TSTP Solution File: SET984+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET984+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n029.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 : Tue Aug 22 10:57:27 EDT 2023
% Result : Theorem 24.84s 11.55s
% Output : CNFRefutation 25.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 19
% Syntax : Number of formulae : 156 ( 122 unt; 11 typ; 0 def)
% Number of atoms : 187 ( 151 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 63 ( 21 ~; 36 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 195 (; 195 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > empty > set_intersection2 > cartesian_product2 > #nlpp > empty_set > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(f_65,negated_conjecture,
~ ! [A,B,C,D] :
( subset(cartesian_product2(A,B),cartesian_product2(C,D))
=> ( ( cartesian_product2(A,B) = empty_set )
| ( subset(A,C)
& subset(B,D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
tff(f_46,axiom,
! [A,B,C,D] : ( cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).
tff(f_71,axiom,
! [A,B] :
( subset(A,B)
=> ( set_intersection2(A,B) = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
tff(f_56,axiom,
! [A,B,C,D] :
( ( cartesian_product2(A,B) = cartesian_product2(C,D) )
=> ( ( A = empty_set )
| ( B = empty_set )
| ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).
tff(f_28,axiom,
! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
tff(f_67,axiom,
! [A,B] : subset(set_intersection2(A,B),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
tff(f_44,axiom,
! [A,B] :
( ( cartesian_product2(A,B) = empty_set )
<=> ( ( A = empty_set )
| ( B = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
tff(f_31,axiom,
! [A,B] : ( set_intersection2(A,A) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
tff(c_28,plain,
cartesian_product2('#skF_3','#skF_4') != empty_set,
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_26,plain,
( ~ subset('#skF_4','#skF_6')
| ~ subset('#skF_3','#skF_5') ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_72,plain,
~ subset('#skF_3','#skF_5'),
inference(splitLeft,[status(thm)],[c_26]) ).
tff(c_746,plain,
! [A_57,C_58,B_59,D_60] : ( set_intersection2(cartesian_product2(A_57,C_58),cartesian_product2(B_59,D_60)) = cartesian_product2(set_intersection2(A_57,B_59),set_intersection2(C_58,D_60)) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_30,plain,
subset(cartesian_product2('#skF_3','#skF_4'),cartesian_product2('#skF_5','#skF_6')),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_126,plain,
! [A_31,B_32] :
( ( set_intersection2(A_31,B_32) = A_31 )
| ~ subset(A_31,B_32) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_139,plain,
set_intersection2(cartesian_product2('#skF_3','#skF_4'),cartesian_product2('#skF_5','#skF_6')) = cartesian_product2('#skF_3','#skF_4'),
inference(resolution,[status(thm)],[c_30,c_126]) ).
tff(c_770,plain,
cartesian_product2(set_intersection2('#skF_3','#skF_5'),set_intersection2('#skF_4','#skF_6')) = cartesian_product2('#skF_3','#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_746,c_139]) ).
tff(c_24,plain,
! [C_15,A_13,B_14,D_16] :
( ( C_15 = A_13 )
| ( empty_set = B_14 )
| ( empty_set = A_13 )
| ( cartesian_product2(C_15,D_16) != cartesian_product2(A_13,B_14) ) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_987,plain,
! [A_13,B_14] :
( ( set_intersection2('#skF_3','#skF_5') = A_13 )
| ( empty_set = B_14 )
| ( empty_set = A_13 )
| ( cartesian_product2(A_13,B_14) != cartesian_product2('#skF_3','#skF_4') ) ),
inference(superposition,[status(thm),theory(equality)],[c_770,c_24]) ).
tff(c_24913,plain,
( ( set_intersection2('#skF_3','#skF_5') = '#skF_3' )
| ( empty_set = '#skF_4' )
| ( empty_set = '#skF_3' ) ),
inference(reflexivity,[status(thm),theory(equality)],[c_987]) ).
tff(c_24942,plain,
empty_set = '#skF_3',
inference(splitLeft,[status(thm)],[c_24913]) ).
