TSTP Solution File: KLE063+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : KLE063+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/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 : n011.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 10:44:47 EDT 2023
% Result : Theorem 6.30s 2.55s
% Output : CNFRefutation 6.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of formulae : 53 ( 44 unt; 8 typ; 0 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 4 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 62 (; 62 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ leq > multiplication > addition > #nlpp > domain > zero > one > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(domain,type,
domain: $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_120,axiom,
! [X0,X1] : ( domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain5) ).
tff(f_127,negated_conjecture,
~ ! [X0,X1] :
( ( addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0) )
=> ( addition(domain(X0),domain(X1)) = domain(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(f_52,axiom,
! [A,B] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
tff(f_65,axiom,
! [A] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
tff(f_115,axiom,
! [X0,X1] : ( domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain2) ).
tff(f_63,axiom,
! [A] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
tff(f_117,axiom,
! [X0] : ( addition(domain(X0),one) = one ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain3) ).
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/KLE001+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/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
tff(f_113,axiom,
! [X0] : ( addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain1) ).
tff(c_36,plain,
! [X0_27,X1_28] : ( addition(domain(X0_27),domain(X1_28)) = domain(addition(X0_27,X1_28)) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_38,plain,
addition(domain('#skF_1'),domain('#skF_2')) != domain('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_41,plain,
domain(addition('#skF_1','#skF_2')) != domain('#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_38]) ).
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_306,plain,
! [X0_44,X1_45] : ( domain(multiplication(X0_44,domain(X1_45))) = domain(multiplication(X0_44,X1_45)) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_326,plain,
! [X1_45] : ( domain(multiplication(one,X1_45)) = domain(domain(X1_45)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_306]) ).
tff(c_340,plain,
! [X1_45] : ( domain(domain(X1_45)) = domain(X1_45) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_326]) ).
tff(c_378,plain,
! [X0_47,X1_48] : ( addition(domain(X0_47),domain(X1_48)) = domain(addition(X0_47,X1_48)) ),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_748,plain,
! [X1_57,X0_58] : ( addition(domain(X1_57),domain(X0_58)) = domain(addition(X0_58,X1_57)) ),
inference(superposition,[status(thm),theory(equality)],[c_378,c_2]) ).
tff(c_782,plain,
! [X1_45,X0_58] : ( addition(domain(X1_45),domain(X0_58)) = domain(addition(X0_58,domain(X1_45))) ),
inference(superposition,[status(thm),theory(equality)],[c_340,c_748]) ).
tff(c_815,plain,
! [X0_58,X1_45] : ( domain(addition(X0_58,domain(X1_45))) = domain(addition(X1_45,X0_58)) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_782]) ).
tff(c_12,plain,
! [A_11] : ( multiplication(A_11,one) = A_11 ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_32,plain,
! [X0_26] : ( addition(domain(X0_26),one) = one ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_161,plain,
! [B_36,A_37] : ( addition(B_36,A_37) = addition(A_37,B_36) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_214,plain,
! [X0_26] : ( addition(one,domain(X0_26)) = one ),
inference(superposition,[status(thm),theory(equality)],[c_32,c_161]) ).
tff(c_2137,plain,
! [A_79,C_80,B_81] : ( addition(multiplication(A_79,C_80),multiplication(B_81,C_80)) = multiplication(addition(A_79,B_81),C_80) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_2721,plain,
! [B_87,A_88] : ( multiplication(addition(one,B_87),A_88) = addition(A_88,multiplication(B_87,A_88)) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_2137]) ).
tff(c_2816,plain,
! [A_88,X0_26] : ( addition(A_88,multiplication(domain(X0_26),A_88)) = multiplication(one,A_88) ),
inference(superposition,[status(thm),theory(equality)],[c_214,c_2721]) ).
tff(c_2861,plain,
! [A_88,X0_26] : ( addition(A_88,multiplication(domain(X0_26),A_88)) = A_88 ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_2816]) ).
tff(c_40,plain,
addition('#skF_1',multiplication(domain('#skF_2'),'#skF_1')) = multiplication(domain('#skF_2'),'#skF_1'),
inference(cnfTransformation,[status(thm)],[f_127]) ).
tff(c_2968,plain,
multiplication(domain('#skF_2'),'#skF_1') = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_2861,c_40]) ).
