TSTP Solution File: ALG216+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ALG216+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 10:32:22 EDT 2023
% Result : Theorem 6.91s 2.57s
% Output : CNFRefutation 7.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 64
% Syntax : Number of formulae : 149 ( 52 unt; 52 typ; 0 def)
% Number of atoms : 260 ( 24 equ)
% Maximal formula atoms : 23 ( 2 avg)
% Number of connectives : 273 ( 110 ~; 100 |; 44 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 47 ( 37 >; 10 *; 0 +; 0 <<)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 15 con; 0-3 aty)
% Number of variables : 64 (; 64 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ v1_rmod_5 > v5_vectsp_2 > r2_hidden > r1_tarski > m1_subset_1 > l1_vectsp_2 > v8_vectsp_1 > v7_vectsp_1 > v6_vectsp_1 > v6_rlvect_1 > v5_rlvect_1 > v4_rlvect_1 > v4_group_1 > v3_struct_0 > v3_rlvect_1 > v1_xboole_0 > v1_finset_1 > l3_vectsp_1 > l2_vectsp_1 > l2_struct_0 > l1_vectsp_1 > l1_struct_0 > l1_rlvect_1 > l1_group_1 > k8_rlvect_2 > k2_tarski > #nlpp > u1_struct_0 > k2_group_1 > k1_zfmisc_1 > k1_rlvect_1 > k1_xboole_0 > #skF_7 > #skF_5 > #skF_21 > #skF_20 > #skF_18 > #skF_17 > #skF_11 > #skF_15 > #skF_19 > #skF_8 > #skF_16 > #skF_14 > #skF_10 > #skF_6 > #skF_13 > #skF_2 > #skF_3 > #skF_1 > #skF_9 > #skF_4 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff('#skF_21',type,
'#skF_21': $i > $i ).
tff('#skF_20',type,
'#skF_20': $i ).
tff('#skF_18',type,
'#skF_18': $i > $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff(l3_vectsp_1,type,
l3_vectsp_1: $i > $o ).
tff(k8_rlvect_2,type,
k8_rlvect_2: ( $i * $i * $i ) > $i ).
tff(r2_hidden,type,
r2_hidden: ( $i * $i ) > $o ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(v4_rlvect_1,type,
v4_rlvect_1: $i > $o ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(v8_vectsp_1,type,
v8_vectsp_1: $i > $o ).
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(r1_tarski,type,
r1_tarski: ( $i * $i ) > $o ).
tff('#skF_16',type,
'#skF_16': $i ).
tff(k2_tarski,type,
k2_tarski: ( $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(v1_rmod_5,type,
v1_rmod_5: ( $i * $i * $i ) > $o ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_13',type,
'#skF_13': $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(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(l1_vectsp_1,type,
l1_vectsp_1: $i > $o ).
tff(v7_vectsp_1,type,
v7_vectsp_1: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(v4_group_1,type,
v4_group_1: $i > $o ).
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(v1_finset_1,type,
v1_finset_1: $i > $o ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(v3_rlvect_1,type,
v3_rlvect_1: $i > $o ).
tff(v3_struct_0,type,
v3_struct_0: $i > $o ).
tff(m1_subset_1,type,
m1_subset_1: ( $i * $i ) > $o ).
tff(f_78,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)
& 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) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ( ( k1_rlvect_1(A) != k2_group_1(A) )
=> ( ~ v1_rmod_5(k8_rlvect_2(B,C,k1_rlvect_1(B)),A,B)
& ~ v1_rmod_5(k8_rlvect_2(B,k1_rlvect_1(B),C),A,B) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_rmod_5) ).
tff(f_311,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_206,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_200,axiom,
! [A] :
( l2_struct_0(A)
=> l1_struct_0(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_struct_0) ).
tff(f_305,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_vectsp_2(B,A)
=> l1_rlvect_1(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_vectsp_2) ).
tff(f_196,axiom,
! [A] :
( l1_rlvect_1(A)
=> l2_struct_0(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_rlvect_1) ).
tff(f_278,axiom,
! [A] :
( l2_struct_0(A)
=> m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_rlvect_1) ).