tff(c_2,plain,
! [B_2,A_1] : ( set_intersection2(B_2,A_1) = set_intersection2(A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_32,plain,
! [A_17,B_18] : subset(set_intersection2(A_17,B_18),A_17),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_155,plain,
! [A_35,B_36] : ( set_intersection2(set_intersection2(A_35,B_36),A_35) = set_intersection2(A_35,B_36) ),
inference(resolution,[status(thm)],[c_32,c_126]) ).
tff(c_193,plain,
! [A_1,B_36] : ( set_intersection2(A_1,set_intersection2(A_1,B_36)) = set_intersection2(A_1,B_36) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_155]) ).
tff(c_18,plain,
! [B_8] : ( cartesian_product2(empty_set,B_8) = empty_set ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_6,plain,
! [A_3] : ( set_intersection2(A_3,A_3) = A_3 ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_16,plain,
! [A_7] : ( cartesian_product2(A_7,empty_set) = empty_set ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_2006,plain,
! [A_94,B_95,D_96] : ( cartesian_product2(set_intersection2(A_94,B_95),set_intersection2(empty_set,D_96)) = set_intersection2(empty_set,cartesian_product2(B_95,D_96)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_746]) ).
tff(c_2137,plain,
! [A_3,D_96] : ( set_intersection2(empty_set,cartesian_product2(A_3,D_96)) = cartesian_product2(A_3,set_intersection2(empty_set,D_96)) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_2006]) ).
tff(c_2130,plain,
! [A_1,B_2,D_96] : ( cartesian_product2(set_intersection2(A_1,B_2),set_intersection2(empty_set,D_96)) = set_intersection2(empty_set,cartesian_product2(A_1,D_96)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_2006]) ).
tff(c_6791,plain,
! [A_171,B_172,D_173] : ( cartesian_product2(set_intersection2(A_171,B_172),set_intersection2(empty_set,D_173)) = cartesian_product2(A_171,set_intersection2(empty_set,D_173)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2137,c_2130]) ).
tff(c_2450,plain,
! [B_106,B_107,D_108] : ( cartesian_product2(set_intersection2(empty_set,B_106),set_intersection2(B_107,D_108)) = set_intersection2(empty_set,cartesian_product2(B_106,D_108)) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_746]) ).
tff(c_2611,plain,
! [B_106,A_3] : ( set_intersection2(empty_set,cartesian_product2(B_106,A_3)) = cartesian_product2(set_intersection2(empty_set,B_106),A_3) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_2450]) ).
tff(c_3153,plain,
! [B_106,A_3] : ( cartesian_product2(set_intersection2(empty_set,B_106),A_3) = cartesian_product2(B_106,set_intersection2(empty_set,A_3)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2137,c_2611]) ).
tff(c_6841,plain,
! [B_172,D_173] : ( cartesian_product2(B_172,set_intersection2(empty_set,set_intersection2(empty_set,D_173))) = cartesian_product2(empty_set,set_intersection2(empty_set,D_173)) ),
inference(superposition,[status(thm),theory(equality)],[c_6791,c_3153]) ).
tff(c_7046,plain,
! [B_172,D_173] : ( cartesian_product2(B_172,set_intersection2(empty_set,D_173)) = empty_set ),
inference(demodulation,[status(thm),theory(equality)],[c_193,c_18,c_6841]) ).
tff(c_820,plain,
! [A_57,C_58,B_8] : ( cartesian_product2(set_intersection2(A_57,empty_set),set_intersection2(C_58,B_8)) = set_intersection2(cartesian_product2(A_57,C_58),empty_set) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_746]) ).
tff(c_1253,plain,
! [A_69,C_70,B_71] : ( cartesian_product2(set_intersection2(A_69,empty_set),set_intersection2(C_70,B_71)) = set_intersection2(empty_set,cartesian_product2(A_69,C_70)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_820]) ).
tff(c_1353,plain,
! [A_69,A_3] : ( set_intersection2(empty_set,cartesian_product2(A_69,A_3)) = cartesian_product2(set_intersection2(A_69,empty_set),A_3) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_1253]) ).
