%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SEU267+1 : TPTP v9.0.0. Released v3.3.0.
% 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 : n007.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 08:53:26 PM UTC 2025
% Result : Theorem 3.49s 1.87s
% Output : CNFRefutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 17 ( 7 ~; 3 |; 1 &)
% ( 2 <=>; 4 =>; 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 : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 26 ( 22 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > element > empty > ordered_pair > #nlpp > pair_second > pair_first > empty_set > #skF_11 > #skF_1 > #skF_7 > #skF_5 > #skF_6 > #skF_2 > #skF_10 > #skF_3 > #skF_8 > #skF_4 > #skF_9
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff(pair_second,type,
pair_second: $i > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff(pair_first,type,
pair_first: $i > $i ).
tff(f_87,axiom,
! [A] :
( ? [B,C] : ( A = ordered_pair(B,C) )
=> ! [B] :
( ( B = pair_first(A) )
<=> ! [C,D] :
( ( A = ordered_pair(C,D) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_mcart_1) ).
tff(f_98,axiom,
! [A] :
( ? [B,C] : ( A = ordered_pair(B,C) )
=> ! [B] :
( ( B = pair_second(A) )
<=> ! [C,D] :
( ( A = ordered_pair(C,D) )
=> ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_mcart_1) ).
tff(f_76,negated_conjecture,
~ ! [A,B] :
( ( pair_first(ordered_pair(A,B)) = A )
& ( pair_second(ordered_pair(A,B)) = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_mcart_1) ).
tff(c_36,plain,
! [C_35,D_36,B_28,C_29] :
( ( pair_first(ordered_pair(C_35,D_36)) = C_35 )
| ( ordered_pair(C_35,D_36) != ordered_pair(B_28,C_29) ) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_166,plain,
! [B_28,C_29] : ( pair_first(ordered_pair(B_28,C_29)) = B_28 ),
inference(reflexivity,[status(thm),theory(equality)],[c_36]) ).
tff(c_42,plain,
! [C_56,D_57,B_49,C_50] :
( ( pair_second(ordered_pair(C_56,D_57)) = D_57 )
| ( ordered_pair(C_56,D_57) != ordered_pair(B_49,C_50) ) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_122,plain,
! [B_49,C_50] : ( pair_second(ordered_pair(B_49,C_50)) = C_50 ),
inference(reflexivity,[status(thm),theory(equality)],[c_42]) ).
tff(c_34,plain,
( ( pair_first(ordered_pair('#skF_6','#skF_7')) != '#skF_6' )
| ( pair_second(ordered_pair('#skF_4','#skF_5')) != '#skF_5' ) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_73,plain,
pair_second(ordered_pair('#skF_4','#skF_5')) != '#skF_5',
inference(splitLeft,[status(thm)],[c_34]) ).
tff(c_128,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_122,c_73]) ).
tff(c_129,plain,
pair_first(ordered_pair('#skF_6','#skF_7')) != '#skF_6',
inference(splitRight,[status(thm)],[c_34]) ).
tff(c_172,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_166,c_129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU267+1 : TPTP v9.0.0. Released v3.3.0.
% 0.06/0.13 % 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
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 8 22:35:39 EDT 2025
% 0.12/0.35 % CPUTime :
% 3.49/1.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.49/1.87
% 3.49/1.87 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------