tff(f_298,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( v1_finset_1(k8_rlvect_2(A,B,C))
& m1_subset_1(k8_rlvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_rlvect_2) ).
tff(f_178,axiom,
! [A,B] : ( k2_tarski(A,B) = k2_tarski(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
tff(f_274,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( k8_rlvect_2(A,B,C) = k2_tarski(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_rlvect_2) ).
tff(f_364,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) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( v1_rmod_5(k8_rlvect_2(B,C,D),A,B)
=> ( ( k1_rlvect_1(A) = k2_group_1(A) )
| ( ( C != k1_rlvect_1(B) )
& ( D != k1_rlvect_1(B) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_rmod_5) ).
tff(f_253,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( k8_rlvect_2(A,B,C) = k8_rlvect_2(A,C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k8_rlvect_2) ).
tff(c_22,plain,
l3_vectsp_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_174,plain,
! [A_84] :
( l2_vectsp_1(A_84)
| ~ l3_vectsp_1(A_84) ),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_181,plain,
l2_vectsp_1('#skF_1'),
inference(resolution,[status(thm)],[c_22,c_174]) ).
tff(c_193,plain,
! [A_87] :
( l2_struct_0(A_87)
| ~ l2_vectsp_1(A_87) ),
inference(cnfTransformation,[status(thm)],[f_206]) ).
tff(c_204,plain,
l2_struct_0('#skF_1'),
inference(resolution,[status(thm)],[c_181,c_193]) ).
tff(c_207,plain,
! [A_89] :
( l1_struct_0(A_89)
| ~ l2_struct_0(A_89) ),
inference(cnfTransformation,[status(thm)],[f_200]) ).
tff(c_226,plain,
l1_struct_0('#skF_1'),
inference(resolution,[status(thm)],[c_204,c_207]) ).
tff(c_8,plain,
l1_vectsp_2('#skF_2','#skF_1'),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_950,plain,
! [B_213,A_214] :
( l1_rlvect_1(B_213)
| ~ l1_vectsp_2(B_213,A_214)
| ~ l1_struct_0(A_214) ),
inference(cnfTransformation,[status(thm)],[f_305]) ).
tff(c_959,plain,
( l1_rlvect_1('#skF_2')
| ~ l1_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_8,c_950]) ).
tff(c_964,plain,
l1_rlvect_1('#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_226,c_959]) ).
tff(c_108,plain,
! [A_36] :
( l2_struct_0(A_36)
| ~ l1_rlvect_1(A_36) ),
inference(cnfTransformation,[status(thm)],[f_196]) ).
tff(c_150,plain,
! [A_57] :
( m1_subset_1(k1_rlvect_1(A_57),u1_struct_0(A_57))
| ~ l2_struct_0(A_57) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_229,plain,
! [A_36] :
( l1_struct_0(A_36)
| ~ l1_rlvect_1(A_36) ),
inference(resolution,[status(thm)],[c_108,c_207]) ).
tff(c_20,plain,
~ v3_struct_0('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_6,plain,
m1_subset_1('#skF_3',u1_struct_0('#skF_2')),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_1167,plain,
! [A_264,B_265,C_266] :
( v1_finset_1(k8_rlvect_2(A_264,B_265,C_266))
| ~ m1_subset_1(C_266,u1_struct_0(A_264))
| ~ m1_subset_1(B_265,u1_struct_0(A_264))
| ~ l1_struct_0(A_264)
| v3_struct_0(A_264) ),
inference(cnfTransformation,[status(thm)],[f_298]) ).
tff(c_1176,plain,
! [B_265] :
( v1_finset_1(k8_rlvect_2('#skF_2',B_265,'#skF_3'))
| ~ m1_subset_1(B_265,u1_struct_0('#skF_2'))
| ~ l1_struct_0('#skF_2')
| v3_struct_0('#skF_2') ),
inference(resolution,[status(thm)],[c_6,c_1167]) ).
tff(c_1182,plain,
! [B_265] :
( v1_finset_1(k8_rlvect_2('#skF_2',B_265,'#skF_3'))
| ~ m1_subset_1(B_265,u1_struct_0('#skF_2'))
| ~ l1_struct_0('#skF_2') ),
inference(negUnitSimplification,[status(thm)],[c_20,c_1176]) ).
