TSTP Solution File: SEU277+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU277+1 : TPTP v8.1.2. 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 : 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 10:58:15 EDT 2023
% Result : Theorem 48.21s 33.07s
% Output : CNFRefutation 48.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 40
% Syntax : Number of formulae : 327 ( 76 unt; 37 typ; 0 def)
% Number of atoms : 1094 ( 351 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1472 ( 668 ~; 783 |; 14 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 55 ( 26 >; 29 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 11 con; 0-4 aty)
% Number of variables : 454 (; 443 !; 11 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > relation > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > ordered_pair > cartesian_product2 > apply > #nlpp > #skF_7 > #skF_5 > #skF_17 > #skF_4 > #skF_11 > #skF_24 > #skF_15 > #skF_18 > #skF_22 > #skF_10 > #skF_14 > #skF_25 > #skF_23 > #skF_26 > #skF_13 > #skF_19 > #skF_2 > #skF_3 > #skF_1 > #skF_9 > #skF_20 > #skF_8 > #skF_21 > #skF_6 > #skF_12 > #skF_16
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_17',type,
'#skF_17': ( $i * $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff('#skF_24',type,
'#skF_24': ( $i * $i * $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i * $i ) > $i ).
tff(epsilon_transitive,type,
epsilon_transitive: $i > $o ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff('#skF_22',type,
'#skF_22': ( $i * $i * $i ) > $i ).
tff(function,type,
function: $i > $o ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(ordinal,type,
ordinal: $i > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_25',type,
'#skF_25': ( $i * $i * $i * $i ) > $i ).
tff('#skF_23',type,
'#skF_23': ( $i * $i * $i ) > $i ).
tff('#skF_26',type,
'#skF_26': ( $i * $i * $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_20',type,
'#skF_20': ( $i * $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': ( $i * $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i ) > $i ).
tff(f_44,negated_conjecture,
~ ! [A,B,C] :
( ( relation(B)
& relation(C)
& function(C) )
=> ? [D] :
! [E] :
( in(E,D)
<=> ( in(E,cartesian_product2(A,A))
& ? [F,G] :
( ( E = ordered_pair(F,G) )
& in(ordered_pair(apply(C,F),apply(C,G)),B) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_21__wellord2__1) ).
tff(f_176,axiom,
! [A,B,C] :
( ( relation(B)
& relation(C)
& function(C) )
=> ( ! [D,E,F] :
( ( ( D = E )
& ? [G,H] :
( ( E = ordered_pair(G,H) )
& in(ordered_pair(apply(C,G),apply(C,H)),B) )
& ( D = F )
& ? [I,J] :
( ( F = ordered_pair(I,J) )
& in(ordered_pair(apply(C,I),apply(C,J)),B) ) )
=> ( E = F ) )
=> ? [D] :
! [E] :
( in(E,D)
<=> ? [F] :
( in(F,cartesian_product2(A,A))
& ( F = E )
& ? [K,L] :
( ( E = ordered_pair(K,L) )
& in(ordered_pair(apply(C,K),apply(C,L)),B) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_21__wellord2__1) ).
tff(f_131,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
tff(c_20,plain,
! [D_20] :
( ( ordered_pair('#skF_5'(D_20),'#skF_6'(D_20)) = '#skF_4'(D_20) )
| in('#skF_7'(D_20),D_20) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_22,plain,
! [D_20] :
( in('#skF_4'(D_20),cartesian_product2('#skF_1','#skF_1'))
| in('#skF_7'(D_20),D_20) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_6,plain,
relation('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_4,plain,
relation('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_2,plain,
function('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_18,plain,
! [D_20] :
( in(ordered_pair(apply('#skF_3','#skF_5'(D_20)),apply('#skF_3','#skF_6'(D_20))),'#skF_2')
| in('#skF_7'(D_20),D_20) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_1447,plain,
! [B_467,C_469,L_465,K_466,A_468] :
( ( '#skF_17'(A_468,B_467,C_469) = '#skF_16'(A_468,B_467,C_469) )
| in(ordered_pair(K_466,L_465),'#skF_23'(A_468,B_467,C_469))
| ~ in(ordered_pair(apply(C_469,K_466),apply(C_469,L_465)),B_467)
| ~ in(ordered_pair(K_466,L_465),cartesian_product2(A_468,A_468))
| ~ function(C_469)
| ~ relation(C_469)
| ~ relation(B_467) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_1459,plain,
! [A_468,D_20] :
( ( '#skF_17'(A_468,'#skF_2','#skF_3') = '#skF_16'(A_468,'#skF_2','#skF_3') )
| in(ordered_pair('#skF_5'(D_20),'#skF_6'(D_20)),'#skF_23'(A_468,'#skF_2','#skF_3'))
| ~ in(ordered_pair('#skF_5'(D_20),'#skF_6'(D_20)),cartesian_product2(A_468,A_468))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2')
| in('#skF_7'(D_20),D_20) ),
inference(resolution,[status(thm)],[c_18,c_1447]) ).
tff(c_1468,plain,
! [A_470,D_471] :
( ( '#skF_17'(A_470,'#skF_2','#skF_3') = '#skF_16'(A_470,'#skF_2','#skF_3') )
| in(ordered_pair('#skF_5'(D_471),'#skF_6'(D_471)),'#skF_23'(A_470,'#skF_2','#skF_3'))
| ~ in(ordered_pair('#skF_5'(D_471),'#skF_6'(D_471)),cartesian_product2(A_470,A_470))
| in('#skF_7'(D_471),D_471) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_1459]) ).
tff(c_1472,plain,
! [A_472,D_473] :
( ( '#skF_17'(A_472,'#skF_2','#skF_3') = '#skF_16'(A_472,'#skF_2','#skF_3') )
| in(ordered_pair('#skF_5'(D_473),'#skF_6'(D_473)),'#skF_23'(A_472,'#skF_2','#skF_3'))
| ~ in('#skF_4'(D_473),cartesian_product2(A_472,A_472))
| in('#skF_7'(D_473),D_473)
| in('#skF_7'(D_473),D_473) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_1468]) ).
tff(c_1505,plain,
! [D_20] :
( ( '#skF_17'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3') )
| in(ordered_pair('#skF_5'(D_20),'#skF_6'(D_20)),'#skF_23'('#skF_1','#skF_2','#skF_3'))
| in('#skF_7'(D_20),D_20) ),
inference(resolution,[status(thm)],[c_22,c_1472]) ).
tff(c_1506,plain,
'#skF_17'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3'),
inference(splitLeft,[status(thm)],[c_1505]) ).
tff(c_1382,plain,
! [K_439,L_438,B_440,C_442,A_441] :
( ( '#skF_17'(A_441,B_440,C_442) != '#skF_18'(A_441,B_440,C_442) )
| in(ordered_pair(K_439,L_438),'#skF_23'(A_441,B_440,C_442))
| ~ in(ordered_pair(apply(C_442,K_439),apply(C_442,L_438)),B_440)
| ~ in(ordered_pair(K_439,L_438),cartesian_product2(A_441,A_441))
| ~ function(C_442)
| ~ relation(C_442)
| ~ relation(B_440) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_1394,plain,
! [A_441,D_20] :
( ( '#skF_17'(A_441,'#skF_2','#skF_3') != '#skF_18'(A_441,'#skF_2','#skF_3') )
| in(ordered_pair('#skF_5'(D_20),'#skF_6'(D_20)),'#skF_23'(A_441,'#skF_2','#skF_3'))
| ~ in(ordered_pair('#skF_5'(D_20),'#skF_6'(D_20)),cartesian_product2(A_441,A_441))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2')
| in('#skF_7'(D_20),D_20) ),
inference(resolution,[status(thm)],[c_18,c_1382]) ).
tff(c_1403,plain,
! [A_443,D_444] :
( ( '#skF_17'(A_443,'#skF_2','#skF_3') != '#skF_18'(A_443,'#skF_2','#skF_3') )
| in(ordered_pair('#skF_5'(D_444),'#skF_6'(D_444)),'#skF_23'(A_443,'#skF_2','#skF_3'))
| ~ in(ordered_pair('#skF_5'(D_444),'#skF_6'(D_444)),cartesian_product2(A_443,A_443))
| in('#skF_7'(D_444),D_444) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_1394]) ).
tff(c_1407,plain,
! [A_445,D_446] :
( ( '#skF_17'(A_445,'#skF_2','#skF_3') != '#skF_18'(A_445,'#skF_2','#skF_3') )
| in(ordered_pair('#skF_5'(D_446),'#skF_6'(D_446)),'#skF_23'(A_445,'#skF_2','#skF_3'))
| ~ in('#skF_4'(D_446),cartesian_product2(A_445,A_445))
| in('#skF_7'(D_446),D_446)
| in('#skF_7'(D_446),D_446) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_1403]) ).
tff(c_1440,plain,
! [D_20] :
( ( '#skF_17'('#skF_1','#skF_2','#skF_3') != '#skF_18'('#skF_1','#skF_2','#skF_3') )
| in(ordered_pair('#skF_5'(D_20),'#skF_6'(D_20)),'#skF_23'('#skF_1','#skF_2','#skF_3'))
| in('#skF_7'(D_20),D_20) ),
inference(resolution,[status(thm)],[c_22,c_1407]) ).
tff(c_1441,plain,
'#skF_17'('#skF_1','#skF_2','#skF_3') != '#skF_18'('#skF_1','#skF_2','#skF_3'),
inference(splitLeft,[status(thm)],[c_1440]) ).
tff(c_1508,plain,
'#skF_18'('#skF_1','#skF_2','#skF_3') != '#skF_16'('#skF_1','#skF_2','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_1506,c_1441]) ).
tff(c_16,plain,
! [D_20] :
( ~ in('#skF_4'(D_20),D_20)
| in('#skF_7'(D_20),D_20) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_1515,plain,
! [C_487,K_484,L_483,A_486,B_485] :
( ( '#skF_18'(A_486,B_485,C_487) = '#skF_16'(A_486,B_485,C_487) )
| in(ordered_pair(K_484,L_483),'#skF_23'(A_486,B_485,C_487))
| ~ in(ordered_pair(apply(C_487,K_484),apply(C_487,L_483)),B_485)
| ~ in(ordered_pair(K_484,L_483),cartesian_product2(A_486,A_486))
| ~ function(C_487)
| ~ relation(C_487)
| ~ relation(B_485) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_1527,plain,
! [A_486,D_20] :
( ( '#skF_18'(A_486,'#skF_2','#skF_3') = '#skF_16'(A_486,'#skF_2','#skF_3') )
| in(ordered_pair('#skF_5'(D_20),'#skF_6'(D_20)),'#skF_23'(A_486,'#skF_2','#skF_3'))
| ~ in(ordered_pair('#skF_5'(D_20),'#skF_6'(D_20)),cartesian_product2(A_486,A_486))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2')
| in('#skF_7'(D_20),D_20) ),
inference(resolution,[status(thm)],[c_18,c_1515]) ).
tff(c_1708,plain,
! [A_496,D_497] :
( ( '#skF_18'(A_496,'#skF_2','#skF_3') = '#skF_16'(A_496,'#skF_2','#skF_3') )
| in(ordered_pair('#skF_5'(D_497),'#skF_6'(D_497)),'#skF_23'(A_496,'#skF_2','#skF_3'))
| ~ in(ordered_pair('#skF_5'(D_497),'#skF_6'(D_497)),cartesian_product2(A_496,A_496))
| in('#skF_7'(D_497),D_497) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_1527]) ).
