TSTP Solution File: KLE039+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : KLE039+1 : 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 : n026.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 10:44:44 EDT 2023
% Result : Theorem 193.80s 160.46s
% Output : CNFRefutation 194.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 24
% Syntax : Number of formulae : 159 ( 96 unt; 7 typ; 0 def)
% Number of atoms : 211 ( 143 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 120 ( 61 ~; 56 |; 0 &)
% ( 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 : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 244 (; 244 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ leq > multiplication > addition > #nlpp > star > zero > one > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(star,type,
star: $i > $i ).
tff(multiplication,type,
multiplication: ( $i * $i ) > $i ).
tff(addition,type,
addition: ( $i * $i ) > $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_63,axiom,
! [A] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
tff(f_56,axiom,
! [A] : ( addition(A,zero) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_identity) ).
tff(f_65,axiom,
! [A] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).
tff(f_58,axiom,
! [A] : ( addition(A,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
tff(f_80,axiom,
! [A,B] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',order) ).
tff(f_52,axiom,
! [A,B] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
tff(f_75,axiom,
! [A] : ( multiplication(zero,A) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',left_annihilation) ).
tff(f_91,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),B)
=> leq(multiplication(star(A),C),B) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_induction_left) ).
tff(f_73,axiom,
! [A] : ( multiplication(A,zero) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',right_annihilation) ).
tff(f_86,axiom,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_left) ).
tff(f_61,axiom,
! [A,B,C] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_associativity) ).
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/KLE002+0.ax',left_distributivity) ).
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/KLE002+0.ax',right_distributivity) ).
tff(f_54,axiom,
! [C,B,A] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_associativity) ).
tff(f_95,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),A)
=> leq(multiplication(C,star(B)),A) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_induction_right) ).
tff(f_84,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).
tff(f_100,negated_conjecture,
~ ! [X0] : ( star(star(X0)) = star(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
tff(c_12,plain,
! [A_11] : ( multiplication(A_11,one) = A_11 ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_6,plain,
! [A_6] : ( addition(A_6,zero) = A_6 ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_14,plain,
! [A_12] : ( multiplication(one,A_12) = A_12 ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_8,plain,
! [A_7] : ( addition(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_26,plain,
! [A_21,B_22] :
( leq(A_21,B_22)
| ( addition(A_21,B_22) != B_22 ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
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_135,plain,
! [B_37,A_38] : ( addition(B_37,A_38) = addition(A_38,B_37) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_151,plain,
! [A_38] : ( addition(zero,A_38) = A_38 ),
inference(superposition,[status(thm),theory(equality)],[c_135,c_6]) ).
tff(c_22,plain,
! [A_20] : ( multiplication(zero,A_20) = zero ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_1369,plain,
! [A_69,C_70,B_71] :
( leq(multiplication(star(A_69),C_70),B_71)
| ~ leq(addition(multiplication(A_69,B_71),C_70),B_71) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_1413,plain,
! [C_70,A_20] :
( leq(multiplication(star(zero),C_70),A_20)
| ~ leq(addition(zero,C_70),A_20) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_1369]) ).
tff(c_1907,plain,
! [C_85,A_86] :
( leq(multiplication(star(zero),C_85),A_86)
| ~ leq(C_85,A_86) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_1413]) ).
tff(c_1922,plain,
! [A_87] :
( leq(star(zero),A_87)
| ~ leq(one,A_87) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_1907]) ).
tff(c_24,plain,
! [A_21,B_22] :
( ( addition(A_21,B_22) = B_22 )
| ~ leq(A_21,B_22) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_2116,plain,
! [A_90] :
( ( addition(star(zero),A_90) = A_90 )
| ~ leq(one,A_90) ),
inference(resolution,[status(thm)],[c_1922,c_24]) ).
tff(c_2353,plain,
! [A_96] :
( ( addition(A_96,star(zero)) = A_96 )
| ~ leq(one,A_96) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_2116]) ).
tff(c_20,plain,
! [A_19] : ( multiplication(A_19,zero) = zero ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_238,plain,
! [A_44] : leq(addition(one,multiplication(star(A_44),A_44)),star(A_44)),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_249,plain,
leq(addition(one,zero),star(zero)),
inference(superposition,[status(thm),theory(equality)],[c_20,c_238]) ).
tff(c_251,plain,
leq(one,star(zero)),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_249]) ).
