%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET906+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 : n031.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 08:39:33 PM UTC 2025
% Result : Theorem 5.56s 2.49s
% Output : CNFRefutation 5.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 23 ( 8 ~; 8 |; 0 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 31 ( 31 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > empty > unordered_pair > set_union2 > #nlpp > #skF_1 > #skF_4 > #skF_7 > #skF_10 > #skF_6 > #skF_2 > #skF_9 > #skF_8 > #skF_3 > #skF_5
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff(f_86,negated_conjecture,
~ ! [A,B,C] :
( subset(set_union2(unordered_pair(A,B),C),C)
=> in(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_zfmisc_1) ).
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_35,axiom,
! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
tff(f_53,axiom,
! [A,B,C] :
( ( C = set_union2(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
tff(f_60,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
tff(c_62,plain,
~ in('#skF_8','#skF_10'),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_12,plain,
! [D_12,B_8] : in(D_12,unordered_pair(D_12,B_8)),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_6,plain,
! [B_6,A_5] : ( set_union2(B_6,A_5) = set_union2(A_5,B_6) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_64,plain,
subset(set_union2(unordered_pair('#skF_8','#skF_9'),'#skF_10'),'#skF_10'),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_65,plain,
subset(set_union2('#skF_10',unordered_pair('#skF_8','#skF_9')),'#skF_10'),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_64]) ).
tff(c_28,plain,
! [D_18,B_14,A_13] :
( ~ in(D_18,B_14)
| in(D_18,set_union2(A_13,B_14)) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_410,plain,
! [C_77,B_78,A_79] :
( in(C_77,B_78)
| ~ in(C_77,A_79)
| ~ subset(A_79,B_78) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_2934,plain,
! [D_2879,B_2880,A_2881,B_2882] :
( in(D_2879,B_2880)
| ~ subset(set_union2(A_2881,B_2882),B_2880)
| ~ in(D_2879,B_2882) ),
inference(resolution,[status(thm)],[c_28,c_410]) ).
tff(c_2950,plain,
! [D_2919] :
( in(D_2919,'#skF_10')
| ~ in(D_2919,unordered_pair('#skF_8','#skF_9')) ),
inference(resolution,[status(thm)],[c_65,c_2934]) ).
tff(c_2990,plain,
in('#skF_8','#skF_10'),
inference(resolution,[status(thm)],[c_12,c_2950]) ).
tff(c_3001,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_62,c_2990]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15 % Problem : SET906+1 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.16 % 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
% 0.16/0.38 % Computer : n031.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Tue Apr 8 21:49:52 EDT 2025
% 0.16/0.38 % CPUTime :
% 5.56/2.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.79/2.50
% 5.79/2.50 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------