%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ALG214+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:01:39 PM UTC 2026
% Result : Theorem 1.55s 0.57s
% Output : CNFRefutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 48 ( 27 unt; 0 def)
% Number of atoms : 487 ( 19 equ)
% Maximal formula atoms : 82 ( 10 avg)
% Number of connectives : 698 ( 259 ~; 268 |; 132 &)
% ( 2 <=>; 37 =>; 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 : 66 ( 0 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t2_rmod_5,conjecture,
! [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)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_vectsp_2(X2,X1)
& v5_vectsp_2(X2,X1)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))
=> ( ( v1_rmod_5(X4,X1,X2)
& r1_tarski(X3,X4) )
=> v1_rmod_5(X3,X1,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_rmod_5) ).
fof(t25_rmod_4,axiom,
! [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)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_vectsp_2(X2,X1)
& v5_vectsp_2(X2,X1)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) )
=> ! [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/sandbox2/benchmark/theBenchmark.p',t25_rmod_4) ).
fof(d1_rmod_5,axiom,
! [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)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_vectsp_2(X2,X1)
& v5_vectsp_2(X2,X1)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) )
=> ! [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/sandbox2/benchmark/theBenchmark.p',d1_rmod_5) ).
fof(c_0_3,negated_conjecture,
~ ! [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)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_vectsp_2(X2,X1)
& v5_vectsp_2(X2,X1)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))
=> ( ( v1_rmod_5(X4,X1,X2)
& r1_tarski(X3,X4) )
=> v1_rmod_5(X3,X1,X2) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t2_rmod_5]) ).
fof(c_0_4,plain,
! [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)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_vectsp_2(X2,X1)
& v5_vectsp_2(X2,X1)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) )
=> ! [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_5,negated_conjecture,
~ ! [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)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_vectsp_2(X2,X1)
& v5_vectsp_2(X2,X1)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))
=> ( ( v1_rmod_5(X4,X1,X2)
& r1_tarski(X3,X4) )
=> v1_rmod_5(X3,X1,X2) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_6,plain,
! [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)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_vectsp_2(X2,X1)
& v5_vectsp_2(X2,X1)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) )
=> ! [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_7,plain,
! [X132,X133,X134,X135,X136] :
( m2_rmod_4(X136,X132,X133,X135)
| ~ r1_tarski(X134,X135)
| ~ m2_rmod_4(X136,X132,X133,X134)
| ~ m1_subset_1(X135,k1_zfmisc_1(u1_struct_0(X133)))
| ~ m1_subset_1(X134,k1_zfmisc_1(u1_struct_0(X133)))
| ~ l1_vectsp_2(X133,X132)
| ~ v5_vectsp_2(X133,X132)
| ~ v6_rlvect_1(X133)
| ~ v5_rlvect_1(X133)