tff(c_3339,plain,
! [A_69,A_3] : ( cartesian_product2(set_intersection2(A_69,empty_set),A_3) = cartesian_product2(A_69,set_intersection2(empty_set,A_3)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2137,c_1353]) ).
tff(c_7786,plain,
! [A_184,A_185] : ( cartesian_product2(set_intersection2(A_184,empty_set),A_185) = empty_set ),
inference(demodulation,[status(thm),theory(equality)],[c_7046,c_3339]) ).
tff(c_14,plain,
! [B_8,A_7] :
( ( empty_set = B_8 )
| ( empty_set = A_7 )
| ( cartesian_product2(A_7,B_8) != empty_set ) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_7994,plain,
! [A_185,A_184] :
( ( empty_set = A_185 )
| ( set_intersection2(A_184,empty_set) = empty_set ) ),
inference(superposition,[status(thm),theory(equality)],[c_7786,c_14]) ).
tff(c_8231,plain,
! [A_188] : ( set_intersection2(A_188,empty_set) = empty_set ),
inference(splitLeft,[status(thm)],[c_7994]) ).
tff(c_8363,plain,
! [A_188] : subset(empty_set,A_188),
inference(superposition,[status(thm),theory(equality)],[c_8231,c_32]) ).
tff(c_24952,plain,
! [A_188] : subset('#skF_3',A_188),
inference(demodulation,[status(thm),theory(equality)],[c_24942,c_8363]) ).
tff(c_24967,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_24952,c_72]) ).
tff(c_24968,plain,
( ( empty_set = '#skF_4' )
| ( set_intersection2('#skF_3','#skF_5') = '#skF_3' ) ),
inference(splitRight,[status(thm)],[c_24913]) ).
tff(c_24970,plain,
set_intersection2('#skF_3','#skF_5') = '#skF_3',
inference(splitLeft,[status(thm)],[c_24968]) ).
tff(c_73,plain,
! [B_27,A_28] : ( set_intersection2(B_27,A_28) = set_intersection2(A_28,B_27) ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_88,plain,
! [B_27,A_28] : subset(set_intersection2(B_27,A_28),A_28),
inference(superposition,[status(thm),theory(equality)],[c_73,c_32]) ).
tff(c_25369,plain,
subset('#skF_3','#skF_5'),
inference(superposition,[status(thm),theory(equality)],[c_24970,c_88]) ).
tff(c_25452,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_72,c_25369]) ).
tff(c_25453,plain,
empty_set = '#skF_4',
inference(splitRight,[status(thm)],[c_24968]) ).
tff(c_25472,plain,
! [A_7] : ( cartesian_product2(A_7,'#skF_4') = '#skF_4' ),
inference(demodulation,[status(thm),theory(equality)],[c_25453,c_25453,c_16]) ).
tff(c_25471,plain,
cartesian_product2('#skF_3','#skF_4') != '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_25453,c_28]) ).
tff(c_25844,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_25472,c_25471]) ).
tff(c_25846,plain,
! [A_403] : ( empty_set = A_403 ),
inference(splitRight,[status(thm)],[c_7994]) ).
tff(c_1010,plain,
! [A_63,B_64,C_65,D_66] : subset(cartesian_product2(set_intersection2(A_63,B_64),set_intersection2(C_65,D_66)),cartesian_product2(A_63,C_65)),
inference(superposition,[status(thm),theory(equality)],[c_746,c_32]) ).
tff(c_5540,plain,
! [B_151,A_152,C_153,D_154] : subset(cartesian_product2(set_intersection2(B_151,A_152),set_intersection2(C_153,D_154)),cartesian_product2(A_152,C_153)),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1010]) ).
tff(c_5634,plain,
subset(cartesian_product2('#skF_3','#skF_4'),cartesian_product2('#skF_5','#skF_4')),
inference(superposition,[status(thm),theory(equality)],[c_770,c_5540]) ).
