%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG219+1 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n019.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 May 5 04:08:17 PM UTC 2026
% Result : Theorem 1.36s 1.75s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 77 ( 30 unt; 0 def)
% Number of atoms : 544 ( 39 equ)
% Maximal formula atoms : 36 ( 7 avg)
% Number of connectives : 718 ( 251 ~; 248 |; 184 &)
% ( 1 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-5 aty)
% Number of variables : 83 ( 1 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc2_vectsp_2,axiom,
! [X1] :
( l1_vectsp_1(X1)
=> ( ( ~ v3_struct_0(X1)
& v7_group_1(X1)
& v8_vectsp_1(X1) )
=> ( ~ v3_struct_0(X1)
& v2_group_1(X1)
& v6_vectsp_1(X1)
& v8_vectsp_1(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_vectsp_2) ).
fof(dt_l2_vectsp_1,axiom,
! [X1] :
( l2_vectsp_1(X1)
=> ( l1_vectsp_1(X1)
& l2_struct_0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_vectsp_1) ).
fof(dt_l3_vectsp_1,axiom,
! [X1] :
( l3_vectsp_1(X1)
=> ( l1_rlvect_1(X1)
& l2_vectsp_1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_vectsp_1) ).
fof(d4_rmod_2,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> k2_rmod_2(X1,X2) = g1_vectsp_2(X1,u1_struct_0(X2),u1_rlvect_1(X2),u2_struct_0(X2),u1_vectsp_2(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_rmod_2) ).
fof(t14_rmod_5,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v7_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& ~ v10_vectsp_1(X1)
& v2_vectsp_2(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v3_vectsp_2(X2,X1)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ( X3 = u1_struct_0(X2)
=> ( k1_rlvect_1(X1) = k2_group_1(X1)
| k1_rmod_5(X1,X2,X3) = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_rmod_5) ).
fof(dt_l1_group_1,axiom,
! [X1] :
( l1_group_1(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(dt_l1_vectsp_1,axiom,
! [X1] :
( l1_vectsp_1(X1)
=> l1_group_1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_vectsp_1) ).
fof(t13_rmod_5,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v7_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& ~ v10_vectsp_1(X1)
& v2_vectsp_2(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ! [X4] :
( ( v3_vectsp_2(X4,X1)
& m1_rmod_2(X4,X1,X2) )
=> ( X3 = u1_struct_0(X4)
=> ( k1_rlvect_1(X1) = k2_group_1(X1)
| k1_rmod_5(X1,X2,X3) = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_rmod_5) ).
fof(abstractness_v3_vectsp_2,axiom,
! [X1,X2] :
( ( l1_struct_0(X1)
& l1_vectsp_2(X2,X1) )
=> ( v3_vectsp_2(X2,X1)
=> X2 = g1_vectsp_2(X1,u1_struct_0(X2),u1_rlvect_1(X2),u2_struct_0(X2),u1_vectsp_2(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v3_vectsp_2) ).
fof(dt_k2_rmod_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& l3_vectsp_1(X1)
& ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> ( v3_vectsp_2(k2_rmod_2(X1,X2),X1)
& m1_rmod_2(k2_rmod_2(X1,X2),X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_rmod_2) ).
fof(t3_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,k1_zfmisc_1(X2))
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : r1_tarski(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(c_0_12,plain,
! [X1] :
( l1_vectsp_1(X1)
=> ( ( ~ v3_struct_0(X1)
& v7_group_1(X1)
& v8_vectsp_1(X1) )
=> ( ~ v3_struct_0(X1)
& v2_group_1(X1)
& v6_vectsp_1(X1)
& v8_vectsp_1(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc2_vectsp_2]) ).
fof(c_0_13,plain,
! [X173] :
( ( l1_vectsp_1(X173)
| ~ l2_vectsp_1(X173) )
& ( l2_struct_0(X173)
| ~ l2_vectsp_1(X173) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_vectsp_1])])]) ).