tff(c_1712,plain,
! [A_498,D_499] :
( ( '#skF_18'(A_498,'#skF_2','#skF_3') = '#skF_16'(A_498,'#skF_2','#skF_3') )
| in(ordered_pair('#skF_5'(D_499),'#skF_6'(D_499)),'#skF_23'(A_498,'#skF_2','#skF_3'))
| ~ in('#skF_4'(D_499),cartesian_product2(A_498,A_498))
| in('#skF_7'(D_499),D_499)
| in('#skF_7'(D_499),D_499) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_1708]) ).
tff(c_1734,plain,
! [D_20] :
( ( '#skF_18'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3') )
| in(ordered_pair('#skF_5'(D_20),'#skF_6'(D_20)),'#skF_23'('#skF_1','#skF_2','#skF_3'))
| in('#skF_7'(D_20),D_20) ),
inference(resolution,[status(thm)],[c_22,c_1712]) ).
tff(c_1857,plain,
! [D_503] :
( in(ordered_pair('#skF_5'(D_503),'#skF_6'(D_503)),'#skF_23'('#skF_1','#skF_2','#skF_3'))
| in('#skF_7'(D_503),D_503) ),
inference(negUnitSimplification,[status(thm)],[c_1508,c_1734]) ).
tff(c_1894,plain,
! [D_20] :
( in('#skF_4'(D_20),'#skF_23'('#skF_1','#skF_2','#skF_3'))
| in('#skF_7'(D_20),D_20)
| in('#skF_7'(D_20),D_20) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_1857]) ).
tff(c_2081,plain,
! [D_506] :
( in('#skF_4'(D_506),'#skF_23'('#skF_1','#skF_2','#skF_3'))
| in('#skF_7'(D_506),D_506) ),
inference(factorization,[status(thm),theory(equality)],[c_1894]) ).
tff(c_136,plain,
! [A_45,B_46,C_47,E_127] :
( ( '#skF_18'(A_45,B_46,C_47) = '#skF_16'(A_45,B_46,C_47) )
| ( '#skF_24'(A_45,B_46,C_47,E_127) = E_127 )
| ~ in(E_127,'#skF_23'(A_45,B_46,C_47))
| ~ function(C_47)
| ~ relation(C_47)
| ~ relation(B_46) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_31021,plain,
! [A_1532,B_1533,C_1534] :
( ( '#skF_18'(A_1532,B_1533,C_1534) = '#skF_16'(A_1532,B_1533,C_1534) )
| ( '#skF_24'(A_1532,B_1533,C_1534,'#skF_7'('#skF_23'(A_1532,B_1533,C_1534))) = '#skF_7'('#skF_23'(A_1532,B_1533,C_1534)) )
| ~ function(C_1534)
| ~ relation(C_1534)
| ~ relation(B_1533)
| in('#skF_4'('#skF_23'(A_1532,B_1533,C_1534)),'#skF_23'('#skF_1','#skF_2','#skF_3')) ),
inference(resolution,[status(thm)],[c_2081,c_136]) ).
tff(c_319,plain,
! [A_184,B_185,C_186,E_187] :
( ( '#skF_18'(A_184,B_185,C_186) = '#skF_16'(A_184,B_185,C_186) )
| ( '#skF_24'(A_184,B_185,C_186,E_187) = E_187 )
| ~ in(E_187,'#skF_23'(A_184,B_185,C_186))
| ~ function(C_186)
| ~ relation(C_186)
| ~ relation(B_185) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_334,plain,
! [A_184,B_185,C_186] :
( ( '#skF_18'(A_184,B_185,C_186) = '#skF_16'(A_184,B_185,C_186) )
| ( '#skF_24'(A_184,B_185,C_186,'#skF_7'('#skF_23'(A_184,B_185,C_186))) = '#skF_7'('#skF_23'(A_184,B_185,C_186)) )
| ~ function(C_186)
| ~ relation(C_186)
| ~ relation(B_185)
| ~ in('#skF_4'('#skF_23'(A_184,B_185,C_186)),'#skF_23'(A_184,B_185,C_186)) ),
inference(resolution,[status(thm)],[c_16,c_319]) ).
tff(c_31221,plain,
( ( '#skF_18'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3') )
| ( '#skF_24'('#skF_1','#skF_2','#skF_3','#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3'))) = '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_31021,c_334]) ).
tff(c_31432,plain,
( ( '#skF_18'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3') )
| ( '#skF_24'('#skF_1','#skF_2','#skF_3','#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3'))) = '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_31221]) ).
tff(c_31433,plain,
'#skF_24'('#skF_1','#skF_2','#skF_3','#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3'))) = '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(negUnitSimplification,[status(thm)],[c_1508,c_31432]) ).
tff(c_375,plain,
! [A_204,B_205,C_206,E_207] :
( ( '#skF_18'(A_204,B_205,C_206) = '#skF_16'(A_204,B_205,C_206) )
| in('#skF_24'(A_204,B_205,C_206,E_207),cartesian_product2(A_204,A_204))
| ~ in(E_207,'#skF_23'(A_204,B_205,C_206))
| ~ function(C_206)
| ~ relation(C_206)
| ~ relation(B_205) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_88,plain,
! [B_42,A_41] :
( ~ in(B_42,A_41)
| ~ in(A_41,B_42) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_378,plain,
! [A_204,B_205,C_206,E_207] :
( ~ in(cartesian_product2(A_204,A_204),'#skF_24'(A_204,B_205,C_206,E_207))
| ( '#skF_18'(A_204,B_205,C_206) = '#skF_16'(A_204,B_205,C_206) )
| ~ in(E_207,'#skF_23'(A_204,B_205,C_206))
| ~ function(C_206)
| ~ relation(C_206)
| ~ relation(B_205) ),
inference(resolution,[status(thm)],[c_375,c_88]) ).
tff(c_31590,plain,
( ~ in(cartesian_product2('#skF_1','#skF_1'),'#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')))
| ( '#skF_18'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_31433,c_378]) ).
tff(c_31656,plain,
( ~ in(cartesian_product2('#skF_1','#skF_1'),'#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')))
| ( '#skF_18'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_31590]) ).
tff(c_31657,plain,
( ~ in(cartesian_product2('#skF_1','#skF_1'),'#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')))
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')) ),
inference(negUnitSimplification,[status(thm)],[c_1508,c_31656]) ).
tff(c_31677,plain,
~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(splitLeft,[status(thm)],[c_31657]) ).
tff(c_31750,plain,
~ in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(resolution,[status(thm)],[c_16,c_31677]) ).
tff(c_1949,plain,
! [D_20] :
( in('#skF_4'(D_20),'#skF_23'('#skF_1','#skF_2','#skF_3'))
| in('#skF_7'(D_20),D_20) ),
inference(factorization,[status(thm),theory(equality)],[c_1894]) ).
tff(c_31747,plain,
in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(resolution,[status(thm)],[c_1949,c_31677]) ).
tff(c_31931,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_31750,c_31747]) ).
tff(c_31933,plain,
in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(splitRight,[status(thm)],[c_31657]) ).
tff(c_122,plain,
! [A_45,B_46,C_47,E_127] :
( ( '#skF_18'(A_45,B_46,C_47) = '#skF_16'(A_45,B_46,C_47) )
| ( ordered_pair('#skF_25'(A_45,B_46,C_47,E_127),'#skF_26'(A_45,B_46,C_47,E_127)) = E_127 )
| ~ in(E_127,'#skF_23'(A_45,B_46,C_47))
| ~ function(C_47)
| ~ relation(C_47)
| ~ relation(B_46) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_108,plain,
! [A_45,B_46,C_47,E_127] :
( ( '#skF_18'(A_45,B_46,C_47) = '#skF_16'(A_45,B_46,C_47) )
| in(ordered_pair(apply(C_47,'#skF_25'(A_45,B_46,C_47,E_127)),apply(C_47,'#skF_26'(A_45,B_46,C_47,E_127))),B_46)
| ~ in(E_127,'#skF_23'(A_45,B_46,C_47))
| ~ function(C_47)
| ~ relation(C_47)
| ~ relation(B_46) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_150,plain,
! [A_45,B_46,C_47,E_127] :
( ( '#skF_18'(A_45,B_46,C_47) = '#skF_16'(A_45,B_46,C_47) )
| in('#skF_24'(A_45,B_46,C_47,E_127),cartesian_product2(A_45,A_45))
| ~ in(E_127,'#skF_23'(A_45,B_46,C_47))
| ~ function(C_47)
| ~ relation(C_47)
| ~ relation(B_46) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_31596,plain,
( ( '#skF_18'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3') )
| in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1'))
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_31433,c_150]) ).
tff(c_31661,plain,
( ( '#skF_18'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3') )
| in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1'))
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_31596]) ).
tff(c_31662,plain,
( in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1'))
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')) ),
inference(negUnitSimplification,[status(thm)],[c_1508,c_31661]) ).
tff(c_32111,plain,
in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_31933,c_31662]) ).
tff(c_1029,plain,
! [A_382,B_383,C_384,E_385] :
( ( '#skF_18'(A_382,B_383,C_384) = '#skF_16'(A_382,B_383,C_384) )
| in(ordered_pair(apply(C_384,'#skF_25'(A_382,B_383,C_384,E_385)),apply(C_384,'#skF_26'(A_382,B_383,C_384,E_385))),B_383)
| ~ in(E_385,'#skF_23'(A_382,B_383,C_384))
| ~ function(C_384)
| ~ relation(C_384)
| ~ relation(B_383) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_14,plain,
! [D_20,F_34,G_35] :
( in('#skF_4'(D_20),cartesian_product2('#skF_1','#skF_1'))
| ~ in(ordered_pair(apply('#skF_3',F_34),apply('#skF_3',G_35)),'#skF_2')
| ( ordered_pair(F_34,G_35) != '#skF_7'(D_20) )
| ~ in('#skF_7'(D_20),cartesian_product2('#skF_1','#skF_1')) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_1074,plain,
! [D_20,A_382,E_385] :
( in('#skF_4'(D_20),cartesian_product2('#skF_1','#skF_1'))
| ( ordered_pair('#skF_25'(A_382,'#skF_2','#skF_3',E_385),'#skF_26'(A_382,'#skF_2','#skF_3',E_385)) != '#skF_7'(D_20) )
| ~ in('#skF_7'(D_20),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_382,'#skF_2','#skF_3') = '#skF_16'(A_382,'#skF_2','#skF_3') )
| ~ in(E_385,'#skF_23'(A_382,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_1029,c_14]) ).
tff(c_6242,plain,
! [D_667,A_668,E_669] :
( in('#skF_4'(D_667),cartesian_product2('#skF_1','#skF_1'))
| ( ordered_pair('#skF_25'(A_668,'#skF_2','#skF_3',E_669),'#skF_26'(A_668,'#skF_2','#skF_3',E_669)) != '#skF_7'(D_667) )
| ~ in('#skF_7'(D_667),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_668,'#skF_2','#skF_3') = '#skF_16'(A_668,'#skF_2','#skF_3') )
| ~ in(E_669,'#skF_23'(A_668,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_1074]) ).
tff(c_6257,plain,
! [D_667,E_127,A_45] :
( in('#skF_4'(D_667),cartesian_product2('#skF_1','#skF_1'))
| ( E_127 != '#skF_7'(D_667) )
| ~ in('#skF_7'(D_667),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_122,c_6242]) ).
