%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET878+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/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 : n011.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 08:39:30 PM UTC 2025
% Result : Theorem 2.89s 1.77s
% Output : CNFRefutation 3.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 20 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 12 ( 6 ~; 3 |; 0 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 22 ( 22 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > unordered_pair > set_intersection2 > #nlpp > singleton > #skF_1 > #skF_5 > #skF_6 > #skF_3 > #skF_2 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(f_44,axiom,
! [A,B,C] :
( ( C = unordered_pair(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
tff(f_50,axiom,
! [A,B] :
( in(A,B)
=> ( set_intersection2(B,singleton(A)) = singleton(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_zfmisc_1) ).
tff(f_35,axiom,
! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
tff(f_33,axiom,
! [A,B] : ( unordered_pair(A,B) = unordered_pair(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
tff(f_58,negated_conjecture,
~ ! [A,B] : ( set_intersection2(singleton(A),unordered_pair(A,B)) = singleton(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_zfmisc_1) ).
tff(c_10,plain,
! [D_12,A_7] : in(D_12,unordered_pair(A_7,D_12)),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_167,plain,
! [B_35,A_36] :
( ( set_intersection2(B_35,singleton(A_36)) = singleton(A_36) )
| ~ in(A_36,B_35) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_6,plain,
! [B_6,A_5] : ( set_intersection2(B_6,A_5) = set_intersection2(A_5,B_6) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_218,plain,
! [A_43,B_44] :
( ( set_intersection2(singleton(A_43),B_44) = singleton(A_43) )
| ~ in(A_43,B_44) ),
inference(superposition,[status(thm),theory(equality)],[c_167,c_6]) ).
tff(c_4,plain,
! [B_4,A_3] : ( unordered_pair(B_4,A_3) = unordered_pair(A_3,B_4) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_34,plain,
set_intersection2(singleton('#skF_5'),unordered_pair('#skF_5','#skF_6')) != singleton('#skF_5'),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_35,plain,
set_intersection2(singleton('#skF_5'),unordered_pair('#skF_6','#skF_5')) != singleton('#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_34]) ).
tff(c_228,plain,
~ in('#skF_5',unordered_pair('#skF_6','#skF_5')),
inference(superposition,[status(thm),theory(equality)],[c_218,c_35]) ).
tff(c_262,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_228]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET878+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/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
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 8 21:48:48 EDT 2025
% 0.12/0.34 % CPUTime :
% 2.89/1.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.89/1.78
% 2.89/1.78 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------