%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG215+1 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.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 04:08:15 PM UTC 2026
% Result : Theorem 2.16s 1.95s
% Output : CNFRefutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 27 unt; 0 def)
% Number of atoms : 506 ( 17 equ)
% Maximal formula atoms : 82 ( 9 avg)
% Number of connectives : 717 ( 265 ~; 273 |; 147 &)
% ( 4 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 75 ( 3 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t6_boole,axiom,
! [X1] :
( v1_xboole_0(X1)
=> X1 = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(dt_k1_subset_1,axiom,
! [X1] :
( v1_xboole_0(k1_subset_1(X1))
& m1_subset_1(k1_subset_1(X1),k1_zfmisc_1(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_subset_1) ).
fof(d7_rmod_4,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) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ! [X4] :
( m1_rmod_4(X4,X1,X2)
=> ( m2_rmod_4(X4,X1,X2,X3)
<=> r1_tarski(k2_rmod_4(X1,X2,X4),X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_rmod_4) ).
fof(dt_m2_rmod_4,axiom,
! [X1,X2,X3] :
( ( ~ 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)
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2))) )
=> ! [X4] :
( m2_rmod_4(X4,X1,X2,X3)
=> m1_rmod_4(X4,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_rmod_4) ).
fof(d1_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)
& 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) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ( v1_rmod_5(X3,X1,X2)
<=> ! [X4] :
( m2_rmod_4(X4,X1,X2,X3)
=> ( k5_rmod_4(X1,X2,X4) = k1_rlvect_1(X2)
=> k2_rmod_4(X1,X2,X4) = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_rmod_5) ).
fof(t4_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)
& 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) )
=> v1_rmod_5(k1_subset_1(u1_struct_0(X2)),X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_rmod_5) ).
fof(t3_xboole_1,axiom,
! [X1] :
( r1_tarski(X1,k1_xboole_0)
=> X1 = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(c_0_7,plain,
! [X296] :
( ~ v1_xboole_0(X296)
| X296 = k1_xboole_0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_8,plain,
! [X175] :
( v1_xboole_0(k1_subset_1(X175))
& m1_subset_1(k1_subset_1(X175),k1_zfmisc_1(X175)) ),
inference(variable_rename,[status(thm)],[dt_k1_subset_1]) ).
fof(c_0_9,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) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ! [X4] :
( m1_rmod_4(X4,X1,X2)
=> ( m2_rmod_4(X4,X1,X2,X3)
<=> r1_tarski(k2_rmod_4(X1,X2,X4),X3) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d7_rmod_4]) ).
fof(c_0_10,plain,
! [X1,X2,X3] :
( ( ~ 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)
& m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2))) )
=> ! [X4] :
( m2_rmod_4(X4,X1,X2,X3)
=> m1_rmod_4(X4,X1,X2) ) ),
inference(fof_simplification,[status(thm)],[dt_m2_rmod_4]) ).
fof(c_0_11,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) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ( v1_rmod_5(X3,X1,X2)
<=> ! [X4] :
( m2_rmod_4(X4,X1,X2,X3)
=> ( k5_rmod_4(X1,X2,X4) = k1_rlvect_1(X2)
=> k2_rmod_4(X1,X2,X4) = k1_xboole_0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[d1_rmod_5]) ).
cnf(c_0_12,plain,
( X1 = k1_xboole_0
| ~ v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
v1_xboole_0(k1_subset_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_14,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)
& 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) )
=> v1_rmod_5(k1_subset_1(u1_struct_0(X2)),X1,X2) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t4_rmod_5])]) ).
