TSTP Solution File: KLE142+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : KLE142+2 : TPTP v8.1.2. Released v4.0.0.
% 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 : n010.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 10:44:55 EDT 2023
% Result : Theorem 18.49s 6.43s
% Output : CNFRefutation 18.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 24
% Syntax : Number of formulae : 130 ( 97 unt; 9 typ; 0 def)
% Number of atoms : 145 ( 88 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 53 ( 29 ~; 20 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 162 (; 162 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ leq > multiplication > addition > #nlpp > strong_iteration > star > zero > one > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(strong_iteration,type,
strong_iteration: $i > $i ).
tff(star,type,
star: $i > $i ).
tff(multiplication,type,
multiplication: ( $i * $i ) > $i ).
tff(addition,type,
addition: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(one,type,
one: $i ).
tff(leq,type,
leq: ( $i * $i ) > $o ).
tff(zero,type,
zero: $i ).
tff(f_52,axiom,
! [A,B] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
tff(f_65,axiom,
! [A] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
tff(f_63,axiom,
! [A] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
tff(f_56,axiom,
! [A] : ( addition(A,zero) = A ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
tff(f_68,axiom,
! [A,B,C] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity1) ).
tff(f_58,axiom,
! [A] : ( addition(A,A) = A ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
tff(f_54,axiom,
! [C,B,A] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
tff(f_100,axiom,
! [A,B] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
tff(f_93,axiom,
! [A,B,C] :
( leq(C,addition(multiplication(A,C),B))
=> leq(C,multiplication(strong_iteration(A),B)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
tff(f_107,negated_conjecture,
~ ! [X0] :
( leq(strong_iteration(strong_iteration(X0)),strong_iteration(one))
& leq(strong_iteration(one),strong_iteration(strong_iteration(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(f_86,axiom,
! [A,B,C] :
( leq(addition(multiplication(C,A),B),C)
=> leq(multiplication(B,star(A)),C) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_induction2) ).
tff(f_89,axiom,
! [A] : ( strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
tff(f_70,axiom,
! [A,B,C] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
tff(f_73,axiom,
! [A] : ( multiplication(zero,A) = zero ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
tff(f_61,axiom,
! [A,B,C] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
tff(c_2,plain,
! [B_2,A_1] : ( addition(B_2,A_1) = addition(A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_14,plain,
! [A_12] : ( multiplication(one,A_12) = A_12 ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_12,plain,
! [A_11] : ( multiplication(A_11,one) = A_11 ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_114,plain,
! [B_40,A_41] : ( addition(B_40,A_41) = addition(A_41,B_40) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_6,plain,
! [A_6] : ( addition(A_6,zero) = A_6 ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_130,plain,
! [A_41] : ( addition(zero,A_41) = A_41 ),
inference(superposition,[status(thm),theory(equality)],[c_114,c_6]) ).
tff(c_22276,plain,
! [A_360,B_361,C_362] : ( addition(multiplication(A_360,B_361),multiplication(A_360,C_362)) = multiplication(A_360,addition(B_361,C_362)) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_28023,plain,
! [A_426,B_427] : ( multiplication(A_426,addition(B_427,one)) = addition(multiplication(A_426,B_427),A_426) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_22276]) ).
tff(c_28239,plain,
! [A_426] : ( addition(multiplication(A_426,zero),A_426) = multiplication(A_426,one) ),
inference(superposition,[status(thm),theory(equality)],[c_130,c_28023]) ).
tff(c_28312,plain,
! [A_428] : ( addition(multiplication(A_428,zero),A_428) = A_428 ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_28239]) ).
tff(c_22327,plain,
! [A_11,B_361] : ( multiplication(A_11,addition(B_361,one)) = addition(multiplication(A_11,B_361),A_11) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_22276]) ).
tff(c_28319,plain,
! [A_11] : ( addition(multiplication(A_11,multiplication(one,zero)),A_11) = multiplication(A_11,one) ),
inference(superposition,[status(thm),theory(equality)],[c_28312,c_22327]) ).
tff(c_28479,plain,
! [A_11] : ( addition(A_11,multiplication(A_11,zero)) = A_11 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_14,c_12,c_28319]) ).