tff(c_1186,plain,
~ l1_struct_0('#skF_2'),
inference(splitLeft,[status(thm)],[c_1182]) ).
tff(c_1189,plain,
~ l1_rlvect_1('#skF_2'),
inference(resolution,[status(thm)],[c_229,c_1186]) ).
tff(c_1196,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_964,c_1189]) ).
tff(c_1199,plain,
! [B_269] :
( v1_finset_1(k8_rlvect_2('#skF_2',B_269,'#skF_3'))
| ~ m1_subset_1(B_269,u1_struct_0('#skF_2')) ),
inference(splitRight,[status(thm)],[c_1182]) ).
tff(c_1218,plain,
( v1_finset_1(k8_rlvect_2('#skF_2',k1_rlvect_1('#skF_2'),'#skF_3'))
| ~ l2_struct_0('#skF_2') ),
inference(resolution,[status(thm)],[c_150,c_1199]) ).
tff(c_1238,plain,
~ l2_struct_0('#skF_2'),
inference(splitLeft,[status(thm)],[c_1218]) ).
tff(c_1241,plain,
~ l1_rlvect_1('#skF_2'),
inference(resolution,[status(thm)],[c_108,c_1238]) ).
tff(c_1245,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_964,c_1241]) ).
tff(c_1247,plain,
l2_struct_0('#skF_2'),
inference(splitRight,[status(thm)],[c_1218]) ).
tff(c_90,plain,
! [B_34,A_33] : ( k2_tarski(B_34,A_33) = k2_tarski(A_33,B_34) ),
inference(cnfTransformation,[status(thm)],[f_178]) ).
tff(c_1198,plain,
l1_struct_0('#skF_2'),
inference(splitRight,[status(thm)],[c_1182]) ).
tff(c_1221,plain,
! [A_270,B_271,C_272] :
( ( k8_rlvect_2(A_270,B_271,C_272) = k2_tarski(B_271,C_272) )
| ~ m1_subset_1(C_272,u1_struct_0(A_270))
| ~ m1_subset_1(B_271,u1_struct_0(A_270))
| ~ l1_struct_0(A_270)
| v3_struct_0(A_270) ),
inference(cnfTransformation,[status(thm)],[f_274]) ).
tff(c_1230,plain,
! [B_271] :
( ( k8_rlvect_2('#skF_2',B_271,'#skF_3') = k2_tarski(B_271,'#skF_3') )
| ~ m1_subset_1(B_271,u1_struct_0('#skF_2'))
| ~ l1_struct_0('#skF_2')
| v3_struct_0('#skF_2') ),
inference(resolution,[status(thm)],[c_6,c_1221]) ).
tff(c_1236,plain,
! [B_271] :
( ( k8_rlvect_2('#skF_2',B_271,'#skF_3') = k2_tarski(B_271,'#skF_3') )
| ~ m1_subset_1(B_271,u1_struct_0('#skF_2'))
| v3_struct_0('#skF_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_1198,c_1230]) ).
tff(c_1255,plain,
! [B_274] :
( ( k8_rlvect_2('#skF_2',B_274,'#skF_3') = k2_tarski(B_274,'#skF_3') )
| ~ m1_subset_1(B_274,u1_struct_0('#skF_2')) ),
inference(negUnitSimplification,[status(thm)],[c_20,c_1236]) ).
tff(c_1263,plain,
( ( k8_rlvect_2('#skF_2',k1_rlvect_1('#skF_2'),'#skF_3') = k2_tarski(k1_rlvect_1('#skF_2'),'#skF_3') )
| ~ l2_struct_0('#skF_2') ),
inference(resolution,[status(thm)],[c_150,c_1255]) ).
tff(c_1276,plain,
k8_rlvect_2('#skF_2',k1_rlvect_1('#skF_2'),'#skF_3') = k2_tarski('#skF_3',k1_rlvect_1('#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_1247,c_90,c_1263]) ).