tff(c_6273,plain,
! [D_667,E_127,A_45] :
( in('#skF_4'(D_667),cartesian_product2('#skF_1','#skF_1'))
| ( E_127 != '#skF_7'(D_667) )
| ~ in('#skF_7'(D_667),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_6257]) ).
tff(c_6281,plain,
! [D_667,A_45] :
( in('#skF_4'(D_667),cartesian_product2('#skF_1','#skF_1'))
| ~ in('#skF_7'(D_667),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in('#skF_7'(D_667),'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_6273]) ).
tff(c_32155,plain,
! [A_45] :
( in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(resolution,[status(thm)],[c_32111,c_6281]) ).
tff(c_32430,plain,
in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1')),
inference(splitLeft,[status(thm)],[c_32155]) ).
tff(c_12,plain,
! [D_20,F_34,G_35] :
( ( ordered_pair('#skF_5'(D_20),'#skF_6'(D_20)) = '#skF_4'(D_20) )
| ~ in(ordered_pair(apply('#skF_3',F_34),apply('#skF_3',G_35)),'#skF_2')
| ( ordered_pair(F_34,G_35) != '#skF_7'(D_20) )
| ~ in('#skF_7'(D_20),cartesian_product2('#skF_1','#skF_1')) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_1071,plain,
! [D_20,A_382,E_385] :
( ( ordered_pair('#skF_5'(D_20),'#skF_6'(D_20)) = '#skF_4'(D_20) )
| ( ordered_pair('#skF_25'(A_382,'#skF_2','#skF_3',E_385),'#skF_26'(A_382,'#skF_2','#skF_3',E_385)) != '#skF_7'(D_20) )
| ~ in('#skF_7'(D_20),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_382,'#skF_2','#skF_3') = '#skF_16'(A_382,'#skF_2','#skF_3') )
| ~ in(E_385,'#skF_23'(A_382,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_1029,c_12]) ).
tff(c_8496,plain,
! [D_766,A_767,E_768] :
( ( ordered_pair('#skF_5'(D_766),'#skF_6'(D_766)) = '#skF_4'(D_766) )
| ( ordered_pair('#skF_25'(A_767,'#skF_2','#skF_3',E_768),'#skF_26'(A_767,'#skF_2','#skF_3',E_768)) != '#skF_7'(D_766) )
| ~ in('#skF_7'(D_766),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_767,'#skF_2','#skF_3') = '#skF_16'(A_767,'#skF_2','#skF_3') )
| ~ in(E_768,'#skF_23'(A_767,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_1071]) ).
tff(c_8511,plain,
! [D_766,E_127,A_45] :
( ( ordered_pair('#skF_5'(D_766),'#skF_6'(D_766)) = '#skF_4'(D_766) )
| ( E_127 != '#skF_7'(D_766) )
| ~ in('#skF_7'(D_766),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_122,c_8496]) ).
tff(c_8527,plain,
! [D_766,E_127,A_45] :
( ( ordered_pair('#skF_5'(D_766),'#skF_6'(D_766)) = '#skF_4'(D_766) )
| ( E_127 != '#skF_7'(D_766) )
| ~ in('#skF_7'(D_766),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_8511]) ).
tff(c_9640,plain,
! [D_766,A_45] :
( ( ordered_pair('#skF_5'(D_766),'#skF_6'(D_766)) = '#skF_4'(D_766) )
| ~ in('#skF_7'(D_766),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in('#skF_7'(D_766),'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_8527]) ).
tff(c_32150,plain,
! [A_45] :
( ( ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))) = '#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(resolution,[status(thm)],[c_32111,c_9640]) ).
tff(c_32639,plain,
ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))) = '#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(splitLeft,[status(thm)],[c_32150]) ).
tff(c_10,plain,
! [D_20,F_34,G_35] :
( in(ordered_pair(apply('#skF_3','#skF_5'(D_20)),apply('#skF_3','#skF_6'(D_20))),'#skF_2')
| ~ in(ordered_pair(apply('#skF_3',F_34),apply('#skF_3',G_35)),'#skF_2')
| ( ordered_pair(F_34,G_35) != '#skF_7'(D_20) )
| ~ in('#skF_7'(D_20),cartesian_product2('#skF_1','#skF_1')) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_1056,plain,
! [D_20,A_382,E_385] :
( in(ordered_pair(apply('#skF_3','#skF_5'(D_20)),apply('#skF_3','#skF_6'(D_20))),'#skF_2')
| ( ordered_pair('#skF_25'(A_382,'#skF_2','#skF_3',E_385),'#skF_26'(A_382,'#skF_2','#skF_3',E_385)) != '#skF_7'(D_20) )
| ~ in('#skF_7'(D_20),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_382,'#skF_2','#skF_3') = '#skF_16'(A_382,'#skF_2','#skF_3') )
| ~ in(E_385,'#skF_23'(A_382,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_1029,c_10]) ).
tff(c_13092,plain,
! [D_954,A_955,E_956] :
( in(ordered_pair(apply('#skF_3','#skF_5'(D_954)),apply('#skF_3','#skF_6'(D_954))),'#skF_2')
| ( ordered_pair('#skF_25'(A_955,'#skF_2','#skF_3',E_956),'#skF_26'(A_955,'#skF_2','#skF_3',E_956)) != '#skF_7'(D_954) )
| ~ in('#skF_7'(D_954),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_955,'#skF_2','#skF_3') = '#skF_16'(A_955,'#skF_2','#skF_3') )
| ~ in(E_956,'#skF_23'(A_955,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_1056]) ).
tff(c_13111,plain,
! [D_954,E_127,A_45] :
( in(ordered_pair(apply('#skF_3','#skF_5'(D_954)),apply('#skF_3','#skF_6'(D_954))),'#skF_2')
| ( E_127 != '#skF_7'(D_954) )
| ~ in('#skF_7'(D_954),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_122,c_13092]) ).
tff(c_13127,plain,
! [D_954,E_127,A_45] :
( in(ordered_pair(apply('#skF_3','#skF_5'(D_954)),apply('#skF_3','#skF_6'(D_954))),'#skF_2')
| ( E_127 != '#skF_7'(D_954) )
| ~ in('#skF_7'(D_954),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_13111]) ).
tff(c_13192,plain,
! [D_954,A_45] :
( in(ordered_pair(apply('#skF_3','#skF_5'(D_954)),apply('#skF_3','#skF_6'(D_954))),'#skF_2')
| ~ in('#skF_7'(D_954),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in('#skF_7'(D_954),'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_13127]) ).
tff(c_31986,plain,
( in(ordered_pair(apply('#skF_3','#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3'))),apply('#skF_3','#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3')))),'#skF_2')
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3') ) ),
inference(resolution,[status(thm)],[c_31933,c_13192]) ).
tff(c_32052,plain,
( in(ordered_pair(apply('#skF_3','#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3'))),apply('#skF_3','#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3')))),'#skF_2')
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_1508,c_31986]) ).
tff(c_32235,plain,
in(ordered_pair(apply('#skF_3','#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3'))),apply('#skF_3','#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3')))),'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_32111,c_32052]) ).
tff(c_164,plain,
! [C_47,A_45,K_141,B_46,L_142] :
( ( '#skF_18'(A_45,B_46,C_47) = '#skF_16'(A_45,B_46,C_47) )
| in(ordered_pair(K_141,L_142),'#skF_23'(A_45,B_46,C_47))
| ~ in(ordered_pair(apply(C_47,K_141),apply(C_47,L_142)),B_46)
| ~ in(ordered_pair(K_141,L_142),cartesian_product2(A_45,A_45))
| ~ function(C_47)
| ~ relation(C_47)
| ~ relation(B_46) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_32248,plain,
! [A_45] :
( ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| in(ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))),'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ in(ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))),cartesian_product2(A_45,A_45))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_32235,c_164]) ).
tff(c_32276,plain,
! [A_45] :
( ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| in(ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))),'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ in(ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))),cartesian_product2(A_45,A_45)) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_32248]) ).
tff(c_48768,plain,
! [A_2029] :
( ( '#skF_18'(A_2029,'#skF_2','#skF_3') = '#skF_16'(A_2029,'#skF_2','#skF_3') )
| in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'(A_2029,'#skF_2','#skF_3'))
| ~ in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2(A_2029,A_2029)) ),
inference(demodulation,[status(thm),theory(equality)],[c_32639,c_32639,c_32276]) ).
tff(c_48771,plain,
( ( '#skF_18'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3') )
| in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')) ),
inference(resolution,[status(thm)],[c_32430,c_48768]) ).
tff(c_48876,plain,
in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(negUnitSimplification,[status(thm)],[c_1508,c_48771]) ).
tff(c_8,plain,
! [D_20,F_34,G_35] :
( ~ in('#skF_4'(D_20),D_20)
| ~ in(ordered_pair(apply('#skF_3',F_34),apply('#skF_3',G_35)),'#skF_2')
| ( ordered_pair(F_34,G_35) != '#skF_7'(D_20) )
| ~ in('#skF_7'(D_20),cartesian_product2('#skF_1','#skF_1')) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_49110,plain,
! [F_34,G_35] :
( ~ in(ordered_pair(apply('#skF_3',F_34),apply('#skF_3',G_35)),'#skF_2')
| ( ordered_pair(F_34,G_35) != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1')) ),
inference(resolution,[status(thm)],[c_48876,c_8]) ).
tff(c_50030,plain,
! [F_2035,G_2036] :
( ~ in(ordered_pair(apply('#skF_3',F_2035),apply('#skF_3',G_2036)),'#skF_2')
| ( ordered_pair(F_2035,G_2036) != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_32111,c_49110]) ).
tff(c_50192,plain,
! [A_45,E_127] :
( ( ordered_pair('#skF_25'(A_45,'#skF_2','#skF_3',E_127),'#skF_26'(A_45,'#skF_2','#skF_3',E_127)) != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_108,c_50030]) ).
tff(c_53587,plain,
! [A_2114,E_2115] :
( ( ordered_pair('#skF_25'(A_2114,'#skF_2','#skF_3',E_2115),'#skF_26'(A_2114,'#skF_2','#skF_3',E_2115)) != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ( '#skF_18'(A_2114,'#skF_2','#skF_3') = '#skF_16'(A_2114,'#skF_2','#skF_3') )
| ~ in(E_2115,'#skF_23'(A_2114,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_50192]) ).
tff(c_53613,plain,
! [E_127,A_45] :
( ( E_127 != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_122,c_53587]) ).
tff(c_53637,plain,
! [E_2116,A_2117] :
( ( E_2116 != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ( '#skF_18'(A_2117,'#skF_2','#skF_3') = '#skF_16'(A_2117,'#skF_2','#skF_3') )
| ~ in(E_2116,'#skF_23'(A_2117,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_53613]) ).
tff(c_53696,plain,
'#skF_18'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3'),
inference(resolution,[status(thm)],[c_31933,c_53637]) ).
tff(c_54007,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1508,c_53696]) ).
tff(c_54028,plain,
! [A_2120] :
( ( '#skF_18'(A_2120,'#skF_2','#skF_3') = '#skF_16'(A_2120,'#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'(A_2120,'#skF_2','#skF_3')) ),
inference(splitRight,[status(thm)],[c_32150]) ).
tff(c_54031,plain,
'#skF_18'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3'),
inference(resolution,[status(thm)],[c_31933,c_54028]) ).
tff(c_54083,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1508,c_54031]) ).