tff(c_34,plain,
! [A_19,B_20] :
( ( set_intersection2(A_19,B_20) = A_19 )
| ~ subset(A_19,B_20) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_5745,plain,
set_intersection2(cartesian_product2('#skF_3','#skF_4'),cartesian_product2('#skF_5','#skF_4')) = cartesian_product2('#skF_3','#skF_4'),
inference(resolution,[status(thm)],[c_5634,c_34]) ).
tff(c_785,plain,
! [B_59,D_60,A_57,C_58] : ( set_intersection2(cartesian_product2(B_59,D_60),cartesian_product2(A_57,C_58)) = cartesian_product2(set_intersection2(A_57,B_59),set_intersection2(C_58,D_60)) ),
inference(superposition,[status(thm),theory(equality)],[c_746,c_2]) ).
tff(c_5782,plain,
cartesian_product2(set_intersection2('#skF_5','#skF_3'),set_intersection2('#skF_4','#skF_4')) = cartesian_product2('#skF_3','#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_5745,c_785]) ).
tff(c_5857,plain,
cartesian_product2(set_intersection2('#skF_3','#skF_5'),'#skF_4') = cartesian_product2('#skF_3','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6,c_5782]) ).
tff(c_25938,plain,
cartesian_product2('#skF_3','#skF_4') = empty_set,
inference(superposition,[status(thm),theory(equality)],[c_25846,c_5857]) ).
tff(c_26186,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_25938]) ).
tff(c_26187,plain,
~ subset('#skF_4','#skF_6'),
inference(splitRight,[status(thm)],[c_26]) ).
tff(c_26188,plain,
subset('#skF_3','#skF_5'),
inference(splitRight,[status(thm)],[c_26]) ).
tff(c_26242,plain,
! [A_640,B_641] :
( ( set_intersection2(A_640,B_641) = A_640 )
| ~ subset(A_640,B_641) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_26260,plain,
set_intersection2('#skF_3','#skF_5') = '#skF_3',
inference(resolution,[status(thm)],[c_26188,c_26242]) ).
tff(c_26800,plain,
! [A_664,C_665,B_666,D_667] : ( set_intersection2(cartesian_product2(A_664,C_665),cartesian_product2(B_666,D_667)) = cartesian_product2(set_intersection2(A_664,B_666),set_intersection2(C_665,D_667)) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_26258,plain,
set_intersection2(cartesian_product2('#skF_3','#skF_4'),cartesian_product2('#skF_5','#skF_6')) = cartesian_product2('#skF_3','#skF_4'),
inference(resolution,[status(thm)],[c_30,c_26242]) ).
tff(c_26812,plain,
cartesian_product2(set_intersection2('#skF_3','#skF_5'),set_intersection2('#skF_4','#skF_6')) = cartesian_product2('#skF_3','#skF_4'),
inference(superposition,[status(thm),theory(equality)],[c_26800,c_26258]) ).
tff(c_26875,plain,
cartesian_product2('#skF_3',set_intersection2('#skF_4','#skF_6')) = cartesian_product2('#skF_3','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_26260,c_26812]) ).
tff(c_26905,plain,
! [C_15,D_16] :
( ( C_15 = '#skF_3' )
| ( set_intersection2('#skF_4','#skF_6') = empty_set )
| ( empty_set = '#skF_3' )
| ( cartesian_product2(C_15,D_16) != cartesian_product2('#skF_3','#skF_4') ) ),
inference(superposition,[status(thm),theory(equality)],[c_26875,c_24]) ).
tff(c_70035,plain,
empty_set = '#skF_3',
inference(splitLeft,[status(thm)],[c_26905]) ).
tff(c_70052,plain,
! [B_8] : ( cartesian_product2('#skF_3',B_8) = '#skF_3' ),
inference(demodulation,[status(thm),theory(equality)],[c_70035,c_70035,c_18]) ).
tff(c_70050,plain,
cartesian_product2('#skF_3','#skF_4') != '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_70035,c_28]) ).