tff(c_369,plain,
! [B_118,A_119] :
( l1_rlvect_1(B_118)
| ~ l1_vectsp_2(B_118,A_119)
| ~ l1_struct_0(A_119) ),
inference(cnfTransformation,[status(thm)],[f_305]) ).
tff(c_378,plain,
( l1_rlvect_1('#skF_2')
| ~ l1_struct_0('#skF_1') ),
inference(resolution,[status(thm)],[c_8,c_369]) ).
tff(c_383,plain,
l1_rlvect_1('#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_226,c_378]) ).
tff(c_548,plain,
! [A_163,B_164,C_165] :
( v1_finset_1(k8_rlvect_2(A_163,B_164,C_165))
| ~ m1_subset_1(C_165,u1_struct_0(A_163))
| ~ m1_subset_1(B_164,u1_struct_0(A_163))
| ~ l1_struct_0(A_163)
| v3_struct_0(A_163) ),
inference(cnfTransformation,[status(thm)],[f_298]) ).
tff(c_557,plain,
! [B_164] :
( v1_finset_1(k8_rlvect_2('#skF_2',B_164,'#skF_3'))
| ~ m1_subset_1(B_164,u1_struct_0('#skF_2'))
| ~ l1_struct_0('#skF_2')
| v3_struct_0('#skF_2') ),
inference(resolution,[status(thm)],[c_6,c_548]) ).
tff(c_563,plain,
! [B_164] :
( v1_finset_1(k8_rlvect_2('#skF_2',B_164,'#skF_3'))
| ~ m1_subset_1(B_164,u1_struct_0('#skF_2'))
| ~ l1_struct_0('#skF_2') ),
inference(negUnitSimplification,[status(thm)],[c_20,c_557]) ).
tff(c_571,plain,
~ l1_struct_0('#skF_2'),
inference(splitLeft,[status(thm)],[c_563]) ).
tff(c_574,plain,
~ l1_rlvect_1('#skF_2'),
inference(resolution,[status(thm)],[c_229,c_571]) ).
tff(c_581,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_383,c_574]) ).
tff(c_584,plain,
! [B_169] :
( v1_finset_1(k8_rlvect_2('#skF_2',B_169,'#skF_3'))
| ~ m1_subset_1(B_169,u1_struct_0('#skF_2')) ),
inference(splitRight,[status(thm)],[c_563]) ).
tff(c_603,plain,
( v1_finset_1(k8_rlvect_2('#skF_2',k1_rlvect_1('#skF_2'),'#skF_3'))
| ~ l2_struct_0('#skF_2') ),
inference(resolution,[status(thm)],[c_150,c_584]) ).
tff(c_651,plain,
~ l2_struct_0('#skF_2'),
inference(splitLeft,[status(thm)],[c_603]) ).
tff(c_654,plain,
~ l1_rlvect_1('#skF_2'),
inference(resolution,[status(thm)],[c_108,c_651]) ).
tff(c_658,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_383,c_654]) ).
tff(c_660,plain,
l2_struct_0('#skF_2'),
inference(splitRight,[status(thm)],[c_603]) ).
tff(c_40,plain,
~ v3_struct_0('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_4,plain,
k2_group_1('#skF_1') != k1_rlvect_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_38,plain,
v3_rlvect_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_36,plain,
v4_rlvect_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_34,plain,
v5_rlvect_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_32,plain,
v6_rlvect_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_30,plain,
v4_group_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_28,plain,
v6_vectsp_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_26,plain,
v7_vectsp_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_24,plain,
v8_vectsp_1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_18,plain,
v3_rlvect_1('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_16,plain,
v4_rlvect_1('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_14,plain,
v5_rlvect_1('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_12,plain,
v6_rlvect_1('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_10,plain,
v5_vectsp_2('#skF_2','#skF_1'),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_2,plain,
( v1_rmod_5(k8_rlvect_2('#skF_2',k1_rlvect_1('#skF_2'),'#skF_3'),'#skF_1','#skF_2')
| v1_rmod_5(k8_rlvect_2('#skF_2','#skF_3',k1_rlvect_1('#skF_2')),'#skF_1','#skF_2') ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_265,plain,
v1_rmod_5(k8_rlvect_2('#skF_2','#skF_3',k1_rlvect_1('#skF_2')),'#skF_1','#skF_2'),
inference(splitLeft,[status(thm)],[c_2]) ).