tff(c_54225,plain,
! [A_2121] :
( ( '#skF_18'(A_2121,'#skF_2','#skF_3') = '#skF_16'(A_2121,'#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'(A_2121,'#skF_2','#skF_3')) ),
inference(splitRight,[status(thm)],[c_32155]) ).
tff(c_54228,plain,
'#skF_18'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3'),
inference(resolution,[status(thm)],[c_31933,c_54225]) ).
tff(c_54280,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1508,c_54228]) ).
tff(c_54282,plain,
'#skF_17'('#skF_1','#skF_2','#skF_3') != '#skF_16'('#skF_1','#skF_2','#skF_3'),
inference(splitRight,[status(thm)],[c_1505]) ).
tff(c_54304,plain,
! [D_2127] :
( in(ordered_pair('#skF_5'(D_2127),'#skF_6'(D_2127)),'#skF_23'('#skF_1','#skF_2','#skF_3'))
| in('#skF_7'(D_2127),D_2127) ),
inference(splitRight,[status(thm)],[c_1505]) ).
tff(c_54339,plain,
! [D_20] :
( in('#skF_4'(D_20),'#skF_23'('#skF_1','#skF_2','#skF_3'))
| in('#skF_7'(D_20),D_20)
| in('#skF_7'(D_20),D_20) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_54304]) ).
tff(c_54515,plain,
! [D_2131] :
( in('#skF_4'(D_2131),'#skF_23'('#skF_1','#skF_2','#skF_3'))
| in('#skF_7'(D_2131),D_2131) ),
inference(factorization,[status(thm),theory(equality)],[c_54339]) ).
tff(c_142,plain,
! [A_45,B_46,C_47,E_127] :
( ( '#skF_17'(A_45,B_46,C_47) = '#skF_16'(A_45,B_46,C_47) )
| ( '#skF_24'(A_45,B_46,C_47,E_127) = E_127 )
| ~ in(E_127,'#skF_23'(A_45,B_46,C_47))
| ~ function(C_47)
| ~ relation(C_47)
| ~ relation(B_46) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_82632,plain,
! [A_3199,B_3200,C_3201] :
( ( '#skF_17'(A_3199,B_3200,C_3201) = '#skF_16'(A_3199,B_3200,C_3201) )
| ( '#skF_24'(A_3199,B_3200,C_3201,'#skF_7'('#skF_23'(A_3199,B_3200,C_3201))) = '#skF_7'('#skF_23'(A_3199,B_3200,C_3201)) )
| ~ function(C_3201)
| ~ relation(C_3201)
| ~ relation(B_3200)
| in('#skF_4'('#skF_23'(A_3199,B_3200,C_3201)),'#skF_23'('#skF_1','#skF_2','#skF_3')) ),
inference(resolution,[status(thm)],[c_54515,c_142]) ).
tff(c_351,plain,
! [A_192,B_193,C_194,E_195] :
( ( '#skF_17'(A_192,B_193,C_194) = '#skF_16'(A_192,B_193,C_194) )
| ( '#skF_24'(A_192,B_193,C_194,E_195) = E_195 )
| ~ in(E_195,'#skF_23'(A_192,B_193,C_194))
| ~ function(C_194)
| ~ relation(C_194)
| ~ relation(B_193) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_366,plain,
! [A_192,B_193,C_194] :
( ( '#skF_17'(A_192,B_193,C_194) = '#skF_16'(A_192,B_193,C_194) )
| ( '#skF_24'(A_192,B_193,C_194,'#skF_7'('#skF_23'(A_192,B_193,C_194))) = '#skF_7'('#skF_23'(A_192,B_193,C_194)) )
| ~ function(C_194)
| ~ relation(C_194)
| ~ relation(B_193)
| ~ in('#skF_4'('#skF_23'(A_192,B_193,C_194)),'#skF_23'(A_192,B_193,C_194)) ),
inference(resolution,[status(thm)],[c_16,c_351]) ).
tff(c_82824,plain,
( ( '#skF_17'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3') )
| ( '#skF_24'('#skF_1','#skF_2','#skF_3','#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3'))) = '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_82632,c_366]) ).
tff(c_83022,plain,
( ( '#skF_17'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3') )
| ( '#skF_24'('#skF_1','#skF_2','#skF_3','#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3'))) = '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_82824]) ).
tff(c_83023,plain,
'#skF_24'('#skF_1','#skF_2','#skF_3','#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3'))) = '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(negUnitSimplification,[status(thm)],[c_54282,c_83022]) ).
tff(c_371,plain,
! [A_200,B_201,C_202,E_203] :
( ( '#skF_17'(A_200,B_201,C_202) = '#skF_16'(A_200,B_201,C_202) )
| in('#skF_24'(A_200,B_201,C_202,E_203),cartesian_product2(A_200,A_200))
| ~ in(E_203,'#skF_23'(A_200,B_201,C_202))
| ~ function(C_202)
| ~ relation(C_202)
| ~ relation(B_201) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_374,plain,
! [A_200,B_201,C_202,E_203] :
( ~ in(cartesian_product2(A_200,A_200),'#skF_24'(A_200,B_201,C_202,E_203))
| ( '#skF_17'(A_200,B_201,C_202) = '#skF_16'(A_200,B_201,C_202) )
| ~ in(E_203,'#skF_23'(A_200,B_201,C_202))
| ~ function(C_202)
| ~ relation(C_202)
| ~ relation(B_201) ),
inference(resolution,[status(thm)],[c_371,c_88]) ).
tff(c_83174,plain,
( ~ in(cartesian_product2('#skF_1','#skF_1'),'#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')))
| ( '#skF_17'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_83023,c_374]) ).
tff(c_83239,plain,
( ~ in(cartesian_product2('#skF_1','#skF_1'),'#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')))
| ( '#skF_17'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_83174]) ).
tff(c_83240,plain,
( ~ in(cartesian_product2('#skF_1','#skF_1'),'#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')))
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')) ),
inference(negUnitSimplification,[status(thm)],[c_54282,c_83239]) ).
tff(c_83262,plain,
~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(splitLeft,[status(thm)],[c_83240]) ).
tff(c_83335,plain,
~ in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(resolution,[status(thm)],[c_16,c_83262]) ).
tff(c_54391,plain,
! [D_20] :
( in('#skF_4'(D_20),'#skF_23'('#skF_1','#skF_2','#skF_3'))
| in('#skF_7'(D_20),D_20) ),
inference(factorization,[status(thm),theory(equality)],[c_54339]) ).
tff(c_83332,plain,
in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(resolution,[status(thm)],[c_54391,c_83262]) ).
tff(c_83498,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_83335,c_83332]) ).
tff(c_83500,plain,
in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(splitRight,[status(thm)],[c_83240]) ).
tff(c_128,plain,
! [A_45,B_46,C_47,E_127] :
( ( '#skF_17'(A_45,B_46,C_47) = '#skF_16'(A_45,B_46,C_47) )
| ( ordered_pair('#skF_25'(A_45,B_46,C_47,E_127),'#skF_26'(A_45,B_46,C_47,E_127)) = E_127 )
| ~ in(E_127,'#skF_23'(A_45,B_46,C_47))
| ~ function(C_47)
| ~ relation(C_47)
| ~ relation(B_46) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_114,plain,
! [A_45,B_46,C_47,E_127] :
( ( '#skF_17'(A_45,B_46,C_47) = '#skF_16'(A_45,B_46,C_47) )
| in(ordered_pair(apply(C_47,'#skF_25'(A_45,B_46,C_47,E_127)),apply(C_47,'#skF_26'(A_45,B_46,C_47,E_127))),B_46)
| ~ in(E_127,'#skF_23'(A_45,B_46,C_47))
| ~ function(C_47)
| ~ relation(C_47)
| ~ relation(B_46) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_156,plain,
! [A_45,B_46,C_47,E_127] :
( ( '#skF_17'(A_45,B_46,C_47) = '#skF_16'(A_45,B_46,C_47) )
| in('#skF_24'(A_45,B_46,C_47,E_127),cartesian_product2(A_45,A_45))
| ~ in(E_127,'#skF_23'(A_45,B_46,C_47))
| ~ function(C_47)
| ~ relation(C_47)
| ~ relation(B_46) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_83186,plain,
( ( '#skF_17'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3') )
| in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1'))
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_83023,c_156]) ).
tff(c_83248,plain,
( ( '#skF_17'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3') )
| in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1'))
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_83186]) ).
tff(c_83249,plain,
( in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1'))
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')) ),
inference(negUnitSimplification,[status(thm)],[c_54282,c_83248]) ).
tff(c_83670,plain,
in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_83500,c_83249]) ).
tff(c_60049,plain,
! [D_2417,A_2418,E_2419] :
( in('#skF_4'(D_2417),cartesian_product2('#skF_1','#skF_1'))
| ( ordered_pair('#skF_25'(A_2418,'#skF_2','#skF_3',E_2419),'#skF_26'(A_2418,'#skF_2','#skF_3',E_2419)) != '#skF_7'(D_2417) )
| ~ in('#skF_7'(D_2417),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_2418,'#skF_2','#skF_3') = '#skF_16'(A_2418,'#skF_2','#skF_3') )
| ~ in(E_2419,'#skF_23'(A_2418,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_1074]) ).
tff(c_60064,plain,
! [D_2417,E_127,A_45] :
( in('#skF_4'(D_2417),cartesian_product2('#skF_1','#skF_1'))
| ( E_127 != '#skF_7'(D_2417) )
| ~ in('#skF_7'(D_2417),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_122,c_60049]) ).
tff(c_60080,plain,
! [D_2417,E_127,A_45] :
( in('#skF_4'(D_2417),cartesian_product2('#skF_1','#skF_1'))
| ( E_127 != '#skF_7'(D_2417) )
| ~ in('#skF_7'(D_2417),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_60064]) ).
tff(c_61130,plain,
! [D_2417,A_45] :
( in('#skF_4'(D_2417),cartesian_product2('#skF_1','#skF_1'))
| ~ in('#skF_7'(D_2417),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in('#skF_7'(D_2417),'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_60080]) ).
tff(c_83712,plain,
! [A_45] :
( in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(resolution,[status(thm)],[c_83670,c_61130]) ).
tff(c_83994,plain,
in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1')),
inference(splitLeft,[status(thm)],[c_83712]) ).
tff(c_961,plain,
! [A_378,B_379,C_380,E_381] :
( ( '#skF_17'(A_378,B_379,C_380) = '#skF_16'(A_378,B_379,C_380) )
| in(ordered_pair(apply(C_380,'#skF_25'(A_378,B_379,C_380,E_381)),apply(C_380,'#skF_26'(A_378,B_379,C_380,E_381))),B_379)
| ~ in(E_381,'#skF_23'(A_378,B_379,C_380))
| ~ function(C_380)
| ~ relation(C_380)
| ~ relation(B_379) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_1003,plain,
! [D_20,A_378,E_381] :
( ( ordered_pair('#skF_5'(D_20),'#skF_6'(D_20)) = '#skF_4'(D_20) )
| ( ordered_pair('#skF_25'(A_378,'#skF_2','#skF_3',E_381),'#skF_26'(A_378,'#skF_2','#skF_3',E_381)) != '#skF_7'(D_20) )
| ~ in('#skF_7'(D_20),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_378,'#skF_2','#skF_3') = '#skF_16'(A_378,'#skF_2','#skF_3') )
| ~ in(E_381,'#skF_23'(A_378,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_961,c_12]) ).
