TSTP Solution File: ARI678_1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ARI678_1 : TPTP v8.1.2. Released v6.3.0.
% 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 : n031.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 10:34:14 EDT 2023
% Result : Theorem 30.48s 10.92s
% Output : CNFRefutation 31.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 13
% Syntax : Number of formulae : 413 ( 297 unt; 4 typ; 0 def)
% Number of atoms : 540 ( 417 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 341 ( 210 ~; 128 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number arithmetic : 1471 ( 92 atm; 752 fun; 539 num; 88 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 4 usr; 15 con; 0-2 aty)
% Number of variables : 88 (; 88 !; 0 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp
%Foreground sorts:
%Background operators:
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
tff(a,type,
a: $int ).
%Foreground operators:
tff(f_81,axiom,
! [C: $int,B: $int] :
( ( $product(C,B) = C )
<=> ( ( C = 0 )
| ( B = 1 ) ) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_cancel_right1) ).
tff(f_65,axiom,
! [A: $int,B: $int] : ( $product(A,B) = $product(B,A) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_comm) ).
tff(f_30,axiom,
$greatereq(7,$product($product(a,a),a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f_33,negated_conjecture,
~ $greatereq(1,$product($product($product(a,a),a),a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_002) ).
tff(f_67,axiom,
! [A: $int,B: $int,C: $int] : ( $product(A,$sum(B,C)) = $sum($product(A,B),$product(A,C)) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_dist) ).
tff(f_62,axiom,
! [M: $int,N: $int] : ( $product($sum(1,M),N) = $sum(N,$product(M,N)) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_def_2) ).
tff(f_90,axiom,
! [A: $int,B: $int] :
( ( $less(0,A)
& $less(0,B) )
=> $less(0,$product(A,B)) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_nonneg_nonneg) ).
tff(f_31,axiom,
$lesseq(0,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_001) ).
tff(f_73,axiom,
! [A: $int,B: $int] : ( $uminus($product(A,B)) = $product($uminus(A),B) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',minus_mult_left) ).
tff(c_43,plain,
! [C_23: $int] : ( $product(C_23,1) = C_23 ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_42,plain,
! [B_24: $int] : ( $product(0,B_24) = 0 ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_50,plain,
! [B_7: $int,A_8: $int] : ( $product(B_7,A_8) = $product(A_8,B_7) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_2,plain,
$greatereq(7,$product($product(a,a),a)),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_40,plain,
~ $less(7,$product($product(a,a),a)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).
tff(c_64,plain,
~ $less(7,$product(a,$product(a,a))),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_40]) ).
tff(c_82,plain,
$product(a,a) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_64]) ).
tff(c_225,plain,
( ( '#skE_1' = 0 )
| ( a != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_42,c_82]) ).
tff(c_239,plain,
a != 0,
inference(splitLeft,[status(thm)],[c_225]) ).
tff(c_81,plain,
$product(a,a) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_64]) ).
tff(c_7,plain,
~ $greatereq(1,$product($product($product(a,a),a),a)),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_35,plain,
$less(1,$product($product($product(a,a),a),a)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_7]) ).
tff(c_244,plain,
$less(1,$product(a,$product('#skE_1',a))),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_81,c_50,c_50,c_35]) ).
tff(c_267,plain,
$product('#skE_1',a) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_244]) ).
tff(c_16,plain,
! [A_9: $int,C_11: $int,B_10: $int] : ( $product(A_9,$sum(C_11,B_10)) = $sum($product(A_9,B_10),$product(A_9,C_11)) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_58,plain,
! [A_12: $int,B_13: $int,C_14: $int] : ( $product(A_12,$sum(B_13,C_14)) = $sum($product(A_12,B_13),$product(A_12,C_14)) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_16]) ).
tff(c_431,plain,
$product('#skE_1',a) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_244]) ).
tff(c_49,plain,
! [A_12: $int,X_44: $int,B_13: $int,C_14: $int] :
( ( $product(A_12,X_44) = $sum($product(A_12,B_13),$product(A_12,C_14)) )
| ( X_44 != $sum(B_13,C_14) ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_16]) ).
tff(c_540,plain,
! [B_13: $int,X_44: $int] :
( ( $sum($product('#skE_1',B_13),'#skE_2') = $product('#skE_1',X_44) )
| ( X_44 != $sum(B_13,a) ) ),
inference(superposition,[status(thm),theory(equality)],[c_431,c_49]) ).
tff(c_4672,plain,
! [X_825: $int,B_828: $int] :
( ( $sum($uminus('#skE_2'),$product('#skE_1',X_825)) = $product('#skE_1',B_828) )
| ( X_825 != $sum(a,B_828) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_540]) ).
tff(c_4786,plain,
$sum($uminus('#skE_2'),$product('#skE_1',$sum(a,1))) = '#skE_1',
inference(superposition,[status(thm),theory(equality)],[c_4672,c_43]) ).
tff(c_5095,plain,
$sum($uminus('#skE_2'),$sum('#skE_2',$product(1,'#skE_1'))) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_267,c_50,c_58,c_4786]) ).
tff(c_5328,plain,
$product(1,'#skE_1') = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5095]) ).
tff(c_52,plain,
! [X_45: $int,N_4: $int,M_3: $int] :
( ( $product(X_45,N_4) = $sum(N_4,$product(M_3,N_4)) )
| ( X_45 != $sum(1,M_3) ) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_5564,plain,
$product($sum(1,1),'#skE_1') = $sum('#skE_1','#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_5328,c_52]) ).
tff(c_123467,plain,
$product(2,'#skE_1') = $product(2,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5564]) ).
tff(c_123606,plain,
$product($sum(1,2),'#skE_1') = $sum('#skE_1',$product(2,'#skE_1')),
inference(superposition,[status(thm),theory(equality)],[c_123467,c_52]) ).
tff(c_126147,plain,
$product(3,'#skE_1') = $product(3,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_123606]) ).
tff(c_126794,plain,
$product('#skE_1',3) = $product(3,'#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_126147,c_50]) ).
tff(c_17865,plain,
$product(2,'#skE_1') = $product(2,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5564]) ).
tff(c_18318,plain,
$product($sum(1,2),'#skE_1') = $sum('#skE_1',$product(2,'#skE_1')),
inference(superposition,[status(thm),theory(equality)],[c_17865,c_52]) ).
tff(c_26209,plain,
$product(3,'#skE_1') = $product(3,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_18318]) ).
tff(c_26726,plain,
$product($sum(1,3),'#skE_1') = $sum('#skE_1',$product(3,'#skE_1')),
inference(superposition,[status(thm),theory(equality)],[c_26209,c_52]) ).
tff(c_71097,plain,
$product(4,'#skE_1') = $product(4,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_26726]) ).
tff(c_71428,plain,
$product($sum(1,4),'#skE_1') = $sum('#skE_1',$product(4,'#skE_1')),
inference(superposition,[status(thm),theory(equality)],[c_71097,c_52]) ).
tff(c_86479,plain,
$product(5,'#skE_1') = $product(5,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_71428]) ).
tff(c_41,plain,
! [A_27: $int,B_28: $int] :
( $less(0,$product(A_27,B_28))
| ~ $less(0,A_27)
| ~ $less(0,B_28) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_199,plain,
( $less(0,'#skE_1')
| ~ $less(0,a) ),
inference(superposition,[status(thm),theory(equality)],[c_82,c_41]) ).
tff(c_265,plain,
~ $less(0,a),
inference(splitLeft,[status(thm)],[c_199]) ).
tff(c_4,plain,
$lesseq(0,a),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_36,plain,
~ $less(a,0),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_4]) ).
tff(c_426,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_265,c_239,c_36]) ).
tff(c_430,plain,
$less(0,a),
inference(splitRight,[status(thm)],[c_199]) ).
tff(c_516,plain,
! [M_3: $int] :
( ( $sum(a,$product(M_3,a)) = '#skE_2' )
| ( $sum(1,M_3) != '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_431,c_52]) ).
