TSTP Solution File: GRP194+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP194+1 : TPTP v8.1.2. Released v2.0.0.
% 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 : n006.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 10:40:27 EDT 2023
% Result : Theorem 3.60s 2.03s
% Output : CNFRefutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 53 ( 13 unt; 9 typ; 0 def)
% Number of atoms : 104 ( 22 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 114 ( 54 ~; 47 |; 6 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 6 >; 5 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 54 (; 53 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ left_zero > group_member > multiply > #nlpp > phi > h > f_left_zero > f > #skF_1 > #skF_2
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(h,type,
h: $i ).
tff(group_member,type,
group_member: ( $i * $i ) > $o ).
tff(f,type,
f: $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(phi,type,
phi: $i > $i ).
tff(f_left_zero,type,
f_left_zero: $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(left_zero,type,
left_zero: ( $i * $i ) > $o ).
tff(multiply,type,
multiply: ( $i * $i * $i ) > $i ).
tff(f_96,hypothesis,
left_zero(f,f_left_zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_zero_for_f) ).
tff(f_94,axiom,
! [G,X] :
( left_zero(G,X)
<=> ( group_member(X,G)
& ! [Y] :
( group_member(Y,G)
=> ( multiply(G,X,Y) = X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_zero) ).
tff(f_71,axiom,
! [X] :
( group_member(X,f)
=> group_member(phi(X),h) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).
tff(f_98,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_left_zero_h) ).
tff(f_84,axiom,
! [X] :
( group_member(X,h)
=> ? [Y] :
( group_member(Y,f)
& ( phi(Y) = X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjective) ).
tff(f_64,axiom,
! [G,X,Y,Z] :
( ( group_member(X,G)
& group_member(Y,G)
& group_member(Z,G) )
=> ( multiply(G,multiply(G,X,Y),Z) = multiply(G,X,multiply(G,Y,Z)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP007+0.ax',associativity) ).
tff(f_56,axiom,
! [G,X,Y] :
( ( group_member(X,G)
& group_member(Y,G) )
=> group_member(multiply(G,X,Y),G) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP007+0.ax',total_function) ).
tff(f_77,axiom,
! [X,Y] :
( ( group_member(X,f)
& group_member(Y,f) )
=> ( multiply(h,phi(X),phi(Y)) = phi(multiply(f,X,Y)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).
tff(c_22,plain,
left_zero(f,f_left_zero),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_25,plain,
! [X_18,G_19] :
( group_member(X_18,G_19)
| ~ left_zero(G_19,X_18) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_29,plain,
group_member(f_left_zero,f),
inference(resolution,[status(thm)],[c_22,c_25]) ).
tff(c_6,plain,
! [X_8] :
( group_member(phi(X_8),h)
| ~ group_member(X_8,f) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_24,plain,
~ left_zero(h,phi(f_left_zero)),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_20,plain,
! [G_13,X_14] :
( group_member('#skF_2'(G_13,X_14),G_13)
| left_zero(G_13,X_14)
| ~ group_member(X_14,G_13) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_12,plain,
! [X_11] :
( group_member('#skF_1'(X_11),f)
| ~ group_member(X_11,h) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_44,plain,
! [G_23,X_24,Y_25] :
( ( multiply(G_23,X_24,Y_25) = X_24 )
| ~ group_member(Y_25,G_23)
| ~ left_zero(G_23,X_24) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_54,plain,
! [X_26] :
( ( multiply(f,X_26,f_left_zero) = X_26 )
| ~ left_zero(f,X_26) ),
inference(resolution,[status(thm)],[c_29,c_44]) ).
tff(c_58,plain,
multiply(f,f_left_zero,f_left_zero) = f_left_zero,
inference(resolution,[status(thm)],[c_22,c_54]) ).