| ~ v4_rlvect_1(X133)
| ~ v3_rlvect_1(X133)
| v3_struct_0(X133)
| ~ l3_vectsp_1(X132)
| ~ v8_vectsp_1(X132)
| ~ v7_vectsp_1(X132)
| ~ v6_vectsp_1(X132)
| ~ v4_group_1(X132)
| ~ v6_rlvect_1(X132)
| ~ v5_rlvect_1(X132)
| ~ v4_rlvect_1(X132)
| ~ v3_rlvect_1(X132)
| v3_struct_0(X132) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_8,negated_conjecture,
( ~ v1_rmod_5(esk3_0,esk1_0,esk2_0)
& v1_rmod_5(esk4_0,esk1_0,esk2_0)
& r1_tarski(esk3_0,esk4_0)
& m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk2_0)))
& m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk2_0)))
& l1_vectsp_2(esk2_0,esk1_0)
& v5_vectsp_2(esk2_0,esk1_0)
& v6_rlvect_1(esk2_0)
& v5_rlvect_1(esk2_0)
& v4_rlvect_1(esk2_0)
& v3_rlvect_1(esk2_0)
& ~ v3_struct_0(esk2_0)
& l3_vectsp_1(esk1_0)
& v8_vectsp_1(esk1_0)
& v7_vectsp_1(esk1_0)
& v6_vectsp_1(esk1_0)
& v4_group_1(esk1_0)
& v6_rlvect_1(esk1_0)
& v5_rlvect_1(esk1_0)
& v4_rlvect_1(esk1_0)
& v3_rlvect_1(esk1_0)
& ~ v3_struct_0(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_9,plain,
! [X15,X16,X17,X18] :
( ( ~ l3_vectsp_1(X15)
| ~ v8_vectsp_1(X15)
| ~ v7_vectsp_1(X15)
| ~ v6_vectsp_1(X15)
| ~ v4_group_1(X15)
| ~ v6_rlvect_1(X15)
| ~ v5_rlvect_1(X15)
| ~ v4_rlvect_1(X15)
| ~ v3_rlvect_1(X15)
| v3_struct_0(X15)
| ~ l1_vectsp_2(X16,X15)
| ~ v5_vectsp_2(X16,X15)
| ~ v6_rlvect_1(X16)
| ~ v5_rlvect_1(X16)
| ~ v4_rlvect_1(X16)
| ~ v3_rlvect_1(X16)
| v3_struct_0(X16)
| ~ m1_subset_1(X17,k1_zfmisc_1(u1_struct_0(X16)))
| v1_rmod_5(X17,X15,X16)
| k2_rmod_4(X15,X16,esk5_3(X15,X16,X17)) != k1_xboole_0 )
& ( ~ l3_vectsp_1(X15)
| ~ v8_vectsp_1(X15)
| ~ v7_vectsp_1(X15)
| ~ v6_vectsp_1(X15)
| ~ v4_group_1(X15)
| ~ v6_rlvect_1(X15)
| ~ v5_rlvect_1(X15)
| ~ v4_rlvect_1(X15)
| ~ v3_rlvect_1(X15)
| v3_struct_0(X15)
| ~ l1_vectsp_2(X16,X15)
| ~ v5_vectsp_2(X16,X15)
| ~ v6_rlvect_1(X16)
| ~ v5_rlvect_1(X16)
| ~ v4_rlvect_1(X16)
| ~ v3_rlvect_1(X16)
| v3_struct_0(X16)
| ~ m1_subset_1(X17,k1_zfmisc_1(u1_struct_0(X16)))
| v1_rmod_5(X17,X15,X16)
| k5_rmod_4(X15,X16,esk5_3(X15,X16,X17)) = k1_rlvect_1(X16) )
& ( ~ l3_vectsp_1(X15)
| ~ v8_vectsp_1(X15)
| ~ v7_vectsp_1(X15)
| ~ v6_vectsp_1(X15)
| ~ v4_group_1(X15)
| ~ v6_rlvect_1(X15)
| ~ v5_rlvect_1(X15)
| ~ v4_rlvect_1(X15)
| ~ v3_rlvect_1(X15)
| v3_struct_0(X15)
| ~ l1_vectsp_2(X16,X15)
| ~ v5_vectsp_2(X16,X15)
| ~ v6_rlvect_1(X16)
| ~ v5_rlvect_1(X16)
| ~ v4_rlvect_1(X16)
| ~ v3_rlvect_1(X16)
| v3_struct_0(X16)
| ~ m1_subset_1(X17,k1_zfmisc_1(u1_struct_0(X16)))
| v1_rmod_5(X17,X15,X16)
| m2_rmod_4(esk5_3(X15,X16,X17),X15,X16,X17) )
& ( ~ l3_vectsp_1(X15)
| ~ v8_vectsp_1(X15)
| ~ v7_vectsp_1(X15)
| ~ v6_vectsp_1(X15)
| ~ v4_group_1(X15)
| ~ v6_rlvect_1(X15)
| ~ v5_rlvect_1(X15)
| ~ v4_rlvect_1(X15)
| ~ v3_rlvect_1(X15)
| v3_struct_0(X15)
| ~ l1_vectsp_2(X16,X15)
| ~ v5_vectsp_2(X16,X15)
| ~ v6_rlvect_1(X16)
| ~ v5_rlvect_1(X16)
| ~ v4_rlvect_1(X16)
| ~ v3_rlvect_1(X16)
| v3_struct_0(X16)
| ~ m1_subset_1(X17,k1_zfmisc_1(u1_struct_0(X16)))
| k2_rmod_4(X15,X16,X18) = k1_xboole_0
| k5_rmod_4(X15,X16,X18) != k1_rlvect_1(X16)
| ~ m2_rmod_4(X18,X15,X16,X17)
| ~ v1_rmod_5(X17,X15,X16) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])])]) ).