tff(c_843,plain,
! [A_188,B_189,C_190] :
( ( k2_group_1(A_188) = k1_rlvect_1(A_188) )
| ~ v1_rmod_5(k8_rlvect_2(B_189,C_190,k1_rlvect_1(B_189)),A_188,B_189)
| ~ m1_subset_1(k1_rlvect_1(B_189),u1_struct_0(B_189))
| ~ m1_subset_1(C_190,u1_struct_0(B_189))
| ~ l1_vectsp_2(B_189,A_188)
| ~ v5_vectsp_2(B_189,A_188)
| ~ v6_rlvect_1(B_189)
| ~ v5_rlvect_1(B_189)
| ~ v4_rlvect_1(B_189)
| ~ v3_rlvect_1(B_189)
| v3_struct_0(B_189)
| ~ l3_vectsp_1(A_188)
| ~ v8_vectsp_1(A_188)
| ~ v7_vectsp_1(A_188)
| ~ v6_vectsp_1(A_188)
| ~ v4_group_1(A_188)
| ~ v6_rlvect_1(A_188)
| ~ v5_rlvect_1(A_188)
| ~ v4_rlvect_1(A_188)
| ~ v3_rlvect_1(A_188)
| v3_struct_0(A_188) ),
inference(cnfTransformation,[status(thm)],[f_364]) ).
tff(c_846,plain,
( ( k2_group_1('#skF_1') = k1_rlvect_1('#skF_1') )
| ~ m1_subset_1(k1_rlvect_1('#skF_2'),u1_struct_0('#skF_2'))
| ~ m1_subset_1('#skF_3',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')
| ~ 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_265,c_843]) ).
tff(c_849,plain,
( ( k2_group_1('#skF_1') = k1_rlvect_1('#skF_1') )
| ~ m1_subset_1(k1_rlvect_1('#skF_2'),u1_struct_0('#skF_2'))
| v3_struct_0('#skF_2')
| v3_struct_0('#skF_1') ),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_36,c_34,c_32,c_30,c_28,c_26,c_24,c_22,c_18,c_16,c_14,c_12,c_10,c_8,c_6,c_846]) ).
tff(c_850,plain,
~ m1_subset_1(k1_rlvect_1('#skF_2'),u1_struct_0('#skF_2')),
inference(negUnitSimplification,[status(thm)],[c_40,c_20,c_4,c_849]) ).
tff(c_853,plain,
~ l2_struct_0('#skF_2'),
inference(resolution,[status(thm)],[c_150,c_850]) ).
tff(c_857,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_660,c_853]) ).
tff(c_858,plain,
v1_rmod_5(k8_rlvect_2('#skF_2',k1_rlvect_1('#skF_2'),'#skF_3'),'#skF_1','#skF_2'),
inference(splitRight,[status(thm)],[c_2]) ).
tff(c_1327,plain,
v1_rmod_5(k2_tarski('#skF_3',k1_rlvect_1('#skF_2')),'#skF_1','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_1276,c_858]) ).
tff(c_1338,plain,
! [A_278,C_279,B_280] :
( ( k8_rlvect_2(A_278,C_279,B_280) = k8_rlvect_2(A_278,B_280,C_279) )
| ~ m1_subset_1(C_279,u1_struct_0(A_278))
| ~ m1_subset_1(B_280,u1_struct_0(A_278))
| ~ l1_struct_0(A_278)
| v3_struct_0(A_278) ),
inference(cnfTransformation,[status(thm)],[f_253]) ).
tff(c_1347,plain,
! [B_280] :
( ( k8_rlvect_2('#skF_2',B_280,'#skF_3') = k8_rlvect_2('#skF_2','#skF_3',B_280) )
| ~ m1_subset_1(B_280,u1_struct_0('#skF_2'))
| ~ l1_struct_0('#skF_2')
| v3_struct_0('#skF_2') ),
inference(resolution,[status(thm)],[c_6,c_1338]) ).