tff(c_8,plain,
! [A_7] : ( addition(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_21312,plain,
! [A_335,B_336,C_337] : ( addition(addition(A_335,B_336),C_337) = addition(A_335,addition(B_336,C_337)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_21392,plain,
! [A_7,C_337] : ( addition(A_7,addition(A_7,C_337)) = addition(A_7,C_337) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_21312]) ).
tff(c_38,plain,
! [A_33,B_34] :
( leq(A_33,B_34)
| ( addition(A_33,B_34) != B_34 ) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_24675,plain,
! [C_385,A_386,B_387] :
( leq(C_385,multiplication(strong_iteration(A_386),B_387))
| ~ leq(C_385,addition(multiplication(A_386,C_385),B_387)) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_35369,plain,
! [A_486,B_487] :
( leq(A_486,multiplication(strong_iteration(one),B_487))
| ~ leq(A_486,addition(A_486,B_487)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_24675]) ).
tff(c_35497,plain,
! [A_33,B_487] :
( leq(A_33,multiplication(strong_iteration(one),B_487))
| ( addition(A_33,addition(A_33,B_487)) != addition(A_33,B_487) ) ),
inference(resolution,[status(thm)],[c_38,c_35369]) ).
tff(c_35538,plain,
! [A_488,B_489] : leq(A_488,multiplication(strong_iteration(one),B_489)),
inference(demodulation,[status(thm),theory(equality)],[c_21392,c_35497]) ).
tff(c_35562,plain,
! [A_488] : leq(A_488,strong_iteration(one)),
inference(superposition,[status(thm),theory(equality)],[c_12,c_35538]) ).
tff(c_371,plain,
! [A_52,B_53,C_54] : ( addition(addition(A_52,B_53),C_54) = addition(A_52,addition(B_53,C_54)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_448,plain,
! [A_7,C_54] : ( addition(A_7,addition(A_7,C_54)) = addition(A_7,C_54) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_371]) ).
tff(c_1348,plain,
! [C_87,A_88,B_89] :
( leq(C_87,multiplication(strong_iteration(A_88),B_89))
| ~ leq(C_87,addition(multiplication(A_88,C_87),B_89)) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_10656,plain,
! [A_186,B_187] :
( leq(A_186,multiplication(strong_iteration(one),B_187))
| ~ leq(A_186,addition(A_186,B_187)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_1348]) ).
tff(c_10750,plain,
! [A_33,B_187] :
( leq(A_33,multiplication(strong_iteration(one),B_187))
| ( addition(A_33,addition(A_33,B_187)) != addition(A_33,B_187) ) ),
inference(resolution,[status(thm)],[c_38,c_10656]) ).
tff(c_11148,plain,
! [A_190,B_191] : leq(A_190,multiplication(strong_iteration(one),B_191)),
inference(demodulation,[status(thm),theory(equality)],[c_448,c_10750]) ).
tff(c_11180,plain,
! [A_192] : leq(A_192,strong_iteration(one)),
inference(superposition,[status(thm),theory(equality)],[c_12,c_11148]) ).
tff(c_36,plain,
! [A_33,B_34] :
( ( addition(A_33,B_34) = B_34 )
| ~ leq(A_33,B_34) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_11268,plain,
! [A_195] : ( addition(A_195,strong_iteration(one)) = strong_iteration(one) ),
inference(resolution,[status(thm)],[c_11180,c_36]) ).
tff(c_11417,plain,
! [A_195] : ( addition(strong_iteration(one),A_195) = strong_iteration(one) ),
inference(superposition,[status(thm),theory(equality)],[c_11268,c_2]) ).
tff(c_11172,plain,
! [A_190] : leq(A_190,strong_iteration(one)),
inference(superposition,[status(thm),theory(equality)],[c_12,c_11148]) ).
tff(c_32,plain,
! [C_31,A_29,B_30] :
( leq(C_31,multiplication(strong_iteration(A_29),B_30))
| ~ leq(C_31,addition(multiplication(A_29,C_31),B_30)) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_11379,plain,
! [C_31,A_29] :
( leq(C_31,multiplication(strong_iteration(A_29),strong_iteration(one)))
| ~ leq(C_31,strong_iteration(one)) ),
inference(superposition,[status(thm),theory(equality)],[c_11268,c_32]) ).
