%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG215+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 11:55:37 AM UTC 2026
% Result : Theorem 1.25s 0.64s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 27 unt; 0 def)
% Number of atoms : 489 ( 17 equ)
% Maximal formula atoms : 82 ( 9 avg)
% Number of connectives : 673 ( 238 ~; 239 |; 162 &)
% ( 4 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 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 : 73 ( 3 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t4_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) )
=> v1_rmod_5(k1_subset_1(u1_struct_0(X2)),X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_rmod_5) ).
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/sandbox/benchmark/theBenchmark.p',d1_rmod_5) ).
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] :
( m1_subset_1(k1_subset_1(X1),k1_zfmisc_1(X1))
& v1_xboole_0(k1_subset_1(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_subset_1) ).
fof(d7_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_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] :
( ( 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)
& ~ v3_struct_0(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)
& ~ v3_struct_0(X1) )
=> ! [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(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,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) )
=> v1_rmod_5(k1_subset_1(u1_struct_0(X2)),X1,X2) ) ),
inference(assume_negation,[status(cth)],[t4_rmod_5]) ).
fof(c_0_8,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_9,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) )
=> v1_rmod_5(k1_subset_1(u1_struct_0(X2)),X1,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X149] :
( X149 = k1_xboole_0
| ~ v1_xboole_0(X149) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])]) ).
fof(c_0_11,plain,
! [X28] :
( m1_subset_1(k1_subset_1(X28),k1_zfmisc_1(X28))
& v1_xboole_0(k1_subset_1(X28)) ),
inference(variable_rename,[status(thm)],[dt_k1_subset_1]) ).
fof(c_0_12,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_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_13,plain,
! [X1,X2,X3] :
( ( 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)
& ~ v3_struct_0(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)
& ~ v3_struct_0(X1) )
=> ! [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_14,plain,
! [X13,X14,X15,X16] :
( ( ~ l3_vectsp_1(X13)
| ~ v8_vectsp_1(X13)
| ~ v7_vectsp_1(X13)
| ~ v6_vectsp_1(X13)
| ~ v4_group_1(X13)
| ~ v6_rlvect_1(X13)
| ~ v5_rlvect_1(X13)
| ~ v4_rlvect_1(X13)
| ~ v3_rlvect_1(X13)
| v3_struct_0(X13)
| ~ l1_vectsp_2(X14,X13)
| ~ v5_vectsp_2(X14,X13)
| ~ v6_rlvect_1(X14)
| ~ v5_rlvect_1(X14)
| ~ v4_rlvect_1(X14)
| ~ v3_rlvect_1(X14)
| v3_struct_0(X14)
| ~ m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(X14)))
| v1_rmod_5(X15,X13,X14)
| k2_rmod_4(X13,X14,esk3_3(X13,X14,X15)) != k1_xboole_0 )
& ( ~ l3_vectsp_1(X13)
| ~ v8_vectsp_1(X13)
| ~ v7_vectsp_1(X13)
| ~ v6_vectsp_1(X13)
| ~ v4_group_1(X13)
| ~ v6_rlvect_1(X13)
| ~ v5_rlvect_1(X13)
| ~ v4_rlvect_1(X13)
| ~ v3_rlvect_1(X13)
| v3_struct_0(X13)
| ~ l1_vectsp_2(X14,X13)
| ~ v5_vectsp_2(X14,X13)
| ~ v6_rlvect_1(X14)
| ~ v5_rlvect_1(X14)
| ~ v4_rlvect_1(X14)
| ~ v3_rlvect_1(X14)
| v3_struct_0(X14)
| ~ m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(X14)))
| v1_rmod_5(X15,X13,X14)
| k5_rmod_4(X13,X14,esk3_3(X13,X14,X15)) = k1_rlvect_1(X14) )
& ( ~ l3_vectsp_1(X13)
| ~ v8_vectsp_1(X13)
| ~ v7_vectsp_1(X13)
| ~ v6_vectsp_1(X13)
| ~ v4_group_1(X13)
| ~ v6_rlvect_1(X13)
| ~ v5_rlvect_1(X13)
| ~ v4_rlvect_1(X13)
| ~ v3_rlvect_1(X13)
| v3_struct_0(X13)
| ~ l1_vectsp_2(X14,X13)
| ~ v5_vectsp_2(X14,X13)
| ~ v6_rlvect_1(X14)
| ~ v5_rlvect_1(X14)
| ~ v4_rlvect_1(X14)
| ~ v3_rlvect_1(X14)
| v3_struct_0(X14)
| ~ m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(X14)))
| v1_rmod_5(X15,X13,X14)
| m2_rmod_4(esk3_3(X13,X14,X15),X13,X14,X15) )
& ( ~ l3_vectsp_1(X13)
| ~ v8_vectsp_1(X13)
| ~ v7_vectsp_1(X13)
| ~ v6_vectsp_1(X13)
| ~ v4_group_1(X13)
| ~ v6_rlvect_1(X13)
| ~ v5_rlvect_1(X13)
| ~ v4_rlvect_1(X13)
| ~ v3_rlvect_1(X13)
| v3_struct_0(X13)
| ~ l1_vectsp_2(X14,X13)
| ~ v5_vectsp_2(X14,X13)
| ~ v6_rlvect_1(X14)
| ~ v5_rlvect_1(X14)
| ~ v4_rlvect_1(X14)
| ~ v3_rlvect_1(X14)
| v3_struct_0(X14)
| ~ m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(X14)))
| k2_rmod_4(X13,X14,X16) = k1_xboole_0
| k5_rmod_4(X13,X14,X16) != k1_rlvect_1(X14)
| ~ m2_rmod_4(X16,X13,X14,X15)
| ~ v1_rmod_5(X15,X13,X14) ) ),
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_8])])])])])]) ).
