TSTP Solution File: KLE144+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : KLE144+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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n014.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 19.41s 7.62s
% Output : CNFRefutation 19.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 25
% Syntax : Number of formulae : 134 ( 103 unt; 9 typ; 0 def)
% Number of atoms : 147 ( 93 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 47 ( 25 ~; 18 |; 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 : 170 (; 170 !; 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/sandbox/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
tff(f_65,axiom,
! [A] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
tff(f_63,axiom,
! [A] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
tff(f_56,axiom,
! [A] : ( addition(A,zero) = A ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity1) ).
tff(f_58,axiom,
! [A] : ( addition(A,A) = A ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
tff(f_100,axiom,
! [A,B] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
tff(f_76,axiom,
! [A] : ( addition(one,multiplication(A,star(A))) = star(A) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold1) ).
tff(f_70,axiom,
! [A,B,C] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
tff(f_107,negated_conjecture,
~ ! [X0] :
( leq(strong_iteration(star(X0)),strong_iteration(one))
& leq(strong_iteration(one),strong_iteration(star(X0))) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
tff(f_73,axiom,
! [A] : ( multiplication(zero,A) = zero ),
file('/export/starexec/sandbox/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/sandbox/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_30926,plain,
! [A_428,B_429,C_430] : ( addition(multiplication(A_428,B_429),multiplication(A_428,C_430)) = multiplication(A_428,addition(B_429,C_430)) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_35871,plain,
! [A_486,B_487] : ( multiplication(A_486,addition(B_487,one)) = addition(multiplication(A_486,B_487),A_486) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_30926]) ).
tff(c_36081,plain,
! [A_486] : ( addition(multiplication(A_486,zero),A_486) = multiplication(A_486,one) ),
inference(superposition,[status(thm),theory(equality)],[c_130,c_35871]) ).
tff(c_36152,plain,
! [A_488] : ( addition(multiplication(A_488,zero),A_488) = A_488 ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_36081]) ).
tff(c_30977,plain,
! [A_11,B_429] : ( multiplication(A_11,addition(B_429,one)) = addition(multiplication(A_11,B_429),A_11) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_30926]) ).
tff(c_36159,plain,
! [A_11] : ( addition(multiplication(A_11,multiplication(one,zero)),A_11) = multiplication(A_11,one) ),
inference(superposition,[status(thm),theory(equality)],[c_36152,c_30977]) ).
tff(c_36311,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_36159]) ).
tff(c_8,plain,
! [A_7] : ( addition(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_29962,plain,
! [A_403,B_404,C_405] : ( addition(addition(A_403,B_404),C_405) = addition(A_403,addition(B_404,C_405)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_30042,plain,
! [A_7,C_405] : ( addition(A_7,addition(A_7,C_405)) = addition(A_7,C_405) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_29962]) ).
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_33325,plain,
! [C_453,A_454,B_455] :
( leq(C_453,multiplication(strong_iteration(A_454),B_455))
| ~ leq(C_453,addition(multiplication(A_454,C_453),B_455)) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_43097,plain,
! [A_566,B_567] :
( leq(A_566,multiplication(strong_iteration(one),B_567))
| ~ leq(A_566,addition(A_566,B_567)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_33325]) ).
tff(c_43221,plain,
! [A_33,B_567] :
( leq(A_33,multiplication(strong_iteration(one),B_567))
| ( addition(A_33,addition(A_33,B_567)) != addition(A_33,B_567) ) ),
inference(resolution,[status(thm)],[c_38,c_43097]) ).
tff(c_43252,plain,
! [A_568,B_569] : leq(A_568,multiplication(strong_iteration(one),B_569)),
inference(demodulation,[status(thm),theory(equality)],[c_30042,c_43221]) ).
tff(c_43282,plain,
! [A_568] : leq(A_568,strong_iteration(one)),
inference(superposition,[status(thm),theory(equality)],[c_12,c_43252]) ).