tff(c_61005,plain,
! [D_2454,A_2455,E_2456] :
( ( ordered_pair('#skF_5'(D_2454),'#skF_6'(D_2454)) = '#skF_4'(D_2454) )
| ( ordered_pair('#skF_25'(A_2455,'#skF_2','#skF_3',E_2456),'#skF_26'(A_2455,'#skF_2','#skF_3',E_2456)) != '#skF_7'(D_2454) )
| ~ in('#skF_7'(D_2454),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_2455,'#skF_2','#skF_3') = '#skF_16'(A_2455,'#skF_2','#skF_3') )
| ~ in(E_2456,'#skF_23'(A_2455,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_1003]) ).
tff(c_61023,plain,
! [D_2454,E_127,A_45] :
( ( ordered_pair('#skF_5'(D_2454),'#skF_6'(D_2454)) = '#skF_4'(D_2454) )
| ( E_127 != '#skF_7'(D_2454) )
| ~ in('#skF_7'(D_2454),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_128,c_61005]) ).
tff(c_61038,plain,
! [D_2454,E_127,A_45] :
( ( ordered_pair('#skF_5'(D_2454),'#skF_6'(D_2454)) = '#skF_4'(D_2454) )
| ( E_127 != '#skF_7'(D_2454) )
| ~ in('#skF_7'(D_2454),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_61023]) ).
tff(c_62975,plain,
! [D_2454,A_45] :
( ( ordered_pair('#skF_5'(D_2454),'#skF_6'(D_2454)) = '#skF_4'(D_2454) )
| ~ in('#skF_7'(D_2454),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in('#skF_7'(D_2454),'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_61038]) ).
tff(c_83710,plain,
! [A_45] :
( ( ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))) = '#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(resolution,[status(thm)],[c_83670,c_62975]) ).
tff(c_84174,plain,
ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))) = '#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(splitLeft,[status(thm)],[c_83710]) ).
tff(c_988,plain,
! [D_20,A_378,E_381] :
( in(ordered_pair(apply('#skF_3','#skF_5'(D_20)),apply('#skF_3','#skF_6'(D_20))),'#skF_2')
| ( ordered_pair('#skF_25'(A_378,'#skF_2','#skF_3',E_381),'#skF_26'(A_378,'#skF_2','#skF_3',E_381)) != '#skF_7'(D_20) )
| ~ in('#skF_7'(D_20),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_378,'#skF_2','#skF_3') = '#skF_16'(A_378,'#skF_2','#skF_3') )
| ~ in(E_381,'#skF_23'(A_378,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_961,c_10]) ).
tff(c_64659,plain,
! [D_2607,A_2608,E_2609] :
( in(ordered_pair(apply('#skF_3','#skF_5'(D_2607)),apply('#skF_3','#skF_6'(D_2607))),'#skF_2')
| ( ordered_pair('#skF_25'(A_2608,'#skF_2','#skF_3',E_2609),'#skF_26'(A_2608,'#skF_2','#skF_3',E_2609)) != '#skF_7'(D_2607) )
| ~ in('#skF_7'(D_2607),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_2608,'#skF_2','#skF_3') = '#skF_16'(A_2608,'#skF_2','#skF_3') )
| ~ in(E_2609,'#skF_23'(A_2608,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_988]) ).
tff(c_64681,plain,
! [D_2607,E_127,A_45] :
( in(ordered_pair(apply('#skF_3','#skF_5'(D_2607)),apply('#skF_3','#skF_6'(D_2607))),'#skF_2')
| ( E_127 != '#skF_7'(D_2607) )
| ~ in('#skF_7'(D_2607),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_128,c_64659]) ).
tff(c_64696,plain,
! [D_2607,E_127,A_45] :
( in(ordered_pair(apply('#skF_3','#skF_5'(D_2607)),apply('#skF_3','#skF_6'(D_2607))),'#skF_2')
| ( E_127 != '#skF_7'(D_2607) )
| ~ in('#skF_7'(D_2607),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_64681]) ).
tff(c_64702,plain,
! [D_2607,A_45] :
( in(ordered_pair(apply('#skF_3','#skF_5'(D_2607)),apply('#skF_3','#skF_6'(D_2607))),'#skF_2')
| ~ in('#skF_7'(D_2607),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in('#skF_7'(D_2607),'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_64696]) ).
tff(c_83559,plain,
( in(ordered_pair(apply('#skF_3','#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3'))),apply('#skF_3','#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3')))),'#skF_2')
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3') ) ),
inference(resolution,[status(thm)],[c_83500,c_64702]) ).
tff(c_83619,plain,
( in(ordered_pair(apply('#skF_3','#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3'))),apply('#skF_3','#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3')))),'#skF_2')
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_54282,c_83559]) ).
tff(c_83795,plain,
in(ordered_pair(apply('#skF_3','#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3'))),apply('#skF_3','#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3')))),'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_83670,c_83619]) ).
tff(c_83808,plain,
! [A_45] :
( ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| in(ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))),'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ in(ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))),cartesian_product2(A_45,A_45))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_83795,c_164]) ).
tff(c_83836,plain,
! [A_45] :
( ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| in(ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))),'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ in(ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))),cartesian_product2(A_45,A_45)) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_83808]) ).
tff(c_101032,plain,
! [A_3715] :
( ( '#skF_18'(A_3715,'#skF_2','#skF_3') = '#skF_16'(A_3715,'#skF_2','#skF_3') )
| in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'(A_3715,'#skF_2','#skF_3'))
| ~ in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2(A_3715,A_3715)) ),
inference(demodulation,[status(thm),theory(equality)],[c_84174,c_84174,c_83836]) ).
tff(c_101138,plain,
( ( '#skF_18'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3') )
| in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')) ),
inference(resolution,[status(thm)],[c_83994,c_101032]) ).
tff(c_101238,plain,
in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(splitLeft,[status(thm)],[c_101138]) ).
tff(c_101387,plain,
! [F_34,G_35] :
( ~ in(ordered_pair(apply('#skF_3',F_34),apply('#skF_3',G_35)),'#skF_2')
| ( ordered_pair(F_34,G_35) != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1')) ),
inference(resolution,[status(thm)],[c_101238,c_8]) ).
tff(c_102249,plain,
! [F_3718,G_3719] :
( ~ in(ordered_pair(apply('#skF_3',F_3718),apply('#skF_3',G_3719)),'#skF_2')
| ( ordered_pair(F_3718,G_3719) != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_83670,c_101387]) ).
tff(c_102415,plain,
! [A_45,E_127] :
( ( ordered_pair('#skF_25'(A_45,'#skF_2','#skF_3',E_127),'#skF_26'(A_45,'#skF_2','#skF_3',E_127)) != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_114,c_102249]) ).
tff(c_105266,plain,
! [A_3799,E_3800] :
( ( ordered_pair('#skF_25'(A_3799,'#skF_2','#skF_3',E_3800),'#skF_26'(A_3799,'#skF_2','#skF_3',E_3800)) != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ( '#skF_17'(A_3799,'#skF_2','#skF_3') = '#skF_16'(A_3799,'#skF_2','#skF_3') )
| ~ in(E_3800,'#skF_23'(A_3799,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_102415]) ).
tff(c_105296,plain,
! [E_127,A_45] :
( ( E_127 != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_128,c_105266]) ).
tff(c_105316,plain,
! [E_3801,A_3802] :
( ( E_3801 != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ( '#skF_17'(A_3802,'#skF_2','#skF_3') = '#skF_16'(A_3802,'#skF_2','#skF_3') )
| ~ in(E_3801,'#skF_23'(A_3802,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_105296]) ).
tff(c_105381,plain,
'#skF_17'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3'),
inference(resolution,[status(thm)],[c_83500,c_105316]) ).
tff(c_105693,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_54282,c_105381]) ).
tff(c_105695,plain,
~ in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(splitRight,[status(thm)],[c_101138]) ).
tff(c_170,plain,
! [C_47,A_45,K_141,B_46,L_142] :
( ( '#skF_17'(A_45,B_46,C_47) = '#skF_16'(A_45,B_46,C_47) )
| in(ordered_pair(K_141,L_142),'#skF_23'(A_45,B_46,C_47))
| ~ in(ordered_pair(apply(C_47,K_141),apply(C_47,L_142)),B_46)
| ~ in(ordered_pair(K_141,L_142),cartesian_product2(A_45,A_45))
| ~ function(C_47)
| ~ relation(C_47)
| ~ relation(B_46) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_83810,plain,
! [A_45] :
( ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| in(ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))),'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ in(ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))),cartesian_product2(A_45,A_45))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_83795,c_170]) ).
tff(c_83839,plain,
! [A_45] :
( ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| in(ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))),'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ in(ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))),cartesian_product2(A_45,A_45)) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_83810]) ).
tff(c_106355,plain,
! [A_3815] :
( ( '#skF_17'(A_3815,'#skF_2','#skF_3') = '#skF_16'(A_3815,'#skF_2','#skF_3') )
| in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'(A_3815,'#skF_2','#skF_3'))
| ~ in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2(A_3815,A_3815)) ),
inference(demodulation,[status(thm),theory(equality)],[c_84174,c_84174,c_83839]) ).
tff(c_106358,plain,
( ( '#skF_17'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3') )
| in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')) ),
inference(resolution,[status(thm)],[c_83994,c_106355]) ).
tff(c_106464,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_105695,c_54282,c_106358]) ).
tff(c_106484,plain,
! [A_3816] :
( ( '#skF_17'(A_3816,'#skF_2','#skF_3') = '#skF_16'(A_3816,'#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'(A_3816,'#skF_2','#skF_3')) ),
inference(splitRight,[status(thm)],[c_83710]) ).
tff(c_106487,plain,
'#skF_17'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3'),
inference(resolution,[status(thm)],[c_83500,c_106484]) ).
tff(c_106539,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_54282,c_106487]) ).
tff(c_106541,plain,
~ in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1')),
inference(splitRight,[status(thm)],[c_83712]) ).
tff(c_1006,plain,
! [D_20,A_378,E_381] :
( in('#skF_4'(D_20),cartesian_product2('#skF_1','#skF_1'))
| ( ordered_pair('#skF_25'(A_378,'#skF_2','#skF_3',E_381),'#skF_26'(A_378,'#skF_2','#skF_3',E_381)) != '#skF_7'(D_20) )
| ~ in('#skF_7'(D_20),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_378,'#skF_2','#skF_3') = '#skF_16'(A_378,'#skF_2','#skF_3') )
| ~ in(E_381,'#skF_23'(A_378,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_961,c_14]) ).
tff(c_59796,plain,
! [D_2406,A_2407,E_2408] :
( in('#skF_4'(D_2406),cartesian_product2('#skF_1','#skF_1'))
| ( ordered_pair('#skF_25'(A_2407,'#skF_2','#skF_3',E_2408),'#skF_26'(A_2407,'#skF_2','#skF_3',E_2408)) != '#skF_7'(D_2406) )
| ~ in('#skF_7'(D_2406),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_2407,'#skF_2','#skF_3') = '#skF_16'(A_2407,'#skF_2','#skF_3') )
| ~ in(E_2408,'#skF_23'(A_2407,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_1006]) ).
tff(c_59814,plain,
! [D_2406,E_127,A_45] :
( in('#skF_4'(D_2406),cartesian_product2('#skF_1','#skF_1'))
| ( E_127 != '#skF_7'(D_2406) )
| ~ in('#skF_7'(D_2406),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_128,c_59796]) ).