tff(c_518,plain,
$product($sum($uminus(1),'#skE_1'),a) = $sum($uminus(a),'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_516]) ).
tff(c_6394,plain,
$product($sum($uminus(1),'#skE_1'),a) = $sum('#skE_2',$uminus(a)),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_518]) ).
tff(c_6508,plain,
( $less(0,$sum('#skE_2',$uminus(a)))
| ~ $less(0,$sum($uminus(1),'#skE_1'))
| ~ $less(0,a) ),
inference(superposition,[status(thm),theory(equality)],[c_6394,c_41]) ).
tff(c_6724,plain,
( $less(0,$sum('#skE_2',$uminus(a)))
| ~ $less(0,$sum($uminus(1),'#skE_1')) ),
inference(demodulation,[status(thm),theory(equality)],[c_430,c_6508]) ).
tff(c_6726,plain,
( $less(a,'#skE_2')
| ~ $less(1,'#skE_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6724]) ).
tff(c_6823,plain,
~ $less(1,'#skE_1'),
inference(splitLeft,[status(thm)],[c_6726]) ).
tff(c_601,plain,
$product(a,'#skE_1') = '#skE_2',
inference(superposition,[status(thm),theory(equality)],[c_50,c_431]) ).
tff(c_734,plain,
( ( a = '#skE_2' )
| ( '#skE_1' != 1 ) ),
inference(superposition,[status(thm),theory(equality)],[c_601,c_43]) ).
tff(c_773,plain,
'#skE_1' != 1,
inference(splitLeft,[status(thm)],[c_734]) ).
tff(c_429,plain,
$less(0,'#skE_1'),
inference(splitRight,[status(thm)],[c_199]) ).
tff(c_6824,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_6823,c_773,c_429]) ).
tff(c_6828,plain,
$less(1,'#skE_1'),
inference(splitRight,[status(thm)],[c_6726]) ).
tff(c_246,plain,
$product('#skE_1',a) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_244]) ).
tff(c_245,plain,
$less(1,$product(a,$product('#skE_1',a))),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_81,c_50,c_50,c_35]) ).
tff(c_249,plain,
$less(1,$product(a,'#skE_2')),
inference(demodulation,[status(thm),theory(equality)],[c_246,c_245]) ).
tff(c_259,plain,
$less(1,$product('#skE_2',a)),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_249]) ).
tff(c_792,plain,
$product('#skE_2',a) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_259]) ).
tff(c_894,plain,
! [M_3: $int] :
( ( $sum(a,$product(M_3,a)) = '#skE_3' )
| ( $sum(1,M_3) != '#skE_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_792,c_52]) ).
tff(c_896,plain,
$product($sum($uminus(1),'#skE_2'),a) = $sum($uminus(a),'#skE_3'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_894]) ).
tff(c_6831,plain,
$product($sum($uminus(1),'#skE_2'),a) = $sum('#skE_3',$uminus(a)),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_896]) ).
tff(c_162,plain,
$product($sum(1,a),a) = $sum(a,'#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_82,c_52]) ).
tff(c_165,plain,
$product($sum(1,a),a) = $sum('#skE_1',a),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_162]) ).
tff(c_7092,plain,
( ( $sum('#skE_3',$uminus(a)) = $sum('#skE_1',a) )
| ( $sum(1,a) != $sum($uminus(1),'#skE_2') ) ),
inference(superposition,[status(thm),theory(equality)],[c_6831,c_165]) ).
tff(c_7094,plain,
( ( $sum($product(2,a),'#skE_1') = '#skE_3' )
| ( a != $sum($uminus(2),'#skE_2') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7092]) ).
tff(c_48493,plain,
a != $sum($uminus(2),'#skE_2'),
inference(splitLeft,[status(thm)],[c_7094]) ).
tff(c_697,plain,
! [M_3: $int] :
( ( $sum('#skE_1',$product(M_3,'#skE_1')) = '#skE_2' )
| ( a != $sum(1,M_3) ) ),
inference(superposition,[status(thm),theory(equality)],[c_601,c_52]) ).
tff(c_40611,plain,
! [M_5342: $int] :
( ( $product(M_5342,'#skE_1') = $sum($uminus('#skE_1'),'#skE_2') )
| ( a != $sum(1,M_5342) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_697]) ).
tff(c_18321,plain,
$product(3,'#skE_1') = $product(3,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_18318]) ).
tff(c_41210,plain,
( ( $sum($uminus('#skE_1'),'#skE_2') = $product(3,'#skE_1') )
| ( a != $sum(1,3) ) ),
inference(superposition,[status(thm),theory(equality)],[c_40611,c_18321]) ).
tff(c_41212,plain,
( ( '#skE_2' = $product(4,'#skE_1') )
| ( a != 4 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_41210]) ).
tff(c_41607,plain,
a != 4,
inference(splitLeft,[status(thm)],[c_41212]) ).
tff(c_73,plain,
$product(a,a) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_64]) ).
tff(c_7247,plain,
( ( $sum('#skE_3',$uminus(a)) = '#skE_1' )
| ( a != $sum($uminus(1),'#skE_2') ) ),
inference(superposition,[status(thm),theory(equality)],[c_73,c_6831]) ).
tff(c_7248,plain,
( ( a = $sum('#skE_3',$uminus('#skE_1')) )
| ( a != $sum($uminus(1),'#skE_2') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7247]) ).
tff(c_7250,plain,
( ( a = $sum($uminus('#skE_1'),'#skE_3') )
| ( a != $sum($uminus(1),'#skE_2') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7248]) ).
tff(c_34447,plain,
a != $sum($uminus(1),'#skE_2'),
inference(splitLeft,[status(thm)],[c_7250]) ).
tff(c_791,plain,
$product('#skE_2',a) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_259]) ).
tff(c_178,plain,
! [X_44: $int,B_13: $int] :
( ( $product(a,X_44) = $sum($product(a,B_13),'#skE_1') )
| ( X_44 != $sum(B_13,a) ) ),
inference(superposition,[status(thm),theory(equality)],[c_82,c_49]) ).
tff(c_12264,plain,
! [B_13: $int] : ( $product(a,$sum(a,B_13)) = $sum('#skE_1',$product(a,B_13)) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_178]) ).
tff(c_918,plain,
! [B_13: $int,X_44: $int] :
( ( $sum($product('#skE_2',B_13),'#skE_3') = $product('#skE_2',X_44) )
| ( X_44 != $sum(B_13,a) ) ),
inference(superposition,[status(thm),theory(equality)],[c_792,c_49]) ).
tff(c_13299,plain,
! [X_2594: $int,B_2595: $int] :
( ( $sum($uminus('#skE_3'),$product('#skE_2',X_2594)) = $product('#skE_2',B_2595) )
| ( X_2594 != $sum(a,B_2595) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_918]) ).
tff(c_13762,plain,
$sum($uminus('#skE_3'),$product('#skE_2',$sum(a,1))) = '#skE_2',
inference(superposition,[status(thm),theory(equality)],[c_43,c_13299]) ).
tff(c_14313,plain,
$sum($uminus('#skE_3'),$sum('#skE_3',$product(1,'#skE_2'))) = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_791,c_50,c_58,c_13762]) ).
tff(c_14323,plain,
$product(1,'#skE_2') = '#skE_2',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_14313]) ).
tff(c_14710,plain,
$product($sum(1,1),'#skE_2') = $sum('#skE_2','#skE_2'),
inference(superposition,[status(thm),theory(equality)],[c_14323,c_52]) ).
tff(c_20404,plain,
$product(2,'#skE_2') = $product(2,'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_14710]) ).
tff(c_20866,plain,
$product($sum(1,2),'#skE_2') = $sum('#skE_2',$product(2,'#skE_2')),
inference(superposition,[status(thm),theory(equality)],[c_20404,c_52]) ).
tff(c_25491,plain,
$product(3,'#skE_2') = $product(3,'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_20866]) ).
