TSTP Solution File: GRP682+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP682+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 : n025.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 10:41:55 EDT 2023
% Result : Theorem 10.62s 3.69s
% Output : CNFRefutation 10.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of formulae : 72 ( 61 unt; 9 typ; 0 def)
% Number of atoms : 65 ( 63 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 1 |; 1 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 139 (; 139 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ rd > mult > ld > #nlpp > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(ld,type,
ld: ( $i * $i ) > $i ).
tff(rd,type,
rd: ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(mult,type,
mult: ( $i * $i ) > $i ).
tff(f_28,axiom,
! [A] : ( ld(A,mult(A,A)) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
tff(f_32,axiom,
! [B,A] : ( mult(A,ld(A,B)) = ld(A,mult(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
tff(f_34,axiom,
! [B,A] : ( mult(rd(A,B),B) = rd(mult(A,B),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
tff(f_30,axiom,
! [A] : ( rd(mult(A,A),A) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
tff(f_40,axiom,
! [B,A] : ( ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
tff(f_36,axiom,
! [D,C,B,A] : ( ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
tff(f_38,axiom,
! [D,C,B,A] : ( rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
tff(f_45,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ld(ld(X0,X1),mult(ld(X0,X1),X2)) = ld(X0,mult(X0,X2)) )
& ( ld(rd(X0,X1),mult(rd(X0,X1),X2)) = ld(X0,mult(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(c_2,plain,
! [A_1] : ( ld(A_1,mult(A_1,A_1)) = A_1 ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_6,plain,
! [A_4,B_3] : ( mult(A_4,ld(A_4,B_3)) = ld(A_4,mult(A_4,B_3)) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_48,plain,
! [A_21,B_22] : ( rd(mult(A_21,B_22),B_22) = mult(rd(A_21,B_22),B_22) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_4,plain,
! [A_2] : ( rd(mult(A_2,A_2),A_2) = A_2 ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_55,plain,
! [B_22] : ( mult(rd(B_22,B_22),B_22) = B_22 ),
inference(superposition,[status(thm),theory(equality)],[c_48,c_4]) ).
tff(c_79,plain,
! [A_24,B_25] : ( rd(mult(rd(A_24,A_24),B_25),B_25) = ld(A_24,mult(A_24,ld(B_25,B_25))) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_95,plain,
! [B_22] : ( ld(B_22,mult(B_22,ld(B_22,B_22))) = rd(B_22,B_22) ),
inference(superposition,[status(thm),theory(equality)],[c_55,c_79]) ).
tff(c_110,plain,
! [B_22] : ( rd(B_22,B_22) = ld(B_22,B_22) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6,c_95]) ).
tff(c_113,plain,
! [B_22] : ( mult(ld(B_22,B_22),B_22) = B_22 ),
inference(demodulation,[status(thm),theory(equality)],[c_110,c_55]) ).
tff(c_9517,plain,
! [A_191,B_192,C_193,D_194] : ( ld(ld(A_191,B_192),mult(ld(A_191,B_192),mult(C_193,D_194))) = mult(ld(A_191,mult(A_191,C_193)),D_194) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_9606,plain,
! [A_1,C_193,D_194] : ( ld(A_1,mult(ld(A_1,mult(A_1,A_1)),mult(C_193,D_194))) = mult(ld(A_1,mult(A_1,C_193)),D_194) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_9517]) ).
tff(c_9630,plain,
! [A_1,C_193,D_194] : ( mult(ld(A_1,mult(A_1,C_193)),D_194) = ld(A_1,mult(A_1,mult(C_193,D_194))) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_9606]) ).
tff(c_10,plain,
! [A_10,B_9,C_8,D_7] : ( ld(ld(A_10,B_9),mult(ld(A_10,B_9),mult(C_8,D_7))) = mult(ld(A_10,mult(A_10,C_8)),D_7) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_11946,plain,
! [A_256,B_257,C_258,D_259] : ( ld(ld(A_256,B_257),mult(ld(A_256,B_257),mult(C_258,D_259))) = ld(A_256,mult(A_256,mult(C_258,D_259))) ),
inference(demodulation,[status(thm),theory(equality)],[c_9630,c_10]) ).