tff(c_59829,plain,
! [D_2406,E_127,A_45] :
( in('#skF_4'(D_2406),cartesian_product2('#skF_1','#skF_1'))
| ( E_127 != '#skF_7'(D_2406) )
| ~ in('#skF_7'(D_2406),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_59814]) ).
tff(c_59835,plain,
! [D_2406,A_45] :
( in('#skF_4'(D_2406),cartesian_product2('#skF_1','#skF_1'))
| ~ in('#skF_7'(D_2406),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in('#skF_7'(D_2406),'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_59829]) ).
tff(c_83713,plain,
! [A_45] :
( in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(resolution,[status(thm)],[c_83670,c_59835]) ).
tff(c_106817,plain,
! [A_3828] :
( ( '#skF_17'(A_3828,'#skF_2','#skF_3') = '#skF_16'(A_3828,'#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'(A_3828,'#skF_2','#skF_3')) ),
inference(negUnitSimplification,[status(thm)],[c_106541,c_83713]) ).
tff(c_106820,plain,
'#skF_17'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3'),
inference(resolution,[status(thm)],[c_83500,c_106817]) ).
tff(c_106872,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_54282,c_106820]) ).
tff(c_106880,plain,
! [D_3832] :
( in(ordered_pair('#skF_5'(D_3832),'#skF_6'(D_3832)),'#skF_23'('#skF_1','#skF_2','#skF_3'))
| in('#skF_7'(D_3832),D_3832) ),
inference(splitRight,[status(thm)],[c_1440]) ).
tff(c_106915,plain,
! [D_20] :
( in('#skF_4'(D_20),'#skF_23'('#skF_1','#skF_2','#skF_3'))
| in('#skF_7'(D_20),D_20)
| in('#skF_7'(D_20),D_20) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_106880]) ).
tff(c_106965,plain,
! [D_20] :
( in('#skF_4'(D_20),'#skF_23'('#skF_1','#skF_2','#skF_3'))
| in('#skF_7'(D_20),D_20) ),
inference(factorization,[status(thm),theory(equality)],[c_106915]) ).
tff(c_106874,plain,
'#skF_17'('#skF_1','#skF_2','#skF_3') = '#skF_18'('#skF_1','#skF_2','#skF_3'),
inference(splitRight,[status(thm)],[c_1440]) ).
tff(c_107086,plain,
! [D_3835] :
( in('#skF_4'(D_3835),'#skF_23'('#skF_1','#skF_2','#skF_3'))
| in('#skF_7'(D_3835),D_3835) ),
inference(factorization,[status(thm),theory(equality)],[c_106915]) ).
tff(c_135395,plain,
! [A_4925,B_4926,C_4927] :
( ( '#skF_17'(A_4925,B_4926,C_4927) = '#skF_16'(A_4925,B_4926,C_4927) )
| ( '#skF_24'(A_4925,B_4926,C_4927,'#skF_7'('#skF_23'(A_4925,B_4926,C_4927))) = '#skF_7'('#skF_23'(A_4925,B_4926,C_4927)) )
| ~ function(C_4927)
| ~ relation(C_4927)
| ~ relation(B_4926)
| in('#skF_4'('#skF_23'(A_4925,B_4926,C_4927)),'#skF_23'('#skF_1','#skF_2','#skF_3')) ),
inference(resolution,[status(thm)],[c_107086,c_142]) ).
tff(c_335,plain,
! [A_188,B_189,C_190,E_191] :
( ( '#skF_17'(A_188,B_189,C_190) != '#skF_18'(A_188,B_189,C_190) )
| ( '#skF_24'(A_188,B_189,C_190,E_191) = E_191 )
| ~ in(E_191,'#skF_23'(A_188,B_189,C_190))
| ~ function(C_190)
| ~ relation(C_190)
| ~ relation(B_189) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_350,plain,
! [A_188,B_189,C_190] :
( ( '#skF_17'(A_188,B_189,C_190) != '#skF_18'(A_188,B_189,C_190) )
| ( '#skF_24'(A_188,B_189,C_190,'#skF_7'('#skF_23'(A_188,B_189,C_190))) = '#skF_7'('#skF_23'(A_188,B_189,C_190)) )
| ~ function(C_190)
| ~ relation(C_190)
| ~ relation(B_189)
| ~ in('#skF_4'('#skF_23'(A_188,B_189,C_190)),'#skF_23'(A_188,B_189,C_190)) ),
inference(resolution,[status(thm)],[c_16,c_335]) ).
tff(c_135587,plain,
( ( '#skF_17'('#skF_1','#skF_2','#skF_3') != '#skF_18'('#skF_1','#skF_2','#skF_3') )
| ( '#skF_17'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3') )
| ( '#skF_24'('#skF_1','#skF_2','#skF_3','#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3'))) = '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_135395,c_350]) ).
tff(c_135778,plain,
( ( '#skF_18'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3') )
| ( '#skF_24'('#skF_1','#skF_2','#skF_3','#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3'))) = '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_106874,c_106874,c_135587]) ).
tff(c_135895,plain,
'#skF_24'('#skF_1','#skF_2','#skF_3','#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3'))) = '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(splitLeft,[status(thm)],[c_135778]) ).
tff(c_367,plain,
! [A_196,B_197,C_198,E_199] :
( ( '#skF_17'(A_196,B_197,C_198) != '#skF_18'(A_196,B_197,C_198) )
| in('#skF_24'(A_196,B_197,C_198,E_199),cartesian_product2(A_196,A_196))
| ~ in(E_199,'#skF_23'(A_196,B_197,C_198))
| ~ function(C_198)
| ~ relation(C_198)
| ~ relation(B_197) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_370,plain,
! [A_196,B_197,C_198,E_199] :
( ~ in(cartesian_product2(A_196,A_196),'#skF_24'(A_196,B_197,C_198,E_199))
| ( '#skF_17'(A_196,B_197,C_198) != '#skF_18'(A_196,B_197,C_198) )
| ~ in(E_199,'#skF_23'(A_196,B_197,C_198))
| ~ function(C_198)
| ~ relation(C_198)
| ~ relation(B_197) ),
inference(resolution,[status(thm)],[c_367,c_88]) ).
tff(c_135962,plain,
( ~ in(cartesian_product2('#skF_1','#skF_1'),'#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')))
| ( '#skF_17'('#skF_1','#skF_2','#skF_3') != '#skF_18'('#skF_1','#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_135895,c_370]) ).
tff(c_136025,plain,
( ~ in(cartesian_product2('#skF_1','#skF_1'),'#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')))
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_106874,c_135962]) ).
tff(c_136042,plain,
~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(splitLeft,[status(thm)],[c_136025]) ).
tff(c_136112,plain,
in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(resolution,[status(thm)],[c_106965,c_136042]) ).
tff(c_136115,plain,
~ in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(resolution,[status(thm)],[c_16,c_136042]) ).
tff(c_136442,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_136112,c_136115]) ).
tff(c_136444,plain,
in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(splitRight,[status(thm)],[c_136025]) ).
tff(c_144,plain,
! [A_45,B_46,C_47,E_127] :
( ( '#skF_17'(A_45,B_46,C_47) != '#skF_18'(A_45,B_46,C_47) )
| in('#skF_24'(A_45,B_46,C_47,E_127),cartesian_product2(A_45,A_45))
| ~ in(E_127,'#skF_23'(A_45,B_46,C_47))
| ~ function(C_47)
| ~ relation(C_47)
| ~ relation(B_46) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_135971,plain,
( ( '#skF_17'('#skF_1','#skF_2','#skF_3') != '#skF_18'('#skF_1','#skF_2','#skF_3') )
| in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1'))
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_135895,c_144]) ).
tff(c_136031,plain,
( in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1'))
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_106874,c_135971]) ).
tff(c_136619,plain,
in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_136444,c_136031]) ).
tff(c_112733,plain,
! [D_4134,A_4135,E_4136] :
( in('#skF_4'(D_4134),cartesian_product2('#skF_1','#skF_1'))
| ( ordered_pair('#skF_25'(A_4135,'#skF_2','#skF_3',E_4136),'#skF_26'(A_4135,'#skF_2','#skF_3',E_4136)) != '#skF_7'(D_4134) )
| ~ in('#skF_7'(D_4134),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_4135,'#skF_2','#skF_3') = '#skF_16'(A_4135,'#skF_2','#skF_3') )
| ~ in(E_4136,'#skF_23'(A_4135,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_1074]) ).
tff(c_112748,plain,
! [D_4134,E_127,A_45] :
( in('#skF_4'(D_4134),cartesian_product2('#skF_1','#skF_1'))
| ( E_127 != '#skF_7'(D_4134) )
| ~ in('#skF_7'(D_4134),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_122,c_112733]) ).
tff(c_112764,plain,
! [D_4134,E_127,A_45] :
( in('#skF_4'(D_4134),cartesian_product2('#skF_1','#skF_1'))
| ( E_127 != '#skF_7'(D_4134) )
| ~ in('#skF_7'(D_4134),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_112748]) ).
tff(c_112774,plain,
! [D_4134,A_45] :
( in('#skF_4'(D_4134),cartesian_product2('#skF_1','#skF_1'))
| ~ in('#skF_7'(D_4134),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in('#skF_7'(D_4134),'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_112764]) ).
tff(c_136663,plain,
! [A_45] :
( in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(resolution,[status(thm)],[c_136619,c_112774]) ).
tff(c_136943,plain,
in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1')),
inference(splitLeft,[status(thm)],[c_136663]) ).
tff(c_114517,plain,
! [D_4221,A_4222,E_4223] :
( ( ordered_pair('#skF_5'(D_4221),'#skF_6'(D_4221)) = '#skF_4'(D_4221) )
| ( ordered_pair('#skF_25'(A_4222,'#skF_2','#skF_3',E_4223),'#skF_26'(A_4222,'#skF_2','#skF_3',E_4223)) != '#skF_7'(D_4221) )
| ~ in('#skF_7'(D_4221),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_4222,'#skF_2','#skF_3') = '#skF_16'(A_4222,'#skF_2','#skF_3') )
| ~ in(E_4223,'#skF_23'(A_4222,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_1071]) ).
tff(c_114532,plain,
! [D_4221,E_127,A_45] :
( ( ordered_pair('#skF_5'(D_4221),'#skF_6'(D_4221)) = '#skF_4'(D_4221) )
| ( E_127 != '#skF_7'(D_4221) )
| ~ in('#skF_7'(D_4221),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_122,c_114517]) ).
tff(c_114548,plain,
! [D_4221,E_127,A_45] :
( ( ordered_pair('#skF_5'(D_4221),'#skF_6'(D_4221)) = '#skF_4'(D_4221) )
| ( E_127 != '#skF_7'(D_4221) )
| ~ in('#skF_7'(D_4221),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_114532]) ).
tff(c_116087,plain,
! [D_4221,A_45] :
( ( ordered_pair('#skF_5'(D_4221),'#skF_6'(D_4221)) = '#skF_4'(D_4221) )
| ~ in('#skF_7'(D_4221),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in('#skF_7'(D_4221),'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_114548]) ).
tff(c_136660,plain,
! [A_45] :
( ( ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))) = '#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ( '#skF_18'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(resolution,[status(thm)],[c_136619,c_116087]) ).
tff(c_137129,plain,
ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))) = '#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(splitLeft,[status(thm)],[c_136660]) ).