tff(c_181,plain,
! [B_13: $int,X_44: $int] :
( ( $sum('#skE_1',$product(a,B_13)) = $product(a,X_44) )
| ( X_44 != $sum(a,B_13) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_178]) ).
tff(c_25552,plain,
( ( $product(a,$sum(a,'#skE_2')) = $sum('#skE_1',$product(3,'#skE_2')) )
| ( a != 3 ) ),
inference(superposition,[status(thm),theory(equality)],[c_25491,c_181]) ).
tff(c_25917,plain,
( ( $sum('#skE_1','#skE_3') = $sum('#skE_1',$product(3,'#skE_2')) )
| ( a != 3 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_791,c_50,c_12264,c_25552]) ).
tff(c_25919,plain,
( ( '#skE_3' = $product(3,'#skE_2') )
| ( a != 3 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_25917]) ).
tff(c_26190,plain,
a != 3,
inference(splitLeft,[status(thm)],[c_25919]) ).
tff(c_17887,plain,
( ( $product(a,$sum(a,'#skE_1')) = $sum('#skE_1',$product(2,'#skE_1')) )
| ( a != 2 ) ),
inference(superposition,[status(thm),theory(equality)],[c_17865,c_181]) ).
tff(c_18205,plain,
( ( $sum('#skE_1','#skE_2') = $sum('#skE_1',$product(2,'#skE_1')) )
| ( a != 2 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_267,c_50,c_12264,c_17887]) ).
tff(c_18207,plain,
( ( '#skE_2' = $product(2,'#skE_1') )
| ( a != 2 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_18205]) ).
tff(c_18469,plain,
a != 2,
inference(splitLeft,[status(thm)],[c_18207]) ).
tff(c_6827,plain,
$less(a,'#skE_2'),
inference(splitRight,[status(thm)],[c_6726]) ).
tff(c_66,plain,
$product(a,a) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_64]) ).
tff(c_65,plain,
~ $less(7,$product(a,$product(a,a))),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_40]) ).
tff(c_69,plain,
~ $less(7,$product(a,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_66,c_65]) ).
tff(c_79,plain,
~ $less(7,$product('#skE_1',a)),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_69]) ).
tff(c_230,plain,
$product('#skE_1',a) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_79]) ).
tff(c_229,plain,
~ $less(7,$product('#skE_1',a)),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_69]) ).
tff(c_237,plain,
~ $less(7,'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_230,c_229]) ).
tff(c_195,plain,
( ( a = '#skE_1' )
| ( a != 1 ) ),
inference(superposition,[status(thm),theory(equality)],[c_82,c_43]) ).
tff(c_227,plain,
a != 1,
inference(splitLeft,[status(thm)],[c_195]) ).
tff(c_48494,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_48493,c_41607,c_34447,c_26190,c_18469,c_6827,c_239,c_237,c_227,c_36]) ).
tff(c_48498,plain,
a = $sum($uminus(2),'#skE_2'),
inference(splitRight,[status(thm)],[c_7094]) ).
tff(c_579,plain,
$product(a,'#skE_1') = '#skE_2',
inference(superposition,[status(thm),theory(equality)],[c_50,c_431]) ).
tff(c_49018,plain,
$product($sum($uminus(2),'#skE_2'),'#skE_1') = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_48498,c_579]) ).
tff(c_55650,plain,
$product(4,'#skE_1') = $product(4,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_26726]) ).
tff(c_55967,plain,
$product($sum(1,4),'#skE_1') = $sum('#skE_1',$product(4,'#skE_1')),
inference(superposition,[status(thm),theory(equality)],[c_55650,c_52]) ).
tff(c_58382,plain,
$product(5,'#skE_1') = $product(5,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_55967]) ).
tff(c_58798,plain,
( ( '#skE_2' = $product(5,'#skE_1') )
| ( $sum($uminus(2),'#skE_2') != 5 ) ),
inference(superposition,[status(thm),theory(equality)],[c_49018,c_58382]) ).
tff(c_58800,plain,
( ( '#skE_2' = $product(5,'#skE_1') )
| ( '#skE_2' != 7 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_58798]) ).
tff(c_58829,plain,
'#skE_2' != 7,
inference(splitLeft,[status(thm)],[c_58800]) ).
tff(c_48857,plain,
~ $less($sum($uminus(2),'#skE_2'),0),
inference(demodulation,[status(thm),theory(equality)],[c_48498,c_36]) ).
tff(c_49027,plain,
~ $less('#skE_2',2),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_48857]) ).
tff(c_48629,plain,
$sum($uminus(2),'#skE_2') != 3,
inference(demodulation,[status(thm),theory(equality)],[c_48498,c_26190]) ).
tff(c_48919,plain,
'#skE_2' != 5,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_48629]) ).
tff(c_48529,plain,
$sum($uminus(2),'#skE_2') != 4,
inference(demodulation,[status(thm),theory(equality)],[c_48498,c_41607]) ).
tff(c_48876,plain,
'#skE_2' != 6,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_48529]) ).
tff(c_48660,plain,
$sum($uminus(2),'#skE_2') != 2,
inference(demodulation,[status(thm),theory(equality)],[c_48498,c_18469]) ).
tff(c_48933,plain,
'#skE_2' != 4,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_48660]) ).
tff(c_48849,plain,
$sum($uminus(2),'#skE_2') != 1,
inference(demodulation,[status(thm),theory(equality)],[c_48498,c_227]) ).
tff(c_49023,plain,
'#skE_2' != 3,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_48849]) ).
tff(c_935,plain,
( ( '#skE_3' = 0 )
| ( '#skE_2' != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_792,c_42]) ).
tff(c_974,plain,
'#skE_2' != 0,
inference(splitLeft,[status(thm)],[c_935]) ).
tff(c_45,plain,
! [A_17: $int,B_18: $int,X_43: $int] :
( ( $uminus($product(A_17,B_18)) = $product(X_43,B_18) )
| ( X_43 != $uminus(A_17) ) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_47,plain,
! [X_43: $int,B_18: $int,A_17: $int] :
( ( $uminus($product(X_43,B_18)) = $product(A_17,B_18) )
| ( X_43 != $uminus(A_17) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_45]) ).
tff(c_14824,plain,
$uminus($product($uminus(1),'#skE_2')) = '#skE_2',
inference(superposition,[status(thm),theory(equality)],[c_47,c_14323]) ).
tff(c_14827,plain,
$product($uminus(1),'#skE_2') = $uminus('#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_14824]) ).
tff(c_21673,plain,
$product('#skE_2',2) = $product(2,'#skE_2'),
inference(superposition,[status(thm),theory(equality)],[c_50,c_20404]) ).
tff(c_21860,plain,
( ( $uminus('#skE_2') = $product(2,'#skE_2') )
| ( '#skE_2' != $uminus(1) )
| ( '#skE_2' != 2 ) ),
inference(superposition,[status(thm),theory(equality)],[c_14827,c_21673]) ).
tff(c_22143,plain,
( ( '#skE_2' = 0 )
| ( '#skE_2' != $uminus(1) )
| ( '#skE_2' != 2 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_21860]) ).
tff(c_22228,plain,
( ( '#skE_2' != $uminus(1) )
| ( '#skE_2' != 2 ) ),
inference(negUnitSimplification,[status(thm)],[c_974,c_22143]) ).
tff(c_22230,plain,
'#skE_2' != 2,
inference(splitLeft,[status(thm)],[c_22228]) ).
tff(c_58830,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_58829,c_49027,c_48919,c_48876,c_48933,c_49023,c_22230,c_237]) ).
tff(c_58834,plain,
'#skE_2' = 7,
inference(splitRight,[status(thm)],[c_58800]) ).
tff(c_58833,plain,
'#skE_2' = $product(5,'#skE_1'),
inference(splitRight,[status(thm)],[c_58800]) ).
