%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG216+3 : 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 : n003.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 33.59s 5.44s
% Output : CNFRefutation 33.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 24 unt; 0 def)
% Number of atoms : 506 ( 26 equ)
% Maximal formula atoms : 44 ( 10 avg)
% Number of connectives : 705 ( 247 ~; 232 |; 196 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 10 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 63 ( 0 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t6_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,u1_struct_0(X2))
=> ( k1_rlvect_1(X1) != k2_group_1(X1)
=> ( ~ v1_rmod_5(k8_rlvect_2(X2,k1_rlvect_1(X2),X3),X1,X2)
& ~ v1_rmod_5(k8_rlvect_2(X2,X3,k1_rlvect_1(X2)),X1,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_rmod_5) ).
fof(dt_k3_rmod_4,axiom,
! [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)
& 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) )
=> m1_rmod_4(k3_rmod_4(X1,X2),X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+280.ax',dt_k3_rmod_4) ).
fof(t41_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) )
=> k5_rmod_4(X1,X2,k3_rmod_4(X1,X2)) = k1_rlvect_1(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+280.ax',t41_rmod_4) ).
fof(t5_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,u1_struct_0(X2))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X2))
=> ( v1_rmod_5(k8_rlvect_2(X2,X3,X4),X1,X2)
=> ( ( X4 != k1_rlvect_1(X2)
& X3 != k1_rlvect_1(X2) )
| k1_rlvect_1(X1) = k2_group_1(X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_rmod_5) ).
fof(dt_k5_rmod_4,axiom,
! [X1,X2,X3] :
( ( m1_rmod_4(X3,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)
& 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) )
=> m1_subset_1(k5_rmod_4(X1,X2,X3),u1_struct_0(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+280.ax',dt_k5_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,u1_struct_0(X2))
=> ( k1_rlvect_1(X1) != k2_group_1(X1)
=> ( ~ v1_rmod_5(k8_rlvect_2(X2,k1_rlvect_1(X2),X3),X1,X2)
& ~ v1_rmod_5(k8_rlvect_2(X2,X3,k1_rlvect_1(X2)),X1,X2) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t6_rmod_5]) ).
fof(c_0_6,plain,
! [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)
& 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) )
=> m1_rmod_4(k3_rmod_4(X1,X2),X1,X2) ),
inference(fof_simplification,[status(thm)],[dt_k3_rmod_4]) ).
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) )
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X2))
=> ( k1_rlvect_1(X1) != k2_group_1(X1)
=> ( ~ v1_rmod_5(k8_rlvect_2(X2,k1_rlvect_1(X2),X3),X1,X2)
& ~ v1_rmod_5(k8_rlvect_2(X2,X3,k1_rlvect_1(X2)),X1,X2) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_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) )
=> k5_rmod_4(X1,X2,k3_rmod_4(X1,X2)) = k1_rlvect_1(X2) ) ),
inference(fof_simplification,[status(thm)],[t41_rmod_4]) ).
fof(c_0_9,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,u1_struct_0(X2))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X2))
=> ( v1_rmod_5(k8_rlvect_2(X2,X3,X4),X1,X2)
=> ( ( X4 != k1_rlvect_1(X2)
& X3 != k1_rlvect_1(X2) )
| k1_rlvect_1(X1) = k2_group_1(X1) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t5_rmod_5]) ).
fof(c_0_10,plain,
! [X1,X2,X3] :
( ( m1_rmod_4(X3,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)
& 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) )
=> m1_subset_1(k5_rmod_4(X1,X2,X3),u1_struct_0(X2)) ),
inference(fof_simplification,[status(thm)],[dt_k5_rmod_4]) ).