tff(c_70164,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_70052,c_70050]) ).
tff(c_70166,plain,
empty_set != '#skF_3',
inference(splitRight,[status(thm)],[c_26905]) ).
tff(c_22,plain,
! [D_16,B_14,A_13,C_15] :
( ( D_16 = B_14 )
| ( empty_set = B_14 )
| ( empty_set = A_13 )
| ( cartesian_product2(C_15,D_16) != cartesian_product2(A_13,B_14) ) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_26896,plain,
! [B_14,A_13] :
( ( set_intersection2('#skF_4','#skF_6') = B_14 )
| ( empty_set = B_14 )
| ( empty_set = A_13 )
| ( cartesian_product2(A_13,B_14) != cartesian_product2('#skF_3','#skF_4') ) ),
inference(superposition,[status(thm),theory(equality)],[c_26875,c_22]) ).
tff(c_74285,plain,
( ( set_intersection2('#skF_4','#skF_6') = '#skF_4' )
| ( empty_set = '#skF_4' )
| ( empty_set = '#skF_3' ) ),
inference(reflexivity,[status(thm),theory(equality)],[c_26896]) ).
tff(c_74286,plain,
( ( set_intersection2('#skF_4','#skF_6') = '#skF_4' )
| ( empty_set = '#skF_4' ) ),
inference(negUnitSimplification,[status(thm)],[c_70166,c_74285]) ).
tff(c_74311,plain,
empty_set = '#skF_4',
inference(splitLeft,[status(thm)],[c_74286]) ).
tff(c_26287,plain,
! [A_644,B_645] : ( set_intersection2(set_intersection2(A_644,B_645),A_644) = set_intersection2(A_644,B_645) ),
inference(resolution,[status(thm)],[c_32,c_26242]) ).
tff(c_26261,plain,
! [A_17,B_18] : ( set_intersection2(set_intersection2(A_17,B_18),A_17) = set_intersection2(A_17,B_18) ),
inference(resolution,[status(thm)],[c_32,c_26242]) ).
tff(c_26290,plain,
! [A_644,B_645] : ( set_intersection2(set_intersection2(A_644,B_645),set_intersection2(A_644,B_645)) = set_intersection2(set_intersection2(A_644,B_645),A_644) ),
inference(superposition,[status(thm),theory(equality)],[c_26287,c_26261]) ).
tff(c_26332,plain,
! [A_644,B_645] : ( set_intersection2(A_644,set_intersection2(A_644,B_645)) = set_intersection2(A_644,B_645) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6,c_26290]) ).
tff(c_27403,plain,
! [A_678,B_679,D_680] : ( cartesian_product2(set_intersection2(A_678,B_679),set_intersection2(empty_set,D_680)) = set_intersection2(empty_set,cartesian_product2(B_679,D_680)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_26800]) ).
tff(c_27498,plain,
! [A_3,D_680] : ( set_intersection2(empty_set,cartesian_product2(A_3,D_680)) = cartesian_product2(A_3,set_intersection2(empty_set,D_680)) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_27403]) ).
tff(c_26871,plain,
! [A_664,C_665,B_8] : ( cartesian_product2(set_intersection2(A_664,empty_set),set_intersection2(C_665,B_8)) = set_intersection2(cartesian_product2(A_664,C_665),empty_set) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_26800]) ).
tff(c_27742,plain,
! [A_685,C_686,B_687] : ( cartesian_product2(set_intersection2(A_685,empty_set),set_intersection2(C_686,B_687)) = set_intersection2(empty_set,cartesian_product2(A_685,C_686)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_26871]) ).
tff(c_27856,plain,
! [A_685,A_3] : ( set_intersection2(empty_set,cartesian_product2(A_685,A_3)) = cartesian_product2(set_intersection2(A_685,empty_set),A_3) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_27742]) ).
tff(c_32182,plain,
! [A_685,A_3] : ( cartesian_product2(set_intersection2(A_685,empty_set),A_3) = cartesian_product2(A_685,set_intersection2(empty_set,A_3)) ),
inference(demodulation,[status(thm),theory(equality)],[c_27498,c_27856]) ).
