TSTP Solution File: ALG219+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ALG219+1 : TPTP v8.1.2. 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 : n009.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 : Tue Aug 22 10:32:23 EDT 2023
% Result : Theorem 28.79s 15.36s
% Output : CNFRefutation 28.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 80
% Syntax : Number of formulae : 128 ( 32 unt; 72 typ; 0 def)
% Number of atoms : 346 ( 27 equ)
% Maximal formula atoms : 26 ( 6 avg)
% Number of connectives : 470 ( 180 ~; 200 |; 73 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 84 ( 57 >; 27 *; 0 +; 0 <<)
% Number of predicates : 35 ( 33 usr; 1 prp; 0-3 aty)
% Number of functors : 39 ( 39 usr; 15 con; 0-5 aty)
% Number of variables : 34 (; 34 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ v1_funct_2 > m2_relset_1 > m1_rmod_2 > m1_relset_1 > v5_vectsp_2 > v3_vectsp_2 > r2_hidden > r1_tarski > m1_subset_1 > l1_vectsp_2 > v8_vectsp_1 > v7_vectsp_1 > v7_group_1 > v6_vectsp_1 > v6_rlvect_1 > v5_rlvect_1 > v4_rlvect_1 > v4_group_1 > v3_struct_0 > v3_rlvect_1 > v2_vectsp_2 > v2_group_1 > v1_xboole_0 > v1_relat_1 > v1_funct_1 > v10_vectsp_1 > l3_vectsp_1 > l2_vectsp_1 > l2_struct_0 > l1_vectsp_1 > l1_struct_0 > l1_rlvect_1 > l1_group_1 > g1_vectsp_2 > k1_rmod_5 > u1_vectsp_2 > k2_zfmisc_1 > k2_rmod_2 > #nlpp > u2_struct_0 > u1_struct_0 > u1_rlvect_1 > k2_group_1 > k1_zfmisc_1 > k1_rlvect_1 > k1_xboole_0 > #skF_25 > #skF_21 > #skF_16 > #skF_20 > #skF_11 > #skF_19 > #skF_8 > #skF_7 > #skF_13 > #skF_10 > #skF_12 > #skF_18 > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_1 > #skF_9 > #skF_26 > #skF_4 > #skF_17 > #skF_22 > #skF_14 > #skF_24 > #skF_23 > #skF_27 > #skF_15
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v2_vectsp_2,type,
v2_vectsp_2: $i > $o ).
tff('#skF_25',type,
'#skF_25': $i > $i ).
tff(v2_group_1,type,
v2_group_1: $i > $o ).
tff(m2_relset_1,type,
m2_relset_1: ( $i * $i * $i ) > $o ).
tff('#skF_21',type,
'#skF_21': $i > $i ).
tff('#skF_16',type,
'#skF_16': $i > $i ).
tff('#skF_20',type,
'#skF_20': $i ).
tff(v1_funct_1,type,
v1_funct_1: $i > $o ).
tff(l3_vectsp_1,type,
l3_vectsp_1: $i > $o ).
tff(r2_hidden,type,
r2_hidden: ( $i * $i ) > $o ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(g1_vectsp_2,type,
g1_vectsp_2: ( $i * $i * $i * $i * $i ) > $i ).
tff(v4_rlvect_1,type,
v4_rlvect_1: $i > $o ).
tff(v8_vectsp_1,type,
v8_vectsp_1: $i > $o ).
tff(u2_struct_0,type,
u2_struct_0: $i > $i ).
tff('#skF_19',type,
'#skF_19': $i > $i ).
tff(k1_rlvect_1,type,
k1_rlvect_1: $i > $i ).
tff(k1_xboole_0,type,
k1_xboole_0: $i ).
tff(v5_vectsp_2,type,
v5_vectsp_2: ( $i * $i ) > $o ).
tff(v6_rlvect_1,type,
v6_rlvect_1: $i > $o ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff(l1_rlvect_1,type,
l1_rlvect_1: $i > $o ).