fof(c_0_11,plain,
! [X1401,X1402] :
( m1_rmod_4(k3_rmod_4(X1401,X1402),X1401,X1402)
| ~ l1_vectsp_2(X1402,X1401)
| ~ v5_vectsp_2(X1402,X1401)
| ~ v6_rlvect_1(X1402)
| ~ v5_rlvect_1(X1402)
| ~ v4_rlvect_1(X1402)
| ~ v3_rlvect_1(X1402)
| v3_struct_0(X1402)
| ~ l3_vectsp_1(X1401)
| ~ v8_vectsp_1(X1401)
| ~ v7_vectsp_1(X1401)
| ~ v6_vectsp_1(X1401)
| ~ v4_group_1(X1401)
| ~ v6_rlvect_1(X1401)
| ~ v5_rlvect_1(X1401)
| ~ v4_rlvect_1(X1401)
| ~ v3_rlvect_1(X1401)
| v3_struct_0(X1401) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_12,negated_conjecture,
( ( v1_rmod_5(k8_rlvect_2(esk2_0,k1_rlvect_1(esk2_0),esk3_0),esk1_0,esk2_0)
| v1_rmod_5(k8_rlvect_2(esk2_0,esk3_0,k1_rlvect_1(esk2_0)),esk1_0,esk2_0) )
& k1_rlvect_1(esk1_0) != k2_group_1(esk1_0)
& m1_subset_1(esk3_0,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_7])])])]) ).
fof(c_0_13,plain,
! [X246,X247] :
( k5_rmod_4(X246,X247,k3_rmod_4(X246,X247)) = k1_rlvect_1(X247)
| ~ l1_vectsp_2(X247,X246)
| ~ v5_vectsp_2(X247,X246)
| ~ v6_rlvect_1(X247)
| ~ v5_rlvect_1(X247)
| ~ v4_rlvect_1(X247)
| ~ v3_rlvect_1(X247)
| v3_struct_0(X247)
| ~ l3_vectsp_1(X246)
| ~ v8_vectsp_1(X246)
| ~ v7_vectsp_1(X246)
| ~ v6_vectsp_1(X246)
| ~ v4_group_1(X246)
| ~ v6_rlvect_1(X246)
| ~ v5_rlvect_1(X246)
| ~ v4_rlvect_1(X246)
| ~ v3_rlvect_1(X246)
| v3_struct_0(X246) ),
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_14,plain,
! [X32,X33,X34,X35] :
( ( ~ l3_vectsp_1(X32)
| ~ v8_vectsp_1(X32)
| ~ v7_vectsp_1(X32)
| ~ v6_vectsp_1(X32)
| ~ v4_group_1(X32)
| ~ v6_rlvect_1(X32)
| ~ v5_rlvect_1(X32)
| ~ v4_rlvect_1(X32)
| ~ v3_rlvect_1(X32)
| v3_struct_0(X32)
| ~ l1_vectsp_2(X33,X32)
| ~ v5_vectsp_2(X33,X32)
| ~ v6_rlvect_1(X33)
| ~ v5_rlvect_1(X33)
| ~ v4_rlvect_1(X33)
| ~ v3_rlvect_1(X33)
| v3_struct_0(X33)
| ~ m1_subset_1(X34,u1_struct_0(X33))
| ~ m1_subset_1(X35,u1_struct_0(X33))
| ~ v1_rmod_5(k8_rlvect_2(X33,X34,X35),X32,X33)
| k1_rlvect_1(X32) = k2_group_1(X32)
| X35 != k1_rlvect_1(X33) )
& ( ~ l3_vectsp_1(X32)
| ~ v8_vectsp_1(X32)
| ~ v7_vectsp_1(X32)
| ~ v6_vectsp_1(X32)
| ~ v4_group_1(X32)
| ~ v6_rlvect_1(X32)
| ~ v5_rlvect_1(X32)
| ~ v4_rlvect_1(X32)
| ~ v3_rlvect_1(X32)
| v3_struct_0(X32)
| ~ l1_vectsp_2(X33,X32)
| ~ v5_vectsp_2(X33,X32)
| ~ v6_rlvect_1(X33)
| ~ v5_rlvect_1(X33)
| ~ v4_rlvect_1(X33)
| ~ v3_rlvect_1(X33)
| v3_struct_0(X33)
| ~ m1_subset_1(X34,u1_struct_0(X33))
| ~ m1_subset_1(X35,u1_struct_0(X33))
| ~ v1_rmod_5(k8_rlvect_2(X33,X34,X35),X32,X33)
| k1_rlvect_1(X32) = k2_group_1(X32)
| X34 != k1_rlvect_1(X33) ) ),
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_9])])])])]) ).