fof(c_0_14,plain,
! [X174] :
( ( l1_rlvect_1(X174)
| ~ l3_vectsp_1(X174) )
& ( l2_vectsp_1(X174)
| ~ l3_vectsp_1(X174) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_vectsp_1])])]) ).
fof(c_0_15,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> k2_rmod_2(X1,X2) = g1_vectsp_2(X1,u1_struct_0(X2),u1_rlvect_1(X2),u2_struct_0(X2),u1_vectsp_2(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[d4_rmod_2]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v7_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& ~ v10_vectsp_1(X1)
& v2_vectsp_2(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v3_vectsp_2(X2,X1)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ( X3 = u1_struct_0(X2)
=> ( k1_rlvect_1(X1) = k2_group_1(X1)
| k1_rmod_5(X1,X2,X3) = X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t14_rmod_5])]) ).
fof(c_0_17,plain,
! [X167] :
( ~ l1_group_1(X167)
| l1_struct_0(X167) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_group_1])]) ).
fof(c_0_18,plain,
! [X169] :
( ~ l1_vectsp_1(X169)
| l1_group_1(X169) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_vectsp_1])]) ).
fof(c_0_19,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v7_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& ~ v10_vectsp_1(X1)
& v2_vectsp_2(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ! [X4] :
( ( v3_vectsp_2(X4,X1)
& m1_rmod_2(X4,X1,X2) )
=> ( X3 = u1_struct_0(X4)
=> ( k1_rlvect_1(X1) = k2_group_1(X1)
| k1_rmod_5(X1,X2,X3) = X4 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t13_rmod_5]) ).
fof(c_0_20,plain,
! [X151] :
( ( ~ v3_struct_0(X151)
| v3_struct_0(X151)
| ~ v7_group_1(X151)
| ~ v8_vectsp_1(X151)
| ~ l1_vectsp_1(X151) )
& ( v2_group_1(X151)
| v3_struct_0(X151)
| ~ v7_group_1(X151)
| ~ v8_vectsp_1(X151)
| ~ l1_vectsp_1(X151) )
& ( v6_vectsp_1(X151)
| v3_struct_0(X151)
| ~ v7_group_1(X151)
| ~ v8_vectsp_1(X151)
| ~ l1_vectsp_1(X151) )
& ( v8_vectsp_1(X151)
| v3_struct_0(X151)
| ~ v7_group_1(X151)
| ~ v8_vectsp_1(X151)
| ~ l1_vectsp_1(X151) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
cnf(c_0_21,plain,
( l1_vectsp_1(X1)
| ~ l2_vectsp_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
( l2_vectsp_1(X1)
| ~ l3_vectsp_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_23,plain,
! [X153,X154] :
( v3_struct_0(X153)
| ~ v3_rlvect_1(X153)
| ~ v4_rlvect_1(X153)
| ~ v5_rlvect_1(X153)
| ~ v6_rlvect_1(X153)
| ~ v4_group_1(X153)
| ~ v6_vectsp_1(X153)
| ~ v7_vectsp_1(X153)
| ~ v8_vectsp_1(X153)
| ~ l3_vectsp_1(X153)
| v3_struct_0(X154)
| ~ v3_rlvect_1(X154)
| ~ v4_rlvect_1(X154)
| ~ v5_rlvect_1(X154)
| ~ v6_rlvect_1(X154)
| ~ v5_vectsp_2(X154,X153)
| ~ l1_vectsp_2(X154,X153)
| k2_rmod_2(X153,X154) = g1_vectsp_2(X153,u1_struct_0(X154),u1_rlvect_1(X154),u2_struct_0(X154),u1_vectsp_2(X153,X154)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
fof(c_0_24,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v3_rlvect_1(esk1_0)
& v4_rlvect_1(esk1_0)
& v5_rlvect_1(esk1_0)
& v6_rlvect_1(esk1_0)
& v4_group_1(esk1_0)
& v7_group_1(esk1_0)
& v6_vectsp_1(esk1_0)
& v7_vectsp_1(esk1_0)
& v8_vectsp_1(esk1_0)
& ~ v10_vectsp_1(esk1_0)
& v2_vectsp_2(esk1_0)
& l3_vectsp_1(esk1_0)
& ~ v3_struct_0(esk2_0)
& v3_rlvect_1(esk2_0)
& v4_rlvect_1(esk2_0)
& v5_rlvect_1(esk2_0)
& v6_rlvect_1(esk2_0)
& v3_vectsp_2(esk2_0,esk1_0)
& v5_vectsp_2(esk2_0,esk1_0)
& l1_vectsp_2(esk2_0,esk1_0)
& m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk2_0)))
& esk3_0 = u1_struct_0(esk2_0)
& k1_rlvect_1(esk1_0) != k2_group_1(esk1_0)
& k1_rmod_5(esk1_0,esk2_0,esk3_0) != esk2_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_25,plain,
! [X144,X145] :
( ~ l1_struct_0(X144)
| ~ l1_vectsp_2(X145,X144)
| ~ v3_vectsp_2(X145,X144)
| X145 = g1_vectsp_2(X144,u1_struct_0(X145),u1_rlvect_1(X145),u2_struct_0(X145),u1_vectsp_2(X144,X145)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v3_vectsp_2])]) ).
