TSTP Solution File: ALG216+2 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ALG216+2 : TPTP v8.2.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 18:05:39 EDT 2024
% Result : Theorem 27.83s 4.29s
% Output : CNFRefutation 27.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 47 ( 24 unt; 0 def)
% Number of atoms : 485 ( 25 equ)
% Maximal formula atoms : 44 ( 10 avg)
% Number of connectives : 679 ( 241 ~; 232 |; 180 &)
% ( 0 <=>; 26 =>; 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 : 60 ( 0 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k3_rmod_4,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& l3_vectsp_1(X1)
& ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> 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(t6_rmod_5,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X2))
=> ( k1_rlvect_1(X1) != k2_group_1(X1)
=> ( ~ v1_rmod_5(k8_rlvect_2(X2,X3,k1_rlvect_1(X2)),X1,X2)
& ~ v1_rmod_5(k8_rlvect_2(X2,k1_rlvect_1(X2),X3),X1,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_rmod_5) ).
fof(t41_rmod_4,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> 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] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X2))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X2))
=> ( v1_rmod_5(k8_rlvect_2(X2,X3,X4),X1,X2)
=> ( k1_rlvect_1(X1) = k2_group_1(X1)
| ( X3 != k1_rlvect_1(X2)
& X4 != k1_rlvect_1(X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_rmod_5) ).
fof(dt_k5_rmod_4,axiom,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& l3_vectsp_1(X1)
& ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1)
& m1_rmod_4(X3,X1,X2) )
=> 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,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& l3_vectsp_1(X1)
& ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> m1_rmod_4(k3_rmod_4(X1,X2),X1,X2) ),
inference(fof_simplification,[status(thm)],[dt_k3_rmod_4]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X2))
=> ( k1_rlvect_1(X1) != k2_group_1(X1)
=> ( ~ v1_rmod_5(k8_rlvect_2(X2,X3,k1_rlvect_1(X2)),X1,X2)
& ~ v1_rmod_5(k8_rlvect_2(X2,k1_rlvect_1(X2),X3),X1,X2) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t6_rmod_5])]) ).
fof(c_0_7,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> 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_8,plain,
! [X1] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& l3_vectsp_1(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1) )
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X2))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X2))
=> ( v1_rmod_5(k8_rlvect_2(X2,X3,X4),X1,X2)
=> ( k1_rlvect_1(X1) = k2_group_1(X1)
| ( X3 != k1_rlvect_1(X2)
& X4 != k1_rlvect_1(X2) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[t5_rmod_5]) ).
fof(c_0_9,plain,
! [X1,X2,X3] :
( ( ~ v3_struct_0(X1)
& v3_rlvect_1(X1)
& v4_rlvect_1(X1)
& v5_rlvect_1(X1)
& v6_rlvect_1(X1)
& v4_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& l3_vectsp_1(X1)
& ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v5_vectsp_2(X2,X1)