tff(c_269,plain,
addition(one,star(zero)) = star(zero),
inference(resolution,[status(thm)],[c_251,c_24]) ).
tff(c_2411,plain,
( ( star(zero) = one )
| ~ leq(one,one) ),
inference(superposition,[status(thm),theory(equality)],[c_2353,c_269]) ).
tff(c_2483,plain,
~ leq(one,one),
inference(splitLeft,[status(thm)],[c_2411]) ).
tff(c_2486,plain,
addition(one,one) != one,
inference(resolution,[status(thm)],[c_26,c_2483]) ).
tff(c_2490,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_2486]) ).
tff(c_2491,plain,
star(zero) = one,
inference(splitRight,[status(thm)],[c_2411]) ).
tff(c_1393,plain,
! [A_69,C_70,B_22] :
( leq(multiplication(star(A_69),C_70),B_22)
| ( addition(addition(multiplication(A_69,B_22),C_70),B_22) != B_22 ) ),
inference(resolution,[status(thm)],[c_26,c_1369]) ).
tff(c_20262,plain,
! [A_238,C_239,B_240] :
( leq(multiplication(star(A_238),C_239),B_240)
| ( addition(B_240,addition(multiplication(A_238,B_240),C_239)) != B_240 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1393]) ).
tff(c_20380,plain,
! [A_238,C_239] :
( leq(multiplication(star(A_238),C_239),zero)
| ( addition(multiplication(A_238,zero),C_239) != zero ) ),
inference(superposition,[status(thm),theory(equality)],[c_151,c_20262]) ).
tff(c_20427,plain,
! [A_241,C_242] :
( leq(multiplication(star(A_241),C_242),zero)
| ( zero != C_242 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_20,c_20380]) ).
tff(c_20433,plain,
! [A_241,C_242] :
( ( addition(multiplication(star(A_241),C_242),zero) = zero )
| ( zero != C_242 ) ),
inference(resolution,[status(thm)],[c_20427,c_24]) ).
tff(c_20590,plain,
! [A_244,C_245] :
( ( multiplication(star(A_244),C_245) = zero )
| ( zero != C_245 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_2,c_20433]) ).
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_20718,plain,
! [A_244,C_245,C_10] :
( ( multiplication(star(A_244),multiplication(C_245,C_10)) = multiplication(zero,C_10) )
| ( zero != C_245 ) ),
inference(superposition,[status(thm),theory(equality)],[c_20590,c_10]) ).
tff(c_23260,plain,
! [A_269,C_270,C_271] :
( ( multiplication(star(A_269),multiplication(C_270,C_271)) = zero )
| ( zero != C_270 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_20718]) ).
tff(c_23485,plain,
! [C_270,C_271] :
( ( multiplication(one,multiplication(C_270,C_271)) = zero )
| ( zero != C_270 ) ),
inference(superposition,[status(thm),theory(equality)],[c_2491,c_23260]) ).
tff(c_23580,plain,
! [C_272,C_273] :
( ( multiplication(C_272,C_273) = zero )
| ( zero != C_272 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_23485]) ).
tff(c_460,plain,
! [A_52,C_53,B_54] : ( addition(multiplication(A_52,C_53),multiplication(B_54,C_53)) = multiplication(addition(A_52,B_54),C_53) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_3246,plain,
! [A_108,A_109] : ( multiplication(addition(A_108,one),A_109) = addition(multiplication(A_108,A_109),A_109) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_460]) ).
tff(c_3413,plain,
! [A_108,A_1] : ( multiplication(addition(A_108,one),A_1) = addition(A_1,multiplication(A_108,A_1)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_3246]) ).
tff(c_23697,plain,
! [C_272,C_273] :
( ( multiplication(addition(C_272,one),C_273) = addition(C_273,zero) )
| ( zero != C_272 ) ),
inference(superposition,[status(thm),theory(equality)],[c_23580,c_3413]) ).
tff(c_25173,plain,
! [C_291,C_292] :
( ( multiplication(addition(C_291,one),C_292) = C_292 )
| ( zero != C_291 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_23697]) ).
tff(c_18,plain,
! [A_16,C_18,B_17] : ( addition(multiplication(A_16,C_18),multiplication(B_17,C_18)) = multiplication(addition(A_16,B_17),C_18) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_9860,plain,
! [B_169,C_170,A_171] : ( addition(multiplication(B_169,C_170),multiplication(A_171,C_170)) = multiplication(addition(A_171,B_169),C_170) ),
inference(superposition,[status(thm),theory(equality)],[c_460,c_2]) ).