tff(c_59440,plain,
$product(5,'#skE_1') = 7,
inference(demodulation,[status(thm),theory(equality)],[c_58834,c_58833]) ).
tff(c_59449,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_59440]) ).
tff(c_59452,plain,
'#skE_2' = $product(4,'#skE_1'),
inference(splitRight,[status(thm)],[c_41212]) ).
tff(c_61275,plain,
~ $less(7,$product(4,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_59452,c_237]) ).
tff(c_61277,plain,
~ $less(1,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_61275]) ).
tff(c_61327,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6828,c_61277]) ).
tff(c_61332,plain,
a = $sum($uminus(1),'#skE_2'),
inference(splitRight,[status(thm)],[c_7250]) ).
tff(c_700,plain,
! [M_3: $int] :
( ( $product(M_3,'#skE_1') = $sum($uminus('#skE_1'),'#skE_2') )
| ( a != $sum(1,M_3) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_697]) ).
tff(c_67968,plain,
! [M_3: $int] :
( ( $product(M_3,'#skE_1') = $sum($uminus('#skE_1'),'#skE_2') )
| ( $sum(1,M_3) != $sum($uminus(1),'#skE_2') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_61332,c_700]) ).
tff(c_67970,plain,
$product($sum($uminus(2),'#skE_2'),'#skE_1') = $sum('#skE_2',$uminus('#skE_1')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_67968]) ).
tff(c_67973,plain,
$product($sum($uminus(2),'#skE_2'),'#skE_1') = $sum($uminus('#skE_1'),'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_67970]) ).
tff(c_86961,plain,
( ( $sum($uminus('#skE_1'),'#skE_2') = $product(5,'#skE_1') )
| ( $sum($uminus(2),'#skE_2') != 5 ) ),
inference(superposition,[status(thm),theory(equality)],[c_86479,c_67973]) ).
tff(c_86963,plain,
( ( '#skE_2' = $product(6,'#skE_1') )
| ( '#skE_2' != 7 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_86961]) ).
tff(c_87123,plain,
'#skE_2' != 7,
inference(splitLeft,[status(thm)],[c_86963]) ).
tff(c_203,plain,
! [M_3: $int] :
( ( $sum(a,$product(M_3,a)) = '#skE_1' )
| ( a != $sum(1,M_3) ) ),
inference(superposition,[status(thm),theory(equality)],[c_52,c_82]) ).
tff(c_4302,plain,
! [M_796: $int] :
( ( $product(M_796,a) = $sum($uminus(a),'#skE_1') )
| ( a != $sum(1,M_796) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_203]) ).
tff(c_4409,plain,
! [M_796: $int] :
( $less(0,$sum($uminus(a),'#skE_1'))
| ~ $less(0,M_796)
| ~ $less(0,a)
| ( a != $sum(1,M_796) ) ),
inference(superposition,[status(thm),theory(equality)],[c_4302,c_41]) ).
tff(c_4589,plain,
! [M_796: $int] :
( $less(0,$sum($uminus(a),'#skE_1'))
| ~ $less(0,M_796)
| ( a != $sum(1,M_796) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_430,c_4409]) ).
tff(c_4591,plain,
! [M_796: $int] :
( $less(a,'#skE_1')
| ~ $less(0,M_796)
| ( a != $sum(1,M_796) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4589]) ).
tff(c_76218,plain,
! [M_796: $int] :
( $less($sum($uminus(1),'#skE_2'),'#skE_1')
| ~ $less(0,M_796)
| ( $sum(1,M_796) != $sum($uminus(1),'#skE_2') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_61332,c_61332,c_4591]) ).
tff(c_76220,plain,
( $less('#skE_2',$sum(1,'#skE_1'))
| ~ $less(0,$sum($uminus(2),'#skE_2')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_76218]) ).
tff(c_76222,plain,
( $less('#skE_2',$sum(1,'#skE_1'))
| ~ $less(2,'#skE_2') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_76220]) ).
tff(c_76224,plain,
~ $less(2,'#skE_2'),
inference(splitLeft,[status(thm)],[c_76222]) ).
tff(c_6948,plain,
( $less(0,$sum('#skE_3',$uminus(a)))
| ~ $less(0,$sum($uminus(1),'#skE_2'))
| ~ $less(0,a) ),
inference(superposition,[status(thm),theory(equality)],[c_6831,c_41]) ).
tff(c_7178,plain,
( $less(0,$sum('#skE_3',$uminus(a)))
| ~ $less(0,$sum($uminus(1),'#skE_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_430,c_6948]) ).
tff(c_7180,plain,
( $less(a,'#skE_3')
| ~ $less(1,'#skE_2') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7178]) ).
tff(c_7282,plain,
~ $less(1,'#skE_2'),
inference(splitLeft,[status(thm)],[c_7180]) ).
tff(c_7283,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_7282,c_6827,c_239,c_36]) ).
tff(c_7287,plain,
$less(1,'#skE_2'),
inference(splitRight,[status(thm)],[c_7180]) ).
tff(c_76226,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_76224,c_22230,c_7287]) ).
tff(c_76230,plain,
$less(2,'#skE_2'),
inference(splitRight,[status(thm)],[c_76222]) ).
tff(c_71396,plain,
( ( $sum($uminus('#skE_1'),'#skE_2') = $product(4,'#skE_1') )
| ( $sum($uminus(2),'#skE_2') != 4 ) ),
inference(superposition,[status(thm),theory(equality)],[c_71097,c_67973]) ).
tff(c_71398,plain,
( ( '#skE_2' = $product(5,'#skE_1') )
| ( '#skE_2' != 6 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_71396]) ).
tff(c_71518,plain,
'#skE_2' != 6,
inference(splitLeft,[status(thm)],[c_71398]) ).
tff(c_67976,plain,
$product($sum($uminus(2),'#skE_2'),'#skE_1') = $sum($uminus('#skE_1'),'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_67970]) ).
tff(c_68449,plain,
( ( $sum($uminus('#skE_1'),'#skE_2') = $product(3,'#skE_1') )
| ( $sum($uminus(2),'#skE_2') != 3 ) ),
inference(superposition,[status(thm),theory(equality)],[c_18321,c_67976]) ).
tff(c_68451,plain,
( ( '#skE_2' = $product(4,'#skE_1') )
| ( '#skE_2' != 5 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_68449]) ).
tff(c_68521,plain,
'#skE_2' != 5,
inference(splitLeft,[status(thm)],[c_68451]) ).
tff(c_61379,plain,
$sum($uminus(1),'#skE_2') != 3,
inference(demodulation,[status(thm),theory(equality)],[c_61332,c_26190]) ).
tff(c_61627,plain,
'#skE_2' != 4,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_61379]) ).
tff(c_61410,plain,
$sum($uminus(1),'#skE_2') != 2,
inference(demodulation,[status(thm),theory(equality)],[c_61332,c_18469]) ).
tff(c_61639,plain,
'#skE_2' != 3,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_61410]) ).
tff(c_87124,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_87123,c_76230,c_71518,c_68521,c_61627,c_61639,c_237]) ).
tff(c_87128,plain,
'#skE_2' = 7,
inference(splitRight,[status(thm)],[c_86963]) ).
tff(c_87127,plain,
'#skE_2' = $product(6,'#skE_1'),
inference(splitRight,[status(thm)],[c_86963]) ).
tff(c_88227,plain,
$product(6,'#skE_1') = 7,
inference(demodulation,[status(thm),theory(equality)],[c_87128,c_87127]) ).
tff(c_88228,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_88227]) ).
tff(c_88232,plain,
'#skE_2' = 6,
inference(splitRight,[status(thm)],[c_71398]) ).
tff(c_88231,plain,
'#skE_2' = $product(5,'#skE_1'),
inference(splitRight,[status(thm)],[c_71398]) ).
tff(c_89072,plain,
$product(5,'#skE_1') = 6,
inference(demodulation,[status(thm),theory(equality)],[c_88232,c_88231]) ).