fof(c_0_15,plain,
! [X168,X169,X170,X171] :
( ( ~ m2_rmod_4(X171,X168,X169,X170)
| r1_tarski(k2_rmod_4(X168,X169,X171),X170)
| ~ m1_rmod_4(X171,X168,X169)
| ~ m1_subset_1(X170,k1_zfmisc_1(u1_struct_0(X169)))
| v3_struct_0(X169)
| ~ v3_rlvect_1(X169)
| ~ v4_rlvect_1(X169)
| ~ v5_rlvect_1(X169)
| ~ v6_rlvect_1(X169)
| ~ v5_vectsp_2(X169,X168)
| ~ l1_vectsp_2(X169,X168)
| v3_struct_0(X168)
| ~ v3_rlvect_1(X168)
| ~ v4_rlvect_1(X168)
| ~ v5_rlvect_1(X168)
| ~ v6_rlvect_1(X168)
| ~ v4_group_1(X168)
| ~ v6_vectsp_1(X168)
| ~ v7_vectsp_1(X168)
| ~ v8_vectsp_1(X168)
| ~ l3_vectsp_1(X168) )
& ( ~ r1_tarski(k2_rmod_4(X168,X169,X171),X170)
| m2_rmod_4(X171,X168,X169,X170)
| ~ m1_rmod_4(X171,X168,X169)
| ~ m1_subset_1(X170,k1_zfmisc_1(u1_struct_0(X169)))
| v3_struct_0(X169)
| ~ v3_rlvect_1(X169)
| ~ v4_rlvect_1(X169)
| ~ v5_rlvect_1(X169)
| ~ v6_rlvect_1(X169)
| ~ v5_vectsp_2(X169,X168)
| ~ l1_vectsp_2(X169,X168)
| v3_struct_0(X168)
| ~ v3_rlvect_1(X168)
| ~ v4_rlvect_1(X168)
| ~ v5_rlvect_1(X168)
| ~ v6_rlvect_1(X168)
| ~ v4_group_1(X168)
| ~ v6_vectsp_1(X168)
| ~ v7_vectsp_1(X168)
| ~ v8_vectsp_1(X168)
| ~ l3_vectsp_1(X168) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_16,plain,
! [X207,X208,X209,X210] :
( v3_struct_0(X207)
| ~ v3_rlvect_1(X207)
| ~ v4_rlvect_1(X207)
| ~ v5_rlvect_1(X207)
| ~ v6_rlvect_1(X207)
| ~ v4_group_1(X207)
| ~ v6_vectsp_1(X207)
| ~ v7_vectsp_1(X207)
| ~ v8_vectsp_1(X207)
| ~ l3_vectsp_1(X207)
| v3_struct_0(X208)
| ~ v3_rlvect_1(X208)
| ~ v4_rlvect_1(X208)
| ~ v5_rlvect_1(X208)
| ~ v6_rlvect_1(X208)
| ~ v5_vectsp_2(X208,X207)
| ~ l1_vectsp_2(X208,X207)
| ~ m1_subset_1(X209,k1_zfmisc_1(u1_struct_0(X208)))
| ~ m2_rmod_4(X210,X207,X208,X209)
| m1_rmod_4(X210,X207,X208) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_17,plain,
! [X160,X161,X162,X163] :
( ( ~ v1_rmod_5(X162,X160,X161)
| ~ m2_rmod_4(X163,X160,X161,X162)
| k5_rmod_4(X160,X161,X163) != k1_rlvect_1(X161)
| k2_rmod_4(X160,X161,X163) = k1_xboole_0
| ~ m1_subset_1(X162,k1_zfmisc_1(u1_struct_0(X161)))
| v3_struct_0(X161)
| ~ v3_rlvect_1(X161)
| ~ v4_rlvect_1(X161)
| ~ v5_rlvect_1(X161)
| ~ v6_rlvect_1(X161)
| ~ v5_vectsp_2(X161,X160)
| ~ l1_vectsp_2(X161,X160)
| v3_struct_0(X160)
| ~ v3_rlvect_1(X160)
| ~ v4_rlvect_1(X160)
| ~ v5_rlvect_1(X160)
| ~ v6_rlvect_1(X160)
| ~ v4_group_1(X160)
| ~ v6_vectsp_1(X160)
| ~ v7_vectsp_1(X160)
| ~ v8_vectsp_1(X160)
| ~ l3_vectsp_1(X160) )
& ( m2_rmod_4(esk3_3(X160,X161,X162),X160,X161,X162)
| v1_rmod_5(X162,X160,X161)
| ~ m1_subset_1(X162,k1_zfmisc_1(u1_struct_0(X161)))
| v3_struct_0(X161)
| ~ v3_rlvect_1(X161)
| ~ v4_rlvect_1(X161)
| ~ v5_rlvect_1(X161)
| ~ v6_rlvect_1(X161)
| ~ v5_vectsp_2(X161,X160)
| ~ l1_vectsp_2(X161,X160)
| v3_struct_0(X160)
| ~ v3_rlvect_1(X160)
| ~ v4_rlvect_1(X160)
| ~ v5_rlvect_1(X160)
| ~ v6_rlvect_1(X160)
| ~ v4_group_1(X160)
| ~ v6_vectsp_1(X160)
| ~ v7_vectsp_1(X160)
| ~ v8_vectsp_1(X160)
| ~ l3_vectsp_1(X160) )
& ( k5_rmod_4(X160,X161,esk3_3(X160,X161,X162)) = k1_rlvect_1(X161)
| v1_rmod_5(X162,X160,X161)
| ~ m1_subset_1(X162,k1_zfmisc_1(u1_struct_0(X161)))
| v3_struct_0(X161)
| ~ v3_rlvect_1(X161)
| ~ v4_rlvect_1(X161)
| ~ v5_rlvect_1(X161)
| ~ v6_rlvect_1(X161)
| ~ v5_vectsp_2(X161,X160)
| ~ l1_vectsp_2(X161,X160)
| v3_struct_0(X160)
| ~ v3_rlvect_1(X160)
| ~ v4_rlvect_1(X160)
| ~ v5_rlvect_1(X160)
