%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : KLE037+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/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 : n008.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 8.63s 3.19s
% Output : CNFRefutation 8.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 23 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 : 42 ( 42 !; 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/sandbox/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/sandbox/benchmark/Axioms/KLE002+0.ax',left_distributivity) ).
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_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_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_80,axiom,
! [A,B] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',order) ).
tff(f_58,axiom,
! [A] : ( addition(A,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
tff(f_100,negated_conjecture,
~ ! [X0] : leq(one,star(X0)),
file('/export/starexec/sandbox/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_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_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_6003,plain,
! [A_133] : ( addition(addition(one,multiplication(A_133,star(A_133))),star(A_133)) = star(A_133) ),
inference(resolution,[status(thm)],[c_268,c_24]) ).
tff(c_6093,plain,
! [A_133] : ( addition(one,addition(multiplication(A_133,star(A_133)),star(A_133))) = star(A_133) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_6003]) ).
tff(c_6127,plain,
! [A_133] : ( addition(one,multiplication(addition(one,A_133),star(A_133))) = star(A_133) ),
inference(demodulation,[status(thm),theory(equality)],[c_1721,c_2,c_6093]) ).
tff(c_8358,plain,
! [A_159] : ( addition(one,multiplication(addition(one,A_159),star(A_159))) = star(A_159) ),
inference(demodulation,[status(thm),theory(equality)],[c_1721,c_2,c_6093]) ).
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_8431,plain,
! [A_159] : ( addition(one,multiplication(addition(one,A_159),star(A_159))) = addition(one,star(A_159)) ),
inference(superposition,[status(thm),theory(equality)],[c_8358,c_367]) ).
tff(c_8521,plain,
! [A_159] : ( addition(one,star(A_159)) = star(A_159) ),
inference(demodulation,[status(thm),theory(equality)],[c_6127,c_8431]) ).
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(one,star('#skF_1')),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_241,plain,
addition(one,star('#skF_1')) != star('#skF_1'),
inference(resolution,[status(thm)],[c_233,c_36]) ).
tff(c_8535,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8521,c_241]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE037+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.13 % 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
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Apr 8 02:31:17 EDT 2025
% 0.13/0.34 % CPUTime :
% 8.63/3.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.63/3.20
% 8.63/3.20 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------