%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : DAT042_1 : TPTP v9.0.0. Released v5.0.0.
% 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 : 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 : Wed Apr 9 06:07:59 PM UTC 2025
% Result : Theorem 19.81s 6.70s
% Output : CNFRefutation 20.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 87 ( 61 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 68 ( 27 ~; 34 |; 1 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 99 ( 0 atm; 10 fun; 25 num; 64 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 98 ( 97 !; 1 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > remove > add > #nlpp > count > empty
%Foreground sorts:
tff(collection,type,
collection: $tType ).
%Background operators:
%Foreground operators:
tff(empty,type,
empty: collection ).
tff(count,type,
count: collection > $int ).
tff(in,type,
in: ( $int * collection ) > $o ).
tff(remove,type,
remove: ( $int * collection ) > collection ).
tff(add,type,
add: ( $int * collection ) > collection ).
tff(f_113,axiom,
! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax2) ).
tff(f_118,axiom,
! [X8a: $int,X9: collection] :
( ~ in(X8a,X9)
<=> ( count(add(X8a,X9)) = $sum(count(X9),1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax3) ).
tff(f_60,axiom,
! [Ua: $int] : ~ in(Ua,empty),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax1) ).
tff(f_131,axiom,
! [X14a: $int,X15: collection] :
( ~ in(X14a,X15)
<=> ( count(remove(X14a,X15)) = count(X15) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax6) ).
tff(f_71,axiom,
! [Za: $int,X1: collection,X2a: $int] :
( ( in(Za,X1)
| ( Za = X2a ) )
<=> in(Za,add(X2a,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax4) ).
tff(f_78,axiom,
! [X3a: $int,X4: collection,X5a: $int] :
( ( in(X3a,X4)
& ( X3a != X5a ) )
<=> in(X3a,remove(X5a,X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax5) ).
tff(f_122,axiom,
! [X10a: $int,X11: collection] :
( in(X10a,X11)
<=> ( count(add(X10a,X11)) = count(X11) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax4) ).
tff(f_140,negated_conjecture,
~ ? [U: collection] : ( count(U) = 3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(c_59,plain,
count(empty) = 0,
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_25,plain,
! [X8_14a: $int,X9_15: collection] :
( ( count(add(X8_14a,X9_15)) = $sum(count(X9_15),1) )
| in(X8_14a,X9_15) ),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_412,plain,
! [X8_70a: $int,X9_71: collection] :
( ( count(add(X8_70a,X9_71)) = $sum(1,count(X9_71)) )
| in(X8_70a,X9_71) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).
tff(c_69,plain,
! [U_1a: $int] : ~ in(U_1a,empty),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_440,plain,
! [X8_70a: $int] : ( count(add(X8_70a,empty)) = $sum(1,count(empty)) ),
inference(resolution,[status(thm)],[c_412,c_69]) ).
tff(c_456,plain,
! [X8_70a: $int] : ( count(add(X8_70a,empty)) = $sum(1,0) ),
inference(demodulation,[status(thm),theory(equality)],[c_59,c_440]) ).
tff(c_458,plain,
! [X8_70a: $int] : ( count(add(X8_70a,empty)) = 1 ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_456]) ).
tff(c_51,plain,
! [X14_20a: $int,X15_21: collection] :
( ( count(remove(X14_20a,X15_21)) = count(X15_21) )
| in(X14_20a,X15_21) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_274,plain,
! [Z_55a: $int,X1_56: collection,X2_57a: $int] :
( in(Z_55a,X1_56)
| ~ in(Z_55a,add(X2_57a,X1_56))
| ( Z_55a = X2_57a ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_11238,plain,
! [X14_323a: $int,X1_324: collection,X2_325a: $int] :
( in(X14_323a,X1_324)
| ( X2_325a = X14_323a )
| ( count(remove(X14_323a,add(X2_325a,X1_324))) = count(add(X2_325a,X1_324)) ) ),
inference(resolution,[status(thm)],[c_51,c_274]) ).
