%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET881+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 : n020.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 3.02s 1.80s
% Output : CNFRefutation 3.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 10 ( 5 ~; 2 |; 0 &)
% ( 3 <=>; 0 =>; 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 : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 16 ( 16 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > empty > unordered_pair > set_difference > #nlpp > singleton > empty_set > #skF_1 > #skF_5 > #skF_6 > #skF_3 > #skF_2 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
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('#skF_3',type,
'#skF_3': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(f_42,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_47,axiom,
! [A,B] :
( ( set_difference(singleton(A),B) = empty_set )
<=> in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).
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_55,negated_conjecture,
~ ! [A,B] : ( set_difference(singleton(A),unordered_pair(A,B)) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).
tff(c_8,plain,
! [D_10,A_5] : in(D_10,unordered_pair(A_5,D_10)),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_109,plain,
! [A_27,B_28] :
( ( set_difference(singleton(A_27),B_28) = empty_set )
| ~ in(A_27,B_28) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
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_difference(singleton('#skF_5'),unordered_pair('#skF_5','#skF_6')) != empty_set,
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_35,plain,
set_difference(singleton('#skF_5'),unordered_pair('#skF_6','#skF_5')) != empty_set,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_34]) ).
tff(c_118,plain,
~ in('#skF_5',unordered_pair('#skF_6','#skF_5')),
inference(superposition,[status(thm),theory(equality)],[c_109,c_35]) ).
tff(c_127,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : SET881+1 : TPTP v9.0.0. Released v3.2.0.
% 0.12/0.15 % 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
% 0.15/0.36 % Computer : n020.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 8 21:48:34 EDT 2025
% 0.15/0.36 % CPUTime :
% 3.02/1.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.02/1.81
% 3.02/1.81 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------