tff(c_116,plain,
! [A_45,B_46,C_47,E_127] :
( ( '#skF_17'(A_45,B_46,C_47) != '#skF_18'(A_45,B_46,C_47) )
| ( ordered_pair('#skF_25'(A_45,B_46,C_47,E_127),'#skF_26'(A_45,B_46,C_47,E_127)) = E_127 )
| ~ in(E_127,'#skF_23'(A_45,B_46,C_47))
| ~ function(C_47)
| ~ relation(C_47)
| ~ relation(B_46) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_892,plain,
! [A_370,B_371,C_372,E_373] :
( ( '#skF_17'(A_370,B_371,C_372) != '#skF_18'(A_370,B_371,C_372) )
| in(ordered_pair(apply(C_372,'#skF_25'(A_370,B_371,C_372,E_373)),apply(C_372,'#skF_26'(A_370,B_371,C_372,E_373))),B_371)
| ~ in(E_373,'#skF_23'(A_370,B_371,C_372))
| ~ function(C_372)
| ~ relation(C_372)
| ~ relation(B_371) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_919,plain,
! [D_20,A_370,E_373] :
( in(ordered_pair(apply('#skF_3','#skF_5'(D_20)),apply('#skF_3','#skF_6'(D_20))),'#skF_2')
| ( ordered_pair('#skF_25'(A_370,'#skF_2','#skF_3',E_373),'#skF_26'(A_370,'#skF_2','#skF_3',E_373)) != '#skF_7'(D_20) )
| ~ in('#skF_7'(D_20),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_370,'#skF_2','#skF_3') != '#skF_18'(A_370,'#skF_2','#skF_3') )
| ~ in(E_373,'#skF_23'(A_370,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_892,c_10]) ).
tff(c_118541,plain,
! [D_4365,A_4366,E_4367] :
( in(ordered_pair(apply('#skF_3','#skF_5'(D_4365)),apply('#skF_3','#skF_6'(D_4365))),'#skF_2')
| ( ordered_pair('#skF_25'(A_4366,'#skF_2','#skF_3',E_4367),'#skF_26'(A_4366,'#skF_2','#skF_3',E_4367)) != '#skF_7'(D_4365) )
| ~ in('#skF_7'(D_4365),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_4366,'#skF_2','#skF_3') != '#skF_18'(A_4366,'#skF_2','#skF_3') )
| ~ in(E_4367,'#skF_23'(A_4366,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_919]) ).
tff(c_118566,plain,
! [D_4365,E_127,A_45] :
( in(ordered_pair(apply('#skF_3','#skF_5'(D_4365)),apply('#skF_3','#skF_6'(D_4365))),'#skF_2')
| ( E_127 != '#skF_7'(D_4365) )
| ~ in('#skF_7'(D_4365),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') != '#skF_18'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') != '#skF_18'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_116,c_118541]) ).
tff(c_118580,plain,
! [D_4365,E_127,A_45] :
( in(ordered_pair(apply('#skF_3','#skF_5'(D_4365)),apply('#skF_3','#skF_6'(D_4365))),'#skF_2')
| ( E_127 != '#skF_7'(D_4365) )
| ~ in('#skF_7'(D_4365),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') != '#skF_18'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_118566]) ).
tff(c_118803,plain,
! [D_4365,A_45] :
( in(ordered_pair(apply('#skF_3','#skF_5'(D_4365)),apply('#skF_3','#skF_6'(D_4365))),'#skF_2')
| ~ in('#skF_7'(D_4365),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') != '#skF_18'(A_45,'#skF_2','#skF_3') )
| ~ in('#skF_7'(D_4365),'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_118580]) ).
tff(c_136501,plain,
( in(ordered_pair(apply('#skF_3','#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3'))),apply('#skF_3','#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3')))),'#skF_2')
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'('#skF_1','#skF_2','#skF_3') != '#skF_18'('#skF_1','#skF_2','#skF_3') ) ),
inference(resolution,[status(thm)],[c_136444,c_118803]) ).
tff(c_136566,plain,
( in(ordered_pair(apply('#skF_3','#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3'))),apply('#skF_3','#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3')))),'#skF_2')
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1')) ),
inference(demodulation,[status(thm),theory(equality)],[c_106874,c_136501]) ).
tff(c_136744,plain,
in(ordered_pair(apply('#skF_3','#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3'))),apply('#skF_3','#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3')))),'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_136619,c_136566]) ).
tff(c_158,plain,
! [C_47,A_45,K_141,B_46,L_142] :
( ( '#skF_17'(A_45,B_46,C_47) != '#skF_18'(A_45,B_46,C_47) )
| in(ordered_pair(K_141,L_142),'#skF_23'(A_45,B_46,C_47))
| ~ in(ordered_pair(apply(C_47,K_141),apply(C_47,L_142)),B_46)
| ~ in(ordered_pair(K_141,L_142),cartesian_product2(A_45,A_45))
| ~ function(C_47)
| ~ relation(C_47)
| ~ relation(B_46) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_136761,plain,
! [A_45] :
( ( '#skF_17'(A_45,'#skF_2','#skF_3') != '#skF_18'(A_45,'#skF_2','#skF_3') )
| in(ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))),'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ in(ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))),cartesian_product2(A_45,A_45))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_136744,c_158]) ).
tff(c_136791,plain,
! [A_45] :
( ( '#skF_17'(A_45,'#skF_2','#skF_3') != '#skF_18'(A_45,'#skF_2','#skF_3') )
| in(ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))),'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ in(ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))),cartesian_product2(A_45,A_45)) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_136761]) ).
tff(c_156099,plain,
! [A_5476] :
( ( '#skF_17'(A_5476,'#skF_2','#skF_3') != '#skF_18'(A_5476,'#skF_2','#skF_3') )
| in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'(A_5476,'#skF_2','#skF_3'))
| ~ in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2(A_5476,A_5476)) ),
inference(demodulation,[status(thm),theory(equality)],[c_137129,c_137129,c_136791]) ).
tff(c_156102,plain,
( ( '#skF_17'('#skF_1','#skF_2','#skF_3') != '#skF_18'('#skF_1','#skF_2','#skF_3') )
| in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')) ),
inference(resolution,[status(thm)],[c_136943,c_156099]) ).
tff(c_156207,plain,
in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_106874,c_156102]) ).
tff(c_156472,plain,
! [F_34,G_35] :
( ~ in(ordered_pair(apply('#skF_3',F_34),apply('#skF_3',G_35)),'#skF_2')
| ( ordered_pair(F_34,G_35) != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1')) ),
inference(resolution,[status(thm)],[c_156207,c_8]) ).
tff(c_157394,plain,
! [F_5479,G_5480] :
( ~ in(ordered_pair(apply('#skF_3',F_5479),apply('#skF_3',G_5480)),'#skF_2')
| ( ordered_pair(F_5479,G_5480) != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_136619,c_156472]) ).
tff(c_157560,plain,
! [A_45,E_127] :
( ( ordered_pair('#skF_25'(A_45,'#skF_2','#skF_3',E_127),'#skF_26'(A_45,'#skF_2','#skF_3',E_127)) != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_114,c_157394]) ).
tff(c_161212,plain,
! [A_5578,E_5579] :
( ( ordered_pair('#skF_25'(A_5578,'#skF_2','#skF_3',E_5579),'#skF_26'(A_5578,'#skF_2','#skF_3',E_5579)) != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ( '#skF_17'(A_5578,'#skF_2','#skF_3') = '#skF_16'(A_5578,'#skF_2','#skF_3') )
| ~ in(E_5579,'#skF_23'(A_5578,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_157560]) ).
tff(c_161242,plain,
! [E_127,A_45] :
( ( E_127 != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') = '#skF_16'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_128,c_161212]) ).
tff(c_161262,plain,
! [E_5580,A_5581] :
( ( E_5580 != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ( '#skF_17'(A_5581,'#skF_2','#skF_3') = '#skF_16'(A_5581,'#skF_2','#skF_3') )
| ~ in(E_5580,'#skF_23'(A_5581,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_161242]) ).
tff(c_161336,plain,
'#skF_17'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3'),
inference(resolution,[status(thm)],[c_136444,c_161262]) ).
tff(c_161639,plain,
'#skF_18'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_106874,c_161336]) ).
tff(c_161784,plain,
'#skF_17'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_161639,c_106874]) ).
tff(c_102,plain,
! [A_45,B_46,C_47,E_127] :
( ( '#skF_17'(A_45,B_46,C_47) != '#skF_18'(A_45,B_46,C_47) )
| in(ordered_pair(apply(C_47,'#skF_25'(A_45,B_46,C_47,E_127)),apply(C_47,'#skF_26'(A_45,B_46,C_47,E_127))),B_46)
| ~ in(E_127,'#skF_23'(A_45,B_46,C_47))
| ~ function(C_47)
| ~ relation(C_47)
| ~ relation(B_46) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_157564,plain,
! [A_45,E_127] :
( ( ordered_pair('#skF_25'(A_45,'#skF_2','#skF_3',E_127),'#skF_26'(A_45,'#skF_2','#skF_3',E_127)) != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ( '#skF_17'(A_45,'#skF_2','#skF_3') != '#skF_18'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_102,c_157394]) ).
tff(c_162321,plain,
! [A_5595,E_5596] :
( ( ordered_pair('#skF_25'(A_5595,'#skF_2','#skF_3',E_5596),'#skF_26'(A_5595,'#skF_2','#skF_3',E_5596)) != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ( '#skF_17'(A_5595,'#skF_2','#skF_3') != '#skF_18'(A_5595,'#skF_2','#skF_3') )
| ~ in(E_5596,'#skF_23'(A_5595,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_157564]) ).
tff(c_162355,plain,
! [E_127,A_45] :
( ( E_127 != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ( '#skF_17'(A_45,'#skF_2','#skF_3') != '#skF_18'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') != '#skF_18'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_116,c_162321]) ).
tff(c_162371,plain,
! [E_5597,A_5598] :
( ( E_5597 != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ( '#skF_17'(A_5598,'#skF_2','#skF_3') != '#skF_18'(A_5598,'#skF_2','#skF_3') )
| ~ in(E_5597,'#skF_23'(A_5598,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_162355]) ).
tff(c_162448,plain,
'#skF_17'('#skF_1','#skF_2','#skF_3') != '#skF_18'('#skF_1','#skF_2','#skF_3'),
inference(resolution,[status(thm)],[c_136444,c_162371]) ).
tff(c_162773,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_161784,c_161639,c_162448]) ).
tff(c_162816,plain,
! [A_5604] :
( ( '#skF_18'(A_5604,'#skF_2','#skF_3') = '#skF_16'(A_5604,'#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'(A_5604,'#skF_2','#skF_3')) ),
inference(splitRight,[status(thm)],[c_136660]) ).
tff(c_162868,plain,
'#skF_18'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3'),
inference(resolution,[status(thm)],[c_136444,c_162816]) ).
tff(c_162879,plain,
'#skF_17'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_162868,c_106874]) ).
tff(c_162775,plain,
ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))) != '#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(splitRight,[status(thm)],[c_136660]) ).
tff(c_934,plain,
! [D_20,A_370,E_373] :
( ( ordered_pair('#skF_5'(D_20),'#skF_6'(D_20)) = '#skF_4'(D_20) )
| ( ordered_pair('#skF_25'(A_370,'#skF_2','#skF_3',E_373),'#skF_26'(A_370,'#skF_2','#skF_3',E_373)) != '#skF_7'(D_20) )
| ~ in('#skF_7'(D_20),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_370,'#skF_2','#skF_3') != '#skF_18'(A_370,'#skF_2','#skF_3') )
| ~ in(E_373,'#skF_23'(A_370,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_892,c_12]) ).