tff(c_11323,plain,
! [X2_325a: $int,X14_323a: $int] :
( ( X2_325a = X14_323a )
| ( count(remove(X14_323a,add(X2_325a,empty))) = count(add(X2_325a,empty)) ) ),
inference(resolution,[status(thm)],[c_11238,c_69]) ).
tff(c_11376,plain,
! [X2_325a: $int,X14_323a: $int] :
( ( X2_325a = X14_323a )
| ( count(remove(X14_323a,add(X2_325a,empty))) = 1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_458,c_11323]) ).
tff(c_132,plain,
! [X14_45a: $int,X15_46: collection] :
( ( count(remove(X14_45a,X15_46)) = count(X15_46) )
| in(X14_45a,X15_46) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_61,plain,
! [X3_9a: $int,X4_10: collection,X5_11a: $int] :
( in(X3_9a,X4_10)
| ~ in(X3_9a,remove(X5_11a,X4_10)) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_1695,plain,
! [X14_125a: $int,X4_126: collection,X5_127a: $int] :
( in(X14_125a,X4_126)
| ( count(remove(X14_125a,remove(X5_127a,X4_126))) = count(remove(X5_127a,X4_126)) ) ),
inference(resolution,[status(thm)],[c_132,c_61]) ).
tff(c_50,plain,
! [X14_20a: $int,X15_21: collection] :
( ~ in(X14_20a,X15_21)
| ( count(remove(X14_20a,X15_21)) != count(X15_21) ) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_1749,plain,
! [X14_125a: $int,X4_126: collection,X5_127a: $int] :
( ( count(remove(X14_125a,X4_126)) != count(X4_126) )
| ( count(remove(X14_125a,remove(X5_127a,X4_126))) = count(remove(X5_127a,X4_126)) ) ),
inference(resolution,[status(thm)],[c_1695,c_50]) ).
tff(c_6091,plain,
! [X8_238a: $int,X4_239: collection,X5_240a: $int] :
( in(X8_238a,X4_239)
| ( count(add(X8_238a,remove(X5_240a,X4_239))) = $sum(1,count(remove(X5_240a,X4_239))) ) ),
inference(resolution,[status(thm)],[c_412,c_61]) ).
tff(c_62,plain,
! [X3_9a: $int,X4_10: collection] : ~ in(X3_9a,remove(X3_9a,X4_10)),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_47811,plain,
! [X8_850a: $int,X5_851a: $int,X4_852: collection] : ( count(add(X8_850a,remove(X5_851a,remove(X8_850a,X4_852)))) = $sum(1,count(remove(X5_851a,remove(X8_850a,X4_852)))) ),
inference(resolution,[status(thm)],[c_6091,c_62]) ).
tff(c_55,plain,
! [X10_16a: $int,X11_17: collection] :
( ( count(add(X10_16a,X11_17)) = count(X11_17) )
| ~ in(X10_16a,X11_17) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_157,plain,
! [X14_45a: $int,X15_46: collection] :
( ( count(add(X14_45a,X15_46)) = count(X15_46) )
| ( count(remove(X14_45a,X15_46)) = count(X15_46) ) ),
inference(resolution,[status(thm)],[c_132,c_55]) ).
tff(c_834,plain,
! [X8_91a: $int,X4_92: collection] : ( count(add(X8_91a,remove(X8_91a,X4_92))) = $sum(1,count(remove(X8_91a,X4_92))) ),
inference(resolution,[status(thm)],[c_412,c_62]) ).
tff(c_48,plain,
! [U_24: collection] : ( count(U_24) != 3 ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_849,plain,
! [X8_91a: $int,X4_92: collection] : ( $sum(1,count(remove(X8_91a,X4_92))) != 3 ),
inference(superposition,[status(thm),theory(equality)],[c_834,c_48]) ).
tff(c_889,plain,
! [X8_93a: $int,X4_94: collection] : ( count(remove(X8_93a,X4_94)) != 2 ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_849]) ).
