%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ALG227+1 : TPTP v9.0.0. Released v3.4.0.
% 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 : n020.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 05:24:51 PM UTC 2025
% Result : Theorem 4.52s 2.18s
% Output : CNFRefutation 4.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 69 ( 23 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 56 ( 20 ~; 16 |; 10 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-3 aty)
% Number of variables : 23 ( 19 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ r2_hidden > m1_subset_1 > m1_pboole > v2_funct_1 > v1_xboole_0 > v1_relat_1 > v1_funct_1 > v1_fraenkel > v1_finset_1 > k1_funct_1 > k1_closure3 > a_2_0_closure3 > #nlpp > k1_xboole_0 > #skF_5 > #skF_4 > #skF_11 > #skF_6 > #skF_7 > #skF_10 > #skF_14 > #skF_13 > #skF_2 > #skF_3 > #skF_1 > #skF_9 > #skF_8 > #skF_15 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(v1_funct_1,type,
v1_funct_1: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(v2_funct_1,type,
v2_funct_1: $i > $o ).
tff(r2_hidden,type,
r2_hidden: ( $i * $i ) > $o ).
tff('#skF_11',type,
'#skF_11': $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff(k1_xboole_0,type,
k1_xboole_0: $i ).
tff(m1_pboole,type,
m1_pboole: ( $i * $i ) > $o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(k1_closure3,type,
k1_closure3: ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(k1_funct_1,type,
k1_funct_1: ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff(v1_relat_1,type,
v1_relat_1: $i > $o ).
tff(v1_fraenkel,type,
v1_fraenkel: $i > $o ).
tff(v1_xboole_0,type,
v1_xboole_0: $i > $o ).
tff(v1_finset_1,type,
v1_finset_1: $i > $o ).
tff('#skF_15',type,
'#skF_15': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(a_2_0_closure3,type,
a_2_0_closure3: ( $i * $i ) > $i ).
tff(m1_subset_1,type,
m1_subset_1: ( $i * $i ) > $o ).
tff(f_44,negated_conjecture,
~ ! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ( ~ r2_hidden(C,k1_closure3(A,B))
=> ( k1_funct_1(B,C) = k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_closure3) ).
tff(f_136,axiom,
? [A] : v1_xboole_0(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_172,axiom,
! [A] :
( v1_xboole_0(A)
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
tff(f_125,axiom,
? [A] :
( v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A)
& v1_finset_1(A)
& v1_fraenkel(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_closure2) ).
tff(f_142,axiom,
? [A] :
( v1_relat_1(A)
& v1_xboole_0(A)
& v1_funct_1(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
tff(f_113,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& m1_pboole(C,B) )
=> ( r2_hidden(A,a_2_0_closure3(B,C))
<=> ? [D] :
( m1_subset_1(D,B)
& ( A = D )
& ( k1_funct_1(C,D) != k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_closure3) ).
tff(f_84,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( ( C = k1_closure3(A,B) )
<=> ( C = a_2_0_closure3(A,B) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_closure3) ).
tff(c_10,plain,
~ v1_xboole_0('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_76,plain,
v1_xboole_0('#skF_10'),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_111,plain,
! [A_44] :
( ( k1_xboole_0 = A_44 )
| ~ v1_xboole_0(A_44) ),
inference(cnfTransformation,[status(thm)],[f_172]) ).
tff(c_128,plain,
k1_xboole_0 = '#skF_10',
inference(resolution,[status(thm)],[c_76,c_111]) ).
tff(c_66,plain,
v1_xboole_0('#skF_7'),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_125,plain,
k1_xboole_0 = '#skF_7',
inference(resolution,[status(thm)],[c_66,c_111]) ).
tff(c_142,plain,
'#skF_7' = '#skF_10',
inference(demodulation,[status(thm),theory(equality)],[c_128,c_125]) ).
tff(c_80,plain,
v1_xboole_0('#skF_11'),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_124,plain,
k1_xboole_0 = '#skF_11',
inference(resolution,[status(thm)],[c_80,c_111]) ).
tff(c_137,plain,
'#skF_11' = '#skF_7',
inference(demodulation,[status(thm),theory(equality)],[c_125,c_124]) ).
tff(c_157,plain,
'#skF_11' = '#skF_10',
inference(demodulation,[status(thm),theory(equality)],[c_142,c_137]) ).
tff(c_2,plain,
k1_funct_1('#skF_2','#skF_3') != k1_xboole_0,
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_130,plain,
k1_funct_1('#skF_2','#skF_3') != '#skF_11',
inference(demodulation,[status(thm),theory(equality)],[c_124,c_2]) ).
tff(c_179,plain,
k1_funct_1('#skF_2','#skF_3') != '#skF_10',
inference(demodulation,[status(thm),theory(equality)],[c_157,c_130]) ).
tff(c_8,plain,
m1_pboole('#skF_2','#skF_1'),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_6,plain,
m1_subset_1('#skF_3','#skF_1'),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_48,plain,
! [D_29,B_25,C_26] :
( r2_hidden(D_29,a_2_0_closure3(B_25,C_26))
| ( k1_funct_1(C_26,D_29) = k1_xboole_0 )
| ~ m1_subset_1(D_29,B_25)
| ~ m1_pboole(C_26,B_25)
| v1_xboole_0(B_25) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_616,plain,
! [D_119,B_120,C_121] :
( r2_hidden(D_119,a_2_0_closure3(B_120,C_121))
| ( k1_funct_1(C_121,D_119) = '#skF_10' )
| ~ m1_subset_1(D_119,B_120)
| ~ m1_pboole(C_121,B_120)
| v1_xboole_0(B_120) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_48]) ).
tff(c_243,plain,
! [A_66,B_67] :
( ( k1_closure3(A_66,B_67) = a_2_0_closure3(A_66,B_67) )
| ~ m1_pboole(B_67,A_66)
| v1_xboole_0(A_66) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_249,plain,
( ( k1_closure3('#skF_1','#skF_2') = a_2_0_closure3('#skF_1','#skF_2') )
| v1_xboole_0('#skF_1') ),
inference(resolution,[status(thm)],[c_8,c_243]) ).
tff(c_253,plain,
k1_closure3('#skF_1','#skF_2') = a_2_0_closure3('#skF_1','#skF_2'),
inference(negUnitSimplification,[status(thm)],[c_10,c_249]) ).
tff(c_4,plain,
~ r2_hidden('#skF_3',k1_closure3('#skF_1','#skF_2')),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_254,plain,
~ r2_hidden('#skF_3',a_2_0_closure3('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_253,c_4]) ).
tff(c_642,plain,
( ( k1_funct_1('#skF_2','#skF_3') = '#skF_10' )
| ~ m1_subset_1('#skF_3','#skF_1')
| ~ m1_pboole('#skF_2','#skF_1')
| v1_xboole_0('#skF_1') ),
inference(resolution,[status(thm)],[c_616,c_254]) ).
tff(c_660,plain,
( ( k1_funct_1('#skF_2','#skF_3') = '#skF_10' )
| v1_xboole_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_6,c_642]) ).
tff(c_662,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10,c_179,c_660]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG227+1 : TPTP v9.0.0. Released v3.4.0.
% 0.10/0.13 % 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
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Apr 6 07:18:19 EDT 2025
% 0.13/0.35 % CPUTime :
% 4.52/2.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.52/2.18
% 4.52/2.18 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------