%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG214+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 : n023.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 49.06s 28.72s
% Output : CNFRefutation 49.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 46 ( 27 unt; 0 def)
% Number of atoms : 463 ( 17 equ)
% Maximal formula atoms : 82 ( 10 avg)
% Number of connectives : 672 ( 255 ~; 267 |; 116 &)
% ( 2 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 62 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t25_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_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))
=> ! [X5] :
( m2_rmod_4(X5,X1,X2,X3)
=> ( r1_tarski(X3,X4)
=> m2_rmod_4(X5,X1,X2,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_rmod_4) ).
fof(t2_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) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))
=> ( ( r1_tarski(X3,X4)
& v1_rmod_5(X4,X1,X2) )
=> v1_rmod_5(X3,X1,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_rmod_5) ).
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(c_0_3,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_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))
=> ! [X5] :
( m2_rmod_4(X5,X1,X2,X3)
=> ( r1_tarski(X3,X4)
=> m2_rmod_4(X5,X1,X2,X4) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t25_rmod_4]) ).
fof(c_0_4,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) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))
=> ( ( r1_tarski(X3,X4)
& v1_rmod_5(X4,X1,X2) )
=> v1_rmod_5(X3,X1,X2) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t2_rmod_5])]) ).
fof(c_0_5,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]) ).
fof(c_0_6,plain,
! [X280,X281,X282,X283,X284] :
( v3_struct_0(X280)
| ~ v3_rlvect_1(X280)
| ~ v4_rlvect_1(X280)
| ~ v5_rlvect_1(X280)
| ~ v6_rlvect_1(X280)
| ~ v4_group_1(X280)
| ~ v6_vectsp_1(X280)
| ~ v7_vectsp_1(X280)
| ~ v8_vectsp_1(X280)
| ~ l3_vectsp_1(X280)
| v3_struct_0(X281)
| ~ v3_rlvect_1(X281)
| ~ v4_rlvect_1(X281)
| ~ v5_rlvect_1(X281)
| ~ v6_rlvect_1(X281)
| ~ v5_vectsp_2(X281,X280)
| ~ l1_vectsp_2(X281,X280)
| ~ m1_subset_1(X282,k1_zfmisc_1(u1_struct_0(X281)))
| ~ m1_subset_1(X283,k1_zfmisc_1(u1_struct_0(X281)))
| ~ m2_rmod_4(X284,X280,X281,X282)
| ~ r1_tarski(X282,X283)
| m2_rmod_4(X284,X280,X281,X283) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_7,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)
& m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk2_0)))
& m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk2_0)))
& r1_tarski(esk3_0,esk4_0)
& v1_rmod_5(esk4_0,esk1_0,esk2_0)
& ~ v1_rmod_5(esk3_0,esk1_0,esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_8,plain,
! [X163,X164,X165,X166] :
( ( ~ v1_rmod_5(X165,X163,X164)
| ~ m2_rmod_4(X166,X163,X164,X165)
| k5_rmod_4(X163,X164,X166) != k1_rlvect_1(X164)
| k2_rmod_4(X163,X164,X166) = k1_xboole_0
| ~ m1_subset_1(X165,k1_zfmisc_1(u1_struct_0(X164)))
| v3_struct_0(X164)
| ~ v3_rlvect_1(X164)
| ~ v4_rlvect_1(X164)
| ~ v5_rlvect_1(X164)
| ~ v6_rlvect_1(X164)
| ~ v5_vectsp_2(X164,X163)
| ~ l1_vectsp_2(X164,X163)
| v3_struct_0(X163)
| ~ v3_rlvect_1(X163)
| ~ v4_rlvect_1(X163)
| ~ v5_rlvect_1(X163)
| ~ v6_rlvect_1(X163)
| ~ v4_group_1(X163)
| ~ v6_vectsp_1(X163)
| ~ v7_vectsp_1(X163)
| ~ v8_vectsp_1(X163)
| ~ l3_vectsp_1(X163) )
& ( m2_rmod_4(esk5_3(X163,X164,X165),X163,X164,X165)
| v1_rmod_5(X165,X163,X164)
| ~ m1_subset_1(X165,k1_zfmisc_1(u1_struct_0(X164)))
| v3_struct_0(X164)
| ~ v3_rlvect_1(X164)
| ~ v4_rlvect_1(X164)
| ~ v5_rlvect_1(X164)
| ~ v6_rlvect_1(X164)
| ~ v5_vectsp_2(X164,X163)
| ~ l1_vectsp_2(X164,X163)
| v3_struct_0(X163)
| ~ v3_rlvect_1(X163)
| ~ v4_rlvect_1(X163)
| ~ v5_rlvect_1(X163)
| ~ v6_rlvect_1(X163)
| ~ v4_group_1(X163)
| ~ v6_vectsp_1(X163)
| ~ v7_vectsp_1(X163)
| ~ v8_vectsp_1(X163)