tff(c_115384,plain,
! [D_4241,A_4242,E_4243] :
( ( ordered_pair('#skF_5'(D_4241),'#skF_6'(D_4241)) = '#skF_4'(D_4241) )
| ( ordered_pair('#skF_25'(A_4242,'#skF_2','#skF_3',E_4243),'#skF_26'(A_4242,'#skF_2','#skF_3',E_4243)) != '#skF_7'(D_4241) )
| ~ in('#skF_7'(D_4241),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_4242,'#skF_2','#skF_3') != '#skF_18'(A_4242,'#skF_2','#skF_3') )
| ~ in(E_4243,'#skF_23'(A_4242,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_934]) ).
tff(c_115405,plain,
! [D_4241,E_127,A_45] :
( ( ordered_pair('#skF_5'(D_4241),'#skF_6'(D_4241)) = '#skF_4'(D_4241) )
| ( E_127 != '#skF_7'(D_4241) )
| ~ in('#skF_7'(D_4241),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') != '#skF_18'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') != '#skF_18'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_116,c_115384]) ).
tff(c_115419,plain,
! [D_4241,E_127,A_45] :
( ( ordered_pair('#skF_5'(D_4241),'#skF_6'(D_4241)) = '#skF_4'(D_4241) )
| ( E_127 != '#skF_7'(D_4241) )
| ~ in('#skF_7'(D_4241),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') != '#skF_18'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_115405]) ).
tff(c_116141,plain,
! [D_4241,A_45] :
( ( ordered_pair('#skF_5'(D_4241),'#skF_6'(D_4241)) = '#skF_4'(D_4241) )
| ~ in('#skF_7'(D_4241),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') != '#skF_18'(A_45,'#skF_2','#skF_3') )
| ~ in('#skF_7'(D_4241),'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_115419]) ).
tff(c_136659,plain,
! [A_45] :
( ( ordered_pair('#skF_5'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_6'('#skF_23'('#skF_1','#skF_2','#skF_3'))) = '#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ( '#skF_17'(A_45,'#skF_2','#skF_3') != '#skF_18'(A_45,'#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(resolution,[status(thm)],[c_136619,c_116141]) ).
tff(c_163016,plain,
! [A_5613] :
( ( '#skF_17'(A_5613,'#skF_2','#skF_3') != '#skF_18'(A_5613,'#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'(A_5613,'#skF_2','#skF_3')) ),
inference(negUnitSimplification,[status(thm)],[c_162775,c_136659]) ).
tff(c_163019,plain,
'#skF_17'('#skF_1','#skF_2','#skF_3') != '#skF_18'('#skF_1','#skF_2','#skF_3'),
inference(resolution,[status(thm)],[c_136444,c_163016]) ).
tff(c_163071,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_162879,c_162868,c_163019]) ).
tff(c_163248,plain,
! [A_5619] :
( ( '#skF_18'(A_5619,'#skF_2','#skF_3') = '#skF_16'(A_5619,'#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'(A_5619,'#skF_2','#skF_3')) ),
inference(splitRight,[status(thm)],[c_136663]) ).
tff(c_163300,plain,
'#skF_18'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3'),
inference(resolution,[status(thm)],[c_136444,c_163248]) ).
tff(c_163312,plain,
'#skF_17'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_163300,c_106874]) ).
tff(c_163073,plain,
~ in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1')),
inference(splitRight,[status(thm)],[c_136663]) ).
tff(c_937,plain,
! [D_20,A_370,E_373] :
( in('#skF_4'(D_20),cartesian_product2('#skF_1','#skF_1'))
| ( ordered_pair('#skF_25'(A_370,'#skF_2','#skF_3',E_373),'#skF_26'(A_370,'#skF_2','#skF_3',E_373)) != '#skF_7'(D_20) )
| ~ in('#skF_7'(D_20),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_370,'#skF_2','#skF_3') != '#skF_18'(A_370,'#skF_2','#skF_3') )
| ~ in(E_373,'#skF_23'(A_370,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_892,c_14]) ).
tff(c_113418,plain,
! [D_4162,A_4163,E_4164] :
( in('#skF_4'(D_4162),cartesian_product2('#skF_1','#skF_1'))
| ( ordered_pair('#skF_25'(A_4163,'#skF_2','#skF_3',E_4164),'#skF_26'(A_4163,'#skF_2','#skF_3',E_4164)) != '#skF_7'(D_4162) )
| ~ in('#skF_7'(D_4162),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_4163,'#skF_2','#skF_3') != '#skF_18'(A_4163,'#skF_2','#skF_3') )
| ~ in(E_4164,'#skF_23'(A_4163,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_937]) ).
tff(c_113439,plain,
! [D_4162,E_127,A_45] :
( in('#skF_4'(D_4162),cartesian_product2('#skF_1','#skF_1'))
| ( E_127 != '#skF_7'(D_4162) )
| ~ in('#skF_7'(D_4162),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') != '#skF_18'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') != '#skF_18'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3'))
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_116,c_113418]) ).
tff(c_113453,plain,
! [D_4162,E_127,A_45] :
( in('#skF_4'(D_4162),cartesian_product2('#skF_1','#skF_1'))
| ( E_127 != '#skF_7'(D_4162) )
| ~ in('#skF_7'(D_4162),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') != '#skF_18'(A_45,'#skF_2','#skF_3') )
| ~ in(E_127,'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_113439]) ).
tff(c_114067,plain,
! [D_4162,A_45] :
( in('#skF_4'(D_4162),cartesian_product2('#skF_1','#skF_1'))
| ~ in('#skF_7'(D_4162),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') != '#skF_18'(A_45,'#skF_2','#skF_3') )
| ~ in('#skF_7'(D_4162),'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(reflexivity,[status(thm),theory(equality)],[c_113453]) ).
tff(c_136662,plain,
! [A_45] :
( in('#skF_4'('#skF_23'('#skF_1','#skF_2','#skF_3')),cartesian_product2('#skF_1','#skF_1'))
| ( '#skF_17'(A_45,'#skF_2','#skF_3') != '#skF_18'(A_45,'#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'(A_45,'#skF_2','#skF_3')) ),
inference(resolution,[status(thm)],[c_136619,c_114067]) ).
tff(c_163446,plain,
! [A_5628] :
( ( '#skF_17'(A_5628,'#skF_2','#skF_3') != '#skF_18'(A_5628,'#skF_2','#skF_3') )
| ~ in('#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),'#skF_23'(A_5628,'#skF_2','#skF_3')) ),
inference(negUnitSimplification,[status(thm)],[c_163073,c_136662]) ).
tff(c_163449,plain,
'#skF_17'('#skF_1','#skF_2','#skF_3') != '#skF_18'('#skF_1','#skF_2','#skF_3'),
inference(resolution,[status(thm)],[c_136444,c_163446]) ).
tff(c_163501,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_163312,c_163300,c_163449]) ).
tff(c_163503,plain,
'#skF_24'('#skF_1','#skF_2','#skF_3','#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3'))) != '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(splitRight,[status(thm)],[c_135778]) ).
tff(c_163502,plain,
'#skF_18'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3'),
inference(splitRight,[status(thm)],[c_135778]) ).
tff(c_163504,plain,
'#skF_17'('#skF_1','#skF_2','#skF_3') = '#skF_16'('#skF_1','#skF_2','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_163502,c_106874]) ).
tff(c_130,plain,
! [A_45,B_46,C_47,E_127] :
( ( '#skF_17'(A_45,B_46,C_47) != '#skF_18'(A_45,B_46,C_47) )
| ( '#skF_24'(A_45,B_46,C_47,E_127) = E_127 )
| ~ in(E_127,'#skF_23'(A_45,B_46,C_47))
| ~ function(C_47)
| ~ relation(C_47)
| ~ relation(B_46) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_163627,plain,
! [A_5636,B_5637,C_5638] :
( ( '#skF_17'(A_5636,B_5637,C_5638) != '#skF_18'(A_5636,B_5637,C_5638) )
| ( '#skF_24'(A_5636,B_5637,C_5638,'#skF_7'('#skF_23'(A_5636,B_5637,C_5638))) = '#skF_7'('#skF_23'(A_5636,B_5637,C_5638)) )
| ~ function(C_5638)
| ~ relation(C_5638)
| ~ relation(B_5637)
| in('#skF_4'('#skF_23'(A_5636,B_5637,C_5638)),'#skF_23'('#skF_1','#skF_2','#skF_3')) ),
inference(resolution,[status(thm)],[c_107086,c_130]) ).
tff(c_163823,plain,
( ( '#skF_17'('#skF_1','#skF_2','#skF_3') != '#skF_18'('#skF_1','#skF_2','#skF_3') )
| ( '#skF_24'('#skF_1','#skF_2','#skF_3','#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3'))) = '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')) )
| ~ function('#skF_3')
| ~ relation('#skF_3')
| ~ relation('#skF_2') ),
inference(resolution,[status(thm)],[c_163627,c_350]) ).
tff(c_164036,plain,
'#skF_24'('#skF_1','#skF_2','#skF_3','#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3'))) = '#skF_7'('#skF_23'('#skF_1','#skF_2','#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_4,c_2,c_163504,c_163502,c_163823]) ).
tff(c_164038,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_163503,c_164036]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU277+1 : TPTP v8.1.2. Released v3.3.0.
% 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
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 3 12:11:23 EDT 2023
% 0.14/0.34 % CPUTime :
% 48.21/33.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 48.21/33.11
% 48.21/33.11 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 48.48/33.17
% 48.48/33.17 Inference rules
% 48.48/33.17 ----------------------
% 48.48/33.17 #Ref : 61
% 48.48/33.17 #Sup : 37572
% 48.48/33.17 #Fact : 270
% 48.48/33.17 #Define : 0
% 48.48/33.17 #Split : 31
% 48.48/33.17 #Chain : 0
% 48.48/33.17 #Close : 0
% 48.48/33.17
% 48.48/33.17 Ordering : KBO
% 48.48/33.17
% 48.48/33.17 Simplification rules
% 48.48/33.17 ----------------------
% 48.48/33.17 #Subsume : 19377
% 48.48/33.17 #Demod : 43795
% 48.48/33.17 #Tautology : 3812
% 48.48/33.17 #SimpNegUnit : 964
% 48.48/33.17 #BackRed : 33
% 48.48/33.17
% 48.48/33.17 #Partial instantiations: 0
% 48.48/33.17 #Strategies tried : 1
% 48.48/33.17
% 48.48/33.17 Timing (in seconds)
% 48.48/33.17 ----------------------
% 48.48/33.18 Preprocessing : 0.58
% 48.48/33.18 Parsing : 0.26
% 48.48/33.18 CNF conversion : 0.06
% 48.48/33.18 Main loop : 31.47
% 48.48/33.18 Inferencing : 7.42
% 48.48/33.18 Reduction : 11.06
% 48.48/33.18 Demodulation : 7.94
% 48.48/33.18 BG Simplification : 0.42
% 48.48/33.18 Subsumption : 10.78
% 48.48/33.18 Abstraction : 1.15
% 48.48/33.18 MUC search : 0.00
% 48.48/33.18 Cooper : 0.00
% 48.48/33.18 Total : 32.17
% 48.48/33.18 Index Insertion : 0.00
% 48.48/33.18 Index Deletion : 0.00
% 48.48/33.18 Index Matching : 0.00
% 48.48/33.18 BG Taut test : 0.00
%------------------------------------------------------------------------------