tff(v7_group_1,type,
v7_group_1: $i > $o ).
tff(k2_rmod_2,type,
k2_rmod_2: ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(u1_vectsp_2,type,
u1_vectsp_2: ( $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': ( $i * $i ) > $i ).
tff(r1_tarski,type,
r1_tarski: ( $i * $i ) > $o ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(v3_vectsp_2,type,
v3_vectsp_2: ( $i * $i ) > $o ).
tff(m1_relset_1,type,
m1_relset_1: ( $i * $i * $i ) > $o ).
tff('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff(k1_rmod_5,type,
k1_rmod_5: ( $i * $i * $i ) > $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(v10_vectsp_1,type,
v10_vectsp_1: $i > $o ).
tff(v1_funct_2,type,
v1_funct_2: ( $i * $i * $i ) > $o ).
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(k2_group_1,type,
k2_group_1: $i > $i ).
tff(l1_vectsp_2,type,
l1_vectsp_2: ( $i * $i ) > $o ).
tff(m1_rmod_2,type,
m1_rmod_2: ( $i * $i * $i ) > $o ).
tff(l2_struct_0,type,
l2_struct_0: $i > $o ).
tff(l2_vectsp_1,type,
l2_vectsp_1: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(k1_zfmisc_1,type,
k1_zfmisc_1: $i > $i ).
tff(l1_struct_0,type,
l1_struct_0: $i > $o ).
tff('#skF_26',type,
'#skF_26': $i > $i ).
tff(l1_vectsp_1,type,
l1_vectsp_1: $i > $o ).
tff(v1_relat_1,type,
v1_relat_1: $i > $o ).
tff(k2_zfmisc_1,type,
k2_zfmisc_1: ( $i * $i ) > $i ).
tff(v7_vectsp_1,type,
v7_vectsp_1: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_17',type,
'#skF_17': $i > $i ).
tff('#skF_22',type,
'#skF_22': $i ).
tff('#skF_14',type,
'#skF_14': $i > $i ).
tff('#skF_24',type,
'#skF_24': $i ).
tff('#skF_23',type,
'#skF_23': $i ).
tff(v4_group_1,type,
v4_group_1: $i > $o ).
tff('#skF_27',type,
'#skF_27': $i > $i ).
tff(v5_rlvect_1,type,
v5_rlvect_1: $i > $o ).
tff(u1_struct_0,type,
u1_struct_0: $i > $i ).
tff(v6_vectsp_1,type,
v6_vectsp_1: $i > $o ).
tff(v1_xboole_0,type,
v1_xboole_0: $i > $o ).
tff(l1_group_1,type,
l1_group_1: $i > $o ).
tff('#skF_15',type,
'#skF_15': ( $i * $i ) > $i ).
tff(v3_rlvect_1,type,
v3_rlvect_1: $i > $o ).
tff(u1_rlvect_1,type,
u1_rlvect_1: $i > $i ).
tff(v3_struct_0,type,
v3_struct_0: $i > $o ).
tff(m1_subset_1,type,
m1_subset_1: ( $i * $i ) > $o ).
tff(f_84,negated_conjecture,
~ ! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& ~ v10_vectsp_1(A)
& v2_vectsp_2(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v3_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& l1_vectsp_2(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( C = u1_struct_0(B) )
=> ( ( k1_rlvect_1(A) = k2_group_1(A) )
| ( k1_rmod_5(A,B,C) = B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_rmod_5) ).
tff(f_332,axiom,
! [A] :
( l3_vectsp_1(A)
=> ( l1_rlvect_1(A)
& l2_vectsp_1(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_vectsp_1) ).
tff(f_326,axiom,
! [A] :
( l2_vectsp_1(A)
=> ( l1_vectsp_1(A)
& l2_struct_0(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_vectsp_1) ).
tff(f_320,axiom,
! [A] :
( l2_struct_0(A)
=> l1_struct_0(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_struct_0) ).