fof(c_0_15,negated_conjecture,
( ~ v1_rmod_5(k1_subset_1(u1_struct_0(esk2_0)),esk1_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_9])])])]) ).
cnf(c_0_16,plain,
( ~ v1_xboole_0(X1)
| X1 = k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
v1_xboole_0(k1_subset_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_18,plain,
! [X21,X22,X23,X24] :
( ( ~ l3_vectsp_1(X21)
| ~ v8_vectsp_1(X21)
| ~ v7_vectsp_1(X21)
| ~ v6_vectsp_1(X21)
| ~ v4_group_1(X21)
| ~ v6_rlvect_1(X21)
| ~ v5_rlvect_1(X21)
| ~ v4_rlvect_1(X21)
| ~ v3_rlvect_1(X21)
| v3_struct_0(X21)
| ~ l1_vectsp_2(X22,X21)
| ~ v5_vectsp_2(X22,X21)
| ~ v6_rlvect_1(X22)
| ~ v5_rlvect_1(X22)
| ~ v4_rlvect_1(X22)
| ~ v3_rlvect_1(X22)
| v3_struct_0(X22)
| ~ m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(X22)))
| ~ m1_rmod_4(X24,X21,X22)
| m2_rmod_4(X24,X21,X22,X23)
| ~ r1_tarski(k2_rmod_4(X21,X22,X24),X23) )
& ( ~ l3_vectsp_1(X21)
| ~ v8_vectsp_1(X21)
| ~ v7_vectsp_1(X21)
| ~ v6_vectsp_1(X21)
| ~ v4_group_1(X21)
| ~ v6_rlvect_1(X21)
| ~ v5_rlvect_1(X21)
| ~ v4_rlvect_1(X21)
| ~ v3_rlvect_1(X21)
| v3_struct_0(X21)
| ~ l1_vectsp_2(X22,X21)
| ~ v5_vectsp_2(X22,X21)
| ~ v6_rlvect_1(X22)
| ~ v5_rlvect_1(X22)
| ~ v4_rlvect_1(X22)
| ~ v3_rlvect_1(X22)
| v3_struct_0(X22)
| ~ m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(X22)))
| ~ m1_rmod_4(X24,X21,X22)
| r1_tarski(k2_rmod_4(X21,X22,X24),X23)
| ~ m2_rmod_4(X24,X21,X22,X23) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])])]) ).