& l1_vectsp_2(X2,X1)
& m1_rmod_4(X3,X1,X2) )
=> 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_10,plain,
! [X1307,X1308] :
( v3_struct_0(X1307)
| ~ v3_rlvect_1(X1307)
| ~ v4_rlvect_1(X1307)
| ~ v5_rlvect_1(X1307)
| ~ v6_rlvect_1(X1307)
| ~ v4_group_1(X1307)
| ~ v6_vectsp_1(X1307)
| ~ v7_vectsp_1(X1307)
| ~ v8_vectsp_1(X1307)
| ~ l3_vectsp_1(X1307)
| v3_struct_0(X1308)
| ~ v3_rlvect_1(X1308)
| ~ v4_rlvect_1(X1308)
| ~ v5_rlvect_1(X1308)
| ~ v6_rlvect_1(X1308)
| ~ v5_vectsp_2(X1308,X1307)
| ~ l1_vectsp_2(X1308,X1307)
| m1_rmod_4(k3_rmod_4(X1307,X1308),X1307,X1308) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_11,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v3_rlvect_1(esk1_0)
& v4_rlvect_1(esk1_0)
& v5_rlvect_1(esk1_0)
& v6_rlvect_1(esk1_0)
& v4_group_1(esk1_0)
& v6_vectsp_1(esk1_0)
& v7_vectsp_1(esk1_0)
& v8_vectsp_1(esk1_0)
& l3_vectsp_1(esk1_0)
& ~ v3_struct_0(esk2_0)
& v3_rlvect_1(esk2_0)
& v4_rlvect_1(esk2_0)
& v5_rlvect_1(esk2_0)
& v6_rlvect_1(esk2_0)
& v5_vectsp_2(esk2_0,esk1_0)
& l1_vectsp_2(esk2_0,esk1_0)
& m1_subset_1(esk3_0,u1_struct_0(esk2_0))
& k1_rlvect_1(esk1_0) != k2_group_1(esk1_0)
& ( v1_rmod_5(k8_rlvect_2(esk2_0,esk3_0,k1_rlvect_1(esk2_0)),esk1_0,esk2_0)
| v1_rmod_5(k8_rlvect_2(esk2_0,k1_rlvect_1(esk2_0),esk3_0),esk1_0,esk2_0) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_12,plain,
! [X181,X182] :
( v3_struct_0(X181)
| ~ v3_rlvect_1(X181)
| ~ v4_rlvect_1(X181)
| ~ v5_rlvect_1(X181)
| ~ v6_rlvect_1(X181)
| ~ v4_group_1(X181)
| ~ v6_vectsp_1(X181)
| ~ v7_vectsp_1(X181)
| ~ v8_vectsp_1(X181)
| ~ l3_vectsp_1(X181)
| v3_struct_0(X182)
| ~ v3_rlvect_1(X182)
| ~ v4_rlvect_1(X182)
| ~ v5_rlvect_1(X182)
| ~ v6_rlvect_1(X182)
| ~ v5_vectsp_2(X182,X181)
| ~ l1_vectsp_2(X182,X181)
| k5_rmod_4(X181,X182,k3_rmod_4(X181,X182)) = k1_rlvect_1(X182) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_13,plain,
! [X32,X33,X34,X35] :
( ( X34 != k1_rlvect_1(X33)
| k1_rlvect_1(X32) = k2_group_1(X32)
| ~ v1_rmod_5(k8_rlvect_2(X33,X34,X35),X32,X33)
| ~ m1_subset_1(X35,u1_struct_0(X33))
| ~ m1_subset_1(X34,u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v3_rlvect_1(X33)
| ~ v4_rlvect_1(X33)
| ~ v5_rlvect_1(X33)
| ~ v6_rlvect_1(X33)
| ~ v5_vectsp_2(X33,X32)
| ~ l1_vectsp_2(X33,X32)
| v3_struct_0(X32)
| ~ v3_rlvect_1(X32)
| ~ v4_rlvect_1(X32)
| ~ v5_rlvect_1(X32)
| ~ v6_rlvect_1(X32)
| ~ v4_group_1(X32)
| ~ v6_vectsp_1(X32)
| ~ v7_vectsp_1(X32)
| ~ v8_vectsp_1(X32)
| ~ l3_vectsp_1(X32) )
& ( X35 != k1_rlvect_1(X33)
| k1_rlvect_1(X32) = k2_group_1(X32)
| ~ v1_rmod_5(k8_rlvect_2(X33,X34,X35),X32,X33)
| ~ m1_subset_1(X35,u1_struct_0(X33))
| ~ m1_subset_1(X34,u1_struct_0(X33))
| v3_struct_0(X33)
| ~ v3_rlvect_1(X33)
| ~ v4_rlvect_1(X33)
| ~ v5_rlvect_1(X33)
| ~ v6_rlvect_1(X33)
| ~ v5_vectsp_2(X33,X32)
| ~ l1_vectsp_2(X33,X32)
| v3_struct_0(X32)
| ~ v3_rlvect_1(X32)
| ~ v4_rlvect_1(X32)
| ~ v5_rlvect_1(X32)
| ~ v6_rlvect_1(X32)
| ~ v4_group_1(X32)
| ~ v6_vectsp_1(X32)
| ~ v7_vectsp_1(X32)
| ~ v8_vectsp_1(X32)
| ~ l3_vectsp_1(X32) ) ),
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_8])])])])]) ).