cnf(c_0_26,plain,
( l1_struct_0(X1)
| ~ l1_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
( l1_group_1(X1)
| ~ l1_vectsp_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_28,plain,
! [X249,X250,X251,X252] :
( v3_struct_0(X249)
| ~ v3_rlvect_1(X249)
| ~ v4_rlvect_1(X249)
| ~ v5_rlvect_1(X249)
| ~ v6_rlvect_1(X249)
| ~ v4_group_1(X249)
| ~ v7_group_1(X249)
| ~ v6_vectsp_1(X249)
| ~ v7_vectsp_1(X249)
| ~ v8_vectsp_1(X249)
| v10_vectsp_1(X249)
| ~ v2_vectsp_2(X249)
| ~ l3_vectsp_1(X249)
| v3_struct_0(X250)
| ~ v3_rlvect_1(X250)
| ~ v4_rlvect_1(X250)
| ~ v5_rlvect_1(X250)
| ~ v6_rlvect_1(X250)
| ~ v5_vectsp_2(X250,X249)
| ~ l1_vectsp_2(X250,X249)
| ~ m1_subset_1(X251,k1_zfmisc_1(u1_struct_0(X250)))
| ~ v3_vectsp_2(X252,X249)
| ~ m1_rmod_2(X252,X249,X250)
| X251 != u1_struct_0(X252)
| k1_rlvect_1(X249) = k2_group_1(X249)
| k1_rmod_5(X249,X250,X251) = X252 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_29,plain,
( v6_vectsp_1(X1)
| v3_struct_0(X1)
| ~ v7_group_1(X1)
| ~ v8_vectsp_1(X1)
| ~ l1_vectsp_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,plain,
( l1_vectsp_1(X1)
| ~ l3_vectsp_1(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_31,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& l3_vectsp_1(X1)
& ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> ( v3_vectsp_2(k2_rmod_2(X1,X2),X1)
& m1_rmod_2(k2_rmod_2(X1,X2),X1,X2) ) ),
inference(fof_simplification,[status(thm)],[dt_k2_rmod_2]) ).
