%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET971+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 : n022.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 08:39:41 PM UTC 2025
% Result : Theorem 2.72s 1.66s
% Output : CNFRefutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 1 |; 1 &)
% ( 0 <=>; 2 =>; 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 : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 20 ( 20 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > empty > set_intersection2 > cartesian_product2 > #nlpp > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $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(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(f_46,negated_conjecture,
~ ! [A,B,C,D] :
( ( subset(A,B)
& subset(C,D) )
=> ( set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) = cartesian_product2(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_zfmisc_1) ).
tff(f_50,axiom,
! [A,B] :
( subset(A,B)
=> ( set_intersection2(A,B) = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
tff(f_28,axiom,
! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
tff(f_39,axiom,
! [A,B,C,D] : ( cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).
tff(c_18,plain,
subset('#skF_3','#skF_4'),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_66,plain,
! [A_17,B_18] :
( ( set_intersection2(A_17,B_18) = A_17 )
| ~ subset(A_17,B_18) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_77,plain,
set_intersection2('#skF_3','#skF_4') = '#skF_3',
inference(resolution,[status(thm)],[c_18,c_66]) ).
tff(c_2,plain,
! [B_2,A_1] : ( set_intersection2(B_2,A_1) = set_intersection2(A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_102,plain,
set_intersection2('#skF_4','#skF_3') = '#skF_3',
inference(superposition,[status(thm),theory(equality)],[c_77,c_2]) ).
tff(c_16,plain,
subset('#skF_5','#skF_6'),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_76,plain,
set_intersection2('#skF_5','#skF_6') = '#skF_5',
inference(resolution,[status(thm)],[c_16,c_66]) ).
tff(c_86,plain,
set_intersection2('#skF_6','#skF_5') = '#skF_5',
inference(superposition,[status(thm),theory(equality)],[c_76,c_2]) ).
tff(c_12,plain,
! [A_7,C_9,B_8,D_10] : ( set_intersection2(cartesian_product2(A_7,C_9),cartesian_product2(B_8,D_10)) = cartesian_product2(set_intersection2(A_7,B_8),set_intersection2(C_9,D_10)) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_14,plain,
set_intersection2(cartesian_product2('#skF_3','#skF_6'),cartesian_product2('#skF_4','#skF_5')) != cartesian_product2('#skF_3','#skF_5'),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_21,plain,
cartesian_product2(set_intersection2('#skF_3','#skF_4'),set_intersection2('#skF_6','#skF_5')) != cartesian_product2('#skF_3','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_14]) ).
tff(c_22,plain,
cartesian_product2(set_intersection2('#skF_4','#skF_3'),set_intersection2('#skF_6','#skF_5')) != cartesian_product2('#skF_3','#skF_5'),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_21]) ).
tff(c_124,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_102,c_86,c_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET971+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
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Apr 8 21:53:06 EDT 2025
% 0.13/0.35 % CPUTime :
% 2.72/1.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.72/1.67
% 2.72/1.67 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------