fof(c_0_19,plain,
! [X60,X61,X62,X63] :
( m1_rmod_4(X63,X60,X61)
| ~ m2_rmod_4(X63,X60,X61,X62)
| ~ m1_subset_1(X62,k1_zfmisc_1(u1_struct_0(X61)))
| ~ l1_vectsp_2(X61,X60)
| ~ v5_vectsp_2(X61,X60)
| ~ v6_rlvect_1(X61)
| ~ v5_rlvect_1(X61)
| ~ v4_rlvect_1(X61)
| ~ v3_rlvect_1(X61)
| v3_struct_0(X61)
| ~ l3_vectsp_1(X60)
| ~ v8_vectsp_1(X60)
| ~ v7_vectsp_1(X60)
| ~ v6_vectsp_1(X60)
| ~ v4_group_1(X60)
| ~ v6_rlvect_1(X60)
| ~ v5_rlvect_1(X60)
| ~ v4_rlvect_1(X60)
| ~ v3_rlvect_1(X60)
| v3_struct_0(X60) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
cnf(c_0_20,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(esk3_3(X1,X2,X3),X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,negated_conjecture,
v5_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
l1_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,negated_conjecture,
l3_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,negated_conjecture,
v8_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,negated_conjecture,
v7_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_26,negated_conjecture,
v6_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_27,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_28,negated_conjecture,
v6_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_29,negated_conjecture,
v6_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_30,negated_conjecture,
v5_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_31,negated_conjecture,
v5_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_32,negated_conjecture,
v4_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_33,negated_conjecture,
v4_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_34,negated_conjecture,
v3_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_35,negated_conjecture,
v3_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_36,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_37,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_38,plain,
m1_subset_1(k1_subset_1(X1),k1_zfmisc_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_39,plain,
k1_subset_1(X1) = k1_xboole_0,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_40,negated_conjecture,
~ v1_rmod_5(k1_subset_1(u1_struct_0(esk2_0)),esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_41,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(X4,k1_zfmisc_1(u1_struct_0(X3)))
| ~ m1_rmod_4(X1,X2,X3)
| ~ m2_rmod_4(X1,X2,X3,X4)
| v3_struct_0(X2)
| v3_struct_0(X3)
| r1_tarski(k2_rmod_4(X2,X3,X1),X4) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_42,plain,
( ~ m2_rmod_4(X4,X1,X2,X3)
| ~ 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)
| m1_rmod_4(X4,X1,X2)
| v3_struct_0(X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_43,negated_conjecture,
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk2_0)))
| v1_rmod_5(X1,esk1_0,esk2_0)
| m2_rmod_4(esk3_3(esk1_0,esk2_0,X1),esk1_0,esk2_0,X1) ),
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_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]),c_0_34]),c_0_35])]),c_0_36]),c_0_37]) ).
cnf(c_0_44,plain,
m1_subset_1(k1_xboole_0,k1_zfmisc_1(X1)),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,negated_conjecture,
~ v1_rmod_5(k1_xboole_0,esk1_0,esk2_0),
inference(rw,[status(thm)],[c_0_40,c_0_39]) ).
fof(c_0_46,plain,
! [X142] :
( X142 = k1_xboole_0
| ~ r1_tarski(X142,k1_xboole_0) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])])]) ).
cnf(c_0_47,plain,
( ~ v3_rlvect_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X1)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X1)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X1)
| ~ v6_rlvect_1(X2)
| ~ v4_group_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ l3_vectsp_1(X1)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1)
| ~ m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))
| ~ m2_rmod_4(X3,X1,X2,X4)
| v3_struct_0(X2)
| v3_struct_0(X1)
| r1_tarski(k2_rmod_4(X1,X2,X3),X4) ),
inference(csr,[status(thm)],[c_0_41,c_0_42]) ).
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(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_49,plain,
( ~ r1_tarski(X1,k1_xboole_0)
| 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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_44]),c_0_22]),c_0_21]),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]),c_0_35])]),c_0_36]),c_0_37]) ).
cnf(c_0_51,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,esk3_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_14]) ).
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_44]),c_0_22]),c_0_21]),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]),c_0_35])]),c_0_45]),c_0_36]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG215+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n015.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 13:06:06 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 1.25/0.64 % Version: 3.5.1
% 1.25/0.64 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.25/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.25/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.25/0.64 % Starting new_bool_3 with 300s (1) cores
% 1.25/0.64 % Starting new_bool_1 with 300s (1) cores
% 1.25/0.64 % Starting sh5l with 300s (1) cores
% 1.25/0.64 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1524539 completed with status 0
% 1.25/0.64 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.25/0.64 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.25/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.25/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.25/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.25/0.64 % No SInE strategy applied
% 1.25/0.64 % Search class: FGHSM-FSMM31-SFFFFFNN
% 1.25/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.25/0.64 % Starting SubtermCWHack with 136s (1) cores
% 1.25/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.25/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 136s (1) cores
% 1.25/0.64 % Starting new_bool_3 with 136s (1) cores
% 1.25/0.64 % Starting new_bool_1 with 136s (1) cores
% 1.25/0.64 % new_bool_1 with pid 1524549 completed with status 0
% 1.25/0.64 % Result found by new_bool_1
% 1.25/0.64 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.25/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.25/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.25/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.25/0.64 % No SInE strategy applied
% 1.25/0.64 % Search class: FGHSM-FSMM31-SFFFFFNN
% 1.25/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.25/0.64 % Starting SubtermCWHack with 136s (1) cores
% 1.25/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.25/0.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 136s (1) cores
% 1.25/0.64 % Starting new_bool_3 with 136s (1) cores
% 1.25/0.64 % Starting new_bool_1 with 136s (1) cores
% 1.25/0.64 % Preprocessing time : 0.002 s
% 1.25/0.64 % Presaturation interreduction done
% 1.25/0.64
% 1.25/0.64 % Proof found!