cnf(c_0_32,plain,
( v3_struct_0(X1)
| v3_struct_0(X2)
| k2_rmod_2(X1,X2) = g1_vectsp_2(X1,u1_struct_0(X2),u1_rlvect_1(X2),u2_struct_0(X2),u1_vectsp_2(X1,X2))
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v4_group_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ l3_vectsp_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,negated_conjecture,
esk3_0 = u1_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,negated_conjecture,
v6_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_35,negated_conjecture,
v5_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_36,negated_conjecture,
v4_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_37,negated_conjecture,
v3_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_38,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_39,plain,
( X2 = g1_vectsp_2(X1,u1_struct_0(X2),u1_rlvect_1(X2),u2_struct_0(X2),u1_vectsp_2(X1,X2))
| ~ l1_struct_0(X1)
| ~ l1_vectsp_2(X2,X1)
| ~ v3_vectsp_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_40,plain,
( l1_struct_0(X1)
| ~ l1_vectsp_1(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_41,plain,
( v3_struct_0(X1)
| v10_vectsp_1(X1)
| v3_struct_0(X2)
| k1_rlvect_1(X1) = k2_group_1(X1)
| k1_rmod_5(X1,X2,X3) = X4
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v4_group_1(X1)
| ~ v7_group_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v2_vectsp_2(X1)
| ~ l3_vectsp_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ v3_vectsp_2(X4,X1)
| ~ m1_rmod_2(X4,X1,X2)
| X3 != u1_struct_0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_42,plain,
( v6_vectsp_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_group_1(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_43,plain,
! [X257,X258] :
( ( ~ m1_subset_1(X257,k1_zfmisc_1(X258))
| r1_tarski(X257,X258) )
& ( ~ r1_tarski(X257,X258)
| m1_subset_1(X257,k1_zfmisc_1(X258)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_44,plain,
! [X248] : r1_tarski(X248,X248),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(c_0_45,plain,
! [X165,X166] :
( ( v3_vectsp_2(k2_rmod_2(X165,X166),X165)
| v3_struct_0(X165)
| ~ v3_rlvect_1(X165)
| ~ v4_rlvect_1(X165)
| ~ v5_rlvect_1(X165)
| ~ v6_rlvect_1(X165)
| ~ v4_group_1(X165)
| ~ v6_vectsp_1(X165)
| ~ v7_vectsp_1(X165)
| ~ v8_vectsp_1(X165)
| ~ l3_vectsp_1(X165)
| v3_struct_0(X166)
| ~ v3_rlvect_1(X166)
| ~ v4_rlvect_1(X166)
| ~ v5_rlvect_1(X166)
| ~ v6_rlvect_1(X166)
| ~ v5_vectsp_2(X166,X165)
| ~ l1_vectsp_2(X166,X165) )
& ( m1_rmod_2(k2_rmod_2(X165,X166),X165,X166)
| v3_struct_0(X165)
| ~ v3_rlvect_1(X165)
| ~ v4_rlvect_1(X165)
| ~ v5_rlvect_1(X165)
| ~ v6_rlvect_1(X165)
| ~ v4_group_1(X165)
| ~ v6_vectsp_1(X165)
| ~ v7_vectsp_1(X165)
| ~ v8_vectsp_1(X165)
| ~ l3_vectsp_1(X165)
| v3_struct_0(X166)
| ~ v3_rlvect_1(X166)
| ~ v4_rlvect_1(X166)
| ~ v5_rlvect_1(X166)
| ~ v6_rlvect_1(X166)
| ~ v5_vectsp_2(X166,X165)
| ~ l1_vectsp_2(X166,X165) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])]) ).
cnf(c_0_46,negated_conjecture,
( g1_vectsp_2(X1,esk3_0,u1_rlvect_1(esk2_0),u2_struct_0(esk2_0),u1_vectsp_2(X1,esk2_0)) = k2_rmod_2(X1,esk2_0)
| v3_struct_0(X1)
| ~ l1_vectsp_2(esk2_0,X1)
| ~ v5_vectsp_2(esk2_0,X1)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35]),c_0_36]),c_0_37])]),c_0_38]) ).
cnf(c_0_47,negated_conjecture,
( g1_vectsp_2(X1,esk3_0,u1_rlvect_1(esk2_0),u2_struct_0(esk2_0),u1_vectsp_2(X1,esk2_0)) = esk2_0
| ~ l1_struct_0(X1)
| ~ l1_vectsp_2(esk2_0,X1)
| ~ v3_vectsp_2(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_33]) ).
cnf(c_0_48,plain,
( l1_struct_0(X1)
| ~ l3_vectsp_1(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_30]) ).