| ~ l3_vectsp_1(X163) )
& ( k5_rmod_4(X163,X164,esk5_3(X163,X164,X165)) = k1_rlvect_1(X164)
| v1_rmod_5(X165,X163,X164)
| ~ m1_subset_1(X165,k1_zfmisc_1(u1_struct_0(X164)))
| v3_struct_0(X164)
| ~ v3_rlvect_1(X164)
| ~ v4_rlvect_1(X164)
| ~ v5_rlvect_1(X164)
| ~ v6_rlvect_1(X164)
| ~ v5_vectsp_2(X164,X163)
| ~ l1_vectsp_2(X164,X163)
| v3_struct_0(X163)
| ~ v3_rlvect_1(X163)
| ~ v4_rlvect_1(X163)
| ~ v5_rlvect_1(X163)
| ~ v6_rlvect_1(X163)
| ~ v4_group_1(X163)
| ~ v6_vectsp_1(X163)
| ~ v7_vectsp_1(X163)
| ~ v8_vectsp_1(X163)
| ~ l3_vectsp_1(X163) )
& ( k2_rmod_4(X163,X164,esk5_3(X163,X164,X165)) != k1_xboole_0
| v1_rmod_5(X165,X163,X164)
| ~ m1_subset_1(X165,k1_zfmisc_1(u1_struct_0(X164)))
| v3_struct_0(X164)
| ~ v3_rlvect_1(X164)
| ~ v4_rlvect_1(X164)
| ~ v5_rlvect_1(X164)
| ~ v6_rlvect_1(X164)
| ~ v5_vectsp_2(X164,X163)
| ~ l1_vectsp_2(X164,X163)
| v3_struct_0(X163)
| ~ v3_rlvect_1(X163)
| ~ v4_rlvect_1(X163)
| ~ v5_rlvect_1(X163)
| ~ v6_rlvect_1(X163)
| ~ v4_group_1(X163)
| ~ v6_vectsp_1(X163)
| ~ v7_vectsp_1(X163)
| ~ v8_vectsp_1(X163)
| ~ l3_vectsp_1(X163) ) ),
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_5])])])])]) ).
cnf(c_0_9,plain,
( v3_struct_0(X1)
| v3_struct_0(X2)
| m2_rmod_4(X5,X1,X2,X4)
| ~ 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)))
| ~ m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))
| ~ m2_rmod_4(X5,X1,X2,X3)
| ~ r1_tarski(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
v6_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
v5_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
v4_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
v3_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,plain,
( m2_rmod_4(esk5_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_8]) ).
cnf(c_0_17,negated_conjecture,
m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,negated_conjecture,
( m2_rmod_4(X1,X2,esk2_0,esk4_0)
| v3_struct_0(X2)
| ~ m2_rmod_4(X1,X2,esk2_0,X3)
| ~ r1_tarski(X3,esk4_0)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(esk2_0)))
| ~ l1_vectsp_2(esk2_0,X2)
| ~ v5_vectsp_2(esk2_0,X2)
| ~ l3_vectsp_1(X2)
| ~ v8_vectsp_1(X2)
| ~ v7_vectsp_1(X2)
| ~ v6_vectsp_1(X2)
| ~ v4_group_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2) ),
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_9,c_0_10]),c_0_11]),c_0_12]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_19,negated_conjecture,
r1_tarski(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,negated_conjecture,
( m2_rmod_4(esk5_3(X1,esk2_0,esk3_0),X1,esk2_0,esk3_0)
| v1_rmod_5(esk3_0,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_16,c_0_17]),c_0_11]),c_0_12]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_21,negated_conjecture,
l1_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,negated_conjecture,
v5_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,negated_conjecture,
l3_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,negated_conjecture,
v8_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_25,negated_conjecture,
v7_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_26,negated_conjecture,
v6_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_27,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_28,negated_conjecture,
v6_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_29,negated_conjecture,
v5_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_30,negated_conjecture,
v4_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_31,negated_conjecture,
v3_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_32,negated_conjecture,
~ v1_rmod_5(esk3_0,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_33,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_34,plain,
( k5_rmod_4(X1,X2,esk5_3(X1,X2,X3)) = k1_rlvect_1(X2)
| 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_8]) ).