tff(c_26606,plain,
! [A_656,B_657] : ( set_intersection2(A_656,set_intersection2(A_656,B_657)) = set_intersection2(A_656,B_657) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6,c_26290]) ).
tff(c_26660,plain,
! [B_2,A_1] : ( set_intersection2(B_2,set_intersection2(A_1,B_2)) = set_intersection2(B_2,A_1) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_26606]) ).
tff(c_26865,plain,
! [A_664,A_7,C_665] : ( cartesian_product2(set_intersection2(A_664,A_7),set_intersection2(C_665,empty_set)) = set_intersection2(cartesian_product2(A_664,C_665),empty_set) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_26800]) ).
tff(c_28186,plain,
! [A_696,A_697,C_698] : ( cartesian_product2(set_intersection2(A_696,A_697),set_intersection2(C_698,empty_set)) = set_intersection2(empty_set,cartesian_product2(A_696,C_698)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_26865]) ).
tff(c_31063,plain,
! [C_759] : ( set_intersection2(empty_set,cartesian_product2('#skF_3',C_759)) = cartesian_product2('#skF_3',set_intersection2(C_759,empty_set)) ),
inference(superposition,[status(thm),theory(equality)],[c_26260,c_28186]) ).
tff(c_26886,plain,
! [A_664,C_665,B_8] : ( cartesian_product2(set_intersection2(A_664,empty_set),set_intersection2(C_665,B_8)) = set_intersection2(empty_set,cartesian_product2(A_664,C_665)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_26871]) ).
tff(c_31124,plain,
! [A_664,C_759] : ( cartesian_product2(set_intersection2(A_664,empty_set),cartesian_product2('#skF_3',set_intersection2(C_759,empty_set))) = set_intersection2(empty_set,cartesian_product2(A_664,empty_set)) ),
inference(superposition,[status(thm),theory(equality)],[c_31063,c_26886]) ).
tff(c_35991,plain,
! [A_834,C_835] : ( cartesian_product2(set_intersection2(A_834,empty_set),cartesian_product2('#skF_3',set_intersection2(C_835,empty_set))) = empty_set ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_16,c_31124]) ).
tff(c_28311,plain,
! [A_3,C_698] : ( set_intersection2(empty_set,cartesian_product2(A_3,C_698)) = cartesian_product2(A_3,set_intersection2(C_698,empty_set)) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_28186]) ).
tff(c_36005,plain,
! [A_834,C_835] : ( cartesian_product2(set_intersection2(A_834,empty_set),set_intersection2(cartesian_product2('#skF_3',set_intersection2(C_835,empty_set)),empty_set)) = set_intersection2(empty_set,empty_set) ),
inference(superposition,[status(thm),theory(equality)],[c_35991,c_28311]) ).
tff(c_36170,plain,
! [A_836,C_837] : ( cartesian_product2(A_836,cartesian_product2('#skF_3',set_intersection2(empty_set,C_837))) = empty_set ),
inference(demodulation,[status(thm),theory(equality)],[c_26332,c_27498,c_32182,c_26660,c_27498,c_2,c_6,c_36005]) ).
tff(c_36391,plain,
! [C_837,A_836] :
( ( cartesian_product2('#skF_3',set_intersection2(empty_set,C_837)) = empty_set )
| ( empty_set = A_836 ) ),
inference(superposition,[status(thm),theory(equality)],[c_36170,c_14]) ).
tff(c_36762,plain,
! [A_843] : ( empty_set = A_843 ),
inference(splitLeft,[status(thm)],[c_36391]) ).
tff(c_37734,plain,
cartesian_product2('#skF_3','#skF_4') = empty_set,
inference(superposition,[status(thm),theory(equality)],[c_36762,c_26875]) ).
tff(c_37862,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_37734]) ).
tff(c_37863,plain,
! [C_837] : ( cartesian_product2('#skF_3',set_intersection2(empty_set,C_837)) = empty_set ),
inference(splitRight,[status(thm)],[c_36391]) ).