tff(c_89073,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_89072]) ).
tff(c_89077,plain,
'#skE_2' = 5,
inference(splitRight,[status(thm)],[c_68451]) ).
tff(c_89076,plain,
'#skE_2' = $product(4,'#skE_1'),
inference(splitRight,[status(thm)],[c_68451]) ).
tff(c_89902,plain,
$product(4,'#skE_1') = 5,
inference(demodulation,[status(thm),theory(equality)],[c_89077,c_89076]) ).
tff(c_89903,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_89902]) ).
tff(c_89907,plain,
a = 3,
inference(splitRight,[status(thm)],[c_25919]) ).
tff(c_750,plain,
! [M_3: $int] :
( ( $sum('#skE_1',$product(M_3,'#skE_1')) = '#skE_2' )
| ( a != $sum(1,M_3) ) ),
inference(superposition,[status(thm),theory(equality)],[c_52,c_601]) ).
tff(c_753,plain,
! [M_3: $int] :
( ( $product(M_3,'#skE_1') = $sum($uminus('#skE_1'),'#skE_2') )
| ( a != $sum(1,M_3) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_750]) ).
tff(c_111002,plain,
! [M_3: $int] :
( ( $product(M_3,'#skE_1') = $sum($uminus('#skE_1'),'#skE_2') )
| ( $sum(1,M_3) != 3 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_89907,c_753]) ).
tff(c_111004,plain,
$product(2,'#skE_1') = $sum('#skE_2',$uminus('#skE_1')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_111002]) ).
tff(c_111009,plain,
$product(2,'#skE_1') = $sum($uminus('#skE_1'),'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_111004]) ).
tff(c_5567,plain,
$product(2,'#skE_1') = $product(2,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5564]) ).
tff(c_111242,plain,
$sum($uminus('#skE_1'),'#skE_2') = $product(2,'#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_111009,c_5567]) ).
tff(c_111244,plain,
'#skE_2' = $product(3,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_111242]) ).
tff(c_111581,plain,
~ $less(7,$product(3,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_111244,c_237]) ).
tff(c_44,plain,
! [C_21: $int,B_22: $int] :
( ( $product(C_21,B_22) != C_21 )
| ( C_21 = 0 )
| ( B_22 = 1 ) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_554,plain,
( ( '#skE_2' = 0 )
| ( a = 1 )
| ( '#skE_2' != '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_431,c_44]) ).
tff(c_596,plain,
( ( '#skE_2' = 0 )
| ( '#skE_2' != '#skE_1' ) ),
inference(negUnitSimplification,[status(thm)],[c_227,c_554]) ).
tff(c_598,plain,
'#skE_2' != '#skE_1',
inference(splitLeft,[status(thm)],[c_596]) ).
tff(c_21852,plain,
( ( $product(2,'#skE_2') = $product(2,'#skE_1') )
| ( '#skE_2' != 2 )
| ( '#skE_1' != 2 ) ),
inference(superposition,[status(thm),theory(equality)],[c_5567,c_21673]) ).
tff(c_22139,plain,
( ( '#skE_2' = '#skE_1' )
| ( '#skE_2' != 2 )
| ( '#skE_1' != 2 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_21852]) ).
tff(c_22223,plain,
( ( '#skE_2' != 2 )
| ( '#skE_1' != 2 ) ),
inference(negUnitSimplification,[status(thm)],[c_598,c_22139]) ).
tff(c_22225,plain,
'#skE_1' != 2,
inference(splitLeft,[status(thm)],[c_22223]) ).
tff(c_111767,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_111581,c_22225,c_6828]) ).
tff(c_111771,plain,
'#skE_2' = 2,
inference(splitRight,[status(thm)],[c_22228]) ).
tff(c_111957,plain,
$less(a,2),
inference(demodulation,[status(thm),theory(equality)],[c_111771,c_6827]) ).
tff(c_112006,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_111957,c_239,c_227,c_36]) ).
tff(c_112010,plain,
'#skE_1' = 2,
inference(splitRight,[status(thm)],[c_22223]) ).
tff(c_112017,plain,
$product(2,2) = $product(2,2),
inference(demodulation,[status(thm),theory(equality)],[c_112010,c_112010,c_5567]) ).
tff(c_112162,plain,
$product(2,2) = 4,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_112017]) ).
tff(c_113115,plain,
$product($sum(1,2),2) = $sum(2,4),
inference(superposition,[status(thm),theory(equality)],[c_112162,c_52]) ).
tff(c_113117,plain,
$product(3,2) = 6,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_113115]) ).
tff(c_114348,plain,
$product($sum(1,3),2) = $sum(2,6),
inference(superposition,[status(thm),theory(equality)],[c_113117,c_52]) ).
tff(c_114350,plain,
$product(4,2) = 8,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_114348]) ).
tff(c_114995,plain,
$product($sum(1,4),2) = $sum(2,8),
inference(superposition,[status(thm),theory(equality)],[c_114350,c_52]) ).
tff(c_114997,plain,
$product(5,2) = 10,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_114995]) ).
tff(c_112221,plain,
$product(a,2) = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_112010,c_579]) ).
tff(c_118959,plain,
$product($sum(1,5),2) = $sum(2,10),
inference(superposition,[status(thm),theory(equality)],[c_114997,c_52]) ).
tff(c_118961,plain,
$product(6,2) = 12,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_118959]) ).
tff(c_119540,plain,
( ( '#skE_2' = 12 )
| ( a != 6 ) ),
inference(superposition,[status(thm),theory(equality)],[c_112221,c_118961]) ).
tff(c_120002,plain,
a != 6,
inference(splitLeft,[status(thm)],[c_119540]) ).
tff(c_118928,plain,
( ( '#skE_2' = 10 )
| ( a != 5 ) ),
inference(superposition,[status(thm),theory(equality)],[c_114997,c_112221]) ).
tff(c_119017,plain,
a != 5,
inference(splitLeft,[status(thm)],[c_118928]) ).
tff(c_115040,plain,
$product(2,4) = 8,
inference(superposition,[status(thm),theory(equality)],[c_50,c_114350]) ).
tff(c_253,plain,
$product('#skE_1',a) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_244]) ).
tff(c_112225,plain,
$product(2,a) = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_112010,c_253]) ).
tff(c_115476,plain,
( ( '#skE_2' = 8 )
| ( a != 4 ) ),
inference(superposition,[status(thm),theory(equality)],[c_115040,c_112225]) ).
tff(c_115551,plain,
a != 4,
inference(splitLeft,[status(thm)],[c_115476]) ).
tff(c_4638,plain,
( ( $sum($uminus(a),'#skE_1') = '#skE_2' )
| ( a != $sum(1,'#skE_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_253,c_4302]) ).
tff(c_4639,plain,
( ( a = $sum('#skE_1',$uminus('#skE_2')) )
| ( a != $sum(1,'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4638]) ).
tff(c_4641,plain,
( ( a = $sum($uminus('#skE_2'),'#skE_1') )
| ( a != $sum(1,'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4639]) ).
tff(c_12254,plain,
a != $sum(1,'#skE_1'),
inference(splitLeft,[status(thm)],[c_4641]) ).
tff(c_112043,plain,
a != $sum(1,2),
inference(demodulation,[status(thm),theory(equality)],[c_112010,c_12254]) ).
tff(c_112170,plain,
a != 3,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_112043]) ).
tff(c_120003,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_120002,c_119017,c_115551,c_112170,c_18469,c_6827,c_239,c_237,c_227,c_36]) ).
tff(c_120006,plain,
'#skE_2' = 12,
inference(splitRight,[status(thm)],[c_119540]) ).
tff(c_120202,plain,
~ $less(7,12),
inference(demodulation,[status(thm),theory(equality)],[c_120006,c_237]) ).
tff(c_120213,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_120202]) ).
tff(c_120217,plain,
a = 5,
inference(splitRight,[status(thm)],[c_118928]) ).