cnf(c_0_10,plain,
( ~ r1_tarski(X3,X4)
| ~ m2_rmod_4(X5,X1,X2,X3)
| ~ m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| ~ 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)
| m2_rmod_4(X5,X1,X2,X4)
| v3_struct_0(X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
v6_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
v5_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
v4_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
v3_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,plain,
( ~ 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)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X1)
| v3_struct_0(X2)
| v1_rmod_5(X3,X1,X2)
| m2_rmod_4(esk5_3(X1,X2,X3),X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,negated_conjecture,
( ~ 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)
| ~ v5_vectsp_2(esk2_0,X2)
| ~ l1_vectsp_2(esk2_0,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(esk2_0)))
| ~ r1_tarski(X3,esk4_0)
| ~ m2_rmod_4(X1,X2,esk2_0,X3)
| v3_struct_0(X2)
| m2_rmod_4(X1,X2,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(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13]),c_0_14]),c_0_15])]),c_0_16]) ).
cnf(c_0_20,negated_conjecture,
r1_tarski(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
( ~ 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)
| ~ v5_vectsp_2(esk2_0,X1)
| ~ l1_vectsp_2(esk2_0,X1)
| v3_struct_0(X1)
| v1_rmod_5(esk3_0,X1,esk2_0)
| m2_rmod_4(esk5_3(X1,esk2_0,esk3_0),X1,esk2_0,esk3_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(spm,[status(thm)],[c_0_17,c_0_18]),c_0_12]),c_0_13]),c_0_14]),c_0_15])]),c_0_16]) ).
cnf(c_0_22,negated_conjecture,
l1_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,negated_conjecture,
v5_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_24,negated_conjecture,
l3_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,negated_conjecture,
v8_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,negated_conjecture,
v7_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,negated_conjecture,
v6_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_28,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_29,negated_conjecture,
v6_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_30,negated_conjecture,
v5_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_31,negated_conjecture,
v4_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_32,negated_conjecture,
v3_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_33,negated_conjecture,
~ v1_rmod_5(esk3_0,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_34,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_35,plain,
( ~ 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)
| ~ l1_vectsp_2(X3,X2)
| ~ v5_vectsp_2(X3,X2)
| ~ v6_rlvect_1(X3)
| ~ v5_rlvect_1(X3)
| ~ v4_rlvect_1(X3)
| ~ v3_rlvect_1(X3)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X3)))
| k5_rmod_4(X2,X3,X4) != k1_rlvect_1(X3)
| ~ m2_rmod_4(X4,X2,X3,X1)
| ~ v1_rmod_5(X1,X2,X3)
| v3_struct_0(X2)
| v3_struct_0(X3)
| k2_rmod_4(X2,X3,X4) = k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_36,negated_conjecture,
( ~ 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)
| ~ v5_vectsp_2(esk2_0,X2)
| ~ l1_vectsp_2(esk2_0,X2)
| ~ m2_rmod_4(X1,X2,esk2_0,esk3_0)
| v3_struct_0(X2)
| m2_rmod_4(X1,X2,esk2_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_18]),c_0_20])]) ).
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_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]),c_0_34]) ).
cnf(c_0_38,plain,
( ~ 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)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| v3_struct_0(X1)
| v3_struct_0(X2)
| v1_rmod_5(X3,X1,X2)
| k5_rmod_4(X1,X2,esk5_3(X1,X2,X3)) = k1_rlvect_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_39,negated_conjecture,
( ~ 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)
| ~ v5_vectsp_2(esk2_0,X1)
| ~ l1_vectsp_2(esk2_0,X1)
| ~ v1_rmod_5(esk4_0,X1,esk2_0)
| ~ m2_rmod_4(X2,X1,esk2_0,esk4_0)
| k5_rmod_4(X1,esk2_0,X2) != k1_rlvect_1(esk2_0)
| v3_struct_0(X1)
| k2_rmod_4(X1,esk2_0,X2) = 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(spm,[status(thm)],[c_0_35,c_0_11]),c_0_12]),c_0_13]),c_0_14]),c_0_15])]),c_0_16]) ).