tff(c_16,plain,
! [A_13,B_14,C_15] : ( addition(multiplication(A_13,B_14),multiplication(A_13,C_15)) = multiplication(A_13,addition(B_14,C_15)) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_5575,plain,
! [C_116] : ( multiplication(domain('#skF_2'),addition('#skF_1',C_116)) = addition('#skF_1',multiplication(domain('#skF_2'),C_116)) ),
inference(superposition,[status(thm),theory(equality)],[c_2968,c_16]) ).
tff(c_1625,plain,
! [X0_73] : ( addition(X0_73,multiplication(domain(X0_73),X0_73)) = multiplication(domain(X0_73),X0_73) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_1697,plain,
multiplication(domain(one),one) = addition(one,domain(one)),
inference(superposition,[status(thm),theory(equality)],[c_12,c_1625]) ).
tff(c_1720,plain,
domain(one) = one,
inference(demodulation,[status(thm),theory(equality)],[c_214,c_12,c_1697]) ).
tff(c_1747,plain,
! [X0_27] : ( addition(domain(X0_27),one) = domain(addition(X0_27,one)) ),
inference(superposition,[status(thm),theory(equality)],[c_1720,c_36]) ).
tff(c_1924,plain,
! [X0_75] : ( domain(addition(X0_75,one)) = one ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_1747]) ).
tff(c_30,plain,
! [X0_24,X1_25] : ( domain(multiplication(X0_24,domain(X1_25))) = domain(multiplication(X0_24,X1_25)) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_1963,plain,
! [X0_24,X0_75] : ( domain(multiplication(X0_24,addition(X0_75,one))) = domain(multiplication(X0_24,one)) ),
inference(superposition,[status(thm),theory(equality)],[c_1924,c_30]) ).
tff(c_2015,plain,
! [X0_24,X0_75] : ( domain(multiplication(X0_24,addition(X0_75,one))) = domain(X0_24) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_1963]) ).
tff(c_5585,plain,
domain(addition('#skF_1',multiplication(domain('#skF_2'),one))) = domain(domain('#skF_2')),
inference(superposition,[status(thm),theory(equality)],[c_5575,c_2015]) ).
tff(c_5655,plain,
domain(addition('#skF_1','#skF_2')) = domain('#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_815,c_340,c_12,c_5585]) ).
tff(c_5657,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_41,c_5655]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : KLE063+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % 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
% 0.14/0.37 % Computer : n011.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Thu Aug 3 23:25:36 EDT 2023
% 0.14/0.37 % CPUTime :
% 6.30/2.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.30/2.55
% 6.30/2.55 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.42/2.58
% 6.42/2.58 Inference rules
% 6.42/2.58 ----------------------
% 6.42/2.58 #Ref : 0
% 6.42/2.58 #Sup : 1383
% 6.42/2.58 #Fact : 0
% 6.42/2.58 #Define : 0
% 6.42/2.58 #Split : 0
% 6.42/2.58 #Chain : 0
% 6.42/2.58 #Close : 0
% 6.42/2.58
% 6.42/2.58 Ordering : KBO
% 6.42/2.58
% 6.42/2.58 Simplification rules
% 6.42/2.58 ----------------------
% 6.42/2.58 #Subsume : 49
% 6.42/2.58 #Demod : 1467
% 6.42/2.58 #Tautology : 843
% 6.42/2.58 #SimpNegUnit : 1
% 6.42/2.58 #BackRed : 7
% 6.42/2.58
% 6.42/2.58 #Partial instantiations: 0
% 6.42/2.58 #Strategies tried : 1
% 6.42/2.58
% 6.42/2.58 Timing (in seconds)
% 6.42/2.58 ----------------------
% 6.42/2.59 Preprocessing : 0.48
% 6.42/2.59 Parsing : 0.26
% 6.42/2.59 CNF conversion : 0.03
% 6.42/2.59 Main loop : 1.02
% 6.42/2.59 Inferencing : 0.31
% 6.42/2.59 Reduction : 0.48
% 6.42/2.59 Demodulation : 0.41
% 6.42/2.59 BG Simplification : 0.04
% 6.42/2.59 Subsumption : 0.15
% 6.42/2.59 Abstraction : 0.05
% 6.42/2.59 MUC search : 0.00
% 6.42/2.59 Cooper : 0.00
% 6.42/2.59 Total : 1.56
% 6.42/2.59 Index Insertion : 0.00
% 6.42/2.59 Index Deletion : 0.00
% 6.42/2.59 Index Matching : 0.00
% 6.42/2.59 BG Taut test : 0.00
%------------------------------------------------------------------------------