tff(f_176,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v5_vectsp_2(B,A)
& l1_vectsp_2(B,A) )
=> ( k2_rmod_2(A,B) = g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_rmod_2) ).
tff(f_92,axiom,
! [A,B] :
( ( l1_struct_0(A)
& l1_vectsp_2(B,A) )
=> ( v3_vectsp_2(B,A)
=> ( B = g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v3_vectsp_2) ).
tff(f_297,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v5_vectsp_2(B,A)
& l1_vectsp_2(B,A) )
=> ( v3_vectsp_2(k2_rmod_2(A,B),A)
& m1_rmod_2(k2_rmod_2(A,B),A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_rmod_2) ).
tff(f_802,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& ~ v10_vectsp_1(A)
& v2_vectsp_2(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v5_vectsp_2(B,A)
& l1_vectsp_2(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ! [D] :
( ( v3_vectsp_2(D,A)
& m1_rmod_2(D,A,B) )
=> ( ( C = u1_struct_0(D) )
=> ( ( k1_rlvect_1(A) = k2_group_1(A) )
| ( k1_rmod_5(A,B,C) = D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_rmod_5) ).
tff(c_50,plain,
~ v3_struct_0('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_30,plain,
~ v10_vectsp_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_24,plain,
~ v3_struct_0('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_4,plain,
k2_group_1('#skF_1') != k1_rlvect_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_2,plain,
k1_rmod_5('#skF_1','#skF_2','#skF_3') != '#skF_2',
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_48,plain,
v3_rlvect_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_46,plain,
v4_rlvect_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_44,plain,
v5_rlvect_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_42,plain,
v6_rlvect_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_40,plain,
v4_group_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_38,plain,
v7_group_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_36,plain,
v6_vectsp_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_34,plain,
v7_vectsp_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_32,plain,
v8_vectsp_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_28,plain,
v2_vectsp_2('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_26,plain,
l3_vectsp_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_22,plain,
v3_rlvect_1('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_20,plain,
v4_rlvect_1('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_18,plain,
v5_rlvect_1('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_16,plain,
v6_rlvect_1('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_12,plain,
v5_vectsp_2('#skF_2','#skF_1'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_10,plain,
l1_vectsp_2('#skF_2','#skF_1'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_6,plain,
u1_struct_0('#skF_2') = '#skF_3',
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_8,plain,
m1_subset_1('#skF_3',k1_zfmisc_1(u1_struct_0('#skF_2'))),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_303,plain,
m1_subset_1('#skF_3',k1_zfmisc_1('#skF_3')),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_8]) ).
tff(c_14,plain,
v3_vectsp_2('#skF_2','#skF_1'),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_334,plain,
! [A_146] :
( l2_vectsp_1(A_146)
| ~ l3_vectsp_1(A_146) ),
inference(cnfTransformation,[status(thm)],[f_332]) ).
tff(c_341,plain,
l2_vectsp_1('#skF_1'),
inference(resolution,[status(thm)],[c_26,c_334]) ).
tff(c_393,plain,
! [A_152] :
( l2_struct_0(A_152)
| ~ l2_vectsp_1(A_152) ),
inference(cnfTransformation,[status(thm)],[f_326]) ).
tff(c_404,plain,
l2_struct_0('#skF_1'),
inference(resolution,[status(thm)],[c_341,c_393]) ).
tff(c_108,plain,
! [A_35] :
( l1_struct_0(A_35)
| ~ l2_struct_0(A_35) ),
inference(cnfTransformation,[status(thm)],[f_320]) ).
tff(c_430,plain,
l1_struct_0('#skF_1'),
inference(resolution,[status(thm)],[c_404,c_108]) ).