fof(c_0_15,plain,
! [X255,X256,X257] :
( m1_subset_1(k5_rmod_4(X255,X256,X257),u1_struct_0(X256))
| ~ m1_rmod_4(X257,X255,X256)
| ~ l1_vectsp_2(X256,X255)
| ~ v5_vectsp_2(X256,X255)
| ~ v6_rlvect_1(X256)
| ~ v5_rlvect_1(X256)
| ~ v4_rlvect_1(X256)
| ~ v3_rlvect_1(X256)
| v3_struct_0(X256)
| ~ l3_vectsp_1(X255)
| ~ v8_vectsp_1(X255)
| ~ v7_vectsp_1(X255)
| ~ v6_vectsp_1(X255)
| ~ v4_group_1(X255)
| ~ v6_rlvect_1(X255)
| ~ v5_rlvect_1(X255)
| ~ v4_rlvect_1(X255)
| ~ v3_rlvect_1(X255)
| v3_struct_0(X255) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_16,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_4(k3_rmod_4(X1,X2),X1,X2)
| v3_struct_0(X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
v5_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
l1_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
v8_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,negated_conjecture,
v7_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,negated_conjecture,
v6_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,negated_conjecture,
l3_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_24,negated_conjecture,
v6_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,negated_conjecture,
v6_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_26,negated_conjecture,
v5_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,negated_conjecture,
v5_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_28,negated_conjecture,
v4_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_29,negated_conjecture,
v4_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_30,negated_conjecture,
v3_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_31,negated_conjecture,
v3_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_32,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_33,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_34,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)
| k5_rmod_4(X1,X2,k3_rmod_4(X1,X2)) = k1_rlvect_1(X2)
| v3_struct_0(X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_35,plain,
( ~ l3_vectsp_1(X3)
| ~ v8_vectsp_1(X3)
| ~ v7_vectsp_1(X3)
| ~ v6_vectsp_1(X3)
| ~ v4_group_1(X3)
| ~ v6_rlvect_1(X3)
| ~ v5_rlvect_1(X3)
| ~ v4_rlvect_1(X3)
| ~ v3_rlvect_1(X3)
| ~ l1_vectsp_2(X2,X3)
| ~ v5_vectsp_2(X2,X3)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| ~ m1_subset_1(X1,u1_struct_0(X2))
| ~ m1_subset_1(X4,u1_struct_0(X2))
| ~ v1_rmod_5(k8_rlvect_2(X2,X1,X4),X3,X2)
| X1 != k1_rlvect_1(X2)
| v3_struct_0(X3)
| v3_struct_0(X2)
| k1_rlvect_1(X3) = k2_group_1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_36,plain,
( ~ m1_rmod_4(X3,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)
| ~ 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_subset_1(k5_rmod_4(X1,X2,X3),u1_struct_0(X2))
| v3_struct_0(X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_37,negated_conjecture,
m1_rmod_4(k3_rmod_4(esk1_0,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_16,c_0_17]),c_0_18]),c_0_19]),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(esk1_0,esk2_0,k3_rmod_4(esk1_0,esk2_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(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_18]),c_0_19]),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_39,plain,
( ~ l3_vectsp_1(X3)
| ~ v8_vectsp_1(X3)
| ~ v7_vectsp_1(X3)
| ~ v6_vectsp_1(X3)
| ~ v4_group_1(X3)
| ~ v6_rlvect_1(X3)
| ~ v5_rlvect_1(X3)
| ~ v4_rlvect_1(X3)
| ~ v3_rlvect_1(X3)
| ~ l1_vectsp_2(X2,X3)
| ~ v5_vectsp_2(X2,X3)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| ~ m1_subset_1(X4,u1_struct_0(X2))
| ~ m1_subset_1(X1,u1_struct_0(X2))
| ~ v1_rmod_5(k8_rlvect_2(X2,X4,X1),X3,X2)
| X1 != k1_rlvect_1(X2)
| v3_struct_0(X3)
| v3_struct_0(X2)
| k1_rlvect_1(X3) = k2_group_1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_40,plain,
( ~ m1_subset_1(X3,u1_struct_0(X2))
| ~ m1_subset_1(k1_rlvect_1(X2),u1_struct_0(X2))
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X1)
| ~ v4_group_1(X1)
| ~ l3_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ v1_rmod_5(k8_rlvect_2(X2,k1_rlvect_1(X2),X3),X1,X2)
| v3_struct_0(X2)
| v3_struct_0(X1)
| k2_group_1(X1) = k1_rlvect_1(X1) ),
inference(er,[status(thm)],[c_0_35]) ).
