%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG219+4 : 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 : n001.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 11:55:38 AM UTC 2026
% Result : Theorem 0.15s 15.51s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 55 ( 33 unt; 0 def)
% Number of atoms : 391 ( 41 equ)
% Maximal formula atoms : 26 ( 7 avg)
% Number of connectives : 492 ( 156 ~; 151 |; 154 &)
% ( 2 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 54 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t14_rmod_5,conjecture,
! [X1] :
( ( l3_vectsp_1(X1)
& v2_vectsp_2(X1)
& ~ v10_vectsp_1(X1)
& v8_vectsp_1(X1)
& v7_vectsp_1(X1)
& v6_vectsp_1(X1)
& v7_group_1(X1)
& v4_group_1(X1)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_vectsp_2(X2,X1)
& v5_vectsp_2(X2,X1)
& v3_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)))
=> ( X3 = u1_struct_0(X2)
=> ( k1_rmod_5(X1,X2,X3) = X2
| k1_rlvect_1(X1) = k2_group_1(X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_rmod_5) ).
fof(t13_rmod_5,axiom,
! [X1] :
( ( l3_vectsp_1(X1)
& v2_vectsp_2(X1)
& ~ v10_vectsp_1(X1)
& v8_vectsp_1(X1)
& v7_vectsp_1(X1)
& v6_vectsp_1(X1)
& v7_group_1(X1)
& v4_group_1(X1)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ 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_2(X4,X1,X2)
& v3_vectsp_2(X4,X1) )
=> ( X3 = u1_struct_0(X4)
=> ( k1_rmod_5(X1,X2,X3) = X4
| k1_rlvect_1(X1) = k2_group_1(X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_rmod_5) ).
fof(d21_vectsp_1,axiom,
! [X1] :
( ( l2_vectsp_1(X1)
& ~ v3_struct_0(X1) )
=> ( v10_vectsp_1(X1)
<=> k1_rlvect_1(X1) = k2_group_1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+213.ax',d21_vectsp_1) ).
fof(dt_l3_vectsp_1,axiom,
! [X1] :
( l3_vectsp_1(X1)
=> ( l2_vectsp_1(X1)
& l1_rlvect_1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+213.ax',dt_l3_vectsp_1) ).
fof(t32_rmod_2,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) )
=> m1_rmod_2(X2,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+278.ax',t32_rmod_2) ).
fof(dt_k2_subset_1,axiom,
! [X1] : m1_subset_1(k2_subset_1(X1),k1_zfmisc_1(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+7.ax',dt_k2_subset_1) ).
fof(d4_subset_1,axiom,
! [X1] : k2_subset_1(X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+7.ax',d4_subset_1) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ( l3_vectsp_1(X1)
& v2_vectsp_2(X1)
& ~ v10_vectsp_1(X1)
& v8_vectsp_1(X1)
& v7_vectsp_1(X1)
& v6_vectsp_1(X1)
& v7_group_1(X1)
& v4_group_1(X1)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_vectsp_2(X2,X1)
& v5_vectsp_2(X2,X1)
& v3_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)))
=> ( X3 = u1_struct_0(X2)
=> ( k1_rmod_5(X1,X2,X3) = X2
| k1_rlvect_1(X1) = k2_group_1(X1) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t14_rmod_5]) ).
fof(c_0_8,plain,
! [X1] :
( ( l3_vectsp_1(X1)
& v2_vectsp_2(X1)
& ~ v10_vectsp_1(X1)
& v8_vectsp_1(X1)
& v7_vectsp_1(X1)
& v6_vectsp_1(X1)
& v7_group_1(X1)
& v4_group_1(X1)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ 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_2(X4,X1,X2)
& v3_vectsp_2(X4,X1) )
=> ( X3 = u1_struct_0(X4)
=> ( k1_rmod_5(X1,X2,X3) = X4
| k1_rlvect_1(X1) = k2_group_1(X1) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t13_rmod_5]) ).