tff(c_1353,plain,
! [B_280] :
( ( k8_rlvect_2('#skF_2',B_280,'#skF_3') = k8_rlvect_2('#skF_2','#skF_3',B_280) )
| ~ m1_subset_1(B_280,u1_struct_0('#skF_2'))
| v3_struct_0('#skF_2') ),
inference(demodulation,[status(thm),theory(equality)],[c_1198,c_1347]) ).
tff(c_1363,plain,
! [B_282] :
( ( k8_rlvect_2('#skF_2',B_282,'#skF_3') = k8_rlvect_2('#skF_2','#skF_3',B_282) )
| ~ m1_subset_1(B_282,u1_struct_0('#skF_2')) ),
inference(negUnitSimplification,[status(thm)],[c_20,c_1353]) ).
tff(c_1371,plain,
( ( k8_rlvect_2('#skF_2',k1_rlvect_1('#skF_2'),'#skF_3') = k8_rlvect_2('#skF_2','#skF_3',k1_rlvect_1('#skF_2')) )
| ~ l2_struct_0('#skF_2') ),
inference(resolution,[status(thm)],[c_150,c_1363]) ).
tff(c_1383,plain,
k8_rlvect_2('#skF_2','#skF_3',k1_rlvect_1('#skF_2')) = k2_tarski('#skF_3',k1_rlvect_1('#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_1247,c_1276,c_1371]) ).
tff(c_859,plain,
~ v1_rmod_5(k8_rlvect_2('#skF_2','#skF_3',k1_rlvect_1('#skF_2')),'#skF_1','#skF_2'),
inference(splitRight,[status(thm)],[c_2]) ).
tff(c_1387,plain,
~ v1_rmod_5(k2_tarski('#skF_3',k1_rlvect_1('#skF_2')),'#skF_1','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_1383,c_859]) ).
tff(c_1390,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1327,c_1387]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : ALG216+1 : TPTP v8.1.2. Released v3.4.0.
% 0.13/0.15 % 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
% 0.16/0.36 % Computer : n009.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu Aug 3 20:24:53 EDT 2023
% 0.16/0.36 % CPUTime :
% 6.91/2.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.91/2.58
% 6.91/2.58 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.10/2.63
% 7.10/2.63 Inference rules
% 7.10/2.63 ----------------------
% 7.10/2.63 #Ref : 0
% 7.10/2.63 #Sup : 255
% 7.10/2.63 #Fact : 0
% 7.10/2.63 #Define : 0
% 7.10/2.63 #Split : 13
% 7.10/2.63 #Chain : 0
% 7.10/2.63 #Close : 0
% 7.10/2.63
% 7.10/2.63 Ordering : KBO
% 7.10/2.63
% 7.10/2.63 Simplification rules
% 7.10/2.63 ----------------------
% 7.10/2.63 #Subsume : 28
% 7.10/2.63 #Demod : 82
% 7.10/2.63 #Tautology : 59
% 7.10/2.63 #SimpNegUnit : 42
% 7.10/2.63 #BackRed : 10
% 7.10/2.63
% 7.10/2.63 #Partial instantiations: 0
% 7.10/2.63 #Strategies tried : 1
% 7.10/2.63
% 7.10/2.63 Timing (in seconds)
% 7.10/2.63 ----------------------
% 7.10/2.63 Preprocessing : 0.65
% 7.10/2.63 Parsing : 0.33
% 7.10/2.63 CNF conversion : 0.05
% 7.10/2.63 Main loop : 0.86
% 7.10/2.63 Inferencing : 0.30
% 7.10/2.63 Reduction : 0.28
% 7.10/2.63 Demodulation : 0.18
% 7.10/2.63 BG Simplification : 0.04
% 7.10/2.63 Subsumption : 0.16
% 7.10/2.63 Abstraction : 0.03
% 7.10/2.63 MUC search : 0.00
% 7.10/2.63 Cooper : 0.00
% 7.10/2.63 Total : 1.58
% 7.10/2.63 Index Insertion : 0.00
% 7.10/2.63 Index Deletion : 0.00
% 7.10/2.63 Index Matching : 0.00
% 7.10/2.63 BG Taut test : 0.00
%------------------------------------------------------------------------------