cnf(c_0_41,negated_conjecture,
( v1_rmod_5(k8_rlvect_2(esk2_0,k1_rlvect_1(esk2_0),esk3_0),esk1_0,esk2_0)
| v1_rmod_5(k8_rlvect_2(esk2_0,esk3_0,k1_rlvect_1(esk2_0)),esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_42,negated_conjecture,
m1_subset_1(k1_rlvect_1(esk2_0),u1_struct_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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_17]),c_0_18]),c_0_19]),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_43,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_44,negated_conjecture,
k1_rlvect_1(esk1_0) != k2_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_45,plain,
( ~ m1_subset_1(X3,u1_struct_0(X2))
| ~ m1_subset_1(k1_rlvect_1(X2),u1_struct_0(X2))
| ~ v3_rlvect_1(X2)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X2)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X2)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X2)
| ~ v6_rlvect_1(X1)
| ~ v4_group_1(X1)
| ~ l3_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ v1_rmod_5(k8_rlvect_2(X2,X3,k1_rlvect_1(X2)),X1,X2)
| v3_struct_0(X2)
| v3_struct_0(X1)
| k2_group_1(X1) = k1_rlvect_1(X1) ),
inference(er,[status(thm)],[c_0_39]) ).
cnf(c_0_46,negated_conjecture,
v1_rmod_5(k8_rlvect_2(esk2_0,esk3_0,k1_rlvect_1(esk2_0)),esk1_0,esk2_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_17]),c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22]),c_0_23]),c_0_25]),c_0_24]),c_0_27]),c_0_26]),c_0_29]),c_0_28]),c_0_31]),c_0_30]),c_0_42]),c_0_43])]),c_0_44]),c_0_32]),c_0_33]) ).
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_17]),c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22]),c_0_23]),c_0_25]),c_0_24]),c_0_27]),c_0_26]),c_0_29]),c_0_28]),c_0_31]),c_0_30]),c_0_42]),c_0_43])]),c_0_44]),c_0_32]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG216+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 13:04:17 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 33.59/5.44 % Version: 3.5.1
% 33.59/5.44 % Preprocessing class: FMLLSMLLSSSNFFN.
% 33.59/5.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 33.59/5.44 % Starting new_bool_3 with 900s (3) cores
% 33.59/5.44 % Starting new_bool_1 with 900s (3) cores
% 33.59/5.44 % Starting sh5l with 300s (1) cores
% 33.59/5.44 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 33.59/5.44 % new_bool_1 with pid 159524 completed with status 0
% 33.59/5.44 % Result found by new_bool_1
% 33.59/5.44 % Preprocessing class: FMLLSMLLSSSNFFN.
% 33.59/5.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 33.59/5.44 % Starting new_bool_3 with 900s (3) cores
% 33.59/5.44 % Starting new_bool_1 with 900s (3) cores
% 33.59/5.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 33.59/5.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 33.59/5.44 % Search class: FGHSM-SMLM32-MFFFFFNN
% 33.59/5.44 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 33.59/5.44 % Starting SubtermCWHack with 82s (1) cores
% 33.59/5.44 % Starting new_bool_1 with 91s (1) cores
% 33.59/5.44 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 68s (1) cores
% 33.59/5.44 % new_bool_1 with pid 159530 completed with status 0
% 33.59/5.44 % Result found by new_bool_1
% 33.59/5.44 % Preprocessing class: FMLLSMLLSSSNFFN.
% 33.59/5.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 33.59/5.44 % Starting new_bool_3 with 900s (3) cores
% 33.59/5.44 % Starting new_bool_1 with 900s (3) cores
% 33.59/5.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 33.59/5.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 33.59/5.44 % Search class: FGHSM-SMLM32-MFFFFFNN
% 33.59/5.44 % Scheduled 13 strats onto 3 cores with 900 seconds (900 total)
% 33.59/5.44 % Starting SubtermCWHack with 82s (1) cores
% 33.59/5.44 % Starting new_bool_1 with 91s (1) cores
% 33.59/5.44 % Preprocessing time : 0.047 s
% 33.59/5.44 % Presaturation interreduction done
% 33.59/5.44
% 33.59/5.44 % Proof found!