tff(c_11451,plain,
! [B_185,A_186,C_187] : ( multiplication(addition(B_185,A_186),C_187) = multiplication(addition(A_186,B_185),C_187) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_9860]) ).
tff(c_11635,plain,
! [B_185,A_186] : ( multiplication(addition(B_185,A_186),one) = addition(A_186,B_185) ),
inference(superposition,[status(thm),theory(equality)],[c_11451,c_12]) ).
tff(c_25476,plain,
! [C_293] :
( ( addition(one,C_293) = one )
| ( zero != C_293 ) ),
inference(superposition,[status(thm),theory(equality)],[c_25173,c_11635]) ).
tff(c_702,plain,
! [A_59,B_60,C_61] : ( addition(multiplication(A_59,B_60),multiplication(A_59,C_61)) = multiplication(A_59,addition(B_60,C_61)) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_754,plain,
! [A_11,C_61] : ( multiplication(A_11,addition(one,C_61)) = addition(A_11,multiplication(A_11,C_61)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_702]) ).
tff(c_4,plain,
! [A_5,B_4,C_3] : ( addition(addition(A_5,B_4),C_3) = addition(A_5,addition(B_4,C_3)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_7777,plain,
! [A_145] : ( addition(addition(one,multiplication(star(A_145),A_145)),star(A_145)) = star(A_145) ),
inference(resolution,[status(thm)],[c_238,c_24]) ).
tff(c_7887,plain,
! [A_145] : ( addition(one,addition(multiplication(star(A_145),A_145),star(A_145))) = star(A_145) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_7777]) ).
tff(c_7926,plain,
! [A_145] : ( addition(one,multiplication(star(A_145),addition(one,A_145))) = star(A_145) ),
inference(demodulation,[status(thm),theory(equality)],[c_754,c_2,c_7887]) ).
tff(c_9245,plain,
! [A_164] : ( addition(one,multiplication(star(A_164),addition(one,A_164))) = star(A_164) ),
inference(demodulation,[status(thm),theory(equality)],[c_754,c_2,c_7887]) ).
tff(c_358,plain,
! [A_49,B_50,C_51] : ( addition(addition(A_49,B_50),C_51) = addition(A_49,addition(B_50,C_51)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_419,plain,
! [A_7,C_51] : ( addition(A_7,addition(A_7,C_51)) = addition(A_7,C_51) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_358]) ).
tff(c_9326,plain,
! [A_164] : ( addition(one,multiplication(star(A_164),addition(one,A_164))) = addition(one,star(A_164)) ),
inference(superposition,[status(thm),theory(equality)],[c_9245,c_419]) ).
tff(c_9423,plain,
! [A_164] : ( addition(one,star(A_164)) = star(A_164) ),
inference(demodulation,[status(thm),theory(equality)],[c_7926,c_9326]) ).
tff(c_530,plain,
! [A_55,C_56] : ( addition(A_55,addition(A_55,C_56)) = addition(A_55,C_56) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_358]) ).
tff(c_579,plain,
! [A_1,B_2] : ( addition(A_1,addition(B_2,A_1)) = addition(A_1,B_2) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_530]) ).
tff(c_792,plain,
! [C_62,A_63,B_64] : ( addition(C_62,addition(A_63,B_64)) = addition(A_63,addition(B_64,C_62)) ),
inference(superposition,[status(thm),theory(equality)],[c_358,c_2]) ).
tff(c_1210,plain,
! [A_67,C_68] : ( addition(A_67,addition(A_67,C_68)) = addition(C_68,A_67) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_792]) ).
tff(c_1292,plain,
! [B_2,A_1] : ( addition(addition(B_2,A_1),A_1) = addition(A_1,addition(A_1,B_2)) ),
inference(superposition,[status(thm),theory(equality)],[c_579,c_1210]) ).
tff(c_1358,plain,
! [B_2,A_1] : ( addition(addition(B_2,A_1),A_1) = addition(A_1,B_2) ),
inference(demodulation,[status(thm),theory(equality)],[c_419,c_1292]) ).
tff(c_6990,plain,
! [A_133,C_134] :
( leq(multiplication(star(A_133),C_134),one)
| ~ leq(addition(A_133,C_134),one) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_1369]) ).