tff(c_12753,plain,
! [C_205,A_206] : leq(C_205,multiplication(strong_iteration(A_206),strong_iteration(one))),
inference(demodulation,[status(thm),theory(equality)],[c_11172,c_11379]) ).
tff(c_1387,plain,
! [C_87,A_88] :
( leq(C_87,multiplication(strong_iteration(A_88),zero))
| ~ leq(C_87,multiplication(A_88,C_87)) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_1348]) ).
tff(c_20998,plain,
! [A_324] : leq(strong_iteration(one),multiplication(strong_iteration(strong_iteration(A_324)),zero)),
inference(resolution,[status(thm)],[c_12753,c_1387]) ).
tff(c_21001,plain,
! [A_324] : ( addition(strong_iteration(one),multiplication(strong_iteration(strong_iteration(A_324)),zero)) = multiplication(strong_iteration(strong_iteration(A_324)),zero) ),
inference(resolution,[status(thm)],[c_20998,c_36]) ).
tff(c_21015,plain,
! [A_325] : ( multiplication(strong_iteration(strong_iteration(A_325)),zero) = strong_iteration(one) ),
inference(demodulation,[status(thm),theory(equality)],[c_11417,c_21001]) ).
tff(c_949,plain,
! [A_70,B_71,C_72] : ( addition(multiplication(A_70,B_71),multiplication(A_70,C_72)) = multiplication(A_70,addition(B_71,C_72)) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_997,plain,
! [A_11,C_72] : ( multiplication(A_11,addition(one,C_72)) = addition(A_11,multiplication(A_11,C_72)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_949]) ).
tff(c_21057,plain,
! [A_325] : ( multiplication(strong_iteration(strong_iteration(A_325)),addition(one,zero)) = addition(strong_iteration(strong_iteration(A_325)),strong_iteration(one)) ),
inference(superposition,[status(thm),theory(equality)],[c_21015,c_997]) ).
tff(c_21116,plain,
! [A_325] : ( strong_iteration(strong_iteration(A_325)) = strong_iteration(one) ),
inference(demodulation,[status(thm),theory(equality)],[c_11417,c_2,c_12,c_6,c_21057]) ).
tff(c_213,plain,
! [A_45,B_46] :
( leq(A_45,B_46)
| ( addition(A_45,B_46) != B_46 ) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_40,plain,
( ~ leq(strong_iteration(strong_iteration('#skF_2')),strong_iteration(one))
| ~ leq(strong_iteration(one),strong_iteration(strong_iteration('#skF_1'))) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_210,plain,
~ leq(strong_iteration(one),strong_iteration(strong_iteration('#skF_1'))),
inference(splitLeft,[status(thm)],[c_40]) ).
tff(c_221,plain,
addition(strong_iteration(one),strong_iteration(strong_iteration('#skF_1'))) != strong_iteration(strong_iteration('#skF_1')),
inference(resolution,[status(thm)],[c_213,c_210]) ).
tff(c_11649,plain,
strong_iteration(strong_iteration('#skF_1')) != strong_iteration(one),
inference(demodulation,[status(thm),theory(equality)],[c_11417,c_221]) ).
tff(c_21137,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_21116,c_11649]) ).
tff(c_21139,plain,
leq(strong_iteration(one),strong_iteration(strong_iteration('#skF_1'))),
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_21147,plain,
! [A_328,B_329] :
( ( addition(A_328,B_329) = B_329 )
| ~ leq(A_328,B_329) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_21155,plain,
addition(strong_iteration(one),strong_iteration(strong_iteration('#skF_1'))) = strong_iteration(strong_iteration('#skF_1')),
inference(resolution,[status(thm)],[c_21139,c_21147]) ).
tff(c_25577,plain,
! [B_393,A_394,C_395] :
( leq(multiplication(B_393,star(A_394)),C_395)
| ~ leq(addition(multiplication(C_395,A_394),B_393),C_395) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_32169,plain,
! [B_459,A_460] :
( leq(multiplication(B_459,star(one)),A_460)
| ~ leq(addition(A_460,B_459),A_460) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_25577]) ).