tff(c_120230,plain,
$product(5,2) = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_120217,c_112221]) ).
tff(c_120328,plain,
'#skE_2' = 10,
inference(demodulation,[status(thm),theory(equality)],[c_114997,c_120230]) ).
tff(c_120501,plain,
~ $less(7,10),
inference(demodulation,[status(thm),theory(equality)],[c_120328,c_237]) ).
tff(c_120513,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_120501]) ).
tff(c_120516,plain,
'#skE_2' = 8,
inference(splitRight,[status(thm)],[c_115476]) ).
tff(c_120624,plain,
~ $less(7,8),
inference(demodulation,[status(thm),theory(equality)],[c_120516,c_237]) ).
tff(c_120673,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_120624]) ).
tff(c_120676,plain,
'#skE_2' = $product(2,'#skE_1'),
inference(splitRight,[status(thm)],[c_18207]) ).
tff(c_121421,plain,
~ $less(7,$product(2,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_120676,c_237]) ).
tff(c_121440,plain,
~ $less(3,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_121421]) ).
tff(c_120677,plain,
a = 2,
inference(splitRight,[status(thm)],[c_18207]) ).
tff(c_193,plain,
( ( '#skE_1' = 0 )
| ( a = 1 )
| ( a != '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_82,c_44]) ).
tff(c_261,plain,
( ( '#skE_1' = 0 )
| ( a != '#skE_1' ) ),
inference(negUnitSimplification,[status(thm)],[c_227,c_193]) ).
tff(c_263,plain,
a != '#skE_1',
inference(splitLeft,[status(thm)],[c_261]) ).
tff(c_120930,plain,
'#skE_1' != 2,
inference(demodulation,[status(thm),theory(equality)],[c_120677,c_263]) ).
tff(c_2442,plain,
$product($sum(1,a),a) = $sum('#skE_1',a),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_162]) ).
tff(c_2707,plain,
( ( $sum('#skE_1',a) = '#skE_2' )
| ( $sum(1,a) != '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_253,c_2442]) ).
tff(c_2708,plain,
( ( a = $sum($uminus('#skE_1'),'#skE_2') )
| ( a != $sum($uminus(1),'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2707]) ).
tff(c_2710,plain,
( ( a = $sum('#skE_2',$uminus('#skE_1')) )
| ( a != $sum($uminus(1),'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2708]) ).
tff(c_15985,plain,
a != $sum($uminus(1),'#skE_1'),
inference(splitLeft,[status(thm)],[c_2710]) ).
tff(c_120681,plain,
$sum($uminus(1),'#skE_1') != 2,
inference(demodulation,[status(thm),theory(equality)],[c_120677,c_15985]) ).
tff(c_120851,plain,
'#skE_1' != 3,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_120681]) ).
tff(c_121441,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_121440,c_120930,c_120851,c_6828]) ).
tff(c_121446,plain,
a = $sum($uminus(1),'#skE_1'),
inference(splitRight,[status(thm)],[c_2710]) ).
tff(c_121442,plain,
a = $sum('#skE_2',$uminus('#skE_1')),
inference(splitRight,[status(thm)],[c_2710]) ).
tff(c_121445,plain,
a = $sum($uminus('#skE_1'),'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_121442]) ).
tff(c_121767,plain,
$sum($uminus('#skE_1'),'#skE_2') = $sum($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_121446,c_121445]) ).
tff(c_121770,plain,
'#skE_2' = $sum($uminus(1),$product(2,'#skE_1')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_121767]) ).
tff(c_532,plain,
! [B_13: $int,C_14: $int] :
( ( $sum($product('#skE_1',B_13),$product('#skE_1',C_14)) = '#skE_2' )
| ( a != $sum(B_13,C_14) ) ),
inference(superposition,[status(thm),theory(equality)],[c_431,c_49]) ).
tff(c_535,plain,
! [C_14: $int,B_13: $int] :
( ( $sum('#skE_2',$uminus($product('#skE_1',C_14))) = $product('#skE_1',B_13) )
| ( a != $sum(C_14,B_13) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_532]) ).
tff(c_3069,plain,
! [C_575: $int,B_577: $int] :
( ( $sum('#skE_2',$uminus($product('#skE_1',C_575))) = $product('#skE_1',B_577) )
| ( a != $sum(C_575,B_577) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_532]) ).
tff(c_3383,plain,
! [C_575: $int] :
( ( $sum('#skE_2',$uminus($product('#skE_1',C_575))) = '#skE_2' )
| ( $sum(C_575,a) != a ) ),
inference(superposition,[status(thm),theory(equality)],[c_3069,c_253]) ).
tff(c_3657,plain,
$product('#skE_1',0) = 0,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3383]) ).
tff(c_3889,plain,
! [C_14: $int] :
( ( $sum('#skE_2',$uminus($product('#skE_1',C_14))) = 0 )
| ( a != $sum(C_14,0) ) ),
inference(superposition,[status(thm),theory(equality)],[c_535,c_3657]) ).
tff(c_3893,plain,
$product('#skE_1',a) = '#skE_2',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3889]) ).
tff(c_122964,plain,
$product('#skE_1',$sum($uminus(1),'#skE_1')) = $sum($uminus(1),$product(2,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_121770,c_121446,c_3893]) ).
tff(c_126966,plain,
( ( $sum($uminus(1),$product(2,'#skE_1')) = $product(3,'#skE_1') )
| ( $sum($uminus(1),'#skE_1') != 3 ) ),
inference(superposition,[status(thm),theory(equality)],[c_126794,c_122964]) ).
tff(c_126968,plain,
( ( '#skE_1' = $uminus(1) )
| ( '#skE_1' != 4 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_126966]) ).
tff(c_127064,plain,
'#skE_1' != 4,
inference(splitLeft,[status(thm)],[c_126968]) ).
tff(c_125894,plain,
$product('#skE_1',2) = $product(2,'#skE_1'),
inference(superposition,[status(thm),theory(equality)],[c_123467,c_50]) ).
tff(c_126048,plain,
( ( $sum($uminus(1),$product(2,'#skE_1')) = $product(2,'#skE_1') )
| ( $sum($uminus(1),'#skE_1') != 2 ) ),
inference(superposition,[status(thm),theory(equality)],[c_125894,c_122964]) ).
tff(c_126050,plain,
'#skE_1' != 3,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_126048]) ).
tff(c_122087,plain,
~ $less(7,$sum($uminus(1),$product(2,'#skE_1'))),
inference(demodulation,[status(thm),theory(equality)],[c_121770,c_237]) ).
tff(c_122112,plain,
~ $less(4,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_122087]) ).
tff(c_7121,plain,
( ( $sum('#skE_3',$uminus(a)) = '#skE_2' )
| ( $sum($uminus(1),'#skE_2') != '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_6831,c_253]) ).
tff(c_7122,plain,
( ( a = $sum('#skE_3',$uminus('#skE_2')) )
| ( '#skE_2' != $sum(1,'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7121]) ).
tff(c_7124,plain,
( ( a = $sum($uminus('#skE_2'),'#skE_3') )
| ( '#skE_2' != $sum(1,'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7122]) ).
tff(c_13288,plain,
'#skE_2' != $sum(1,'#skE_1'),
inference(splitLeft,[status(thm)],[c_7124]) ).
tff(c_122056,plain,
$sum($uminus(1),$product(2,'#skE_1')) != $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_121770,c_13288]) ).
tff(c_122102,plain,
'#skE_1' != 2,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_122056]) ).
tff(c_127065,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_127064,c_126050,c_122112,c_122102,c_6828]) ).
tff(c_127069,plain,
'#skE_1' = 4,
inference(splitRight,[status(thm)],[c_126968]) ).
tff(c_127068,plain,
'#skE_1' = $uminus(1),
inference(splitRight,[status(thm)],[c_126968]) ).
tff(c_127319,plain,
$uminus(1) = 4,
inference(demodulation,[status(thm),theory(equality)],[c_127069,c_127068]) ).