tff(c_15510,plain,
! [A_964,B_965] :
( ( g1_vectsp_2(A_964,u1_struct_0(B_965),u1_rlvect_1(B_965),u2_struct_0(B_965),u1_vectsp_2(A_964,B_965)) = k2_rmod_2(A_964,B_965) )
| ~ l1_vectsp_2(B_965,A_964)
| ~ v5_vectsp_2(B_965,A_964)
| ~ v6_rlvect_1(B_965)
| ~ v5_rlvect_1(B_965)
| ~ v4_rlvect_1(B_965)
| ~ v3_rlvect_1(B_965)
| v3_struct_0(B_965)
| ~ l3_vectsp_1(A_964)
| ~ v8_vectsp_1(A_964)
| ~ v7_vectsp_1(A_964)
| ~ v6_vectsp_1(A_964)
| ~ v4_group_1(A_964)
| ~ v6_rlvect_1(A_964)
| ~ v5_rlvect_1(A_964)
| ~ v4_rlvect_1(A_964)
| ~ v3_rlvect_1(A_964)
| v3_struct_0(A_964) ),
inference(cnfTransformation,[status(thm)],[f_176]) ).
tff(c_52,plain,
! [A_5,B_6] :
( ( g1_vectsp_2(A_5,u1_struct_0(B_6),u1_rlvect_1(B_6),u2_struct_0(B_6),u1_vectsp_2(A_5,B_6)) = B_6 )
| ~ v3_vectsp_2(B_6,A_5)
| ~ l1_vectsp_2(B_6,A_5)
| ~ l1_struct_0(A_5) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_45756,plain,
! [A_1233,B_1234] :
( ( k2_rmod_2(A_1233,B_1234) = B_1234 )
| ~ v3_vectsp_2(B_1234,A_1233)
| ~ l1_vectsp_2(B_1234,A_1233)
| ~ l1_struct_0(A_1233)
| ~ l1_vectsp_2(B_1234,A_1233)
| ~ v5_vectsp_2(B_1234,A_1233)
| ~ v6_rlvect_1(B_1234)
| ~ v5_rlvect_1(B_1234)
| ~ v4_rlvect_1(B_1234)
| ~ v3_rlvect_1(B_1234)
| v3_struct_0(B_1234)
| ~ l3_vectsp_1(A_1233)
| ~ v8_vectsp_1(A_1233)
| ~ v7_vectsp_1(A_1233)
| ~ v6_vectsp_1(A_1233)
| ~ v4_group_1(A_1233)
| ~ v6_rlvect_1(A_1233)
| ~ v5_rlvect_1(A_1233)
| ~ v4_rlvect_1(A_1233)
| ~ v3_rlvect_1(A_1233)
| v3_struct_0(A_1233) ),
inference(superposition,[status(thm),theory(equality)],[c_15510,c_52]) ).
tff(c_45774,plain,
( ( k2_rmod_2('#skF_1','#skF_2') = '#skF_2' )
| ~ v3_vectsp_2('#skF_2','#skF_1')
| ~ l1_struct_0('#skF_1')
| ~ l1_vectsp_2('#skF_2','#skF_1')
| ~ v6_rlvect_1('#skF_2')
| ~ v5_rlvect_1('#skF_2')
| ~ v4_rlvect_1('#skF_2')
| ~ v3_rlvect_1('#skF_2')
| v3_struct_0('#skF_2')
| ~ l3_vectsp_1('#skF_1')
| ~ v8_vectsp_1('#skF_1')
| ~ v7_vectsp_1('#skF_1')
| ~ v6_vectsp_1('#skF_1')
| ~ v4_group_1('#skF_1')
| ~ v6_rlvect_1('#skF_1')
| ~ v5_rlvect_1('#skF_1')
| ~ v4_rlvect_1('#skF_1')
| ~ v3_rlvect_1('#skF_1')
| v3_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_12,c_45756]) ).
tff(c_45782,plain,
( ( k2_rmod_2('#skF_1','#skF_2') = '#skF_2' )
| v3_struct_0('#skF_2')
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_46,c_44,c_42,c_40,c_36,c_34,c_32,c_26,c_22,c_20,c_18,c_16,c_10,c_430,c_14,c_45774]) ).