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_12634,plain,
! [A_203,B_204] :
( leq(A_203,multiplication(strong_iteration(one),B_204))
| ~ leq(A_203,addition(A_203,B_204)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_1348]) ).
tff(c_12749,plain,
! [A_33,B_204] :
( leq(A_33,multiplication(strong_iteration(one),B_204))
| ( addition(A_33,addition(A_33,B_204)) != addition(A_33,B_204) ) ),
inference(resolution,[status(thm)],[c_38,c_12634]) ).
tff(c_12783,plain,
! [A_205,B_206] : leq(A_205,multiplication(strong_iteration(one),B_206)),
inference(demodulation,[status(thm),theory(equality)],[c_448,c_12749]) ).
tff(c_12815,plain,
! [A_205] : leq(A_205,strong_iteration(one)),
inference(superposition,[status(thm),theory(equality)],[c_12,c_12783]) ).
tff(c_12828,plain,
! [A_207] : leq(A_207,strong_iteration(one)),
inference(superposition,[status(thm),theory(equality)],[c_12,c_12783]) ).
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_12859,plain,
! [A_207] : ( addition(A_207,strong_iteration(one)) = strong_iteration(one) ),
inference(resolution,[status(thm)],[c_12828,c_36]) ).
tff(c_22,plain,
! [A_20] : ( addition(one,multiplication(A_20,star(A_20))) = star(A_20) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_3940,plain,
! [C_128,A_129,B_130] : ( addition(C_128,addition(A_129,B_130)) = addition(A_129,addition(B_130,C_128)) ),
inference(superposition,[status(thm),theory(equality)],[c_371,c_2]) ).
tff(c_5763,plain,
! [A_144,C_145] : ( addition(zero,addition(A_144,C_145)) = addition(C_145,A_144) ),
inference(superposition,[status(thm),theory(equality)],[c_130,c_3940]) ).
tff(c_5950,plain,
! [A_20] : ( addition(multiplication(A_20,star(A_20)),one) = addition(zero,star(A_20)) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_5763]) ).
tff(c_6025,plain,
! [A_20] : ( addition(multiplication(A_20,star(A_20)),one) = star(A_20) ),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_5950]) ).
tff(c_12860,plain,
! [A_208] : ( addition(A_208,strong_iteration(one)) = strong_iteration(one) ),
inference(resolution,[status(thm)],[c_12828,c_36]) ).
tff(c_677,plain,
! [A_63,C_64,B_65] : ( addition(multiplication(A_63,C_64),multiplication(B_65,C_64)) = multiplication(addition(A_63,B_65),C_64) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_723,plain,
! [A_63,A_12] : ( multiplication(addition(A_63,one),A_12) = addition(multiplication(A_63,A_12),A_12) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_677]) ).
tff(c_15389,plain,
! [A_227] : ( multiplication(addition(A_227,one),strong_iteration(one)) = strong_iteration(one) ),
inference(superposition,[status(thm),theory(equality)],[c_12860,c_723]) ).
tff(c_15475,plain,
! [A_20] : ( multiplication(star(A_20),strong_iteration(one)) = strong_iteration(one) ),
inference(superposition,[status(thm),theory(equality)],[c_6025,c_15389]) ).
tff(c_19721,plain,
! [C_291,A_292,B_293] :
( leq(C_291,multiplication(strong_iteration(A_292),B_293))
| ~ leq(C_291,addition(B_293,multiplication(A_292,C_291))) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1348]) ).
tff(c_19725,plain,
! [A_20,B_293] :
( leq(strong_iteration(one),multiplication(strong_iteration(star(A_20)),B_293))
| ~ leq(strong_iteration(one),addition(B_293,strong_iteration(one))) ),
inference(superposition,[status(thm),theory(equality)],[c_15475,c_19721]) ).
tff(c_29700,plain,
! [A_392,B_393] : leq(strong_iteration(one),multiplication(strong_iteration(star(A_392)),B_393)),
inference(demodulation,[status(thm),theory(equality)],[c_12815,c_12859,c_19725]) ).
tff(c_29764,plain,
! [A_392] : leq(strong_iteration(one),strong_iteration(star(A_392))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_29700]) ).
tff(c_40,plain,
( ~ leq(strong_iteration(star('#skF_2')),strong_iteration(one))
| ~ leq(strong_iteration(one),strong_iteration(star('#skF_1'))) ),
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_210,plain,
~ leq(strong_iteration(one),strong_iteration(star('#skF_1'))),
inference(splitLeft,[status(thm)],[c_40]) ).
tff(c_29787,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_29764,c_210]) ).
tff(c_29789,plain,
leq(strong_iteration(one),strong_iteration(star('#skF_1'))),
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_29797,plain,
! [A_396,B_397] :
( ( addition(A_396,B_397) = B_397 )
| ~ leq(A_396,B_397) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_29805,plain,
addition(strong_iteration(one),strong_iteration(star('#skF_1'))) = strong_iteration(star('#skF_1')),
inference(resolution,[status(thm)],[c_29789,c_29797]) ).
