%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU167+3 : 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 : n006.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 08:53:03 PM UTC 2025
% Result : Theorem 2.98s 1.73s
% Output : CNFRefutation 2.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 27 ( 12 ~; 9 |; 3 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 27 ( 27 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > empty > 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('#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) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
tff(f_39,axiom,
! [A,B,C] :
( subset(A,B)
=> ( subset(cartesian_product2(A,C),cartesian_product2(B,C))
& subset(cartesian_product2(C,A),cartesian_product2(C,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
tff(f_52,axiom,
! [A,B,C] :
( ( subset(A,B)
& subset(B,C) )
=> subset(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
tff(c_14,plain,
subset('#skF_5','#skF_6'),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_16,plain,
subset('#skF_3','#skF_4'),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_8,plain,
! [C_5,A_3,B_4] :
( subset(cartesian_product2(C_5,A_3),cartesian_product2(C_5,B_4))
| ~ subset(A_3,B_4) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_44,plain,
! [A_15,C_16,B_17] :
( subset(cartesian_product2(A_15,C_16),cartesian_product2(B_17,C_16))
| ~ subset(A_15,B_17) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_18,plain,
! [A_6,C_8,B_7] :
( subset(A_6,C_8)
| ~ subset(B_7,C_8)
| ~ subset(A_6,B_7) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_52,plain,
! [A_21,B_22,C_23,A_24] :
( subset(A_21,cartesian_product2(B_22,C_23))
| ~ subset(A_21,cartesian_product2(A_24,C_23))
| ~ subset(A_24,B_22) ),
inference(resolution,[status(thm)],[c_44,c_18]) ).
tff(c_103,plain,
! [C_35,A_36,B_37,B_38] :
( subset(cartesian_product2(C_35,A_36),cartesian_product2(B_37,B_38))
| ~ subset(C_35,B_37)
| ~ subset(A_36,B_38) ),
inference(resolution,[status(thm)],[c_8,c_52]) ).
tff(c_12,plain,
~ subset(cartesian_product2('#skF_3','#skF_5'),cartesian_product2('#skF_4','#skF_6')),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_114,plain,
( ~ subset('#skF_3','#skF_4')
| ~ subset('#skF_5','#skF_6') ),
inference(resolution,[status(thm)],[c_103,c_12]) ).
tff(c_122,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_14,c_16,c_114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU167+3 : 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
% 0.13/0.34 % Computer : n006.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 22:11:07 EDT 2025
% 0.13/0.34 % CPUTime :
% 2.98/1.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.98/1.74
% 2.98/1.74 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------