tff(c_45783,plain,
k2_rmod_2('#skF_1','#skF_2') = '#skF_2',
inference(negUnitSimplification,[status(thm)],[c_50,c_24,c_45782]) ).
tff(c_92,plain,
! [A_27,B_28] :
( m1_rmod_2(k2_rmod_2(A_27,B_28),A_27,B_28)
| ~ l1_vectsp_2(B_28,A_27)
| ~ v5_vectsp_2(B_28,A_27)
| ~ v6_rlvect_1(B_28)
| ~ v5_rlvect_1(B_28)
| ~ v4_rlvect_1(B_28)
| ~ v3_rlvect_1(B_28)
| v3_struct_0(B_28)
| ~ l3_vectsp_1(A_27)
| ~ v8_vectsp_1(A_27)
| ~ v7_vectsp_1(A_27)
| ~ v6_vectsp_1(A_27)
| ~ v4_group_1(A_27)
| ~ v6_rlvect_1(A_27)
| ~ v5_rlvect_1(A_27)
| ~ v4_rlvect_1(A_27)
| ~ v3_rlvect_1(A_27)
| v3_struct_0(A_27) ),
inference(cnfTransformation,[status(thm)],[f_297]) ).
tff(c_45808,plain,
( m1_rmod_2('#skF_2','#skF_1','#skF_2')
| ~ l1_vectsp_2('#skF_2','#skF_1')
| ~ v5_vectsp_2('#skF_2','#skF_1')
| ~ v6_rlvect_1('#skF_2')
| ~ v5_rlvect_1('#skF_2')
| ~ v4_rlvect_1('#skF_2')
| ~ v3_rlvect_1('#skF_2')
| v3_struct_0('#skF_2')
| ~ l3_vectsp_1('#skF_1')
| ~ v8_vectsp_1('#skF_1')
| ~ v7_vectsp_1('#skF_1')
| ~ v6_vectsp_1('#skF_1')
| ~ v4_group_1('#skF_1')
| ~ v6_rlvect_1('#skF_1')
| ~ v5_rlvect_1('#skF_1')
| ~ v4_rlvect_1('#skF_1')
| ~ v3_rlvect_1('#skF_1')
| v3_struct_0('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_45783,c_92]) ).
tff(c_45836,plain,
( m1_rmod_2('#skF_2','#skF_1','#skF_2')
| v3_struct_0('#skF_2')
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_46,c_44,c_42,c_40,c_36,c_34,c_32,c_26,c_22,c_20,c_18,c_16,c_12,c_10,c_45808]) ).
tff(c_45837,plain,
m1_rmod_2('#skF_2','#skF_1','#skF_2'),
inference(negUnitSimplification,[status(thm)],[c_50,c_24,c_45836]) ).
tff(c_19557,plain,
! [A_1005,B_1006,D_1007] :
( ( k1_rmod_5(A_1005,B_1006,u1_struct_0(D_1007)) = D_1007 )
| ( k2_group_1(A_1005) = k1_rlvect_1(A_1005) )
| ~ m1_rmod_2(D_1007,A_1005,B_1006)
| ~ v3_vectsp_2(D_1007,A_1005)
| ~ m1_subset_1(u1_struct_0(D_1007),k1_zfmisc_1(u1_struct_0(B_1006)))
| ~ l1_vectsp_2(B_1006,A_1005)
| ~ v5_vectsp_2(B_1006,A_1005)
| ~ v6_rlvect_1(B_1006)
| ~ v5_rlvect_1(B_1006)
| ~ v4_rlvect_1(B_1006)
| ~ v3_rlvect_1(B_1006)
| v3_struct_0(B_1006)
| ~ l3_vectsp_1(A_1005)
| ~ v2_vectsp_2(A_1005)
| v10_vectsp_1(A_1005)
| ~ v8_vectsp_1(A_1005)
| ~ v7_vectsp_1(A_1005)
| ~ v6_vectsp_1(A_1005)
| ~ v7_group_1(A_1005)
| ~ v4_group_1(A_1005)
| ~ v6_rlvect_1(A_1005)
| ~ v5_rlvect_1(A_1005)
| ~ v4_rlvect_1(A_1005)
| ~ v3_rlvect_1(A_1005)
| v3_struct_0(A_1005) ),
inference(cnfTransformation,[status(thm)],[f_802]) ).