tff(c_34227,plain,
! [B_461,A_462,C_463] :
( leq(multiplication(B_461,star(A_462)),C_463)
| ~ leq(addition(multiplication(C_463,A_462),B_461),C_463) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_41344,plain,
! [B_541,A_542] :
( leq(multiplication(B_541,star(one)),A_542)
| ~ leq(addition(A_542,B_541),A_542) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_34227]) ).
tff(c_41454,plain,
( leq(multiplication(strong_iteration(star('#skF_1')),star(one)),strong_iteration(one))
| ~ leq(strong_iteration(star('#skF_1')),strong_iteration(one)) ),
inference(superposition,[status(thm),theory(equality)],[c_29805,c_41344]) ).
tff(c_41489,plain,
~ leq(strong_iteration(star('#skF_1')),strong_iteration(one)),
inference(splitLeft,[status(thm)],[c_41454]) ).
tff(c_43298,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_43282,c_41489]) ).
tff(c_43300,plain,
leq(strong_iteration(star('#skF_1')),strong_iteration(one)),
inference(splitRight,[status(thm)],[c_41454]) ).
tff(c_43307,plain,
addition(strong_iteration(star('#skF_1')),strong_iteration(one)) = strong_iteration(one),
inference(resolution,[status(thm)],[c_43300,c_36]) ).
tff(c_31138,plain,
! [B_433,A_434,B_435] : ( addition(B_433,addition(A_434,B_435)) = addition(A_434,addition(B_435,B_433)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_29962]) ).
tff(c_31576,plain,
! [A_436,B_437] : ( addition(zero,addition(A_436,B_437)) = addition(B_437,A_436) ),
inference(superposition,[status(thm),theory(equality)],[c_130,c_31138]) ).
tff(c_31718,plain,
addition(strong_iteration(star('#skF_1')),strong_iteration(one)) = addition(zero,strong_iteration(star('#skF_1'))),
inference(superposition,[status(thm),theory(equality)],[c_29805,c_31576]) ).
tff(c_31782,plain,
addition(strong_iteration(star('#skF_1')),strong_iteration(one)) = strong_iteration(star('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_31718]) ).
tff(c_52698,plain,
strong_iteration(star('#skF_1')) = strong_iteration(one),
inference(demodulation,[status(thm),theory(equality)],[c_43307,c_31782]) ).
tff(c_52857,plain,
leq(strong_iteration(one),strong_iteration(one)),
inference(demodulation,[status(thm),theory(equality)],[c_52698,c_43300]) ).
tff(c_30055,plain,
! [A_406,C_407] : ( addition(A_406,addition(A_406,C_407)) = addition(A_406,C_407) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_29962]) ).
tff(c_30100,plain,
! [A_20] : ( addition(one,multiplication(A_20,star(A_20))) = addition(one,star(A_20)) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_30055]) ).
tff(c_30145,plain,
! [A_20] : ( addition(one,star(A_20)) = star(A_20) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_30100]) ).
tff(c_30774,plain,
! [A_423,C_424,B_425] : ( addition(multiplication(A_423,C_424),multiplication(B_425,C_424)) = multiplication(addition(A_423,B_425),C_424) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_30820,plain,
! [B_425,A_12] : ( multiplication(addition(one,B_425),A_12) = addition(A_12,multiplication(B_425,A_12)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_30774]) ).
tff(c_29806,plain,
! [A_398] : ( addition(multiplication(A_398,strong_iteration(A_398)),one) = strong_iteration(A_398) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_29815,plain,
! [A_398] : ( addition(one,multiplication(A_398,strong_iteration(A_398))) = strong_iteration(A_398) ),
inference(superposition,[status(thm),theory(equality)],[c_29806,c_2]) ).