tff(c_184,plain,
! [G_49,X_50,Y_51,Z_52] :
( ( multiply(G_49,multiply(G_49,X_50,Y_51),Z_52) = multiply(G_49,X_50,multiply(G_49,Y_51,Z_52)) )
| ~ group_member(Z_52,G_49)
| ~ group_member(Y_51,G_49)
| ~ group_member(X_50,G_49) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_256,plain,
! [Z_52] :
( ( multiply(f,f_left_zero,multiply(f,f_left_zero,Z_52)) = multiply(f,f_left_zero,Z_52) )
| ~ group_member(Z_52,f)
| ~ group_member(f_left_zero,f)
| ~ group_member(f_left_zero,f) ),
inference(superposition,[status(thm),theory(equality)],[c_58,c_184]) ).
tff(c_261,plain,
! [Z_53] :
( ( multiply(f,f_left_zero,multiply(f,f_left_zero,Z_53)) = multiply(f,f_left_zero,Z_53) )
| ~ group_member(Z_53,f) ),
inference(demodulation,[status(thm),theory(equality)],[c_29,c_29,c_256]) ).
tff(c_67,plain,
! [G_29,X_30,Y_31] :
( group_member(multiply(G_29,X_30,Y_31),G_29)
| ~ group_member(Y_31,G_29)
| ~ group_member(X_30,G_29) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_14,plain,
! [G_13,X_14,Y_17] :
( ( multiply(G_13,X_14,Y_17) = X_14 )
| ~ group_member(Y_17,G_13)
| ~ left_zero(G_13,X_14) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_73,plain,
! [G_29,X_14,X_30,Y_31] :
( ( multiply(G_29,X_14,multiply(G_29,X_30,Y_31)) = X_14 )
| ~ left_zero(G_29,X_14)
| ~ group_member(Y_31,G_29)
| ~ group_member(X_30,G_29) ),
inference(resolution,[status(thm)],[c_67,c_14]) ).
tff(c_276,plain,
! [Z_53] :
( ( multiply(f,f_left_zero,Z_53) = f_left_zero )
| ~ left_zero(f,f_left_zero)
| ~ group_member(Z_53,f)
| ~ group_member(f_left_zero,f)
| ~ group_member(Z_53,f) ),
inference(superposition,[status(thm),theory(equality)],[c_261,c_73]) ).
tff(c_327,plain,
! [Z_54] :
( ( multiply(f,f_left_zero,Z_54) = f_left_zero )
| ~ group_member(Z_54,f) ),
inference(demodulation,[status(thm),theory(equality)],[c_29,c_22,c_276]) ).
tff(c_344,plain,
! [X_11] :
( ( multiply(f,f_left_zero,'#skF_1'(X_11)) = f_left_zero )
| ~ group_member(X_11,h) ),
inference(resolution,[status(thm)],[c_12,c_327]) ).
tff(c_10,plain,
! [X_11] :
( ( phi('#skF_1'(X_11)) = X_11 )
| ~ group_member(X_11,h) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_104,plain,
! [X_38,Y_39] :
( ( multiply(h,phi(X_38),phi(Y_39)) = phi(multiply(f,X_38,Y_39)) )
| ~ group_member(Y_39,f)
| ~ group_member(X_38,f) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_577,plain,
! [X_61,X_62] :
( ( phi(multiply(f,X_61,'#skF_1'(X_62))) = multiply(h,phi(X_61),X_62) )
| ~ group_member('#skF_1'(X_62),f)
| ~ group_member(X_61,f)
| ~ group_member(X_62,h) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_104]) ).
tff(c_603,plain,
! [X_11] :
( ( multiply(h,phi(f_left_zero),X_11) = phi(f_left_zero) )
| ~ group_member('#skF_1'(X_11),f)
| ~ group_member(f_left_zero,f)
| ~ group_member(X_11,h)
| ~ group_member(X_11,h) ),
inference(superposition,[status(thm),theory(equality)],[c_344,c_577]) ).
tff(c_615,plain,
! [X_63] :
( ( multiply(h,phi(f_left_zero),X_63) = phi(f_left_zero) )
| ~ group_member('#skF_1'(X_63),f)
| ~ group_member(X_63,h) ),
inference(demodulation,[status(thm),theory(equality)],[c_29,c_603]) ).
tff(c_620,plain,
! [X_64] :
( ( multiply(h,phi(f_left_zero),X_64) = phi(f_left_zero) )
| ~ group_member(X_64,h) ),
inference(resolution,[status(thm)],[c_12,c_615]) ).