tff(c_27481,plain,
! [D_680] : ( set_intersection2(empty_set,cartesian_product2('#skF_5',D_680)) = cartesian_product2('#skF_3',set_intersection2(empty_set,D_680)) ),
inference(superposition,[status(thm),theory(equality)],[c_26260,c_27403]) ).
tff(c_33120,plain,
! [A_800,C_801] : ( set_intersection2(empty_set,cartesian_product2(A_800,C_801)) = cartesian_product2(A_800,set_intersection2(C_801,empty_set)) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_28186]) ).
tff(c_33233,plain,
! [D_680] : ( cartesian_product2('#skF_5',set_intersection2(D_680,empty_set)) = cartesian_product2('#skF_3',set_intersection2(empty_set,D_680)) ),
inference(superposition,[status(thm),theory(equality)],[c_27481,c_33120]) ).
tff(c_38466,plain,
! [D_1161] : ( cartesian_product2('#skF_5',set_intersection2(D_1161,empty_set)) = empty_set ),
inference(demodulation,[status(thm),theory(equality)],[c_37863,c_33233]) ).
tff(c_38639,plain,
! [D_1161] :
( ( set_intersection2(D_1161,empty_set) = empty_set )
| ( empty_set = '#skF_5' ) ),
inference(superposition,[status(thm),theory(equality)],[c_38466,c_14]) ).
tff(c_38656,plain,
empty_set = '#skF_5',
inference(splitLeft,[status(thm)],[c_38639]) ).
tff(c_37873,plain,
! [C_1156] : ( cartesian_product2('#skF_3',set_intersection2(empty_set,C_1156)) = empty_set ),
inference(splitRight,[status(thm)],[c_36391]) ).
tff(c_38035,plain,
! [C_1156] :
( ( set_intersection2(empty_set,C_1156) = empty_set )
| ( empty_set = '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_37873,c_14]) ).
tff(c_39522,plain,
! [C_1156] :
( ( set_intersection2('#skF_5',C_1156) = '#skF_5' )
| ( '#skF_5' = '#skF_3' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_38656,c_38656,c_38656,c_38035]) ).
tff(c_39523,plain,
'#skF_5' = '#skF_3',
inference(splitLeft,[status(thm)],[c_39522]) ).
tff(c_38689,plain,
! [B_8] : ( cartesian_product2('#skF_5',B_8) = '#skF_5' ),
inference(demodulation,[status(thm),theory(equality)],[c_38656,c_38656,c_18]) ).
tff(c_39534,plain,
! [B_8] : ( cartesian_product2('#skF_3',B_8) = '#skF_3' ),
inference(demodulation,[status(thm),theory(equality)],[c_39523,c_39523,c_38689]) ).
tff(c_38687,plain,
cartesian_product2('#skF_3','#skF_4') != '#skF_5',
inference(demodulation,[status(thm),theory(equality)],[c_38656,c_28]) ).
tff(c_39536,plain,
cartesian_product2('#skF_3','#skF_4') != '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_39523,c_38687]) ).
tff(c_39556,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_39534,c_39536]) ).
tff(c_39558,plain,
'#skF_5' != '#skF_3',
inference(splitRight,[status(thm)],[c_39522]) ).
tff(c_39563,plain,
! [C_1174] : ( set_intersection2('#skF_5',C_1174) = '#skF_5' ),
inference(splitRight,[status(thm)],[c_39522]) ).
tff(c_26189,plain,
! [B_636,A_637] : ( set_intersection2(B_636,A_637) = set_intersection2(A_637,B_636) ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_26204,plain,
! [B_636,A_637] : subset(set_intersection2(B_636,A_637),A_637),
inference(superposition,[status(thm),theory(equality)],[c_26189,c_32]) ).
tff(c_26359,plain,
! [B_650,A_651] : ( set_intersection2(set_intersection2(B_650,A_651),A_651) = set_intersection2(B_650,A_651) ),
inference(resolution,[status(thm)],[c_26204,c_26242]) ).