tff(c_19562,plain,
! [A_1005,B_1006] :
( ( k1_rmod_5(A_1005,B_1006,u1_struct_0('#skF_2')) = '#skF_2' )
| ( k2_group_1(A_1005) = k1_rlvect_1(A_1005) )
| ~ m1_rmod_2('#skF_2',A_1005,B_1006)
| ~ v3_vectsp_2('#skF_2',A_1005)
| ~ m1_subset_1('#skF_3',k1_zfmisc_1(u1_struct_0(B_1006)))
| ~ l1_vectsp_2(B_1006,A_1005)
| ~ v5_vectsp_2(B_1006,A_1005)
| ~ v6_rlvect_1(B_1006)
| ~ v5_rlvect_1(B_1006)
| ~ v4_rlvect_1(B_1006)
| ~ v3_rlvect_1(B_1006)
| v3_struct_0(B_1006)
| ~ l3_vectsp_1(A_1005)
| ~ v2_vectsp_2(A_1005)
| v10_vectsp_1(A_1005)
| ~ v8_vectsp_1(A_1005)
| ~ v7_vectsp_1(A_1005)
| ~ v6_vectsp_1(A_1005)
| ~ v7_group_1(A_1005)
| ~ v4_group_1(A_1005)
| ~ v6_rlvect_1(A_1005)
| ~ v5_rlvect_1(A_1005)
| ~ v4_rlvect_1(A_1005)
| ~ v3_rlvect_1(A_1005)
| v3_struct_0(A_1005) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_19557]) ).
tff(c_63794,plain,
! [A_1517,B_1518] :
( ( k1_rmod_5(A_1517,B_1518,'#skF_3') = '#skF_2' )
| ( k2_group_1(A_1517) = k1_rlvect_1(A_1517) )
| ~ m1_rmod_2('#skF_2',A_1517,B_1518)
| ~ v3_vectsp_2('#skF_2',A_1517)
| ~ m1_subset_1('#skF_3',k1_zfmisc_1(u1_struct_0(B_1518)))
| ~ l1_vectsp_2(B_1518,A_1517)
| ~ v5_vectsp_2(B_1518,A_1517)
| ~ v6_rlvect_1(B_1518)
| ~ v5_rlvect_1(B_1518)
| ~ v4_rlvect_1(B_1518)
| ~ v3_rlvect_1(B_1518)
| v3_struct_0(B_1518)
| ~ l3_vectsp_1(A_1517)
| ~ v2_vectsp_2(A_1517)
| v10_vectsp_1(A_1517)
| ~ v8_vectsp_1(A_1517)
| ~ v7_vectsp_1(A_1517)
| ~ v6_vectsp_1(A_1517)
| ~ v7_group_1(A_1517)
| ~ v4_group_1(A_1517)
| ~ v6_rlvect_1(A_1517)
| ~ v5_rlvect_1(A_1517)
| ~ v4_rlvect_1(A_1517)
| ~ v3_rlvect_1(A_1517)
| v3_struct_0(A_1517) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_19562]) ).