tff(c_18,plain,
! [G_13,X_14] :
( ( multiply(G_13,X_14,'#skF_2'(G_13,X_14)) != X_14 )
| left_zero(G_13,X_14)
| ~ group_member(X_14,G_13) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_645,plain,
( left_zero(h,phi(f_left_zero))
| ~ group_member(phi(f_left_zero),h)
| ~ group_member('#skF_2'(h,phi(f_left_zero)),h) ),
inference(superposition,[status(thm),theory(equality)],[c_620,c_18]) ).
tff(c_677,plain,
( ~ group_member(phi(f_left_zero),h)
| ~ group_member('#skF_2'(h,phi(f_left_zero)),h) ),
inference(negUnitSimplification,[status(thm)],[c_24,c_645]) ).
tff(c_681,plain,
~ group_member('#skF_2'(h,phi(f_left_zero)),h),
inference(splitLeft,[status(thm)],[c_677]) ).
tff(c_730,plain,
( left_zero(h,phi(f_left_zero))
| ~ group_member(phi(f_left_zero),h) ),
inference(resolution,[status(thm)],[c_20,c_681]) ).
tff(c_733,plain,
~ group_member(phi(f_left_zero),h),
inference(negUnitSimplification,[status(thm)],[c_24,c_730]) ).
tff(c_736,plain,
~ group_member(f_left_zero,f),
inference(resolution,[status(thm)],[c_6,c_733]) ).
tff(c_740,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_29,c_736]) ).
tff(c_741,plain,
~ group_member(phi(f_left_zero),h),
inference(splitRight,[status(thm)],[c_677]) ).
tff(c_745,plain,
~ group_member(f_left_zero,f),
inference(resolution,[status(thm)],[c_6,c_741]) ).
tff(c_749,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_29,c_745]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP194+1 : TPTP v8.1.2. Released v2.0.0.
% 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 : n006.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 21:56:59 EDT 2023
% 0.21/0.36 % CPUTime :
% 3.60/2.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.60/2.04
% 3.60/2.04 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.60/2.07
% 3.60/2.07 Inference rules
% 3.60/2.07 ----------------------
% 3.60/2.07 #Ref : 0
% 3.60/2.07 #Sup : 169
% 3.60/2.07 #Fact : 0
% 3.60/2.07 #Define : 0
% 3.60/2.07 #Split : 1
% 3.60/2.07 #Chain : 0
% 3.60/2.07 #Close : 0
% 3.60/2.07
% 3.60/2.07 Ordering : KBO
% 3.60/2.07
% 3.60/2.07 Simplification rules
% 3.60/2.07 ----------------------
% 3.60/2.07 #Subsume : 43
% 3.60/2.07 #Demod : 72
% 3.60/2.07 #Tautology : 58
% 3.60/2.07 #SimpNegUnit : 2
% 3.60/2.07 #BackRed : 0
% 3.60/2.07
% 3.60/2.07 #Partial instantiations: 0
% 3.60/2.07 #Strategies tried : 1
% 3.60/2.07
% 3.60/2.07 Timing (in seconds)
% 3.60/2.07 ----------------------
% 3.60/2.08 Preprocessing : 0.48
% 3.60/2.08 Parsing : 0.24
% 3.60/2.08 CNF conversion : 0.03
% 3.60/2.08 Main loop : 0.46
% 3.60/2.08 Inferencing : 0.20
% 3.60/2.08 Reduction : 0.11
% 3.60/2.08 Demodulation : 0.07
% 3.60/2.08 BG Simplification : 0.03
% 3.60/2.08 Subsumption : 0.09
% 3.60/2.08 Abstraction : 0.02
% 3.60/2.08 MUC search : 0.00
% 3.60/2.08 Cooper : 0.00
% 3.60/2.08 Total : 1.00
% 3.60/2.08 Index Insertion : 0.00
% 3.60/2.08 Index Deletion : 0.00
% 3.60/2.08 Index Matching : 0.00
% 3.60/2.08 BG Taut test : 0.00
%------------------------------------------------------------------------------