%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM533+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/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 : n032.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 07:56:16 PM UTC 2025
% Result : Theorem 3.36s 2.01s
% Output : CNFRefutation 3.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 7 unt; 0 typ; 1 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 80 ( 35 ~; 37 |; 4 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 23 ( 23 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aElement0 > #nlpp > xC > xB > xA > slcrc0 > #skF_1 > #skF_2
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(aSet0,type,
aSet0: $i > $o ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(aElement0,type,
aElement0: $i > $o ).
tff(xB,type,
xB: $i ).
tff(aSubsetOf0,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(isCountable0,type,
isCountable0: $i > $o ).
tff(aElementOf0,type,
aElementOf0: ( $i * $i ) > $o ).
tff(xC,type,
xC: $i ).
tff(slcrc0,type,
slcrc0: $i ).
tff(isFinite0,type,
isFinite0: $i > $o ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(xA,type,
xA: $i ).
tff(f_112,hypothesis,
( aSet0(xA)
& aSet0(xB)
& aSet0(xC) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__522) ).
tff(f_118,negated_conjecture,
~ ( ( aSubsetOf0(xA,xB)
& aSubsetOf0(xB,xC) )
=> aSubsetOf0(xA,xC) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_84,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
tff(c_42,plain,
aSet0(xA),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_48,plain,
aSubsetOf0(xA,xB),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_38,plain,
aSet0(xC),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_40,plain,
aSet0(xB),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_46,plain,
aSubsetOf0(xB,xC),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_116,plain,
! [W0_46,W1_47] :
( aElementOf0('#skF_2'(W0_46,W1_47),W1_47)
| aSubsetOf0(W1_47,W0_46)
| ~ aSet0(W1_47)
| ~ aSet0(W0_46) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_24,plain,
! [W2_23,W0_14,W1_20] :
( aElementOf0(W2_23,W0_14)
| ~ aElementOf0(W2_23,W1_20)
| ~ aSubsetOf0(W1_20,W0_14)
| ~ aSet0(W0_14) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_202,plain,
! [W0_56,W1_57,W0_58] :
( aElementOf0('#skF_2'(W0_56,W1_57),W0_58)
| ~ aSubsetOf0(W1_57,W0_58)
| ~ aSet0(W0_58)
| aSubsetOf0(W1_57,W0_56)
| ~ aSet0(W1_57)
| ~ aSet0(W0_56) ),
inference(resolution,[status(thm)],[c_116,c_24]) ).
tff(c_254,plain,
! [W0_64,W1_65,W0_66,W0_67] :
( aElementOf0('#skF_2'(W0_64,W1_65),W0_66)
| ~ aSubsetOf0(W0_67,W0_66)
| ~ aSet0(W0_66)
| ~ aSubsetOf0(W1_65,W0_67)
| ~ aSet0(W0_67)
| aSubsetOf0(W1_65,W0_64)
| ~ aSet0(W1_65)
| ~ aSet0(W0_64) ),
inference(resolution,[status(thm)],[c_202,c_24]) ).
tff(c_262,plain,
! [W0_64,W1_65] :
( aElementOf0('#skF_2'(W0_64,W1_65),xC)
| ~ aSet0(xC)
| ~ aSubsetOf0(W1_65,xB)
| ~ aSet0(xB)
| aSubsetOf0(W1_65,W0_64)
| ~ aSet0(W1_65)
| ~ aSet0(W0_64) ),
inference(resolution,[status(thm)],[c_46,c_254]) ).
tff(c_293,plain,
! [W0_70,W1_71] :
( aElementOf0('#skF_2'(W0_70,W1_71),xC)
| ~ aSubsetOf0(W1_71,xB)
| aSubsetOf0(W1_71,W0_70)
| ~ aSet0(W1_71)
| ~ aSet0(W0_70) ),
inference(demodulation,[status(thm),theory(equality)],[c_40,c_38,c_262]) ).
tff(c_28,plain,
! [W0_14,W1_20] :
( ~ aElementOf0('#skF_2'(W0_14,W1_20),W0_14)
| aSubsetOf0(W1_20,W0_14)
| ~ aSet0(W1_20)
| ~ aSet0(W0_14) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_297,plain,
! [W1_71] :
( ~ aSubsetOf0(W1_71,xB)
| aSubsetOf0(W1_71,xC)
| ~ aSet0(W1_71)
| ~ aSet0(xC) ),
inference(resolution,[status(thm)],[c_293,c_28]) ).
tff(c_327,plain,
! [W1_74] :
( ~ aSubsetOf0(W1_74,xB)
| aSubsetOf0(W1_74,xC)
| ~ aSet0(W1_74) ),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_297]) ).
tff(c_44,plain,
~ aSubsetOf0(xA,xC),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_342,plain,
( ~ aSubsetOf0(xA,xB)
| ~ aSet0(xA) ),
inference(resolution,[status(thm)],[c_327,c_44]) ).
tff(c_361,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_42,c_48,c_342]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.16 % Problem : NUM533+1 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.17 % 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
% 0.09/0.41 % Computer : n032.cluster.edu
% 0.09/0.41 % Model : x86_64 x86_64
% 0.09/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.41 % Memory : 8042.1875MB
% 0.09/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.41 % CPULimit : 300
% 0.09/0.41 % WCLimit : 300
% 0.09/0.41 % DateTime : Tue Apr 8 13:20:01 EDT 2025
% 0.15/0.41 % CPUTime :
% 3.36/2.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.36/2.01
% 3.36/2.01 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------