cnf(c_0_49,negated_conjecture,
( k1_rmod_5(X1,esk2_0,X2) = X3
| k2_group_1(X1) = k1_rlvect_1(X1)
| v10_vectsp_1(X1)
| v3_struct_0(X1)
| X2 != u1_struct_0(X3)
| ~ m1_rmod_2(X3,X1,esk2_0)
| ~ m1_subset_1(X2,k1_zfmisc_1(esk3_0))
| ~ l1_vectsp_2(esk2_0,X1)
| ~ v5_vectsp_2(esk2_0,X1)
| ~ v3_vectsp_2(X3,X1)
| ~ l3_vectsp_1(X1)
| ~ v2_vectsp_2(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v7_group_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_33]),c_0_34]),c_0_35]),c_0_36]),c_0_37])]),c_0_38]),c_0_42]) ).
cnf(c_0_50,negated_conjecture,
v3_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_51,negated_conjecture,
l1_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_52,negated_conjecture,
v5_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_53,negated_conjecture,
l3_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_54,negated_conjecture,
v2_vectsp_2(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_55,negated_conjecture,
v8_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_56,negated_conjecture,
v7_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_57,negated_conjecture,
v7_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_58,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_59,negated_conjecture,
v6_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_60,negated_conjecture,
v5_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_61,negated_conjecture,
v4_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_62,negated_conjecture,
v3_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_63,negated_conjecture,
k1_rlvect_1(esk1_0) != k2_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_64,negated_conjecture,
~ v10_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_65,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_66,plain,
( m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_67,plain,
r1_tarski(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_68,plain,
( m1_rmod_2(k2_rmod_2(X1,X2),X1,X2)
| v3_struct_0(X1)
| v3_struct_0(X2)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v4_group_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ l3_vectsp_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_69,negated_conjecture,
( k2_rmod_2(X1,esk2_0) = esk2_0
| v3_struct_0(X1)
| ~ l1_vectsp_2(esk2_0,X1)
| ~ v5_vectsp_2(esk2_0,X1)
| ~ v3_vectsp_2(esk2_0,X1)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_70,negated_conjecture,
k1_rmod_5(esk1_0,esk2_0,esk3_0) != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_71,negated_conjecture,
( k1_rmod_5(esk1_0,esk2_0,X1) = esk2_0
| X1 != esk3_0
| ~ m1_rmod_2(esk2_0,esk1_0,esk2_0)
| ~ m1_subset_1(X1,k1_zfmisc_1(esk3_0)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_33]),c_0_51]),c_0_52]),c_0_53]),c_0_54]),c_0_55]),c_0_56]),c_0_57]),c_0_58]),c_0_59]),c_0_60]),c_0_61]),c_0_62])]),c_0_63]),c_0_64]),c_0_65]) ).
cnf(c_0_72,plain,
m1_subset_1(X1,k1_zfmisc_1(X1)),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_73,negated_conjecture,
( m1_rmod_2(esk2_0,X1,esk2_0)
| v3_struct_0(X1)
| ~ l1_vectsp_2(esk2_0,X1)
| ~ v5_vectsp_2(esk2_0,X1)
| ~ v3_vectsp_2(esk2_0,X1)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_34]),c_0_35]),c_0_36]),c_0_37])]),c_0_38]) ).
cnf(c_0_74,negated_conjecture,
v6_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_75,negated_conjecture,
~ m1_rmod_2(esk2_0,esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72])]) ).
cnf(c_0_76,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_50]),c_0_51]),c_0_52]),c_0_53]),c_0_55]),c_0_56]),c_0_74]),c_0_58]),c_0_59]),c_0_60]),c_0_61]),c_0_62])]),c_0_75]),c_0_65]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ALG219+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n019.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 10:27:00 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.36/1.75 % Version : CSE_E---1.7
% 1.36/1.75 % Problem : theBenchmark.p
% 1.36/1.75 % SZS status Theorem for theBenchmark.p
% 1.36/1.75 % SZS output start CNFRefutation
% See solution above
% 1.36/1.75 % Total time : 1.371s
%------------------------------------------------------------------------------