tff(c_26916,plain,
! [B_668,A_669] : ( set_intersection2(set_intersection2(B_668,A_669),B_668) = set_intersection2(A_669,B_668) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_26359]) ).
tff(c_27007,plain,
set_intersection2('#skF_5','#skF_3') = set_intersection2('#skF_3','#skF_3'),
inference(superposition,[status(thm),theory(equality)],[c_26260,c_26916]) ).
tff(c_27049,plain,
set_intersection2('#skF_5','#skF_3') = '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_6,c_27007]) ).
tff(c_39620,plain,
'#skF_5' = '#skF_3',
inference(superposition,[status(thm),theory(equality)],[c_39563,c_27049]) ).
tff(c_39718,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_39558,c_39620]) ).
tff(c_40042,plain,
! [D_1178] : ( set_intersection2(D_1178,empty_set) = empty_set ),
inference(splitRight,[status(thm)],[c_38639]) ).
tff(c_40181,plain,
! [D_1178] : subset(empty_set,D_1178),
inference(superposition,[status(thm),theory(equality)],[c_40042,c_32]) ).
tff(c_74323,plain,
! [D_1178] : subset('#skF_4',D_1178),
inference(demodulation,[status(thm),theory(equality)],[c_74311,c_40181]) ).
tff(c_74339,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_74323,c_26187]) ).
tff(c_74340,plain,
set_intersection2('#skF_4','#skF_6') = '#skF_4',
inference(splitRight,[status(thm)],[c_74286]) ).
tff(c_74910,plain,
subset('#skF_4','#skF_6'),
inference(superposition,[status(thm),theory(equality)],[c_74340,c_26204]) ).
tff(c_75040,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26187,c_74910]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET984+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % 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 : n029.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 : Thu Aug 3 16:41:52 EDT 2023
% 0.13/0.35 % CPUTime :
% 24.84/11.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.84/11.57
% 24.84/11.57 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 25.11/11.61
% 25.11/11.61 Inference rules
% 25.11/11.61 ----------------------
% 25.11/11.61 #Ref : 7
% 25.11/11.61 #Sup : 19286
% 25.11/11.61 #Fact : 0
% 25.11/11.61 #Define : 0
% 25.11/11.61 #Split : 10
% 25.11/11.61 #Chain : 0
% 25.11/11.61 #Close : 0
% 25.11/11.61
% 25.11/11.61 Ordering : KBO
% 25.11/11.61
% 25.11/11.61 Simplification rules
% 25.11/11.61 ----------------------
% 25.11/11.61 #Subsume : 800
% 25.11/11.61 #Demod : 26059
% 25.11/11.61 #Tautology : 10898
% 25.11/11.61 #SimpNegUnit : 69
% 25.11/11.61 #BackRed : 441
% 25.11/11.61
% 25.11/11.61 #Partial instantiations: 792
% 25.11/11.61 #Strategies tried : 1
% 25.11/11.61
% 25.11/11.61 Timing (in seconds)
% 25.11/11.61 ----------------------
% 25.11/11.61 Preprocessing : 0.50
% 25.11/11.61 Parsing : 0.26
% 25.11/11.61 CNF conversion : 0.03
% 25.11/11.61 Main loop : 10.04
% 25.11/11.61 Inferencing : 1.31
% 25.11/11.61 Reduction : 6.20
% 25.11/11.61 Demodulation : 5.67
% 25.11/11.61 BG Simplification : 0.13
% 25.11/11.61 Subsumption : 1.71
% 25.11/11.61 Abstraction : 0.20
% 25.11/11.61 MUC search : 0.00
% 25.11/11.61 Cooper : 0.00
% 25.11/11.61 Total : 10.61
% 25.11/11.62 Index Insertion : 0.00
% 25.11/11.62 Index Deletion : 0.00
% 25.11/11.62 Index Matching : 0.00
% 25.11/11.62 BG Taut test : 0.00
%------------------------------------------------------------------------------