fof(c_0_9,plain,
! [X1] :
( ( l2_vectsp_1(X1)
& ~ v3_struct_0(X1) )
=> ( v10_vectsp_1(X1)
<=> k1_rlvect_1(X1) = k2_group_1(X1) ) ),
inference(fof_simplification,[status(thm)],[d21_vectsp_1]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ( l3_vectsp_1(X1)
& v2_vectsp_2(X1)
& ~ v10_vectsp_1(X1)
& v8_vectsp_1(X1)
& v7_vectsp_1(X1)
& v6_vectsp_1(X1)
& v7_group_1(X1)
& v4_group_1(X1)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_vectsp_2(X2,X1)
& v5_vectsp_2(X2,X1)
& v3_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)))
=> ( X3 = u1_struct_0(X2)
=> ( k1_rmod_5(X1,X2,X3) = X2
| k1_rlvect_1(X1) = k2_group_1(X1) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X73,X74,X75,X76] :
( k1_rmod_5(X73,X74,X75) = X76
| k1_rlvect_1(X73) = k2_group_1(X73)
| X75 != u1_struct_0(X76)
| ~ m1_rmod_2(X76,X73,X74)
| ~ v3_vectsp_2(X76,X73)
| ~ m1_subset_1(X75,k1_zfmisc_1(u1_struct_0(X74)))
| ~ l1_vectsp_2(X74,X73)
| ~ v5_vectsp_2(X74,X73)
| ~ v6_rlvect_1(X74)
| ~ v5_rlvect_1(X74)
| ~ v4_rlvect_1(X74)
| ~ v3_rlvect_1(X74)
| v3_struct_0(X74)
| ~ l3_vectsp_1(X73)
| ~ v2_vectsp_2(X73)
| v10_vectsp_1(X73)
| ~ v8_vectsp_1(X73)
| ~ v7_vectsp_1(X73)
| ~ v6_vectsp_1(X73)
| ~ v7_group_1(X73)
| ~ v4_group_1(X73)
| ~ v6_rlvect_1(X73)
| ~ v5_rlvect_1(X73)
| ~ v4_rlvect_1(X73)
| ~ v3_rlvect_1(X73)
| v3_struct_0(X73) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_12,plain,
! [X694] :
( ( ~ l2_vectsp_1(X694)
| v3_struct_0(X694)
| v10_vectsp_1(X694)
| k1_rlvect_1(X694) != k2_group_1(X694) )
& ( ~ l2_vectsp_1(X694)
| v3_struct_0(X694)
| k1_rlvect_1(X694) = k2_group_1(X694)
| ~ v10_vectsp_1(X694) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_13,plain,
! [X697] :
( ( ~ l3_vectsp_1(X697)
| l2_vectsp_1(X697) )
& ( ~ l3_vectsp_1(X697)
| l1_rlvect_1(X697) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_vectsp_1])])])]) ).
fof(c_0_14,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) )
=> m1_rmod_2(X2,X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t32_rmod_2]) ).
fof(c_0_15,negated_conjecture,
( k1_rmod_5(esk1_0,esk2_0,esk3_0) != esk2_0
& k1_rlvect_1(esk1_0) != k2_group_1(esk1_0)
& esk3_0 = 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)
& v3_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)
& v2_vectsp_2(esk1_0)
& ~ v10_vectsp_1(esk1_0)
& v8_vectsp_1(esk1_0)
& v7_vectsp_1(esk1_0)
& v6_vectsp_1(esk1_0)
& v7_group_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_10])])])]) ).