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_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_34]) ).
cnf(c_0_41,negated_conjecture,
v1_rmod_5(esk4_0,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_42,negated_conjecture,
( ~ 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)
| ~ v5_vectsp_2(esk2_0,X1)
| ~ l1_vectsp_2(esk2_0,X1)
| v3_struct_0(X1)
| v1_rmod_5(esk3_0,X1,esk2_0)
| k5_rmod_4(X1,esk2_0,esk5_3(X1,esk2_0,esk3_0)) = k1_rlvect_1(esk2_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(spm,[status(thm)],[c_0_38,c_0_18]),c_0_12]),c_0_13]),c_0_14]),c_0_15])]),c_0_16]) ).
cnf(c_0_43,negated_conjecture,
( k5_rmod_4(esk1_0,esk2_0,esk5_3(esk1_0,esk2_0,esk3_0)) != k1_rlvect_1(esk2_0)
| 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(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),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_34]) ).
cnf(c_0_44,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_42,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]),c_0_34]) ).
cnf(c_0_45,plain,
( ~ 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)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| k2_rmod_4(X1,X2,esk5_3(X1,X2,X3)) != k1_xboole_0
| v3_struct_0(X1)
| v3_struct_0(X2)
| v1_rmod_5(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_46,negated_conjecture,
k2_rmod_4(esk1_0,esk2_0,esk5_3(esk1_0,esk2_0,esk3_0)) = k1_xboole_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
cnf(c_0_47,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_45,c_0_46]),c_0_18]),c_0_22]),c_0_23]),c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_28]),c_0_12]),c_0_29]),c_0_13]),c_0_30]),c_0_14]),c_0_31]),c_0_15]),c_0_32])]),c_0_33]),c_0_34]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG214+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Mon Sep 21 13:01:51 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.55/0.57 % Version: 3.5.1
% 1.55/0.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.55/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.55/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.55/0.57 % Starting new_bool_3 with 300s (1) cores
% 1.55/0.57 % Starting new_bool_1 with 300s (1) cores
% 1.55/0.57 % Starting sh5l with 300s (1) cores
% 1.55/0.57 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2408343 completed with status 0
% 1.55/0.57 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.55/0.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.55/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.55/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.55/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.55/0.57 % No SInE strategy applied
% 1.55/0.57 % Search class: FGHSM-FSMM32-SFFFFFNN
% 1.55/0.57 % partial match(1): FGHSM-FFMM32-SFFFFFNN
% 1.55/0.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.55/0.57 % Starting SubtermCWHack with 136s (1) cores
% 1.55/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.55/0.57 % Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 316s (1) cores
% 1.55/0.57 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.55/0.57 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 1.55/0.57 % G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with pid 2408358 completed with status 0
% 1.55/0.57 % Result found by G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN
% 1.55/0.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.55/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.55/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.55/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.55/0.57 % No SInE strategy applied
% 1.55/0.57 % Search class: FGHSM-FSMM32-SFFFFFNN
% 1.55/0.57 % partial match(1): FGHSM-FFMM32-SFFFFFNN
% 1.55/0.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.55/0.57 % Starting SubtermCWHack with 136s (1) cores
% 1.55/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.55/0.57 % Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 316s (1) cores
% 1.55/0.57 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.55/0.57 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 1.55/0.57 % Preprocessing time : 0.003 s
% 1.55/0.57
% 1.55/0.57 % Proof found!