tff(c_32283,plain,
( leq(multiplication(strong_iteration(strong_iteration('#skF_1')),star(one)),strong_iteration(one))
| ~ leq(strong_iteration(strong_iteration('#skF_1')),strong_iteration(one)) ),
inference(superposition,[status(thm),theory(equality)],[c_21155,c_32169]) ).
tff(c_32378,plain,
~ leq(strong_iteration(strong_iteration('#skF_1')),strong_iteration(one)),
inference(splitLeft,[status(thm)],[c_32283]) ).
tff(c_35575,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_35562,c_32378]) ).
tff(c_35577,plain,
leq(strong_iteration(strong_iteration('#skF_1')),strong_iteration(one)),
inference(splitRight,[status(thm)],[c_32283]) ).
tff(c_35581,plain,
addition(strong_iteration(strong_iteration('#skF_1')),strong_iteration(one)) = strong_iteration(one),
inference(resolution,[status(thm)],[c_35577,c_36]) ).
tff(c_22488,plain,
! [B_365,A_366,B_367] : ( addition(B_365,addition(A_366,B_367)) = addition(A_366,addition(B_367,B_365)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_21312]) ).
tff(c_22926,plain,
! [A_368,B_369] : ( addition(zero,addition(A_368,B_369)) = addition(B_369,A_368) ),
inference(superposition,[status(thm),theory(equality)],[c_130,c_22488]) ).
tff(c_23068,plain,
addition(strong_iteration(strong_iteration('#skF_1')),strong_iteration(one)) = addition(zero,strong_iteration(strong_iteration('#skF_1'))),
inference(superposition,[status(thm),theory(equality)],[c_21155,c_22926]) ).
tff(c_23132,plain,
addition(strong_iteration(strong_iteration('#skF_1')),strong_iteration(one)) = strong_iteration(strong_iteration('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_23068]) ).
tff(c_35632,plain,
strong_iteration(strong_iteration('#skF_1')) = strong_iteration(one),
inference(demodulation,[status(thm),theory(equality)],[c_35581,c_23132]) ).
tff(c_35718,plain,
leq(strong_iteration(one),strong_iteration(one)),
inference(demodulation,[status(thm),theory(equality)],[c_35632,c_35577]) ).
tff(c_21156,plain,
! [A_330] : ( addition(multiplication(A_330,strong_iteration(A_330)),one) = strong_iteration(A_330) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_21165,plain,
! [A_330] : ( addition(one,multiplication(A_330,strong_iteration(A_330))) = strong_iteration(A_330) ),
inference(superposition,[status(thm),theory(equality)],[c_21156,c_2]) ).
tff(c_21405,plain,
! [A_338,C_339] : ( addition(A_338,addition(A_338,C_339)) = addition(A_338,C_339) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_21312]) ).
tff(c_21441,plain,
! [A_330] : ( addition(one,multiplication(A_330,strong_iteration(A_330))) = addition(one,strong_iteration(A_330)) ),
inference(superposition,[status(thm),theory(equality)],[c_21165,c_21405]) ).
tff(c_21492,plain,
! [A_330] : ( addition(one,strong_iteration(A_330)) = strong_iteration(A_330) ),
inference(demodulation,[status(thm),theory(equality)],[c_21165,c_21441]) ).
tff(c_22124,plain,
! [A_355,C_356,B_357] : ( addition(multiplication(A_355,C_356),multiplication(B_357,C_356)) = multiplication(addition(A_355,B_357),C_356) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_22170,plain,
! [B_357,A_12] : ( multiplication(addition(one,B_357),A_12) = addition(A_12,multiplication(B_357,A_12)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_22124]) ).
tff(c_30,plain,
! [A_28] : ( addition(multiplication(A_28,strong_iteration(A_28)),one) = strong_iteration(A_28) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_21462,plain,
! [A_28] : ( addition(multiplication(A_28,strong_iteration(A_28)),strong_iteration(A_28)) = addition(multiplication(A_28,strong_iteration(A_28)),one) ),
inference(superposition,[status(thm),theory(equality)],[c_30,c_21405]) ).
tff(c_21804,plain,
! [A_349] : ( addition(multiplication(A_349,strong_iteration(A_349)),strong_iteration(A_349)) = strong_iteration(A_349) ),
inference(demodulation,[status(thm),theory(equality)],[c_21165,c_2,c_21462]) ).