cnf(c_0_16,plain,
( X3 != u1_struct_0(X4)
| ~ m1_rmod_2(X4,X1,X2)
| ~ v3_vectsp_2(X4,X1)
| ~ 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)
| ~ v2_vectsp_2(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_group_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| k1_rmod_5(X1,X2,X3) = X4
| k1_rlvect_1(X1) = k2_group_1(X1)
| v3_struct_0(X2)
| v10_vectsp_1(X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( ~ l2_vectsp_1(X1)
| ~ v10_vectsp_1(X1)
| v3_struct_0(X1)
| k1_rlvect_1(X1) = k2_group_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( ~ l3_vectsp_1(X1)
| l2_vectsp_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_19,plain,
! [X236,X237] :
( m1_rmod_2(X237,X236,X237)
| ~ l1_vectsp_2(X237,X236)
| ~ v5_vectsp_2(X237,X236)
| ~ v6_rlvect_1(X237)
| ~ v5_rlvect_1(X237)
| ~ v4_rlvect_1(X237)
| ~ v3_rlvect_1(X237)
| v3_struct_0(X237)
| ~ l3_vectsp_1(X236)
| ~ v8_vectsp_1(X236)
| ~ v7_vectsp_1(X236)
| ~ v6_vectsp_1(X236)
| ~ v4_group_1(X236)
| ~ v6_rlvect_1(X236)
| ~ v5_rlvect_1(X236)
| ~ v4_rlvect_1(X236)
| ~ v3_rlvect_1(X236)
| v3_struct_0(X236) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
fof(c_0_20,plain,
! [X1708] : m1_subset_1(k2_subset_1(X1708),k1_zfmisc_1(X1708)),
inference(variable_rename,[status(thm)],[dt_k2_subset_1]) ).
fof(c_0_21,plain,
! [X1701] : k2_subset_1(X1701) = X1701,
inference(variable_rename,[status(thm)],[d4_subset_1]) ).
cnf(c_0_22,negated_conjecture,
k1_rmod_5(esk1_0,esk2_0,esk3_0) != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,negated_conjecture,
esk3_0 = u1_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
( ~ m1_subset_1(u1_struct_0(X3),k1_zfmisc_1(u1_struct_0(X2)))
| ~ 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)
| ~ v7_group_1(X1)
| ~ l3_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v2_vectsp_2(X1)
| ~ l1_vectsp_2(X2,X1)
| ~ v3_vectsp_2(X3,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ m1_rmod_2(X3,X1,X2)
| v3_struct_0(X1)
| v3_struct_0(X2)
| v10_vectsp_1(X1)
| k2_group_1(X1) = k1_rlvect_1(X1)
| k1_rmod_5(X1,X2,u1_struct_0(X3)) = X3 ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
( ~ l3_vectsp_1(X1)
| ~ v10_vectsp_1(X1)
| v3_struct_0(X1)
| k2_group_1(X1) = k1_rlvect_1(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
( ~ 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_2(X2,X1,X2)
| v3_struct_0(X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,negated_conjecture,
v5_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_28,negated_conjecture,
l1_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_29,negated_conjecture,
v8_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_30,negated_conjecture,
v7_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_31,negated_conjecture,
v6_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_32,negated_conjecture,
l3_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_33,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_34,negated_conjecture,
v6_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_35,negated_conjecture,
v6_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_36,negated_conjecture,
v5_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_37,negated_conjecture,
v5_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_38,negated_conjecture,
v4_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_39,negated_conjecture,
v4_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_40,negated_conjecture,
v3_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_41,negated_conjecture,
v3_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_42,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_43,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_44,plain,
m1_subset_1(k2_subset_1(X1),k1_zfmisc_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_45,plain,
k2_subset_1(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_46,negated_conjecture,
k1_rmod_5(esk1_0,esk2_0,u1_struct_0(esk2_0)) != esk2_0,
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_47,plain,
( ~ m1_subset_1(u1_struct_0(X3),k1_zfmisc_1(u1_struct_0(X2)))
| ~ 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)
| ~ v7_group_1(X1)
| ~ l3_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v2_vectsp_2(X1)
| ~ l1_vectsp_2(X2,X1)
| ~ v3_vectsp_2(X3,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ m1_rmod_2(X3,X1,X2)
| v3_struct_0(X2)
| v3_struct_0(X1)
| k2_group_1(X1) = k1_rlvect_1(X1)
| k1_rmod_5(X1,X2,u1_struct_0(X3)) = X3 ),
inference(csr,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_48,negated_conjecture,
m1_rmod_2(esk2_0,esk1_0,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[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]),c_0_38]),c_0_39]),c_0_40]),c_0_41])]),c_0_42]),c_0_43]) ).