tff(c_7018,plain,
! [A_135] :
( leq(star(A_135),one)
| ~ leq(addition(A_135,one),one) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_6990]) ).
tff(c_7052,plain,
! [A_135] :
( leq(star(A_135),one)
| ( addition(addition(A_135,one),one) != one ) ),
inference(resolution,[status(thm)],[c_26,c_7018]) ).
tff(c_7745,plain,
! [A_143] :
( leq(star(A_143),one)
| ( addition(one,A_143) != one ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1358,c_7052]) ).
tff(c_7748,plain,
! [A_143] :
( ( addition(star(A_143),one) = one )
| ( addition(one,A_143) != one ) ),
inference(resolution,[status(thm)],[c_7745,c_24]) ).
tff(c_7756,plain,
! [A_143] :
( ( addition(one,star(A_143)) = one )
| ( addition(one,A_143) != one ) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_7748]) ).
tff(c_9433,plain,
! [A_143] :
( ( star(A_143) = one )
| ( addition(one,A_143) != one ) ),
inference(demodulation,[status(thm),theory(equality)],[c_9423,c_7756]) ).
tff(c_25907,plain,
! [C_293] :
( ( star(C_293) = one )
| ( zero != C_293 ) ),
inference(superposition,[status(thm),theory(equality)],[c_25476,c_9433]) ).
tff(c_25941,plain,
! [C_294] :
( ( addition(C_294,one) = one )
| ( zero != C_294 ) ),
inference(superposition,[status(thm),theory(equality)],[c_25173,c_12]) ).
tff(c_757,plain,
! [A_11,B_60] : ( multiplication(A_11,addition(B_60,one)) = addition(multiplication(A_11,B_60),A_11) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_702]) ).
tff(c_26128,plain,
! [A_11,C_294] :
( ( addition(multiplication(A_11,C_294),A_11) = multiplication(A_11,one) )
| ( zero != C_294 ) ),
inference(superposition,[status(thm),theory(equality)],[c_25941,c_757]) ).
tff(c_26326,plain,
! [A_11,C_294] :
( ( addition(A_11,multiplication(A_11,C_294)) = A_11 )
| ( zero != C_294 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_2,c_26128]) ).
tff(c_373,plain,
! [C_51,A_49,B_50] : ( addition(C_51,addition(A_49,B_50)) = addition(A_49,addition(B_50,C_51)) ),
inference(superposition,[status(thm),theory(equality)],[c_358,c_2]) ).
tff(c_1477,plain,
! [C_76,B_77,A_78] :
( leq(multiplication(C_76,star(B_77)),A_78)
| ~ leq(addition(multiplication(A_78,B_77),C_76),A_78) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_1501,plain,
! [C_76,B_77,B_22] :
( leq(multiplication(C_76,star(B_77)),B_22)
| ( addition(addition(multiplication(B_22,B_77),C_76),B_22) != B_22 ) ),
inference(resolution,[status(thm)],[c_26,c_1477]) ).
tff(c_21209,plain,
! [C_249,B_250,B_251] :
( leq(multiplication(C_249,star(B_250)),B_251)
| ( addition(B_251,addition(multiplication(B_251,B_250),C_249)) != B_251 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_373,c_4,c_1501]) ).
tff(c_126910,plain,
! [A_712,B_713,B_714] :
( leq(multiplication(A_712,star(B_713)),B_714)
| ( addition(B_714,addition(A_712,multiplication(B_714,B_713))) != B_714 ) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_21209]) ).
tff(c_127044,plain,
! [A_11,C_294] :
( leq(multiplication(A_11,star(C_294)),A_11)
| ( addition(A_11,A_11) != A_11 )
| ( zero != C_294 ) ),
inference(superposition,[status(thm),theory(equality)],[c_26326,c_126910]) ).
tff(c_127327,plain,
! [A_715,C_716] :
( leq(multiplication(A_715,star(C_716)),A_715)
| ( zero != C_716 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_127044]) ).
tff(c_127428,plain,
! [A_715,C_293] :
( leq(multiplication(A_715,one),A_715)
| ( zero != C_293 )
| ( zero != C_293 ) ),
inference(superposition,[status(thm),theory(equality)],[c_25907,c_127327]) ).
tff(c_127528,plain,
! [A_715,C_293] :
( leq(A_715,A_715)
| ( zero != C_293 )
| ( zero != C_293 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_127428]) ).
