%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET907+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 : 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 08:39:33 PM UTC 2025
% Result : Theorem 2.99s 1.75s
% Output : CNFRefutation 3.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 12 ~; 8 |; 2 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 23 ( 23 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > in > empty > unordered_pair > set_union2 > #nlpp > #skF_5 > #skF_2 > #skF_3 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
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(f_73,negated_conjecture,
~ ! [A,B,C] :
( ( in(A,B)
& in(C,B) )
=> ( set_union2(unordered_pair(A,C),B) = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_zfmisc_1) ).
tff(f_66,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(A,C)
& in(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
tff(f_60,axiom,
! [A,B] :
( subset(A,B)
=> ( set_union2(A,B) = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
tff(f_35,axiom,
! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
tff(c_32,plain,
in('#skF_3','#skF_4'),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_30,plain,
in('#skF_5','#skF_4'),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_205,plain,
! [A_48,B_49,C_50] :
( subset(unordered_pair(A_48,B_49),C_50)
| ~ in(B_49,C_50)
| ~ in(A_48,C_50) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_20,plain,
! [A_15,B_16] :
( ( set_union2(A_15,B_16) = B_16 )
| ~ subset(A_15,B_16) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_224,plain,
! [A_51,B_52,C_53] :
( ( set_union2(unordered_pair(A_51,B_52),C_53) = C_53 )
| ~ in(B_52,C_53)
| ~ in(A_51,C_53) ),
inference(resolution,[status(thm)],[c_205,c_20]) ).
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_273,plain,
! [C_54,A_55,B_56] :
( ( set_union2(C_54,unordered_pair(A_55,B_56)) = C_54 )
| ~ in(B_56,C_54)
| ~ in(A_55,C_54) ),
inference(superposition,[status(thm),theory(equality)],[c_224,c_6]) ).
tff(c_28,plain,
set_union2(unordered_pair('#skF_3','#skF_5'),'#skF_4') != '#skF_4',
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_33,plain,
set_union2('#skF_4',unordered_pair('#skF_3','#skF_5')) != '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_6,c_28]) ).
tff(c_292,plain,
( ~ in('#skF_5','#skF_4')
| ~ in('#skF_3','#skF_4') ),
inference(superposition,[status(thm),theory(equality)],[c_273,c_33]) ).
tff(c_329,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_32,c_30,c_292]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET907+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % 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
% 0.13/0.34 % 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 21:49:37 EDT 2025
% 0.13/0.34 % CPUTime :
% 2.99/1.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.99/1.75
% 2.99/1.75 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------