tff(c_21819,plain,
! [A_349] : ( addition(strong_iteration(A_349),multiplication(A_349,strong_iteration(A_349))) = strong_iteration(A_349) ),
inference(superposition,[status(thm),theory(equality)],[c_21804,c_2]) ).
tff(c_35787,plain,
addition(strong_iteration(one),multiplication(strong_iteration('#skF_1'),strong_iteration(strong_iteration('#skF_1')))) = strong_iteration(strong_iteration('#skF_1')),
inference(superposition,[status(thm),theory(equality)],[c_35632,c_21819]) ).
tff(c_35825,plain,
multiplication(strong_iteration('#skF_1'),strong_iteration(one)) = strong_iteration(one),
inference(demodulation,[status(thm),theory(equality)],[c_35632,c_21492,c_22170,c_35632,c_35787]) ).
tff(c_38107,plain,
! [C_507,A_508] :
( leq(C_507,multiplication(strong_iteration(A_508),zero))
| ~ leq(C_507,multiplication(A_508,C_507)) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_24675]) ).
tff(c_38109,plain,
( leq(strong_iteration(one),multiplication(strong_iteration(strong_iteration('#skF_1')),zero))
| ~ leq(strong_iteration(one),strong_iteration(one)) ),
inference(superposition,[status(thm),theory(equality)],[c_35825,c_38107]) ).
tff(c_38149,plain,
leq(strong_iteration(one),multiplication(strong_iteration(one),zero)),
inference(demodulation,[status(thm),theory(equality)],[c_35718,c_35632,c_38109]) ).
tff(c_38158,plain,
addition(strong_iteration(one),multiplication(strong_iteration(one),zero)) = multiplication(strong_iteration(one),zero),
inference(resolution,[status(thm)],[c_38149,c_36]) ).
tff(c_38160,plain,
multiplication(strong_iteration(one),zero) = strong_iteration(one),
inference(demodulation,[status(thm),theory(equality)],[c_28479,c_38158]) ).
tff(c_20,plain,
! [A_19] : ( multiplication(zero,A_19) = zero ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_10,plain,
! [A_8,B_9,C_10] : ( multiplication(multiplication(A_8,B_9),C_10) = multiplication(A_8,multiplication(B_9,C_10)) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_38203,plain,
! [C_10] : ( multiplication(strong_iteration(one),multiplication(zero,C_10)) = multiplication(strong_iteration(one),C_10) ),
inference(superposition,[status(thm),theory(equality)],[c_38160,c_10]) ).
tff(c_38223,plain,
! [C_10] : ( multiplication(strong_iteration(one),C_10) = strong_iteration(one) ),
inference(demodulation,[status(thm),theory(equality)],[c_38160,c_20,c_38203]) ).
tff(c_26549,plain,
! [B_413,A_414] : ( multiplication(addition(one,B_413),A_414) = addition(A_414,multiplication(B_413,A_414)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_22124]) ).
tff(c_26979,plain,
! [A_416] : ( multiplication(addition(one,A_416),strong_iteration(A_416)) = strong_iteration(A_416) ),
inference(superposition,[status(thm),theory(equality)],[c_21819,c_26549]) ).
tff(c_27066,plain,
! [A_1] : ( multiplication(addition(A_1,one),strong_iteration(A_1)) = strong_iteration(A_1) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_26979]) ).
tff(c_21375,plain,
! [B_2,A_335,B_336] : ( addition(B_2,addition(A_335,B_336)) = addition(A_335,addition(B_336,B_2)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_21312]) ).
tff(c_28166,plain,
! [A_1] : ( multiplication(addition(A_1,one),addition(strong_iteration(A_1),one)) = addition(strong_iteration(A_1),addition(A_1,one)) ),
inference(superposition,[status(thm),theory(equality)],[c_27066,c_28023]) ).
tff(c_29008,plain,
! [A_432] : ( addition(A_432,strong_iteration(A_432)) = strong_iteration(A_432) ),
inference(demodulation,[status(thm),theory(equality)],[c_27066,c_21492,c_21375,c_21492,c_2,c_28166]) ).
tff(c_22816,plain,
! [A_41,B_365] : ( addition(zero,addition(A_41,B_365)) = addition(B_365,A_41) ),
inference(superposition,[status(thm),theory(equality)],[c_130,c_22488]) ).