| ~ v6_rlvect_1(X160)
| ~ v4_group_1(X160)
| ~ v6_vectsp_1(X160)
| ~ v7_vectsp_1(X160)
| ~ v8_vectsp_1(X160)
| ~ l3_vectsp_1(X160) )
& ( k2_rmod_4(X160,X161,esk3_3(X160,X161,X162)) != k1_xboole_0
| v1_rmod_5(X162,X160,X161)
| ~ m1_subset_1(X162,k1_zfmisc_1(u1_struct_0(X161)))
| v3_struct_0(X161)
| ~ v3_rlvect_1(X161)
| ~ v4_rlvect_1(X161)
| ~ v5_rlvect_1(X161)
| ~ v6_rlvect_1(X161)
| ~ v5_vectsp_2(X161,X160)
| ~ l1_vectsp_2(X161,X160)
| v3_struct_0(X160)
| ~ v3_rlvect_1(X160)
| ~ v4_rlvect_1(X160)
| ~ v5_rlvect_1(X160)
| ~ v6_rlvect_1(X160)
| ~ v4_group_1(X160)
| ~ v6_vectsp_1(X160)
| ~ v7_vectsp_1(X160)
| ~ v8_vectsp_1(X160)
| ~ l3_vectsp_1(X160) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])]) ).
cnf(c_0_18,plain,
m1_subset_1(k1_subset_1(X1),k1_zfmisc_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,plain,
k1_subset_1(X1) = k1_xboole_0,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_20,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)
& v6_vectsp_1(esk1_0)
& v7_vectsp_1(esk1_0)
& v8_vectsp_1(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)
& v5_vectsp_2(esk2_0,esk1_0)
& l1_vectsp_2(esk2_0,esk1_0)
& ~ v1_rmod_5(k1_subset_1(u1_struct_0(esk2_0)),esk1_0,esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
cnf(c_0_21,plain,
( r1_tarski(k2_rmod_4(X2,X3,X1),X4)
| v3_struct_0(X3)
| v3_struct_0(X2)
| ~ m2_rmod_4(X1,X2,X3,X4)
| ~ m1_rmod_4(X1,X2,X3)
| ~ m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X3)))
| ~ v3_rlvect_1(X3)
| ~ v4_rlvect_1(X3)
| ~ v5_rlvect_1(X3)
| ~ v6_rlvect_1(X3)
| ~ v5_vectsp_2(X3,X2)
| ~ l1_vectsp_2(X3,X2)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v4_group_1(X2)
| ~ v6_vectsp_1(X2)
| ~ v7_vectsp_1(X2)
| ~ v8_vectsp_1(X2)
| ~ l3_vectsp_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( v3_struct_0(X1)
| v3_struct_0(X2)
| m1_rmod_4(X4,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)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ m2_rmod_4(X4,X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( m2_rmod_4(esk3_3(X1,X2,X3),X1,X2,X3)
| v1_rmod_5(X3,X1,X2)
| v3_struct_0(X2)
| v3_struct_0(X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_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_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) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
m1_subset_1(k1_xboole_0,k1_zfmisc_1(X1)),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,negated_conjecture,
~ v1_rmod_5(k1_subset_1(u1_struct_0(esk2_0)),esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
( r1_tarski(k2_rmod_4(X1,X2,X3),X4)
| v3_struct_0(X1)
| v3_struct_0(X2)
| ~ m2_rmod_4(X3,X1,X2,X4)
| ~ m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X1) ),
inference(csr,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( m2_rmod_4(esk3_3(X1,X2,k1_xboole_0),X1,X2,k1_xboole_0)
| v1_rmod_5(k1_xboole_0,X1,X2)
| v3_struct_0(X1)
| v3_struct_0(X2)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,negated_conjecture,
l1_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,negated_conjecture,
v5_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,negated_conjecture,
l3_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31,negated_conjecture,
v8_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,negated_conjecture,
v7_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_33,negated_conjecture,