tff(c_12101,plain,
! [A_256,B_257,B_22] : ( ld(ld(A_256,B_257),mult(ld(A_256,B_257),B_22)) = ld(A_256,mult(A_256,mult(ld(B_22,B_22),B_22))) ),
inference(superposition,[status(thm),theory(equality)],[c_113,c_11946]) ).
tff(c_12156,plain,
! [A_256,B_257,B_22] : ( ld(ld(A_256,B_257),mult(ld(A_256,B_257),B_22)) = ld(A_256,mult(A_256,B_22)) ),
inference(demodulation,[status(thm),theory(equality)],[c_113,c_12101]) ).
tff(c_177,plain,
! [A_31,B_32,C_33,D_34] : ( ld(ld(A_31,B_32),mult(ld(A_31,B_32),mult(C_33,D_34))) = mult(ld(A_31,mult(A_31,C_33)),D_34) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_234,plain,
! [A_1,C_33,D_34] : ( ld(A_1,mult(ld(A_1,mult(A_1,A_1)),mult(C_33,D_34))) = mult(ld(A_1,mult(A_1,C_33)),D_34) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_177]) ).
tff(c_315,plain,
! [A_38,C_39,D_40] : ( mult(ld(A_38,mult(A_38,C_39)),D_40) = ld(A_38,mult(A_38,mult(C_39,D_40))) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_234]) ).
tff(c_408,plain,
! [A_41,D_42] : ( ld(A_41,mult(A_41,mult(A_41,D_42))) = mult(A_41,D_42) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_315]) ).
tff(c_250,plain,
! [A_1,C_33,D_34] : ( mult(ld(A_1,mult(A_1,C_33)),D_34) = ld(A_1,mult(A_1,mult(C_33,D_34))) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_234]) ).
tff(c_414,plain,
! [A_41,D_42,D_34] : ( ld(A_41,mult(A_41,mult(mult(A_41,D_42),D_34))) = mult(mult(A_41,D_42),D_34) ),
inference(superposition,[status(thm),theory(equality)],[c_408,c_250]) ).
tff(c_394,plain,
! [A_1,D_40] : ( ld(A_1,mult(A_1,mult(A_1,D_40))) = mult(A_1,D_40) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_315]) ).
tff(c_1937,plain,
! [A_84,B_85,C_86,D_87] : ( ld(ld(A_84,B_85),mult(ld(A_84,B_85),mult(C_86,D_87))) = ld(A_84,mult(A_84,mult(C_86,D_87))) ),
inference(demodulation,[status(thm),theory(equality)],[c_250,c_10]) ).
tff(c_2063,plain,
! [A_84,B_85,B_22] : ( ld(ld(A_84,B_85),mult(ld(A_84,B_85),B_22)) = ld(A_84,mult(A_84,mult(ld(B_22,B_22),B_22))) ),
inference(superposition,[status(thm),theory(equality)],[c_113,c_1937]) ).
tff(c_5406,plain,
! [A_139,B_140,B_141] : ( ld(ld(A_139,B_140),mult(ld(A_139,B_140),B_141)) = ld(A_139,mult(A_139,B_141)) ),
inference(demodulation,[status(thm),theory(equality)],[c_113,c_2063]) ).
tff(c_5539,plain,
! [A_1,D_40,B_141] : ( ld(mult(A_1,D_40),mult(ld(A_1,mult(A_1,mult(A_1,D_40))),B_141)) = ld(A_1,mult(A_1,B_141)) ),
inference(superposition,[status(thm),theory(equality)],[c_394,c_5406]) ).
tff(c_5599,plain,
! [A_1,D_40,B_141] : ( ld(mult(A_1,D_40),mult(mult(A_1,D_40),B_141)) = ld(A_1,mult(A_1,B_141)) ),
inference(demodulation,[status(thm),theory(equality)],[c_414,c_250,c_5539]) ).
tff(c_8,plain,
! [A_6,B_5] : ( rd(mult(A_6,B_5),B_5) = mult(rd(A_6,B_5),B_5) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_85,plain,
! [A_24,B_25] : ( mult(rd(rd(A_24,A_24),B_25),B_25) = ld(A_24,mult(A_24,ld(B_25,B_25))) ),
inference(superposition,[status(thm),theory(equality)],[c_79,c_8]) ).