fof(c_0_14,plain,
! [X190,X191,X192] :
( v3_struct_0(X190)
| ~ v3_rlvect_1(X190)
| ~ v4_rlvect_1(X190)
| ~ v5_rlvect_1(X190)
| ~ v6_rlvect_1(X190)
| ~ v4_group_1(X190)
| ~ v6_vectsp_1(X190)
| ~ v7_vectsp_1(X190)
| ~ v8_vectsp_1(X190)
| ~ l3_vectsp_1(X190)
| v3_struct_0(X191)
| ~ v3_rlvect_1(X191)
| ~ v4_rlvect_1(X191)
| ~ v5_rlvect_1(X191)
| ~ v6_rlvect_1(X191)
| ~ v5_vectsp_2(X191,X190)
| ~ l1_vectsp_2(X191,X190)
| ~ m1_rmod_4(X192,X190,X191)
| m1_subset_1(k5_rmod_4(X190,X191,X192),u1_struct_0(X191)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_15,plain,
( v3_struct_0(X1)
| v3_struct_0(X2)
| m1_rmod_4(k3_rmod_4(X1,X2),X1,X2)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v4_group_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ l3_vectsp_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
l1_vectsp_2(esk2_0,esk1_0),
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_11]) ).
cnf(c_0_18,negated_conjecture,
v8_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
v7_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
v6_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,negated_conjecture,
l3_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_23,negated_conjecture,
v6_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_24,negated_conjecture,
v6_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_25,negated_conjecture,
v5_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_26,negated_conjecture,
v5_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_27,negated_conjecture,
v4_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_28,negated_conjecture,
v4_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,negated_conjecture,
v3_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,negated_conjecture,
v3_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_31,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_32,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_33,plain,
( v3_struct_0(X1)
| v3_struct_0(X2)
| k5_rmod_4(X1,X2,k3_rmod_4(X1,X2)) = k1_rlvect_1(X2)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v4_group_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ l3_vectsp_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_34,plain,
( k1_rlvect_1(X3) = k2_group_1(X3)
| v3_struct_0(X2)
| v3_struct_0(X3)
| X1 != k1_rlvect_1(X2)
| ~ v1_rmod_5(k8_rlvect_2(X2,X1,X4),X3,X2)
| ~ m1_subset_1(X4,u1_struct_0(X2))
| ~ m1_subset_1(X1,u1_struct_0(X2))
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,X3)
| ~ l1_vectsp_2(X2,X3)
| ~ v3_rlvect_1(X3)
| ~ v4_rlvect_1(X3)
| ~ v5_rlvect_1(X3)
| ~ v6_rlvect_1(X3)
| ~ v4_group_1(X3)
| ~ v6_vectsp_1(X3)
| ~ v7_vectsp_1(X3)
| ~ v8_vectsp_1(X3)
| ~ l3_vectsp_1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_35,plain,
( v3_struct_0(X1)
| v3_struct_0(X2)
| m1_subset_1(k5_rmod_4(X1,X2,X3),u1_struct_0(X2))
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v4_group_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ l3_vectsp_1(X1)
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1)
| ~ m1_rmod_4(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_36,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_15,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]) ).
cnf(c_0_37,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_33,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]) ).
cnf(c_0_38,plain,
( k1_rlvect_1(X3) = k2_group_1(X3)
| v3_struct_0(X2)
| v3_struct_0(X3)
| X1 != k1_rlvect_1(X2)
| ~ v1_rmod_5(k8_rlvect_2(X2,X4,X1),X3,X2)
| ~ m1_subset_1(X1,u1_struct_0(X2))
| ~ m1_subset_1(X4,u1_struct_0(X2))
| ~ v3_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v6_rlvect_1(X2)
| ~ v5_vectsp_2(X2,X3)
| ~ l1_vectsp_2(X2,X3)
| ~ v3_rlvect_1(X3)
| ~ v4_rlvect_1(X3)
| ~ v5_rlvect_1(X3)
| ~ v6_rlvect_1(X3)
| ~ v4_group_1(X3)
| ~ v6_vectsp_1(X3)
| ~ v7_vectsp_1(X3)
| ~ v8_vectsp_1(X3)
| ~ l3_vectsp_1(X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_39,plain,
( k2_group_1(X1) = k1_rlvect_1(X1)
| v3_struct_0(X1)
| v3_struct_0(X2)
| ~ v1_rmod_5(k8_rlvect_2(X2,k1_rlvect_1(X2),X3),X1,X2)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ l3_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X1)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X1)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X1)
| ~ v3_rlvect_1(X2)
| ~ m1_subset_1(k1_rlvect_1(X2),u1_struct_0(X2))
| ~ m1_subset_1(X3,u1_struct_0(X2)) ),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( v1_rmod_5(k8_rlvect_2(esk2_0,esk3_0,k1_rlvect_1(esk2_0)),esk1_0,esk2_0)
| v1_rmod_5(k8_rlvect_2(esk2_0,k1_rlvect_1(esk2_0),esk3_0),esk1_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_41,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_35,c_0_36]),c_0_37]),c_0_17]),c_0_16]),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]) ).