tff(c_29085,plain,
! [A_432] : ( addition(strong_iteration(A_432),A_432) = addition(zero,strong_iteration(A_432)) ),
inference(superposition,[status(thm),theory(equality)],[c_29008,c_22816]) ).
tff(c_29157,plain,
! [A_432] : ( addition(strong_iteration(A_432),A_432) = strong_iteration(A_432) ),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_29085]) ).
tff(c_38231,plain,
! [C_509] : ( multiplication(strong_iteration(one),C_509) = strong_iteration(one) ),
inference(demodulation,[status(thm),theory(equality)],[c_38160,c_20,c_38203]) ).
tff(c_22173,plain,
! [A_355,A_12] : ( multiplication(addition(A_355,one),A_12) = addition(multiplication(A_355,A_12),A_12) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_22124]) ).
tff(c_38252,plain,
! [C_509] : ( multiplication(addition(strong_iteration(one),one),C_509) = addition(strong_iteration(one),C_509) ),
inference(superposition,[status(thm),theory(equality)],[c_38231,c_22173]) ).
tff(c_38357,plain,
! [C_509] : ( addition(strong_iteration(one),C_509) = strong_iteration(one) ),
inference(demodulation,[status(thm),theory(equality)],[c_38223,c_29157,c_38252]) ).
tff(c_21141,plain,
! [A_326,B_327] :
( leq(A_326,B_327)
| ( addition(A_326,B_327) != B_327 ) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_21138,plain,
~ leq(strong_iteration(strong_iteration('#skF_2')),strong_iteration(one)),
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_21144,plain,
addition(strong_iteration(strong_iteration('#skF_2')),strong_iteration(one)) != strong_iteration(one),
inference(resolution,[status(thm)],[c_21141,c_21138]) ).
tff(c_21146,plain,
addition(strong_iteration(one),strong_iteration(strong_iteration('#skF_2'))) != strong_iteration(one),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_21144]) ).
tff(c_39276,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_38357,c_21146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KLE142+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % 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
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 23:10:44 EDT 2023
% 0.13/0.35 % CPUTime :
% 18.49/6.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.49/6.44
% 18.49/6.44 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.49/6.48
% 18.49/6.48 Inference rules
% 18.49/6.48 ----------------------
% 18.49/6.48 #Ref : 0
% 18.49/6.48 #Sup : 10140
% 18.49/6.48 #Fact : 0
% 18.49/6.48 #Define : 0
% 18.49/6.48 #Split : 10
% 18.49/6.48 #Chain : 0
% 18.49/6.48 #Close : 0
% 18.49/6.48
% 18.49/6.48 Ordering : KBO
% 18.49/6.48
% 18.49/6.48 Simplification rules
% 18.49/6.48 ----------------------
% 18.49/6.48 #Subsume : 2143
% 18.49/6.48 #Demod : 9877
% 18.49/6.48 #Tautology : 3455
% 18.49/6.48 #SimpNegUnit : 104
% 18.49/6.48 #BackRed : 46
% 18.49/6.48
% 18.49/6.48 #Partial instantiations: 0
% 18.49/6.48 #Strategies tried : 1
% 18.49/6.48
% 18.49/6.48 Timing (in seconds)
% 18.49/6.48 ----------------------
% 18.49/6.49 Preprocessing : 0.55
% 18.49/6.49 Parsing : 0.28
% 18.49/6.49 CNF conversion : 0.04
% 18.49/6.49 Main loop : 4.80
% 18.49/6.49 Inferencing : 1.05
% 18.49/6.49 Reduction : 2.58
% 18.49/6.49 Demodulation : 2.25
% 18.49/6.49 BG Simplification : 0.11
% 18.49/6.49 Subsumption : 0.76
% 18.49/6.49 Abstraction : 0.16
% 18.49/6.49 MUC search : 0.00
% 18.49/6.49 Cooper : 0.00
% 18.49/6.49 Total : 5.43
% 18.49/6.49 Index Insertion : 0.00
% 18.49/6.49 Index Deletion : 0.00
% 18.49/6.49 Index Matching : 0.00
% 18.49/6.49 BG Taut test : 0.00
%------------------------------------------------------------------------------