tff(c_253,plain,
! [A_24,B_25] : ( mult(rd(ld(A_24,A_24),B_25),B_25) = ld(A_24,mult(A_24,ld(B_25,B_25))) ),
inference(demodulation,[status(thm),theory(equality)],[c_110,c_85]) ).
tff(c_1660,plain,
! [A_79,B_80] : ( rd(ld(A_79,mult(A_79,B_80)),ld(A_79,B_80)) = mult(rd(A_79,ld(A_79,B_80)),ld(A_79,B_80)) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_48]) ).
tff(c_1855,plain,
! [A_83] : ( mult(rd(A_83,ld(A_83,A_83)),ld(A_83,A_83)) = rd(A_83,ld(A_83,A_83)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1660]) ).
tff(c_12,plain,
! [A_14,B_13,C_12,D_11] : ( rd(mult(mult(A_14,B_13),rd(C_12,D_11)),rd(C_12,D_11)) = mult(A_14,rd(mult(B_13,D_11),D_11)) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_499,plain,
! [A_46,B_47,C_48,D_49] : ( rd(mult(mult(A_46,B_47),rd(C_48,D_49)),rd(C_48,D_49)) = mult(A_46,mult(rd(B_47,D_49),D_49)) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_12]) ).
tff(c_559,plain,
! [A_46,B_47,A_2] : ( rd(mult(mult(A_46,B_47),A_2),rd(mult(A_2,A_2),A_2)) = mult(A_46,mult(rd(B_47,A_2),A_2)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_499]) ).
tff(c_580,plain,
! [A_50,B_51,A_52] : ( mult(rd(mult(A_50,B_51),A_52),A_52) = mult(A_50,mult(rd(B_51,A_52),A_52)) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_4,c_559]) ).
tff(c_629,plain,
! [A_6,B_5] : ( mult(mult(rd(A_6,B_5),B_5),B_5) = mult(A_6,mult(rd(B_5,B_5),B_5)) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_580]) ).
tff(c_647,plain,
! [A_6,B_5] : ( mult(mult(rd(A_6,B_5),B_5),B_5) = mult(A_6,B_5) ),
inference(demodulation,[status(thm),theory(equality)],[c_113,c_110,c_629]) ).
tff(c_1879,plain,
! [A_83] : ( mult(rd(A_83,ld(A_83,A_83)),ld(A_83,A_83)) = mult(A_83,ld(A_83,A_83)) ),
inference(superposition,[status(thm),theory(equality)],[c_1855,c_647]) ).
tff(c_1926,plain,
! [A_83] : ( mult(rd(A_83,ld(A_83,A_83)),ld(A_83,A_83)) = A_83 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6,c_1879]) ).
tff(c_1750,plain,
! [A_1] : ( mult(rd(A_1,ld(A_1,A_1)),ld(A_1,A_1)) = rd(A_1,ld(A_1,A_1)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1660]) ).
tff(c_2113,plain,
! [A_1] : ( rd(A_1,ld(A_1,A_1)) = A_1 ),
inference(demodulation,[status(thm),theory(equality)],[c_1926,c_1750]) ).
tff(c_2252,plain,
! [A_90] : ( mult(A_90,ld(A_90,A_90)) = A_90 ),
inference(demodulation,[status(thm),theory(equality)],[c_2113,c_1926]) ).
tff(c_578,plain,
! [A_46,B_47,A_2] : ( mult(rd(mult(A_46,B_47),A_2),A_2) = mult(A_46,mult(rd(B_47,A_2),A_2)) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_4,c_559]) ).
tff(c_2284,plain,
! [A_90,A_2] : ( mult(A_90,mult(rd(ld(A_90,A_90),A_2),A_2)) = mult(rd(A_90,A_2),A_2) ),
inference(superposition,[status(thm),theory(equality)],[c_2252,c_578]) ).
tff(c_2330,plain,
! [A_90,A_2] : ( mult(rd(A_90,A_2),A_2) = mult(A_90,ld(A_2,A_2)) ),
inference(demodulation,[status(thm),theory(equality)],[c_394,c_6,c_253,c_2284]) ).