% 33.59/5.44 % SZS status Theorem
% 33.59/5.44 % SZS output start CNFRefutation
% See solution above
% 33.59/5.44 % Parsed axioms : 9996
% 33.59/5.44 % Removed by relevancy pruning/SinE : 8720
% 33.59/5.44 % Initial clauses : 2577
% 33.59/5.44 % Removed in clause preprocessing : 94
% 33.59/5.44 % Initial clauses in saturation : 2483
% 33.59/5.44 % Processed clauses : 20489
% 33.59/5.44 % ...of these trivial : 167
% 33.59/5.44 % ...subsumed : 12091
% 33.59/5.44 % ...remaining for further processing : 8231
% 33.59/5.44 % Other redundant clauses eliminated : 1199
% 33.59/5.44 % Clauses deleted for lack of memory : 0
% 33.59/5.44 % Backward-subsumed : 159
% 33.59/5.44 % Backward-rewritten : 61
% 33.59/5.44 % Generated clauses : 109702
% 33.59/5.44 % ...of the previous two non-redundant : 99511
% 33.59/5.44 % ...aggressively subsumed : 0
% 33.59/5.44 % Contextual simplify-reflections : 199
% 33.59/5.44 % Paramodulations : 108439
% 33.59/5.44 % Factorizations : 26
% 33.59/5.44 % NegExts : 0
% 33.59/5.44 % Equation resolutions : 1246
% 33.59/5.44 % Disequality decompositions : 0
% 33.59/5.44 % Total rewrite steps : 21001
% 33.59/5.44 % ...of those cached : 18473
% 33.59/5.44 % Propositional unsat checks : 1
% 33.59/5.44 % Propositional check models : 0
% 33.59/5.44 % Propositional check unsatisfiable : 0
% 33.59/5.44 % Propositional clauses : 0
% 33.59/5.44 % Propositional clauses after purity: 0
% 33.59/5.44 % Propositional unsat core size : 0
% 33.59/5.44 % Propositional preprocessing time : 0.000
% 33.59/5.44 % Propositional encoding time : 0.029
% 33.59/5.44 % Propositional solver time : 0.021
% 33.59/5.44 % Success case prop preproc time : 0.000
% 33.59/5.44 % Success case prop encoding time : 0.000
% 33.59/5.44 % Success case prop solver time : 0.000
% 33.59/5.44 % Current number of processed clauses : 5460
% 33.59/5.44 % Positive orientable unit clauses : 670
% 33.59/5.44 % Positive unorientable unit clauses: 3
% 33.59/5.44 % Negative unit clauses : 863
% 33.59/5.44 % Non-unit-clauses : 3924
% 33.59/5.44 % Current number of unprocessed clauses: 83682
% 33.59/5.44 % ...number of literals in the above : 358710
% 33.59/5.44 % Current number of archived formulas : 0
% 33.59/5.44 % Current number of archived clauses : 2544
% 33.59/5.44 % Clause-clause subsumption calls (NU) : 13015812
% 33.59/5.44 % Rec. Clause-clause subsumption calls : 1785828
% 33.59/5.44 % Non-unit clause-clause subsumptions : 5433
% 33.59/5.44 % Unit Clause-clause subsumption calls : 486348
% 33.59/5.44 % Rewrite failures with RHS unbound : 0
% 33.59/5.44 % BW rewrite match attempts : 443
% 33.59/5.44 % BW rewrite match successes : 263
% 33.59/5.44 % Condensation attempts : 0
% 33.59/5.44 % Condensation successes : 0
% 33.59/5.44 % Termbank termtop insertions : 2210006
% 33.59/5.44 % Search garbage collected termcells : 130018
% 33.59/5.44
% 33.59/5.44 % -------------------------------------------------
% 33.59/5.44 % User time : 4.427 s
% 33.59/5.44 % System time : 0.129 s
% 33.59/5.44 % Total time : 4.556 s
% 33.59/5.44 % Maximum resident set size: 28028 pages
% 33.59/5.44
% 33.59/5.44 % -------------------------------------------------
% 33.59/5.44 % User time : 13.128 s
% 33.59/5.44 % System time : 0.339 s
% 33.59/5.44 % Total time : 13.467 s
% 33.59/5.44 % Maximum resident set size: 17408 pages
% 33.59/5.44 % E exiting
%------------------------------------------------------------------------------