%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : KLE038+1 : TPTP v9.0.0. 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 : n020.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 : Wed Apr 9 07:04:39 PM UTC 2025
% Result : Theorem 20.58s 8.25s
% Output : CNFRefutation 20.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 41 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 44 ( 36 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 2 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 65 ( 65 !; 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_65,axiom,
! [A] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).
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/KLE002+0.ax',left_distributivity) ).
tff(f_52,axiom,
! [A,B] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
tff(f_84,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).
tff(f_80,axiom,
! [A,B] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',order) ).
tff(f_54,axiom,
! [C,B,A] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_associativity) ).
tff(f_58,axiom,
! [A] : ( addition(A,A) = A ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
tff(f_63,axiom,
! [A] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_right_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/KLE002+0.ax',right_distributivity) ).
tff(f_100,negated_conjecture,
~ ! [X0] : leq(X0,star(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(c_14,plain,
! [A_12] : ( multiplication(one,A_12) = A_12 ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_1645,plain,
! [A_71,C_72,B_73] : ( addition(multiplication(A_71,C_72),multiplication(B_73,C_72)) = multiplication(addition(A_71,B_73),C_72) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_1721,plain,
! [B_73,A_12] : ( multiplication(addition(one,B_73),A_12) = addition(A_12,multiplication(B_73,A_12)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_1645]) ).
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_268,plain,
! [A_45] : leq(addition(one,multiplication(A_45,star(A_45))),star(A_45)),
inference(cnfTransformation,[status(thm)],[f_84]) ).
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_7098,plain,
! [A_142] : ( addition(addition(one,multiplication(A_142,star(A_142))),star(A_142)) = star(A_142) ),
inference(resolution,[status(thm)],[c_268,c_24]) ).
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_7164,plain,
! [A_142] : ( addition(one,addition(multiplication(A_142,star(A_142)),star(A_142))) = star(A_142) ),
inference(superposition,[status(thm),theory(equality)],[c_7098,c_4]) ).
tff(c_7236,plain,
! [A_142] : ( addition(one,multiplication(addition(one,A_142),star(A_142))) = star(A_142) ),
inference(demodulation,[status(thm),theory(equality)],[c_1721,c_2,c_7164]) ).
tff(c_8928,plain,
! [A_161] : ( addition(one,multiplication(addition(one,A_161),star(A_161))) = star(A_161) ),
inference(demodulation,[status(thm),theory(equality)],[c_1721,c_2,c_7164]) ).
tff(c_8,plain,
! [A_7] : ( addition(A_7,A_7) = A_7 ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_306,plain,
! [A_46,B_47,C_48] : ( addition(addition(A_46,B_47),C_48) = addition(A_46,addition(B_47,C_48)) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_367,plain,
! [A_7,C_48] : ( addition(A_7,addition(A_7,C_48)) = addition(A_7,C_48) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_306]) ).
tff(c_9007,plain,
! [A_161] : ( addition(one,multiplication(addition(one,A_161),star(A_161))) = addition(one,star(A_161)) ),
inference(superposition,[status(thm),theory(equality)],[c_8928,c_367]) ).
tff(c_9103,plain,
! [A_161] : ( addition(one,star(A_161)) = star(A_161) ),
inference(demodulation,[status(thm),theory(equality)],[c_7236,c_9007]) ).
tff(c_353,plain,
! [B_2,A_1,C_48] : ( addition(addition(B_2,A_1),C_48) = addition(A_1,addition(B_2,C_48)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_306]) ).
tff(c_7152,plain,
! [A_142] : ( addition(multiplication(A_142,star(A_142)),addition(one,star(A_142))) = star(A_142) ),
inference(superposition,[status(thm),theory(equality)],[c_7098,c_353]) ).
tff(c_57307,plain,
! [A_142] : ( multiplication(addition(one,A_142),star(A_142)) = star(A_142) ),
inference(demodulation,[status(thm),theory(equality)],[c_1721,c_2,c_9103,c_7152]) ).
tff(c_364,plain,
! [A_46,B_47,A_1] : ( addition(A_46,addition(B_47,A_1)) = addition(A_1,addition(A_46,B_47)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_306]) ).
tff(c_57310,plain,
! [A_441] : ( multiplication(addition(one,A_441),star(A_441)) = star(A_441) ),
inference(demodulation,[status(thm),theory(equality)],[c_1721,c_2,c_9103,c_7152]) ).
tff(c_12,plain,
! [A_11] : ( multiplication(A_11,one) = A_11 ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_1055,plain,
! [A_62,B_63,C_64] : ( addition(multiplication(A_62,B_63),multiplication(A_62,C_64)) = multiplication(A_62,addition(B_63,C_64)) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_4049,plain,
! [A_114,B_115] : ( multiplication(A_114,addition(B_115,one)) = addition(multiplication(A_114,B_115),A_114) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_1055]) ).
tff(c_4239,plain,
! [A_114,B_2] : ( multiplication(A_114,addition(one,B_2)) = addition(multiplication(A_114,B_2),A_114) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_4049]) ).
tff(c_57449,plain,
! [A_441] : ( multiplication(addition(one,A_441),addition(one,star(A_441))) = addition(star(A_441),addition(one,A_441)) ),
inference(superposition,[status(thm),theory(equality)],[c_57310,c_4239]) ).
tff(c_57761,plain,
! [A_441] : ( addition(A_441,star(A_441)) = star(A_441) ),
inference(demodulation,[status(thm),theory(equality)],[c_57307,c_9103,c_9103,c_2,c_364,c_57449]) ).
tff(c_233,plain,
! [A_42,B_43] :
( leq(A_42,B_43)
| ( addition(A_42,B_43) != B_43 ) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_36,plain,
~ leq('#skF_1',star('#skF_1')),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_241,plain,
addition('#skF_1',star('#skF_1')) != star('#skF_1'),
inference(resolution,[status(thm)],[c_233,c_36]) ).
tff(c_57819,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_57761,c_241]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE038+1 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 8 02:31:19 EDT 2025
% 0.12/0.34 % CPUTime :
% 20.58/8.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.58/8.26
% 20.58/8.26 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------