tff(c_6524,plain,
! [A_153,D_154,B_155] : ( ld(mult(A_153,D_154),mult(mult(A_153,D_154),B_155)) = ld(A_153,mult(A_153,B_155)) ),
inference(demodulation,[status(thm),theory(equality)],[c_414,c_250,c_5539]) ).
tff(c_6690,plain,
! [A_90,A_2,B_155] : ( ld(mult(rd(A_90,A_2),A_2),mult(mult(A_90,ld(A_2,A_2)),B_155)) = ld(rd(A_90,A_2),mult(rd(A_90,A_2),B_155)) ),
inference(superposition,[status(thm),theory(equality)],[c_2330,c_6524]) ).
tff(c_6805,plain,
! [A_90,A_2,B_155] : ( ld(rd(A_90,A_2),mult(rd(A_90,A_2),B_155)) = ld(A_90,mult(A_90,B_155)) ),
inference(demodulation,[status(thm),theory(equality)],[c_5599,c_2330,c_6690]) ).
tff(c_16,plain,
( ( ld(ld('#skF_4','#skF_5'),mult(ld('#skF_4','#skF_5'),'#skF_6')) != ld('#skF_4',mult('#skF_4','#skF_6')) )
| ( ld(rd('#skF_1','#skF_2'),mult(rd('#skF_1','#skF_2'),'#skF_3')) != ld('#skF_1',mult('#skF_1','#skF_3')) ) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_136,plain,
ld(rd('#skF_1','#skF_2'),mult(rd('#skF_1','#skF_2'),'#skF_3')) != ld('#skF_1',mult('#skF_1','#skF_3')),
inference(splitLeft,[status(thm)],[c_16]) ).
tff(c_9371,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6805,c_136]) ).
tff(c_9372,plain,
ld(ld('#skF_4','#skF_5'),mult(ld('#skF_4','#skF_5'),'#skF_6')) != ld('#skF_4',mult('#skF_4','#skF_6')),
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_12492,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12156,c_9372]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GRP682+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/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
% 0.14/0.36 % Computer : n025.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 22:28:35 EDT 2023
% 0.14/0.36 % CPUTime :
% 10.62/3.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.62/3.70
% 10.62/3.70 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.62/3.73
% 10.62/3.73 Inference rules
% 10.62/3.74 ----------------------
% 10.62/3.74 #Ref : 0
% 10.62/3.74 #Sup : 3006
% 10.62/3.74 #Fact : 0
% 10.62/3.74 #Define : 0
% 10.62/3.74 #Split : 1
% 10.62/3.74 #Chain : 0
% 10.62/3.74 #Close : 0
% 10.62/3.74
% 10.62/3.74 Ordering : KBO
% 10.62/3.74
% 10.62/3.74 Simplification rules
% 10.62/3.74 ----------------------
% 10.62/3.74 #Subsume : 0
% 10.62/3.74 #Demod : 5174
% 10.62/3.74 #Tautology : 1295
% 10.62/3.74 #SimpNegUnit : 0
% 10.62/3.74 #BackRed : 29
% 10.62/3.74
% 10.62/3.74 #Partial instantiations: 0
% 10.62/3.74 #Strategies tried : 1
% 10.62/3.74
% 10.62/3.74 Timing (in seconds)
% 10.62/3.74 ----------------------
% 10.62/3.74 Preprocessing : 0.44
% 10.62/3.74 Parsing : 0.24
% 10.62/3.74 CNF conversion : 0.03
% 10.62/3.74 Main loop : 2.21
% 10.62/3.74 Inferencing : 0.71
% 10.62/3.74 Reduction : 1.07
% 10.62/3.74 Demodulation : 0.92
% 10.62/3.74 BG Simplification : 0.09
% 10.62/3.74 Subsumption : 0.23
% 10.62/3.74 Abstraction : 0.18
% 10.62/3.74 MUC search : 0.00
% 10.62/3.74 Cooper : 0.00
% 10.62/3.74 Total : 2.71
% 10.62/3.74 Index Insertion : 0.00
% 10.62/3.74 Index Deletion : 0.00
% 10.62/3.74 Index Matching : 0.00
% 10.62/3.74 BG Taut test : 0.00
%------------------------------------------------------------------------------