%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET904+1 : TPTP v9.0.0. Released v3.2.0.
% 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 : n023.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 08:39:33 PM UTC 2025
% Result : Theorem 2.60s 1.70s
% Output : CNFRefutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 12 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > empty > set_union2 > #nlpp > singleton > #skF_2 > #skF_3 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(singleton,type,
singleton: $i > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(f_59,negated_conjecture,
~ ! [A,B] :
( subset(set_union2(singleton(A),B),B)
=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_zfmisc_1) ).
tff(f_40,axiom,
! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
tff(f_63,axiom,
! [A,B] :
( subset(set_union2(singleton(A),B),B)
=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l21_zfmisc_1) ).
tff(c_18,plain,
~ in('#skF_3','#skF_4'),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_6,plain,
! [B_6,A_5] : ( set_union2(B_6,A_5) = set_union2(A_5,B_6) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_20,plain,
subset(set_union2(singleton('#skF_3'),'#skF_4'),'#skF_4'),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_23,plain,
subset(set_union2('#skF_4',singleton('#skF_3')),'#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_20]) ).
tff(c_88,plain,
! [A_25,B_26] :
( in(A_25,B_26)
| ~ subset(set_union2(singleton(A_25),B_26),B_26) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_108,plain,
! [A_29,B_30] :
( in(A_29,B_30)
| ~ subset(set_union2(B_30,singleton(A_29)),B_30) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_88]) ).
tff(c_111,plain,
in('#skF_3','#skF_4'),
inference(resolution,[status(thm)],[c_23,c_108]) ).
tff(c_127,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_18,c_111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET904+1 : TPTP v9.0.0. Released v3.2.0.
% 0.12/0.13 % 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
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 21:49:54 EDT 2025
% 0.13/0.34 % CPUTime :
% 2.60/1.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.60/1.70
% 2.60/1.70 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------