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_30112,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_30055]) ).
tff(c_30454,plain,
! [A_417] : ( addition(multiplication(A_417,strong_iteration(A_417)),strong_iteration(A_417)) = strong_iteration(A_417) ),
inference(demodulation,[status(thm),theory(equality)],[c_29815,c_2,c_30112]) ).
tff(c_30469,plain,
! [A_417] : ( addition(strong_iteration(A_417),multiplication(A_417,strong_iteration(A_417))) = strong_iteration(A_417) ),
inference(superposition,[status(thm),theory(equality)],[c_30454,c_2]) ).
tff(c_52951,plain,
addition(strong_iteration(one),multiplication(star('#skF_1'),strong_iteration(star('#skF_1')))) = strong_iteration(star('#skF_1')),
inference(superposition,[status(thm),theory(equality)],[c_52698,c_30469]) ).
tff(c_52988,plain,
multiplication(star('#skF_1'),strong_iteration(one)) = strong_iteration(one),
inference(demodulation,[status(thm),theory(equality)],[c_52698,c_30145,c_30820,c_52698,c_52951]) ).
tff(c_33377,plain,
! [C_453,A_454] :
( leq(C_453,multiplication(strong_iteration(A_454),zero))
| ~ leq(C_453,multiplication(A_454,C_453)) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_33325]) ).
tff(c_53294,plain,
( leq(strong_iteration(one),multiplication(strong_iteration(star('#skF_1')),zero))
| ~ leq(strong_iteration(one),strong_iteration(one)) ),
inference(superposition,[status(thm),theory(equality)],[c_52988,c_33377]) ).
tff(c_53339,plain,
leq(strong_iteration(one),multiplication(strong_iteration(one),zero)),
inference(demodulation,[status(thm),theory(equality)],[c_52857,c_52698,c_53294]) ).
tff(c_53466,plain,
addition(strong_iteration(one),multiplication(strong_iteration(one),zero)) = multiplication(strong_iteration(one),zero),
inference(resolution,[status(thm)],[c_53339,c_36]) ).
tff(c_53468,plain,
multiplication(strong_iteration(one),zero) = strong_iteration(one),
inference(demodulation,[status(thm),theory(equality)],[c_36311,c_53466]) ).
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_53525,plain,
! [C_10] : ( multiplication(strong_iteration(one),multiplication(zero,C_10)) = multiplication(strong_iteration(one),C_10) ),
inference(superposition,[status(thm),theory(equality)],[c_53468,c_10]) ).
tff(c_53549,plain,
! [C_10] : ( multiplication(strong_iteration(one),C_10) = strong_iteration(one) ),
inference(demodulation,[status(thm),theory(equality)],[c_53468,c_20,c_53525]) ).
tff(c_34853,plain,
! [B_479,A_480] : ( multiplication(addition(one,B_479),A_480) = addition(A_480,multiplication(B_479,A_480)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_30774]) ).
tff(c_35649,plain,
! [A_484] : ( multiplication(addition(one,A_484),strong_iteration(A_484)) = strong_iteration(A_484) ),
inference(superposition,[status(thm),theory(equality)],[c_30469,c_34853]) ).
tff(c_35736,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_35649]) ).
tff(c_30091,plain,
! [A_398] : ( addition(one,multiplication(A_398,strong_iteration(A_398))) = addition(one,strong_iteration(A_398)) ),
inference(superposition,[status(thm),theory(equality)],[c_29815,c_30055]) ).
tff(c_30142,plain,
! [A_398] : ( addition(one,strong_iteration(A_398)) = strong_iteration(A_398) ),
inference(demodulation,[status(thm),theory(equality)],[c_29815,c_30091]) ).
tff(c_30025,plain,
! [B_2,A_403,B_404] : ( addition(B_2,addition(A_403,B_404)) = addition(A_403,addition(B_404,B_2)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_29962]) ).
tff(c_38426,plain,
! [A_505] : ( multiplication(addition(A_505,one),strong_iteration(A_505)) = strong_iteration(A_505) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_35649]) ).
tff(c_30974,plain,
! [A_11,C_430] : ( multiplication(A_11,addition(one,C_430)) = addition(A_11,multiplication(A_11,C_430)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_30926]) ).
tff(c_38432,plain,
! [A_505] : ( multiplication(addition(A_505,one),addition(one,strong_iteration(A_505))) = addition(addition(A_505,one),strong_iteration(A_505)) ),
inference(superposition,[status(thm),theory(equality)],[c_38426,c_30974]) ).
tff(c_38557,plain,
! [A_506] : ( addition(A_506,strong_iteration(A_506)) = strong_iteration(A_506) ),
inference(demodulation,[status(thm),theory(equality)],[c_35736,c_30142,c_30025,c_30142,c_2,c_38432]) ).