tff(c_127321,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_127319]) ).
tff(c_127326,plain,
'#skE_2' = $sum(1,'#skE_1'),
inference(splitRight,[status(thm)],[c_7124]) ).
tff(c_127322,plain,
a = $sum($uminus('#skE_2'),'#skE_3'),
inference(splitRight,[status(thm)],[c_7124]) ).
tff(c_127325,plain,
a = $sum('#skE_3',$uminus('#skE_2')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_127322]) ).
tff(c_128472,plain,
a = $sum('#skE_3',$uminus($sum(1,'#skE_1'))),
inference(demodulation,[status(thm),theory(equality)],[c_127326,c_127325]) ).
tff(c_128474,plain,
a = $sum($uminus(1),$sum($uminus('#skE_1'),'#skE_3')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_128472]) ).
tff(c_128565,plain,
$sum($uminus(1),$sum($uminus('#skE_1'),'#skE_3')) != 1,
inference(demodulation,[status(thm),theory(equality)],[c_128474,c_227]) ).
tff(c_128619,plain,
'#skE_3' != $sum(2,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_128565]) ).
tff(c_130870,plain,
$product(2,'#skE_1') = $product(2,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5564]) ).
tff(c_131037,plain,
$product($sum(1,2),'#skE_1') = $sum('#skE_1',$product(2,'#skE_1')),
inference(superposition,[status(thm),theory(equality)],[c_130870,c_52]) ).
tff(c_132597,plain,
$product(3,'#skE_1') = $product(3,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_131037]) ).
tff(c_132804,plain,
$product($sum(1,3),'#skE_1') = $sum('#skE_1',$product(3,'#skE_1')),
inference(superposition,[status(thm),theory(equality)],[c_132597,c_52]) ).
tff(c_134120,plain,
$product(4,'#skE_1') = $product(4,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_132804]) ).
tff(c_127512,plain,
$product(a,'#skE_1') = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_127326,c_579]) ).
tff(c_128629,plain,
$product($sum($uminus(1),$sum($uminus('#skE_1'),'#skE_3')),'#skE_1') = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_128474,c_127512]) ).
tff(c_134343,plain,
( ( $sum(1,'#skE_1') = $product(4,'#skE_1') )
| ( $sum($uminus(1),$sum($uminus('#skE_1'),'#skE_3')) != 4 ) ),
inference(superposition,[status(thm),theory(equality)],[c_134120,c_128629]) ).
tff(c_134345,plain,
( ( $product(3,'#skE_1') = 1 )
| ( '#skE_3' != $sum(5,'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_134343]) ).
tff(c_136802,plain,
'#skE_3' != $sum(5,'#skE_1'),
inference(splitLeft,[status(thm)],[c_134345]) ).
tff(c_584,plain,
$uminus($product($uminus('#skE_1'),a)) = '#skE_2',
inference(superposition,[status(thm),theory(equality)],[c_47,c_431]) ).
tff(c_587,plain,
$product($uminus('#skE_1'),a) = $uminus('#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_584]) ).
tff(c_6772,plain,
( ( $sum('#skE_2',$uminus(a)) = $uminus('#skE_2') )
| ( $uminus('#skE_1') != $sum($uminus(1),'#skE_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_587,c_6394]) ).
tff(c_6774,plain,
( ( a = $product(2,'#skE_2') )
| ( $product(2,'#skE_1') != 1 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6772]) ).
tff(c_11250,plain,
$product(2,'#skE_1') != 1,
inference(splitLeft,[status(thm)],[c_6774]) ).
tff(c_132796,plain,
( ( $sum(1,'#skE_1') = $product(3,'#skE_1') )
| ( $sum($uminus(1),$sum($uminus('#skE_1'),'#skE_3')) != 3 ) ),
inference(superposition,[status(thm),theory(equality)],[c_132597,c_128629]) ).
tff(c_132798,plain,
( ( $product(2,'#skE_1') = 1 )
| ( '#skE_3' != $sum(4,'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_132796]) ).
tff(c_134453,plain,
'#skE_3' != $sum(4,'#skE_1'),
inference(negUnitSimplification,[status(thm)],[c_11250,c_132798]) ).
tff(c_131029,plain,
( ( $sum(1,'#skE_1') = $product(2,'#skE_1') )
| ( $sum($uminus(1),$sum($uminus('#skE_1'),'#skE_3')) != 2 ) ),
inference(superposition,[status(thm),theory(equality)],[c_130870,c_128629]) ).
tff(c_131031,plain,
( ( '#skE_1' = 1 )
| ( '#skE_3' != $sum(3,'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_131029]) ).
tff(c_131125,plain,
'#skE_3' != $sum(3,'#skE_1'),
inference(negUnitSimplification,[status(thm)],[c_773,c_131031]) ).
tff(c_127518,plain,
$product('#skE_1',a) = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_127326,c_253]) ).
tff(c_57,plain,
! [M_3: $int,N_4: $int] : ( $product($sum(1,M_3),N_4) = $sum(N_4,$product(M_3,N_4)) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_914,plain,
! [C_14: $int,X_44: $int] :
( ( $sum('#skE_3',$product('#skE_2',C_14)) = $product('#skE_2',X_44) )
| ( X_44 != $sum(a,C_14) ) ),
inference(superposition,[status(thm),theory(equality)],[c_792,c_49]) ).
tff(c_917,plain,
! [X_44: $int,C_14: $int] :
( ( $sum($uminus('#skE_3'),$product('#skE_2',X_44)) = $product('#skE_2',C_14) )
| ( X_44 != $sum(C_14,a) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_914]) ).
tff(c_127844,plain,
! [C_14: $int,X_44: $int] :
( ( $sum(C_14,$product('#skE_1',C_14)) = $sum($uminus('#skE_3'),$sum(X_44,$product('#skE_1',X_44))) )
| ( X_44 != $sum(C_14,a) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_57,c_57,c_127326,c_127326,c_917]) ).
tff(c_127848,plain,
! [C_14: $int] : ( $sum($uminus(C_14),$sum($sum(a,C_14),$sum($uminus('#skE_3'),$product('#skE_1',$sum(a,C_14))))) = $product('#skE_1',C_14) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_127844]) ).
tff(c_127849,plain,
! [X_15560: $int,X_15561: $int,C_15559: $int] :
( ( $sum(X_15560,$sum(X_15561,$sum($uminus('#skE_3'),$product('#skE_1',X_15561)))) = $product('#skE_1',C_15559) )
| ( X_15560 != $uminus(C_15559) )
| ( X_15561 != $sum(a,C_15559) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_127844]) ).
tff(c_127910,plain,
( ( $sum($uminus(a),$sum($sum(a,a),$sum($uminus('#skE_3'),$product('#skE_1',$sum(a,a))))) = $sum('#skE_1',a) )
| ( $sum(1,a) != '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_127849,c_165]) ).
tff(c_128206,plain,
( ( $sum('#skE_1',a) = $sum(1,'#skE_1') )
| ( $sum(1,a) != '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_127518,c_127848,c_127910]) ).
tff(c_128208,plain,
( ( a = 1 )
| ( a != $sum($uminus(1),'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_128206]) ).
tff(c_129404,plain,
( ( $sum($uminus(1),$sum($uminus('#skE_1'),'#skE_3')) = 1 )
| ( $sum($uminus(1),$sum($uminus('#skE_1'),'#skE_3')) != $sum($uminus(1),'#skE_1') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_128474,c_128474,c_128208]) ).
tff(c_129406,plain,
( ( '#skE_3' = $sum(2,'#skE_1') )
| ( '#skE_3' != $product(2,'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_129404]) ).
tff(c_129408,plain,
'#skE_3' != $product(2,'#skE_1'),
inference(splitLeft,[status(thm)],[c_129406]) ).
tff(c_127468,plain,
$less(a,$sum(1,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_127326,c_6827]) ).