cnf(c_0_49,negated_conjecture,
v3_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_50,negated_conjecture,
v2_vectsp_2(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_51,negated_conjecture,
v7_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_52,plain,
m1_subset_1(X1,k1_zfmisc_1(X1)),
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_53,negated_conjecture,
k1_rlvect_1(esk1_0) != k2_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_54,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_27]),c_0_49]),c_0_28]),c_0_50]),c_0_29]),c_0_30]),c_0_31]),c_0_32]),c_0_51]),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_52])]),c_0_53]),c_0_43]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG219+4 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/5.36 % Computer : n001.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Mon Sep 21 13:10:45 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.41 Running first-order theorem proving
% 0.13/5.41 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
% 0.15/15.51 % Version: 3.5.1
% 0.15/15.51 % Preprocessing class: FMLLSLLLSSSNFFN.
% 0.15/15.51 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 0.15/15.51 % Starting new_ho_10 with 598s (2) cores
% 0.15/15.51 % Starting sh3 with 598s (2) cores
% 0.15/15.51 % Starting ho_unfolding_3 with 598s (2) cores
% 0.15/15.51 % Starting new_ho_10_cnf2 with 598s (2) cores
% 0.15/15.51 % sh3 with pid 3193877 completed with status 0
% 0.15/15.51 % Result found by sh3
% 0.15/15.51 % Preprocessing class: FMLLSLLLSSSNFFN.
% 0.15/15.51 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 0.15/15.51 % Starting new_ho_10 with 598s (2) cores
% 0.15/15.51 % Starting sh3 with 598s (2) cores
% 0.15/15.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/15.51 % SinE strategy is gf120_h_gu_RUU_F100_L01000
% 0.15/15.51 % Search class: FGHSM-SMLM31-DFFFFFNN
% 0.15/15.51 % Scheduled 7 strats onto 2 cores with 598 seconds (598 total)
% 0.15/15.51 % Starting SubtermCWHack with 54s (1) cores
% 0.15/15.51 % Starting sh3 with 60s (1) cores
% 0.15/15.51 % sh3 with pid 3193886 completed with status 0
% 0.15/15.51 % Result found by sh3
% 0.15/15.51 % Preprocessing class: FMLLSLLLSSSNFFN.
% 0.15/15.51 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 0.15/15.51 % Starting new_ho_10 with 598s (2) cores
% 0.15/15.51 % Starting sh3 with 598s (2) cores
% 0.15/15.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/15.51 % SinE strategy is gf120_h_gu_RUU_F100_L01000
% 0.15/15.51 % Search class: FGHSM-SMLM31-DFFFFFNN
% 0.15/15.51 % Scheduled 7 strats onto 2 cores with 598 seconds (598 total)
% 0.15/15.51 % Starting SubtermCWHack with 54s (1) cores
% 0.15/15.51 % Starting sh3 with 60s (1) cores
% 0.15/15.51 % Preprocessing time : 0.127 s
% 0.15/15.51 % Presaturation interreduction done
% 0.15/15.51
% 0.15/15.51 % Proof found!