% 1.55/0.57 % SZS status Theorem
% 1.55/0.57 % SZS output start CNFRefutation
% See solution above
% 1.55/0.57 % Parsed axioms : 75
% 1.55/0.57 % Removed by relevancy pruning/SinE : 0
% 1.55/0.57 % Initial clauses : 120
% 1.55/0.57 % Removed in clause preprocessing : 9
% 1.55/0.57 % Initial clauses in saturation : 111
% 1.55/0.57 % Processed clauses : 1228
% 1.55/0.57 % ...of these trivial : 0
% 1.55/0.57 % ...subsumed : 282
% 1.55/0.57 % ...remaining for further processing : 946
% 1.55/0.57 % Other redundant clauses eliminated : 1
% 1.55/0.57 % Clauses deleted for lack of memory : 0
% 1.55/0.57 % Backward-subsumed : 34
% 1.55/0.57 % Backward-rewritten : 7
% 1.55/0.57 % Generated clauses : 5506
% 1.55/0.57 % ...of the previous two non-redundant : 5439
% 1.55/0.57 % ...aggressively subsumed : 0
% 1.55/0.57 % Contextual simplify-reflections : 25
% 1.55/0.57 % Paramodulations : 5429
% 1.55/0.57 % Factorizations : 76
% 1.55/0.57 % NegExts : 0
% 1.55/0.57 % Equation resolutions : 1
% 1.55/0.57 % Disequality decompositions : 0
% 1.55/0.57 % Total rewrite steps : 3823
% 1.55/0.57 % ...of those cached : 3751
% 1.55/0.57 % Propositional unsat checks : 0
% 1.55/0.57 % Propositional check models : 0
% 1.55/0.57 % Propositional check unsatisfiable : 0
% 1.55/0.57 % Propositional clauses : 0
% 1.55/0.57 % Propositional clauses after purity: 0
% 1.55/0.57 % Propositional unsat core size : 0
% 1.55/0.57 % Propositional preprocessing time : 0.000
% 1.55/0.57 % Propositional encoding time : 0.000
% 1.55/0.57 % Propositional solver time : 0.000
% 1.55/0.57 % Success case prop preproc time : 0.000
% 1.55/0.57 % Success case prop encoding time : 0.000
% 1.55/0.57 % Success case prop solver time : 0.000
% 1.55/0.57 % Current number of processed clauses : 904
% 1.55/0.57 % Positive orientable unit clauses : 108
% 1.55/0.57 % Positive unorientable unit clauses: 0
% 1.55/0.57 % Negative unit clauses : 28
% 1.55/0.57 % Non-unit-clauses : 768
% 1.55/0.57 % Current number of unprocessed clauses: 4261
% 1.55/0.57 % ...number of literals in the above : 34681
% 1.55/0.57 % Current number of archived formulas : 0
% 1.55/0.57 % Current number of archived clauses : 41
% 1.55/0.57 % Clause-clause subsumption calls (NU) : 344463
% 1.55/0.57 % Rec. Clause-clause subsumption calls : 30713
% 1.55/0.57 % Non-unit clause-clause subsumptions : 258
% 1.55/0.57 % Unit Clause-clause subsumption calls : 3020
% 1.55/0.57 % Rewrite failures with RHS unbound : 0
% 1.55/0.57 % BW rewrite match attempts : 73
% 1.55/0.57 % BW rewrite match successes : 8
% 1.55/0.57 % Condensation attempts : 0
% 1.55/0.57 % Condensation successes : 0
% 1.55/0.57 % Termbank termtop insertions : 179485
% 1.55/0.57 % Search garbage collected termcells : 2425
% 1.55/0.57
% 1.55/0.57 % -------------------------------------------------
% 1.55/0.57 % User time : 0.213 s
% 1.55/0.57 % System time : 0.009 s
% 1.55/0.57 % Total time : 0.222 s
% 1.55/0.57 % Maximum resident set size: 3972 pages
% 1.55/0.57
% 1.55/0.57 % -------------------------------------------------
% 1.55/0.57 % User time : 1.050 s
% 1.55/0.57 % System time : 0.041 s
% 1.55/0.57 % Total time : 1.091 s
% 1.55/0.57 % Maximum resident set size: 4608 pages
% 1.55/0.57 % E exiting
%------------------------------------------------------------------------------