tff(c_63796,plain,
( ( k1_rmod_5('#skF_1','#skF_2','#skF_3') = '#skF_2' )
| ( k2_group_1('#skF_1') = k1_rlvect_1('#skF_1') )
| ~ v3_vectsp_2('#skF_2','#skF_1')
| ~ m1_subset_1('#skF_3',k1_zfmisc_1(u1_struct_0('#skF_2')))
| ~ l1_vectsp_2('#skF_2','#skF_1')
| ~ v5_vectsp_2('#skF_2','#skF_1')
| ~ v6_rlvect_1('#skF_2')
| ~ v5_rlvect_1('#skF_2')
| ~ v4_rlvect_1('#skF_2')
| ~ v3_rlvect_1('#skF_2')
| v3_struct_0('#skF_2')
| ~ l3_vectsp_1('#skF_1')
| ~ v2_vectsp_2('#skF_1')
| v10_vectsp_1('#skF_1')
| ~ v8_vectsp_1('#skF_1')
| ~ v7_vectsp_1('#skF_1')
| ~ v6_vectsp_1('#skF_1')
| ~ v7_group_1('#skF_1')
| ~ v4_group_1('#skF_1')
| ~ v6_rlvect_1('#skF_1')
| ~ v5_rlvect_1('#skF_1')
| ~ v4_rlvect_1('#skF_1')
| ~ v3_rlvect_1('#skF_1')
| v3_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_45837,c_63794]) ).
tff(c_63799,plain,
( ( k1_rmod_5('#skF_1','#skF_2','#skF_3') = '#skF_2' )
| ( k2_group_1('#skF_1') = k1_rlvect_1('#skF_1') )
| v3_struct_0('#skF_2')
| v10_vectsp_1('#skF_1')
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_46,c_44,c_42,c_40,c_38,c_36,c_34,c_32,c_28,c_26,c_22,c_20,c_18,c_16,c_12,c_10,c_303,c_6,c_14,c_63796]) ).
tff(c_63801,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_50,c_30,c_24,c_4,c_2,c_63799]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG219+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.14 % 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
% 0.14/0.36 % Computer : n009.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 20:10:08 EDT 2023
% 0.14/0.36 % CPUTime :
% 28.79/15.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.79/15.36
% 28.79/15.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 28.79/15.40
% 28.79/15.40 Inference rules
% 28.79/15.40 ----------------------
% 28.79/15.40 #Ref : 10
% 28.79/15.40 #Sup : 19180
% 28.79/15.40 #Fact : 2
% 28.79/15.40 #Define : 0
% 28.79/15.40 #Split : 63
% 28.79/15.40 #Chain : 0
% 28.79/15.40 #Close : 0
% 28.79/15.40
% 28.79/15.40 Ordering : KBO
% 28.79/15.40
% 28.79/15.40 Simplification rules
% 28.79/15.40 ----------------------
% 28.79/15.40 #Subsume : 17174
% 28.79/15.40 #Demod : 1861
% 28.79/15.40 #Tautology : 403
% 28.79/15.40 #SimpNegUnit : 3293
% 28.79/15.40 #BackRed : 1870
% 28.79/15.40
% 28.79/15.40 #Partial instantiations: 0
% 28.79/15.40 #Strategies tried : 1
% 28.79/15.40
% 28.79/15.40 Timing (in seconds)
% 28.79/15.40 ----------------------
% 28.79/15.40 Preprocessing : 0.82
% 28.79/15.40 Parsing : 0.41
% 28.79/15.41 CNF conversion : 0.07
% 28.79/15.41 Main loop : 13.43
% 28.79/15.41 Inferencing : 2.31
% 28.79/15.41 Reduction : 5.79
% 28.79/15.41 Demodulation : 4.67
% 28.79/15.41 BG Simplification : 0.14
% 28.79/15.41 Subsumption : 4.84
% 28.79/15.41 Abstraction : 0.21
% 28.79/15.41 MUC search : 0.00
% 28.79/15.41 Cooper : 0.00
% 28.79/15.41 Total : 14.32
% 28.79/15.41 Index Insertion : 0.00
% 28.79/15.41 Index Deletion : 0.00
% 28.79/15.41 Index Matching : 0.00
% 28.79/15.41 BG Taut test : 0.00
%------------------------------------------------------------------------------