% 1.25/0.64 % SZS status Theorem
% 1.25/0.64 % SZS output start CNFRefutation
% See solution above
% 1.25/0.65 % Parsed axioms : 77
% 1.25/0.65 % Removed by relevancy pruning/SinE : 0
% 1.25/0.65 % Initial clauses : 120
% 1.25/0.65 % Removed in clause preprocessing : 9
% 1.25/0.65 % Initial clauses in saturation : 111
% 1.25/0.65 % Processed clauses : 2665
% 1.25/0.65 % ...of these trivial : 3
% 1.25/0.65 % ...subsumed : 1669
% 1.25/0.65 % ...remaining for further processing : 993
% 1.25/0.65 % Other redundant clauses eliminated : 11
% 1.25/0.65 % Clauses deleted for lack of memory : 0
% 1.25/0.65 % Backward-subsumed : 17
% 1.25/0.65 % Backward-rewritten : 14
% 1.25/0.65 % Generated clauses : 7686
% 1.25/0.65 % ...of the previous two non-redundant : 7215
% 1.25/0.65 % ...aggressively subsumed : 0
% 1.25/0.65 % Contextual simplify-reflections : 30
% 1.25/0.65 % Paramodulations : 7673
% 1.25/0.65 % Factorizations : 2
% 1.25/0.65 % NegExts : 0
% 1.25/0.65 % Equation resolutions : 11
% 1.25/0.65 % Disequality decompositions : 0
% 1.25/0.65 % Total rewrite steps : 2548
% 1.25/0.65 % ...of those cached : 2440
% 1.25/0.65 % Propositional unsat checks : 0
% 1.25/0.65 % Propositional check models : 0
% 1.25/0.65 % Propositional check unsatisfiable : 0
% 1.25/0.65 % Propositional clauses : 0
% 1.25/0.65 % Propositional clauses after purity: 0
% 1.25/0.65 % Propositional unsat core size : 0
% 1.25/0.65 % Propositional preprocessing time : 0.000
% 1.25/0.65 % Propositional encoding time : 0.000
% 1.25/0.65 % Propositional solver time : 0.000
% 1.25/0.65 % Success case prop preproc time : 0.000
% 1.25/0.65 % Success case prop encoding time : 0.000
% 1.25/0.65 % Success case prop solver time : 0.000
% 1.25/0.65 % Current number of processed clauses : 850
% 1.25/0.65 % Positive orientable unit clauses : 134
% 1.25/0.65 % Positive unorientable unit clauses: 0
% 1.25/0.65 % Negative unit clauses : 19
% 1.25/0.65 % Non-unit-clauses : 697
% 1.25/0.65 % Current number of unprocessed clauses: 4753
% 1.25/0.65 % ...number of literals in the above : 25423
% 1.25/0.65 % Current number of archived formulas : 0
% 1.25/0.65 % Current number of archived clauses : 142
% 1.25/0.65 % Clause-clause subsumption calls (NU) : 186732
% 1.25/0.65 % Rec. Clause-clause subsumption calls : 65395
% 1.25/0.65 % Non-unit clause-clause subsumptions : 1272
% 1.25/0.65 % Unit Clause-clause subsumption calls : 10422
% 1.25/0.65 % Rewrite failures with RHS unbound : 0
% 1.25/0.65 % BW rewrite match attempts : 230
% 1.25/0.65 % BW rewrite match successes : 11
% 1.25/0.65 % Condensation attempts : 0
% 1.25/0.65 % Condensation successes : 0
% 1.25/0.65 % Termbank termtop insertions : 142846
% 1.25/0.65 % Search garbage collected termcells : 2374
% 1.25/0.65
% 1.25/0.65 % -------------------------------------------------
% 1.25/0.65 % User time : 0.170 s
% 1.25/0.65 % System time : 0.008 s
% 1.25/0.65 % Total time : 0.179 s
% 1.25/0.65 % Maximum resident set size: 3972 pages
% 1.25/0.65
% 1.25/0.65 % -------------------------------------------------
% 1.25/0.65 % User time : 0.880 s
% 1.25/0.65 % System time : 0.047 s
% 1.25/0.65 % Total time : 0.927 s
% 1.25/0.65 % Maximum resident set size: 4608 pages
% 1.25/0.65 % E exiting
%------------------------------------------------------------------------------