tff(c_898,plain,
! [X15_46: collection,X14_45a: $int] :
( ( count(X15_46) != 2 )
| ( count(add(X14_45a,X15_46)) = count(X15_46) ) ),
inference(superposition,[status(thm),theory(equality)],[c_157,c_889]) ).
tff(c_54,plain,
! [X10_16a: $int,X11_17: collection] :
( in(X10_16a,X11_17)
| ( count(add(X10_16a,X11_17)) != count(X11_17) ) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_6921,plain,
! [X10_264a: $int,X1_265: collection,X2_266a: $int] :
( in(X10_264a,X1_265)
| ( X2_266a = X10_264a )
| ( count(add(X10_264a,add(X2_266a,X1_265))) != count(add(X2_266a,X1_265)) ) ),
inference(resolution,[status(thm)],[c_54,c_274]) ).
tff(c_36617,plain,
! [X2_693a: $int,X10_694a: $int,X4_695: collection] :
( ( X2_693a = X10_694a )
| ( count(add(X10_694a,add(X2_693a,remove(X10_694a,X4_695)))) != count(add(X2_693a,remove(X10_694a,X4_695))) ) ),
inference(resolution,[status(thm)],[c_6921,c_62]) ).
tff(c_36789,plain,
! [X2_693a: $int,X14_45a: $int,X4_695: collection] :
( ( X2_693a = X14_45a )
| ( count(add(X2_693a,remove(X14_45a,X4_695))) != 2 ) ),
inference(superposition,[status(thm),theory(equality)],[c_898,c_36617]) ).
tff(c_47847,plain,
! [X8_850a: $int,X5_851a: $int,X4_852: collection] :
( ( X8_850a = X5_851a )
| ( $sum(1,count(remove(X5_851a,remove(X8_850a,X4_852)))) != 2 ) ),
inference(superposition,[status(thm),theory(equality)],[c_47811,c_36789]) ).
tff(c_48401,plain,
! [X8_853a: $int,X5_854a: $int,X4_855: collection] :
( ( X8_853a = X5_854a )
| ( count(remove(X5_854a,remove(X8_853a,X4_855))) != 1 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_47847]) ).
tff(c_51487,plain,
! [X5_907a: $int,X14_908a: $int,X4_909: collection] :
( ( X5_907a = X14_908a )
| ( count(remove(X5_907a,X4_909)) != 1 )
| ( count(remove(X14_908a,X4_909)) != count(X4_909) ) ),
inference(superposition,[status(thm),theory(equality)],[c_1749,c_48401]) ).
tff(c_51537,plain,
! [X14_908a: $int,X14_323a: $int,X2_325a: $int] :
( ( X14_908a = X14_323a )
| ( count(remove(X14_908a,add(X2_325a,empty))) != count(add(X2_325a,empty)) )
| ( X2_325a = X14_323a ) ),
inference(superposition,[status(thm),theory(equality)],[c_11376,c_51487]) ).
tff(c_51621,plain,
! [X14_911a: $int,X14_910a: $int,X2_912a: $int] :
( ( X14_911a = X14_910a )
| ( count(remove(X14_910a,add(X2_912a,empty))) != 1 )
| ( X2_912a = X14_911a ) ),
inference(demodulation,[status(thm),theory(equality)],[c_458,c_51537]) ).
tff(c_51771,plain,
! [X14_911a: $int,X14_323a: $int,X2_325a: $int] :
( ( X14_911a = X14_323a )
| ( X2_325a = X14_911a )
| ( X2_325a = X14_323a ) ),
inference(superposition,[status(thm),theory(equality)],[c_11376,c_51621]) ).
tff(c_51806,plain,
$false,
inference(quantifierElimination,[status(thm),theory('LIA')],[c_51771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : DAT042_1 : TPTP v9.0.0. Released v5.0.0.
% 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 : n025.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 : Mon Apr 7 18:16:20 EDT 2025
% 0.13/0.34 % CPUTime :
% 19.81/6.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.13/6.70
% 20.13/6.70 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------