cnf(c_0_35,plain,
( k2_rmod_4(X2,X3,X4) = k1_xboole_0
| v3_struct_0(X3)
| v3_struct_0(X2)
| ~ v1_rmod_5(X1,X2,X3)
| ~ m2_rmod_4(X4,X2,X3,X1)
| k5_rmod_4(X2,X3,X4) != k1_rlvect_1(X3)
| ~ m1_subset_1(X1,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_8]) ).
cnf(c_0_36,negated_conjecture,
( m2_rmod_4(X1,X2,esk2_0,esk4_0)
| v3_struct_0(X2)
| ~ m2_rmod_4(X1,X2,esk2_0,esk3_0)
| ~ l1_vectsp_2(esk2_0,X2)
| ~ v5_vectsp_2(esk2_0,X2)
| ~ l3_vectsp_1(X2)
| ~ v8_vectsp_1(X2)
| ~ v7_vectsp_1(X2)
| ~ v6_vectsp_1(X2)
| ~ v4_group_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_17]),c_0_19])]) ).
cnf(c_0_37,negated_conjecture,
m2_rmod_4(esk5_3(esk1_0,esk2_0,esk3_0),esk1_0,esk2_0,esk3_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(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23]),c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_28]),c_0_29]),c_0_30]),c_0_31])]),c_0_32]),c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( k5_rmod_4(X1,esk2_0,esk5_3(X1,esk2_0,esk3_0)) = k1_rlvect_1(esk2_0)
| v1_rmod_5(esk3_0,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_34,c_0_17]),c_0_11]),c_0_12]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_39,negated_conjecture,
( k2_rmod_4(X1,esk2_0,X2) = k1_xboole_0
| v3_struct_0(X1)
| k5_rmod_4(X1,esk2_0,X2) != k1_rlvect_1(esk2_0)
| ~ m2_rmod_4(X2,X1,esk2_0,esk4_0)
| ~ v1_rmod_5(esk4_0,X1,esk2_0)
| ~ 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_35,c_0_10]),c_0_11]),c_0_12]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_40,negated_conjecture,
m2_rmod_4(esk5_3(esk1_0,esk2_0,esk3_0),esk1_0,esk2_0,esk4_0),
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_36,c_0_37]),c_0_21]),c_0_22]),c_0_23]),c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_28]),c_0_29]),c_0_30]),c_0_31])]),c_0_33]) ).
cnf(c_0_41,negated_conjecture,
k5_rmod_4(esk1_0,esk2_0,esk5_3(esk1_0,esk2_0,esk3_0)) = k1_rlvect_1(esk2_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(spm,[status(thm)],[c_0_38,c_0_21]),c_0_22]),c_0_23]),c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_28]),c_0_29]),c_0_30]),c_0_31])]),c_0_32]),c_0_33]) ).
cnf(c_0_42,negated_conjecture,
v1_rmod_5(esk4_0,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_43,plain,
( v1_rmod_5(X3,X1,X2)
| v3_struct_0(X2)
| v3_struct_0(X1)
| k2_rmod_4(X1,X2,esk5_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_8]) ).
cnf(c_0_44,negated_conjecture,
k2_rmod_4(esk1_0,esk2_0,esk5_3(esk1_0,esk2_0,esk3_0)) = k1_xboole_0,
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_39,c_0_40]),c_0_41]),c_0_42]),c_0_21]),c_0_22]),c_0_23]),c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_28]),c_0_29]),c_0_30]),c_0_31])]),c_0_33]) ).
cnf(c_0_45,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_43,c_0_44]),c_0_17]),c_0_21]),c_0_22]),c_0_23]),c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_11]),c_0_28]),c_0_12]),c_0_29]),c_0_13]),c_0_30]),c_0_14]),c_0_31])]),c_0_32]),c_0_15]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG214+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
% 0.17/0.33 % Computer : n023.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 10:25:23 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 49.06/28.72 % Version : CSE_E---1.7
% 49.06/28.72 % Problem : theBenchmark.p
% 49.06/28.72 % SZS status Theorem for theBenchmark.p
% 49.06/28.72 % SZS output start CNFRefutation
% See solution above
% 49.26/28.90 % Total time : 21.419s
%------------------------------------------------------------------------------