v6_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_34,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_35,negated_conjecture,
v6_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_36,negated_conjecture,
v6_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_37,negated_conjecture,
v5_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_38,negated_conjecture,
v5_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_39,negated_conjecture,
v4_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_40,negated_conjecture,
v4_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_41,negated_conjecture,
v3_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_42,negated_conjecture,
v3_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_43,negated_conjecture,
~ v1_rmod_5(k1_xboole_0,esk1_0,esk2_0),
inference(rw,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_44,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_45,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_46,plain,
! [X289] :
( ~ r1_tarski(X289,k1_xboole_0)
| X289 = k1_xboole_0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
cnf(c_0_47,plain,
( r1_tarski(k2_rmod_4(X1,X2,X3),k1_xboole_0)
| v3_struct_0(X1)
| v3_struct_0(X2)
| ~ m2_rmod_4(X3,X1,X2,k1_xboole_0)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_48,negated_conjecture,
m2_rmod_4(esk3_3(esk1_0,esk2_0,k1_xboole_0),esk1_0,esk2_0,k1_xboole_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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32]),c_0_33]),c_0_34]),c_0_35]),c_0_36]),c_0_37]),c_0_38]),c_0_39]),c_0_40]),c_0_41]),c_0_42])]),c_0_43]),c_0_44]),c_0_45]) ).
cnf(c_0_49,plain,
( X1 = k1_xboole_0
| ~ r1_tarski(X1,k1_xboole_0) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_50,negated_conjecture,
r1_tarski(k2_rmod_4(esk1_0,esk2_0,esk3_3(esk1_0,esk2_0,k1_xboole_0)),k1_xboole_0),
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32]),c_0_33]),c_0_34]),c_0_35]),c_0_36]),c_0_37]),c_0_38]),c_0_39]),c_0_40]),c_0_41]),c_0_42])]),c_0_44]),c_0_45]) ).
cnf(c_0_51,plain,
( v1_rmod_5(X3,X1,X2)
| v3_struct_0(X2)
| v3_struct_0(X1)
| k2_rmod_4(X1,X2,esk3_3(X1,X2,X3)) != k1_xboole_0
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_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_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) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_52,negated_conjecture,
k2_rmod_4(esk1_0,esk2_0,esk3_3(esk1_0,esk2_0,k1_xboole_0)) = k1_xboole_0,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
$false,
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_24]),c_0_28]),c_0_29]),c_0_30]),c_0_31]),c_0_32]),c_0_33]),c_0_34]),c_0_35]),c_0_36]),c_0_37]),c_0_38]),c_0_39]),c_0_40]),c_0_41]),c_0_42])]),c_0_43]),c_0_45]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG215+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n027.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 10:24:50 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.16/1.95 % Version : CSE_E---1.7
% 2.16/1.95 % Problem : theBenchmark.p
% 2.16/1.95 % SZS status Theorem for theBenchmark.p
% 2.16/1.95 % SZS output start CNFRefutation
% See solution above
% 2.16/1.95 % Total time : 1.371s
%------------------------------------------------------------------------------