrier(A_436),B_437,cast_as_carrier_subset(A_436)) = B_437 )
| ~ element(B_437,powerset(the_carrier(A_436)))
| ~ one_sorted_str(A_436) ),
inference(cnfTransformation,[status(thm)],[f_393]) ).
tff(c_3799,plain,
! [B_437] :
( ( subset_intersection2(the_carrier('#skF_6'),B_437,cast_as_carrier_subset('#skF_6')) = B_437 )
| ~ element(B_437,powerset(cast_as_carrier_subset('#skF_6')))
| ~ one_sorted_str('#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_443,c_3789]) ).
tff(c_4954,plain,
! [B_482] :
( ( subset_intersection2(cast_as_carrier_subset('#skF_6'),B_482,cast_as_carrier_subset('#skF_6')) = B_482 )
| ~ element(B_482,powerset(cast_as_carrier_subset('#skF_6'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_254,c_443,c_3799]) ).
tff(c_4997,plain,
subset_intersection2(cast_as_carrier_subset('#skF_6'),'#skF_7',cast_as_carrier_subset('#skF_6')) = '#skF_7',
inference(resolution,[status(thm)],[c_449,c_4954]) ).
tff(c_4540,plain,
! [A_468,C_469,B_470] :
( ( subset_intersection2(A_468,C_469,B_470) = subset_intersection2(A_468,B_470,C_469) )
| ~ element(C_469,powerset(A_468))
| ~ element(B_470,powerset(A_468)) ),
inference(cnfTransformation,[status(thm)],[f_177]) ).
tff(c_4601,plain,
! [B_474] :
( ( subset_intersection2(cast_as_carrier_subset('#skF_6'),B_474,'#skF_7') = subset_intersection2(cast_as_carrier_subset('#skF_6'),'#skF_7',B_474) )
| ~ element(B_474,powerset(cast_as_carrier_subset('#skF_6'))) ),
inference(resolution,[status(thm)],[c_449,c_4540]) ).
tff(c_4634,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_2234,c_4601]) ).
tff(c_5129,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_4997,c_4634]) ).
tff(c_82,plain,
! [B_39,A_38] : ( set_intersection2(B_39,A_38) = set_intersection2(A_38,B_39) ),
inference(cnfTransformation,[status(thm)],[f_171]) ).
tff(c_244,plain,
! [A_99] : subset(A_99,A_99),
inference(cnfTransformation,[status(thm)],[f_386]) ).
tff(c_264,plain,
! [A_111,B_112] :
( element(A_111,powerset(B_112))
| ~ subset(A_111,B_112) ),
inference(cnfTransformation,[status(thm)],[f_419]) ).
tff(c_3891,plain,
! [A_444,B_445,C_446] :
( ( subset_intersection2(A_444,B_445,C_446) = set_intersection2(B_445,C_446) )
| ~ element(C_446,powerset(A_444))
| ~ element(B_445,powerset(A_444)) ),
inference(cnfTransformation,[status(thm)],[f_378]) ).
tff(c_3934,plain,
! [B_448] :
( ( subset_intersection2(cast_as_carrier_subset('#skF_6'),B_448,'#skF_7') = set_intersection2(B_448,'#skF_7') )
| ~ element(B_448,powerset(cast_as_carrier_subset('#skF_6'))) ),
inference(resolution,[status(thm)],[c_449,c_3891]) ).
tff(c_5440,plain,
! [A_503] :
( ( subset_intersection2(cast_as_carrier_subset('#skF_6'),A_503,'#skF_7') = set_intersection2(A_503,'#skF_7') )
| ~ subset(A_503,cast_as_carrier_subset('#skF_6')) ),
inference(resolution,[status(thm)],[c_264,c_3934]) ).
tff(c_5462,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_244,c_5440]) ).
tff(c_5475,plain,
set_intersection2('#skF_7',cast_as_carrier_subset('#skF_6')) = '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_5129,c_82,c_5462]) ).
tff(c_266,plain,
! [A_113,B_114] : ( set_difference(A_113,set_difference(A_113,B_114)) = set_intersection2(A_113,B_114) ),
inference(cnfTransformation,[status(thm)],[f_421]) ).
tff(c_7841,plain,
! [B_594,B_595,A_596] :
( ( subset_difference(B_594,B_595,A_596) = set_difference(B_595,A_596) )
| ~ element(B_595,powerset(B_594))
| ~ subset(A_596,B_594) ),
inference(resolution,[status(thm)],[c_264,c_4220]) ).
tff(c_79362,plain,
! [A_1754] :
( ( subset_difference(cast_as_carrier_subset('#skF_6'),cast_as_carrier_subset('#skF_6'),A_1754) = set_difference(cast_as_carrier_subset('#skF_6'),A_1754) )
| ~ subset(A_1754,cast_as_carrier_subset('#skF_6')) ),
inference(resolution,[status(thm)],[c_2234,c_7841]) ).
tff(c_250,plain,
subset_difference(the_carrier('#skF_6'),cast_as_carrier_subset('#skF_6'),subset_difference(the_carrier('#skF_6'),cast_as_carrier_subset('#skF_6'),'#skF_7')) != '#skF_7',
inference(cnfTransformation,[status(thm)],[f_405]) ).
tff(c_448,plain,
subset_difference(cast_as_carrier_subset('#skF_6'),cast_as_carrier_subset('#skF_6'),subset_difference(cast_as_carrier_subset('#skF_6'),cast_as_carrier_subset('#skF_6'),'#skF_7')) != '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_443,c_443,c_250]) ).
tff(c_4530,plain,
subset_difference(cast_as_carrier_subset('#skF_6'),cast_as_carrier_subset('#skF_6'),set_difference(cast_as_carrier_subset('#skF_6'),'#skF_7')) != '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_4312,c_448]) ).
tff(c_79574,plain,
( ( set_difference(cast_as_carrier_subset('#skF_6'),set_difference(cast_as_carrier_subset('#skF_6'),'#skF_7')) != '#skF_7' )
| ~ subset(set_difference(cast_as_carrier_subset('#skF_6'),'#skF_7'),cast_as_carrier_subset('#skF_6')) ),
inference(superposition,[status(thm),theory(equality)],[c_79362,c_4530]) ).
tff(c_79735,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4810,c_5475,c_82,c_266,c_79574]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU309+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.13 % 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
% 0.13/0.34 % Computer : n012.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 22:44:29 EDT 2025
% 0.13/0.34 % CPUTime :
% 33.39/17.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.39/17.73
% 33.39/17.73 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------