% 0.15/15.51 % SZS status Theorem
% 0.15/15.51 % SZS output start CNFRefutation
% See solution above
% 0.15/15.51 % Parsed axioms : 24514
% 0.15/15.51 % Removed by relevancy pruning/SinE : 23513
% 0.15/15.51 % Initial clauses : 3592
% 0.15/15.51 % Removed in clause preprocessing : 95
% 0.15/15.51 % Initial clauses in saturation : 3497
% 0.15/15.51 % Processed clauses : 9433
% 0.15/15.51 % ...of these trivial : 25
% 0.15/15.51 % ...subsumed : 1677
% 0.15/15.51 % ...remaining for further processing : 7731
% 0.15/15.51 % Other redundant clauses eliminated : 466
% 0.15/15.51 % Clauses deleted for lack of memory : 0
% 0.15/15.51 % Backward-subsumed : 65
% 0.15/15.51 % Backward-rewritten : 13
% 0.15/15.51 % Generated clauses : 42446
% 0.15/15.51 % ...of the previous two non-redundant : 39926
% 0.15/15.51 % ...aggressively subsumed : 0
% 0.15/15.51 % Contextual simplify-reflections : 141
% 0.15/15.51 % Paramodulations : 41964
% 0.15/15.51 % Factorizations : 12
% 0.15/15.51 % NegExts : 0
% 0.15/15.51 % Equation resolutions : 480
% 0.15/15.51 % Disequality decompositions : 0
% 0.15/15.51 % Total rewrite steps : 5323
% 0.15/15.51 % ...of those cached : 4705
% 0.15/15.51 % Propositional unsat checks : 1
% 0.15/15.51 % Propositional check models : 1
% 0.15/15.51 % Propositional check unsatisfiable : 0
% 0.15/15.51 % Propositional clauses : 0
% 0.15/15.51 % Propositional clauses after purity: 0
% 0.15/15.51 % Propositional unsat core size : 0
% 0.15/15.51 % Propositional preprocessing time : 0.000
% 0.15/15.51 % Propositional encoding time : 0.033
% 0.15/15.51 % Propositional solver time : 0.015
% 0.15/15.51 % Success case prop preproc time : 0.000
% 0.15/15.51 % Success case prop encoding time : 0.000
% 0.15/15.51 % Success case prop solver time : 0.000
% 0.15/15.51 % Current number of processed clauses : 4112
% 0.15/15.51 % Positive orientable unit clauses : 260
% 0.15/15.51 % Positive unorientable unit clauses: 2
% 0.15/15.51 % Negative unit clauses : 200
% 0.15/15.51 % Non-unit-clauses : 3650
% 0.15/15.51 % Current number of unprocessed clauses: 37201
% 0.15/15.51 % ...number of literals in the above : 401367
% 0.15/15.51 % Current number of archived formulas : 0
% 0.15/15.51 % Current number of archived clauses : 3493
% 0.15/15.51 % Clause-clause subsumption calls (NU) : 10403982
% 0.15/15.51 % Rec. Clause-clause subsumption calls : 311280
% 0.15/15.51 % Non-unit clause-clause subsumptions : 948
% 0.15/15.51 % Unit Clause-clause subsumption calls : 63565
% 0.15/15.51 % Rewrite failures with RHS unbound : 0
% 0.15/15.51 % BW rewrite match attempts : 134
% 0.15/15.51 % BW rewrite match successes : 80
% 0.15/15.51 % Condensation attempts : 0
% 0.15/15.51 % Condensation successes : 0
% 0.15/15.51 % Termbank termtop insertions : 2517278
% 0.15/15.51 % Search garbage collected termcells : 280902
% 0.15/15.51
% 0.15/15.51 % -------------------------------------------------
% 0.15/15.51 % User time : 8.608 s
% 0.15/15.51 % System time : 0.182 s
% 0.15/15.51 % Total time : 8.790 s
% 0.15/15.51 % Maximum resident set size: 50248 pages
% 0.15/15.51
% 0.15/15.51 % -------------------------------------------------
% 0.15/15.51 % User time : 17.783 s
% 0.15/15.51 % System time : 0.397 s
% 0.15/15.51 % Total time : 18.181 s
% 0.15/15.51 % Maximum resident set size: 39680 pages
% 0.15/15.51 % E exiting
%------------------------------------------------------------------------------