tff(c_31466,plain,
! [A_41,B_433] : ( addition(zero,addition(A_41,B_433)) = addition(B_433,A_41) ),
inference(superposition,[status(thm),theory(equality)],[c_130,c_31138]) ).
tff(c_38641,plain,
! [A_506] : ( addition(strong_iteration(A_506),A_506) = addition(zero,strong_iteration(A_506)) ),
inference(superposition,[status(thm),theory(equality)],[c_38557,c_31466]) ).
tff(c_38718,plain,
! [A_506] : ( addition(strong_iteration(A_506),A_506) = strong_iteration(A_506) ),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_38641]) ).
tff(c_53559,plain,
! [C_686] : ( multiplication(strong_iteration(one),C_686) = strong_iteration(one) ),
inference(demodulation,[status(thm),theory(equality)],[c_53468,c_20,c_53525]) ).
tff(c_30823,plain,
! [A_423,A_12] : ( multiplication(addition(A_423,one),A_12) = addition(multiplication(A_423,A_12),A_12) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_30774]) ).
tff(c_53609,plain,
! [C_686] : ( multiplication(addition(strong_iteration(one),one),C_686) = addition(strong_iteration(one),C_686) ),
inference(superposition,[status(thm),theory(equality)],[c_53559,c_30823]) ).
tff(c_53720,plain,
! [C_686] : ( addition(strong_iteration(one),C_686) = strong_iteration(one) ),
inference(demodulation,[status(thm),theory(equality)],[c_53549,c_38718,c_53609]) ).
tff(c_29791,plain,
! [A_394,B_395] :
( leq(A_394,B_395)
| ( addition(A_394,B_395) != B_395 ) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_29788,plain,
~ leq(strong_iteration(star('#skF_2')),strong_iteration(one)),
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_29794,plain,
addition(strong_iteration(star('#skF_2')),strong_iteration(one)) != strong_iteration(one),
inference(resolution,[status(thm)],[c_29791,c_29788]) ).
tff(c_29796,plain,
addition(strong_iteration(one),strong_iteration(star('#skF_2'))) != strong_iteration(one),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_29794]) ).
tff(c_54140,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_53720,c_29796]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KLE144+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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.17/0.35 % Computer : n014.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Thu Aug 3 23:16:18 EDT 2023
% 0.17/0.35 % CPUTime :
% 19.41/7.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.41/7.64
% 19.41/7.64 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.53/7.68
% 19.53/7.68 Inference rules
% 19.53/7.68 ----------------------
% 19.53/7.68 #Ref : 0
% 19.53/7.68 #Sup : 14132
% 19.53/7.68 #Fact : 0
% 19.53/7.68 #Define : 0
% 19.53/7.68 #Split : 12
% 19.53/7.68 #Chain : 0
% 19.53/7.68 #Close : 0
% 19.53/7.68
% 19.53/7.68 Ordering : KBO
% 19.53/7.68
% 19.53/7.68 Simplification rules
% 19.53/7.68 ----------------------
% 19.53/7.68 #Subsume : 4139
% 19.53/7.68 #Demod : 12827
% 19.53/7.68 #Tautology : 4145
% 19.53/7.68 #SimpNegUnit : 194
% 19.53/7.68 #BackRed : 59
% 19.53/7.68
% 19.53/7.68 #Partial instantiations: 0
% 19.53/7.68 #Strategies tried : 1
% 19.53/7.68
% 19.53/7.68 Timing (in seconds)
% 19.53/7.68 ----------------------
% 19.53/7.68 Preprocessing : 0.49
% 19.53/7.68 Parsing : 0.26
% 19.53/7.68 CNF conversion : 0.03
% 19.53/7.68 Main loop : 6.10
% 19.53/7.68 Inferencing : 1.20
% 19.53/7.68 Reduction : 3.39
% 19.53/7.68 Demodulation : 2.93
% 19.53/7.68 BG Simplification : 0.11
% 19.53/7.68 Subsumption : 1.03
% 19.53/7.68 Abstraction : 0.18
% 19.53/7.68 MUC search : 0.00
% 19.53/7.68 Cooper : 0.00
% 19.53/7.68 Total : 6.66
% 19.53/7.68 Index Insertion : 0.00
% 19.53/7.68 Index Deletion : 0.00
% 19.53/7.68 Index Matching : 0.00
% 19.53/7.68 BG Taut test : 0.00
%------------------------------------------------------------------------------