tff(c_127544,plain,
! [C_293] :
( ( zero != C_293 )
| ( zero != C_293 ) ),
inference(splitLeft,[status(thm)],[c_127528]) ).
tff(c_127550,plain,
$false,
inference(reflexivity,[status(thm),theory(equality)],[c_127544]) ).
tff(c_127551,plain,
! [A_715] : leq(A_715,A_715),
inference(splitRight,[status(thm)],[c_127528]) ).
tff(c_28,plain,
! [A_23] : leq(addition(one,multiplication(A_23,star(A_23))),star(A_23)),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_16105,plain,
! [A_207,B_208,B_209] :
( leq(multiplication(star(A_207),B_208),B_209)
| ~ leq(addition(B_208,multiplication(A_207,B_209)),B_209) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1369]) ).
tff(c_16190,plain,
! [A_23] : leq(multiplication(star(A_23),one),star(A_23)),
inference(resolution,[status(thm)],[c_28,c_16105]) ).
tff(c_16225,plain,
! [A_23] : leq(star(A_23),star(A_23)),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_16190]) ).
tff(c_16872,plain,
! [B_215,B_216,A_217] :
( leq(multiplication(B_215,star(B_216)),A_217)
| ~ leq(addition(B_215,multiplication(A_217,B_216)),A_217) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1477]) ).
tff(c_16888,plain,
! [A_145] :
( leq(multiplication(one,star(addition(one,A_145))),star(A_145))
| ~ leq(star(A_145),star(A_145)) ),
inference(superposition,[status(thm),theory(equality)],[c_7926,c_16872]) ).
tff(c_17006,plain,
! [A_218] : leq(star(addition(one,A_218)),star(A_218)),
inference(demodulation,[status(thm),theory(equality)],[c_16225,c_14,c_16888]) ).
tff(c_17366,plain,
! [A_220] : ( addition(star(addition(one,A_220)),star(A_220)) = star(A_220) ),
inference(resolution,[status(thm)],[c_17006,c_24]) ).
tff(c_17459,plain,
! [A_220] : ( addition(star(A_220),star(addition(one,A_220))) = star(A_220) ),
inference(superposition,[status(thm),theory(equality)],[c_17366,c_2]) ).
tff(c_412,plain,
! [A_1,B_2,C_51] : ( addition(addition(A_1,B_2),C_51) = addition(B_2,addition(A_1,C_51)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_358]) ).
tff(c_7870,plain,
! [A_145] : ( addition(multiplication(star(A_145),A_145),addition(one,star(A_145))) = star(A_145) ),
inference(superposition,[status(thm),theory(equality)],[c_412,c_7777]) ).
tff(c_62009,plain,
! [A_145] : ( multiplication(star(A_145),addition(one,A_145)) = star(A_145) ),
inference(demodulation,[status(thm),theory(equality)],[c_754,c_2,c_9423,c_7870]) ).
tff(c_4042,plain,
! [A_116,C_117] : ( multiplication(A_116,addition(one,C_117)) = addition(A_116,multiplication(A_116,C_117)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_702]) ).
tff(c_4189,plain,
! [A_116,C_51,B_50] : ( multiplication(A_116,addition(C_51,addition(one,B_50))) = addition(A_116,multiplication(A_116,addition(B_50,C_51))) ),
inference(superposition,[status(thm),theory(equality)],[c_373,c_4042]) ).
tff(c_504,plain,
! [B_54,A_12] : ( multiplication(addition(one,B_54),A_12) = addition(A_12,multiplication(B_54,A_12)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_460]) ).
tff(c_252,plain,
! [A_45] : leq(addition(one,multiplication(A_45,star(A_45))),star(A_45)),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_7321,plain,
! [A_136] : ( addition(addition(one,multiplication(A_136,star(A_136))),star(A_136)) = star(A_136) ),
inference(resolution,[status(thm)],[c_252,c_24]) ).
tff(c_7408,plain,
! [A_136] : ( addition(multiplication(A_136,star(A_136)),addition(one,star(A_136))) = star(A_136) ),
inference(superposition,[status(thm),theory(equality)],[c_412,c_7321]) ).
tff(c_58889,plain,
! [A_136] : ( multiplication(addition(one,A_136),star(A_136)) = star(A_136) ),
inference(demodulation,[status(thm),theory(equality)],[c_504,c_2,c_9423,c_7408]) ).