tff(c_128482,plain,
$less($sum($uminus(1),$sum($uminus('#skE_1'),'#skE_3')),$sum(1,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_128474,c_127468]) ).
tff(c_128580,plain,
$less('#skE_3',$sum(2,$product(2,'#skE_1'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_128482]) ).
tff(c_128559,plain,
$sum($uminus(1),$sum($uminus('#skE_1'),'#skE_3')) != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_128474,c_263]) ).
tff(c_128618,plain,
'#skE_3' != $sum(1,$product(2,'#skE_1')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_128559]) ).
tff(c_128573,plain,
~ $less($sum($uminus(1),$sum($uminus('#skE_1'),'#skE_3')),0),
inference(demodulation,[status(thm),theory(equality)],[c_128474,c_36]) ).
tff(c_128623,plain,
~ $less('#skE_3',$sum(1,'#skE_1')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_128573]) ).
tff(c_932,plain,
( ( '#skE_3' = 0 )
| ( a = 1 )
| ( '#skE_3' != '#skE_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_792,c_44]) ).
tff(c_976,plain,
( ( '#skE_3' = 0 )
| ( '#skE_3' != '#skE_2' ) ),
inference(negUnitSimplification,[status(thm)],[c_227,c_932]) ).
tff(c_978,plain,
'#skE_3' != '#skE_2',
inference(splitLeft,[status(thm)],[c_976]) ).
tff(c_127505,plain,
'#skE_3' != $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_127326,c_978]) ).
tff(c_127448,plain,
~ $less(7,$sum(1,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_127326,c_237]) ).
tff(c_127516,plain,
~ $less(6,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_127448]) ).
tff(c_136803,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_136802,c_134453,c_131125,c_129408,c_128580,c_128618,c_128623,c_128619,c_127505,c_127516]) ).
tff(c_136806,plain,
$product(3,'#skE_1') = 1,
inference(splitRight,[status(thm)],[c_134345]) ).
tff(c_136824,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_136806]) ).
tff(c_136825,plain,
'#skE_3' = $sum(2,'#skE_1'),
inference(splitRight,[status(thm)],[c_129406]) ).
tff(c_136827,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_128619,c_136825]) ).
tff(c_136833,plain,
a = $sum(1,'#skE_1'),
inference(splitRight,[status(thm)],[c_4641]) ).
tff(c_136829,plain,
a = $sum($uminus('#skE_2'),'#skE_1'),
inference(splitRight,[status(thm)],[c_4641]) ).
tff(c_136832,plain,
a = $sum('#skE_1',$uminus('#skE_2')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_136829]) ).
tff(c_139050,plain,
$sum('#skE_1',$uminus('#skE_2')) = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_136833,c_136832]) ).
tff(c_139052,plain,
'#skE_2' = $uminus(1),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_139050]) ).
tff(c_139078,plain,
$less(1,$uminus(1)),
inference(demodulation,[status(thm),theory(equality)],[c_139052,c_7287]) ).
tff(c_139105,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_139078]) ).
tff(c_139109,plain,
$product(2,'#skE_1') = 1,
inference(splitRight,[status(thm)],[c_6774]) ).
tff(c_140109,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_139109]) ).
tff(c_140112,plain,
'#skE_3' = 0,
inference(splitRight,[status(thm)],[c_976]) ).
tff(c_776,plain,
$product('#skE_2',a) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_259]) ).
tff(c_775,plain,
$less(1,$product('#skE_2',a)),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_249]) ).
tff(c_783,plain,
$less(1,'#skE_3'),
inference(demodulation,[status(thm),theory(equality)],[c_776,c_775]) ).
tff(c_140119,plain,
$less(1,0),
inference(demodulation,[status(thm),theory(equality)],[c_140112,c_783]) ).
tff(c_140125,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_140119]) ).
tff(c_140129,plain,
'#skE_1' = 1,
inference(splitRight,[status(thm)],[c_734]) ).
tff(c_140128,plain,
a = '#skE_2',
inference(splitRight,[status(thm)],[c_734]) ).
tff(c_140167,plain,
$product('#skE_2','#skE_2') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_140128,c_140128,c_73]) ).
tff(c_140560,plain,
$product('#skE_2','#skE_2') = 1,
inference(demodulation,[status(thm),theory(equality)],[c_140129,c_140167]) ).
tff(c_140180,plain,
$less(1,$product('#skE_2','#skE_2')),
inference(demodulation,[status(thm),theory(equality)],[c_140128,c_259]) ).
tff(c_140562,plain,
$less(1,1),
inference(demodulation,[status(thm),theory(equality)],[c_140560,c_140180]) ).
tff(c_140565,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_140562]) ).
tff(c_140568,plain,
'#skE_1' = 0,
inference(splitRight,[status(thm)],[c_261]) ).
tff(c_140569,plain,
a = '#skE_1',
inference(splitRight,[status(thm)],[c_261]) ).
tff(c_140744,plain,
a = 0,
inference(demodulation,[status(thm),theory(equality)],[c_140568,c_140569]) ).
tff(c_140745,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_239,c_140744]) ).
tff(c_140749,plain,
a = 0,
inference(splitRight,[status(thm)],[c_225]) ).
tff(c_140863,plain,
$less(1,0),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_140749,c_50,c_50,c_35]) ).
tff(c_140865,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_140863]) ).
tff(c_140869,plain,
a = 1,
inference(splitRight,[status(thm)],[c_195]) ).
tff(c_140901,plain,
$less(1,1),
inference(demodulation,[status(thm),theory(equality)],[c_43,c_43,c_43,c_140869,c_140869,c_140869,c_140869,c_50,c_50,c_35]) ).
tff(c_140903,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_140901]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : ARI678_1 : TPTP v8.1.2. Released v6.3.0.
% 0.13/0.14 % 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
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 4 00:34:15 EDT 2023
% 0.14/0.36 % CPUTime :
% 30.48/10.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.40/11.00
% 31.40/11.00 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 31.89/11.12
% 31.89/11.12 Inference rules
% 31.89/11.12 ----------------------
% 31.89/11.12 #Ref : 0
% 31.89/11.12 #Sup : 21199
% 31.89/11.12 #Fact : 0
% 31.89/11.12 #Define : 4
% 31.89/11.12 #Split : 150
% 31.89/11.12 #Chain : 0
% 31.89/11.12 #Close : 23
% 31.89/11.12
% 31.89/11.12 Ordering : LPO
% 31.89/11.12
% 31.89/11.12 Simplification rules
% 31.89/11.12 ----------------------
% 31.89/11.12 #Subsume : 6866
% 31.89/11.12 #Demod : 9515
% 31.89/11.12 #Tautology : 7790
% 31.89/11.12 #SimpNegUnit : 1922
% 31.89/11.12 #BackRed : 901
% 31.89/11.12
% 31.89/11.12 #Partial instantiations: 0
% 31.89/11.12 #Strategies tried : 1
% 31.89/11.12
% 31.89/11.12 Timing (in seconds)
% 31.89/11.12 ----------------------
% 31.89/11.12 Preprocessing : 0.53
% 31.89/11.12 Parsing : 0.28
% 31.89/11.13 CNF conversion : 0.02
% 31.89/11.13 Main loop : 9.31
% 31.89/11.13 Inferencing : 1.14
% 31.89/11.13 Reduction : 3.54
% 31.89/11.13 Demodulation : 2.72
% 31.89/11.13 BG Simplification : 0.58
% 31.89/11.13 Subsumption : 1.85
% 31.89/11.13 Abstraction : 0.29
% 31.89/11.13 MUC search : 0.51
% 31.89/11.13 Cooper : 0.91
% 31.89/11.13 Total : 10.05
% 31.89/11.13 Index Insertion : 0.00
% 31.89/11.13 Index Deletion : 0.00
% 31.89/11.13 Index Matching : 0.00
% 31.89/11.13 BG Taut test : 0.00
%------------------------------------------------------------------------------