%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : KLE093+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 : n012.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 07:04:46 PM UTC 2025
% Result : Theorem 12.07s 4.56s
% Output : CNFRefutation 12.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 32 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 3 ~; 1 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 49 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ leq > multiplication > addition > #nlpp > star > domain > zero > one > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(domain,type,
domain: $i > $i ).
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_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_132,axiom,
! [X0] : ( addition(domain(X0),one) = one ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain3) ).
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_63,axiom,
! [A] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
tff(f_128,axiom,
! [X0] : ( addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain1) ).
tff(f_135,axiom,
! [X0,X1] : ( domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain5) ).
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_140,negated_conjecture,
~ ! [X0] : ( domain(star(X0)) = one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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_40,plain,
! [X0_34] : ( addition(domain(X0_34),one) = one ),
inference(cnfTransformation,[status(thm)],[f_132]) ).
tff(c_158,plain,
! [B_44,A_45] : ( addition(B_44,A_45) = addition(A_45,B_44) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_199,plain,
! [X0_34] : ( addition(one,domain(X0_34)) = one ),
inference(superposition,[status(thm),theory(equality)],[c_40,c_158]) ).
tff(c_12,plain,
! [A_11] : ( multiplication(A_11,one) = A_11 ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_741,plain,
! [X0_66] : ( addition(X0_66,multiplication(domain(X0_66),X0_66)) = multiplication(domain(X0_66),X0_66) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_775,plain,
multiplication(domain(one),one) = addition(one,domain(one)),
inference(superposition,[status(thm),theory(equality)],[c_12,c_741]) ).
tff(c_786,plain,
domain(one) = one,
inference(demodulation,[status(thm),theory(equality)],[c_199,c_12,c_775]) ).
tff(c_397,plain,
! [X0_56,X1_57] : ( addition(domain(X0_56),domain(X1_57)) = domain(addition(X0_56,X1_57)) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
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_406,plain,
! [X1_57,X0_56] : ( addition(domain(X1_57),domain(X0_56)) = domain(addition(X0_56,X1_57)) ),
inference(superposition,[status(thm),theory(equality)],[c_397,c_2]) ).
tff(c_794,plain,
! [X0_56] : ( addition(one,domain(X0_56)) = domain(addition(X0_56,one)) ),
inference(superposition,[status(thm),theory(equality)],[c_786,c_406]) ).
tff(c_826,plain,
! [X0_67] : ( domain(addition(X0_67,one)) = one ),
inference(demodulation,[status(thm),theory(equality)],[c_199,c_794]) ).
tff(c_44,plain,
! [X0_35,X1_36] : ( addition(domain(X0_35),domain(X1_36)) = domain(addition(X0_35,X1_36)) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_846,plain,
! [X0_67,X1_36] : ( domain(addition(addition(X0_67,one),X1_36)) = addition(one,domain(X1_36)) ),
inference(superposition,[status(thm),theory(equality)],[c_826,c_44]) ).
tff(c_892,plain,
! [X0_67,X1_36] : ( domain(addition(addition(X0_67,one),X1_36)) = one ),
inference(demodulation,[status(thm),theory(equality)],[c_199,c_846]) ).
tff(c_1715,plain,
! [X0_67,X1_36] : ( domain(addition(X0_67,addition(one,X1_36))) = one ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_892]) ).
tff(c_460,plain,
! [A_58] : leq(addition(one,multiplication(A_58,star(A_58))),star(A_58)),
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_12041,plain,
! [A_198] : ( addition(addition(one,multiplication(A_198,star(A_198))),star(A_198)) = star(A_198) ),
inference(resolution,[status(thm)],[c_460,c_24]) ).
tff(c_537,plain,
! [X1_62,X0_63] : ( addition(domain(X1_62),domain(X0_63)) = domain(addition(X0_63,X1_62)) ),
inference(superposition,[status(thm),theory(equality)],[c_397,c_2]) ).
tff(c_543,plain,
! [X1_62,X0_63] : ( domain(addition(X1_62,X0_63)) = domain(addition(X0_63,X1_62)) ),
inference(superposition,[status(thm),theory(equality)],[c_537,c_44]) ).
tff(c_12112,plain,
! [A_198] : ( domain(addition(star(A_198),addition(one,multiplication(A_198,star(A_198))))) = domain(star(A_198)) ),
inference(superposition,[status(thm),theory(equality)],[c_12041,c_543]) ).
tff(c_12177,plain,
! [A_198] : ( domain(star(A_198)) = one ),
inference(demodulation,[status(thm),theory(equality)],[c_1715,c_12112]) ).
tff(c_46,plain,
domain(star('#skF_1')) != one,
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_12191,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12177,c_46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : KLE093+1 : TPTP v9.0.0. Released v4.0.0.
% 0.00/0.10 % 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
% 0.09/0.30 % Computer : n012.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue Apr 8 02:37:45 EDT 2025
% 0.09/0.30 % CPUTime :
% 12.07/4.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.07/4.56
% 12.07/4.56 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------