tff(c_10054,plain,
! [B_17,A_16,C_18] : ( multiplication(addition(B_17,A_16),C_18) = multiplication(addition(A_16,B_17),C_18) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_9860]) ).
tff(c_19038,plain,
! [A_229,B_230] :
( leq(multiplication(star(A_229),multiplication(A_229,B_230)),B_230)
| ~ leq(multiplication(A_229,B_230),B_230) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_1369]) ).
tff(c_19045,plain,
! [A_229,B_230] :
( ( addition(multiplication(star(A_229),multiplication(A_229,B_230)),B_230) = B_230 )
| ~ leq(multiplication(A_229,B_230),B_230) ),
inference(resolution,[status(thm)],[c_19038,c_24]) ).
tff(c_299179,plain,
! [B_1184,A_1185] :
( ( addition(B_1184,multiplication(star(A_1185),multiplication(A_1185,B_1184))) = B_1184 )
| ~ leq(multiplication(A_1185,B_1184),B_1184) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19045]) ).
tff(c_300332,plain,
! [A_136] :
( ( addition(star(A_136),multiplication(star(addition(one,A_136)),star(A_136))) = star(A_136) )
| ~ leq(multiplication(addition(one,A_136),star(A_136)),star(A_136)) ),
inference(superposition,[status(thm),theory(equality)],[c_58889,c_299179]) ).
tff(c_458457,plain,
! [A_1462] : ( multiplication(star(addition(one,A_1462)),star(A_1462)) = star(A_1462) ),
inference(demodulation,[status(thm),theory(equality)],[c_127551,c_58889,c_9423,c_10054,c_3413,c_300332]) ).
tff(c_21266,plain,
! [A_11,B_60] :
( leq(multiplication(A_11,star(B_60)),A_11)
| ( addition(A_11,multiplication(A_11,addition(B_60,one))) != A_11 ) ),
inference(superposition,[status(thm),theory(equality)],[c_757,c_21209]) ).
tff(c_458705,plain,
! [A_1462] :
( leq(star(A_1462),star(addition(one,A_1462)))
| ( addition(star(addition(one,A_1462)),multiplication(star(addition(one,A_1462)),addition(A_1462,one))) != star(addition(one,A_1462)) ) ),
inference(superposition,[status(thm),theory(equality)],[c_458457,c_21266]) ).
tff(c_459595,plain,
! [A_1463] : leq(star(A_1463),star(addition(one,A_1463))),
inference(demodulation,[status(thm),theory(equality)],[c_62009,c_4189,c_458705]) ).
tff(c_459598,plain,
! [A_1463] : ( addition(star(A_1463),star(addition(one,A_1463))) = star(addition(one,A_1463)) ),
inference(resolution,[status(thm)],[c_459595,c_24]) ).
tff(c_460028,plain,
! [A_1463] : ( star(addition(one,A_1463)) = star(A_1463) ),
inference(demodulation,[status(thm),theory(equality)],[c_17459,c_459598]) ).
tff(c_300870,plain,
! [A_136] : ( multiplication(star(addition(one,A_136)),star(A_136)) = star(A_136) ),
inference(demodulation,[status(thm),theory(equality)],[c_127551,c_58889,c_9423,c_10054,c_3413,c_300332]) ).
tff(c_460513,plain,
! [A_136] : ( multiplication(star(A_136),star(A_136)) = star(A_136) ),
inference(demodulation,[status(thm),theory(equality)],[c_460028,c_300870]) ).
tff(c_58892,plain,
! [A_451] : ( multiplication(addition(one,A_451),star(A_451)) = star(A_451) ),
inference(demodulation,[status(thm),theory(equality)],[c_504,c_2,c_9423,c_7408]) ).
tff(c_59310,plain,
! [A_1] : ( multiplication(addition(A_1,one),star(A_1)) = star(A_1) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_58892]) ).
tff(c_60881,plain,
! [A_459] : ( multiplication(addition(A_459,one),star(A_459)) = star(A_459) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_58892]) ).
tff(c_4275,plain,
! [A_118,B_119] : ( multiplication(A_118,addition(B_119,one)) = addition(multiplication(A_118,B_119),A_118) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_702]) ).
tff(c_4479,plain,
! [A_118,B_2] : ( multiplication(A_118,addition(one,B_2)) = addition(multiplication(A_118,B_2),A_118) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_4275]) ).
