%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET968+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 : n013.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 8.15s 2.95s
% Output : CNFRefutation 8.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 8 ~; 0 |; 1 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 36 ( 36 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ empty > set_union2 > 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('#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(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff(cartesian_product2,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(f_51,axiom,
! [A,B,C] :
( ( cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C)) )
& ( cartesian_product2(C,set_union2(A,B)) = set_union2(cartesian_product2(C,A),cartesian_product2(C,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_zfmisc_1) ).
tff(f_28,axiom,
! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
tff(f_56,axiom,
! [A,B,C] : ( set_union2(set_union2(A,B),C) = set_union2(A,set_union2(B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_1) ).
tff(f_54,negated_conjecture,
~ ! [A,B,C,D] : ( cartesian_product2(set_union2(A,B),set_union2(C,D)) = set_union2(set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,C)),cartesian_product2(B,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_zfmisc_1) ).
tff(c_14,plain,
! [A_9,C_11,B_10] : ( set_union2(cartesian_product2(A_9,C_11),cartesian_product2(B_10,C_11)) = cartesian_product2(set_union2(A_9,B_10),C_11) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_2,plain,
! [B_2,A_1] : ( set_union2(B_2,A_1) = set_union2(A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_348,plain,
! [C_35,A_36,B_37] : ( set_union2(cartesian_product2(C_35,A_36),cartesian_product2(C_35,B_37)) = cartesian_product2(C_35,set_union2(A_36,B_37)) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_20,plain,
! [A_12,B_13,C_14] : ( set_union2(set_union2(A_12,B_13),C_14) = set_union2(A_12,set_union2(B_13,C_14)) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_366,plain,
! [C_35,A_36,B_37,C_14] : ( set_union2(cartesian_product2(C_35,A_36),set_union2(cartesian_product2(C_35,B_37),C_14)) = set_union2(cartesian_product2(C_35,set_union2(A_36,B_37)),C_14) ),
inference(superposition,[status(thm),theory(equality)],[c_348,c_20]) ).
tff(c_86,plain,
! [A_22,B_23,C_24] : ( set_union2(set_union2(A_22,B_23),C_24) = set_union2(A_22,set_union2(B_23,C_24)) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_98,plain,
! [C_24,A_22,B_23] : ( set_union2(C_24,set_union2(A_22,B_23)) = set_union2(A_22,set_union2(B_23,C_24)) ),
inference(superposition,[status(thm),theory(equality)],[c_86,c_2]) ).
tff(c_16,plain,
! [C_11,A_9,B_10] : ( set_union2(cartesian_product2(C_11,A_9),cartesian_product2(C_11,B_10)) = cartesian_product2(C_11,set_union2(A_9,B_10)) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_18,plain,
set_union2(set_union2(set_union2(cartesian_product2('#skF_3','#skF_5'),cartesian_product2('#skF_3','#skF_6')),cartesian_product2('#skF_4','#skF_5')),cartesian_product2('#skF_4','#skF_6')) != cartesian_product2(set_union2('#skF_3','#skF_4'),set_union2('#skF_5','#skF_6')),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_21,plain,
set_union2(cartesian_product2('#skF_3','#skF_5'),set_union2(cartesian_product2('#skF_3','#skF_6'),set_union2(cartesian_product2('#skF_4','#skF_5'),cartesian_product2('#skF_4','#skF_6')))) != cartesian_product2(set_union2('#skF_3','#skF_4'),set_union2('#skF_5','#skF_6')),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_20,c_20,c_18]) ).
tff(c_22,plain,
set_union2(cartesian_product2('#skF_3','#skF_5'),set_union2(cartesian_product2('#skF_3','#skF_6'),cartesian_product2('#skF_4',set_union2('#skF_5','#skF_6')))) != cartesian_product2(set_union2('#skF_3','#skF_4'),set_union2('#skF_5','#skF_6')),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_21]) ).
tff(c_23,plain,
set_union2(cartesian_product2('#skF_3','#skF_5'),set_union2(cartesian_product2('#skF_3','#skF_6'),cartesian_product2('#skF_4',set_union2('#skF_6','#skF_5')))) != cartesian_product2(set_union2('#skF_4','#skF_3'),set_union2('#skF_6','#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_2,c_22]) ).
tff(c_421,plain,
set_union2(cartesian_product2('#skF_3','#skF_6'),set_union2(cartesian_product2('#skF_4',set_union2('#skF_6','#skF_5')),cartesian_product2('#skF_3','#skF_5'))) != cartesian_product2(set_union2('#skF_4','#skF_3'),set_union2('#skF_6','#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_98,c_23]) ).
tff(c_422,plain,
set_union2(cartesian_product2('#skF_3','#skF_6'),set_union2(cartesian_product2('#skF_3','#skF_5'),cartesian_product2('#skF_4',set_union2('#skF_6','#skF_5')))) != cartesian_product2(set_union2('#skF_4','#skF_3'),set_union2('#skF_6','#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_421]) ).
tff(c_6861,plain,
set_union2(cartesian_product2('#skF_3',set_union2('#skF_6','#skF_5')),cartesian_product2('#skF_4',set_union2('#skF_6','#skF_5'))) != cartesian_product2(set_union2('#skF_4','#skF_3'),set_union2('#skF_6','#skF_5')),
inference(demodulation,[status(thm),theory(equality)],[c_366,c_422]) ).
tff(c_6864,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_14,c_2,c_6861]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SET968+1 : TPTP v9.0.0. Released v3.2.0.
% 0.00/0.08 % 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
% 0.07/0.26 % Computer : n013.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Tue Apr 8 21:53:17 EDT 2025
% 0.07/0.26 % CPUTime :
% 8.15/2.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.15/2.96
% 8.15/2.96 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------