tff(c_61030,plain,
! [A_459] : ( multiplication(addition(A_459,one),addition(one,star(A_459))) = addition(star(A_459),addition(A_459,one)) ),
inference(superposition,[status(thm),theory(equality)],[c_60881,c_4479]) ).
tff(c_61321,plain,
! [A_459] : ( addition(A_459,star(A_459)) = star(A_459) ),
inference(demodulation,[status(thm),theory(equality)],[c_59310,c_9423,c_9423,c_373,c_61030]) ).
tff(c_62012,plain,
! [A_462] : ( multiplication(star(A_462),addition(one,A_462)) = star(A_462) ),
inference(demodulation,[status(thm),theory(equality)],[c_754,c_2,c_9423,c_7870]) ).
tff(c_62405,plain,
! [A_164] : ( multiplication(star(star(A_164)),star(A_164)) = star(star(A_164)) ),
inference(superposition,[status(thm),theory(equality)],[c_9423,c_62012]) ).
tff(c_463244,plain,
! [A_1467] : ( multiplication(star(A_1467),star(A_1467)) = star(A_1467) ),
inference(demodulation,[status(thm),theory(equality)],[c_460028,c_300870]) ).
tff(c_19174,plain,
! [B_230,A_229] :
( ( addition(B_230,multiplication(star(A_229),multiplication(A_229,B_230))) = B_230 )
| ~ leq(multiplication(A_229,B_230),B_230) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_19045]) ).
tff(c_463378,plain,
! [A_1467] :
( ( addition(star(A_1467),multiplication(star(star(A_1467)),star(A_1467))) = star(A_1467) )
| ~ leq(multiplication(star(A_1467),star(A_1467)),star(A_1467)) ),
inference(superposition,[status(thm),theory(equality)],[c_463244,c_19174]) ).
tff(c_463982,plain,
! [A_1467] : ( star(star(A_1467)) = star(A_1467) ),
inference(demodulation,[status(thm),theory(equality)],[c_127551,c_460513,c_61321,c_62405,c_463378]) ).
tff(c_36,plain,
star(star('#skF_1')) != star('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_464236,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_463982,c_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KLE039+1 : 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
% 0.14/0.35 % Computer : n026.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 : Thu Aug 3 23:43:47 EDT 2023
% 0.14/0.35 % CPUTime :
% 193.80/160.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 193.80/160.48
% 193.80/160.48 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 194.06/160.53
% 194.06/160.53 Inference rules
% 194.06/160.53 ----------------------
% 194.06/160.53 #Ref : 7
% 194.06/160.53 #Sup : 119418
% 194.06/160.53 #Fact : 0
% 194.06/160.53 #Define : 0
% 194.06/160.53 #Split : 8
% 194.06/160.53 #Chain : 0
% 194.06/160.53 #Close : 0
% 194.06/160.53
% 194.06/160.53 Ordering : KBO
% 194.06/160.53
% 194.06/160.53 Simplification rules
% 194.06/160.53 ----------------------
% 194.06/160.53 #Subsume : 34544
% 194.06/160.53 #Demod : 141925
% 194.06/160.53 #Tautology : 18303
% 194.06/160.53 #SimpNegUnit : 679
% 194.06/160.53 #BackRed : 112
% 194.06/160.53
% 194.06/160.53 #Partial instantiations: 0
% 194.06/160.53 #Strategies tried : 1
% 194.06/160.53
% 194.06/160.53 Timing (in seconds)
% 194.06/160.53 ----------------------
% 194.06/160.53 Preprocessing : 0.49
% 194.06/160.53 Parsing : 0.27
% 194.06/160.53 CNF conversion : 0.03
% 194.06/160.53 Main loop : 158.96
% 194.06/160.53 Inferencing : 8.20
% 194.06/160.53 Reduction : 118.17
% 194.06/160.53 Demodulation : 110.86
% 194.06/160.53 BG Simplification : 1.24
% 194.06/160.53 Subsumption : 22.10
% 194.06/160.53 Abstraction : 2.16
% 194.06/160.53 MUC search : 0.00
% 194.06/160.53 Cooper : 0.00
% 194.06/160.53 Total : 159.54
% 194.06/160.53 Index Insertion : 0.00
% 194.06/160.53 Index Deletion : 0.00
% 194.06/160.53 Index Matching : 0.00
% 194.06/160.53 BG Taut test : 0.00
%------------------------------------------------------------------------------