cnf(c_0_42,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_43,negated_conjecture,
k1_rlvect_1(esk1_0) != k2_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_44,plain,
( k2_group_1(X1) = k1_rlvect_1(X1)
| v3_struct_0(X1)
| v3_struct_0(X2)
| ~ v1_rmod_5(k8_rlvect_2(X2,X3,k1_rlvect_1(X2)),X1,X2)
| ~ v5_vectsp_2(X2,X1)
| ~ l1_vectsp_2(X2,X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ l3_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X1)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X1)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X1)
| ~ v3_rlvect_1(X2)
| ~ m1_subset_1(k1_rlvect_1(X2),u1_struct_0(X2))
| ~ m1_subset_1(X3,u1_struct_0(X2)) ),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_45,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_39,c_0_40]),c_0_17]),c_0_16]),c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22]),c_0_24]),c_0_23]),c_0_26]),c_0_25]),c_0_28]),c_0_27]),c_0_30]),c_0_29]),c_0_41]),c_0_42])]),c_0_43]),c_0_31]),c_0_32]) ).
cnf(c_0_46,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_44,c_0_45]),c_0_17]),c_0_16]),c_0_18]),c_0_19]),c_0_20]),c_0_21]),c_0_22]),c_0_24]),c_0_23]),c_0_26]),c_0_25]),c_0_28]),c_0_27]),c_0_30]),c_0_29]),c_0_41]),c_0_42])]),c_0_43]),c_0_31]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : ALG216+2 : TPTP v8.2.0. Released v3.4.0.
% 0.04/0.15 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n004.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sat May 18 22:58:53 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.23/0.53 Running first-order theorem proving
% 0.23/0.53 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
% 27.83/4.29 # Version: 3.1.0
% 27.83/4.29 # Preprocessing class: FMLMSMSLSSSNFFN.
% 27.83/4.29 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.83/4.29 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 27.83/4.29 # Starting new_bool_3 with 600s (2) cores
% 27.83/4.29 # Starting new_bool_1 with 600s (2) cores
% 27.83/4.29 # Starting sh5l with 300s (1) cores
% 27.83/4.29 # new_bool_3 with pid 17026 completed with status 0
% 27.83/4.29 # Result found by new_bool_3
% 27.83/4.29 # Preprocessing class: FMLMSMSLSSSNFFN.
% 27.83/4.29 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.83/4.29 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 27.83/4.29 # Starting new_bool_3 with 600s (2) cores
% 27.83/4.29 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 27.83/4.29 # Search class: FGHSM-SMLM32-MFFFFFNN
% 27.83/4.29 # Scheduled 13 strats onto 2 cores with 600 seconds (600 total)
% 27.83/4.29 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 45s (1) cores
% 27.83/4.29 # Starting new_bool_3 with 61s (1) cores
% 27.83/4.29 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with pid 17031 completed with status 0
% 27.83/4.29 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI
% 27.83/4.29 # Preprocessing class: FMLMSMSLSSSNFFN.
% 27.83/4.29 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.83/4.29 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 27.83/4.29 # Starting new_bool_3 with 600s (2) cores
% 27.83/4.29 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 27.83/4.29 # Search class: FGHSM-SMLM32-MFFFFFNN
% 27.83/4.29 # Scheduled 13 strats onto 2 cores with 600 seconds (600 total)
% 27.83/4.29 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 45s (1) cores
% 27.83/4.29 # Preprocessing time : 0.022 s
% 27.83/4.29 # Presaturation interreduction done
% 27.83/4.29
% 27.83/4.29 # Proof found!
% 27.83/4.29 # SZS status Theorem
% 27.83/4.29 # SZS output start CNFRefutation
% See solution above
% 27.83/4.29 # Parsed axioms : 3449
% 27.83/4.29 # Removed by relevancy pruning/SinE : 2509
% 27.83/4.29 # Initial clauses : 1814
% 27.83/4.29 # Removed in clause preprocessing : 75
% 27.83/4.29 # Initial clauses in saturation : 1739
% 27.83/4.29 # Processed clauses : 15110
% 27.83/4.29 # ...of these trivial : 134
% 27.83/4.29 # ...subsumed : 6898
% 27.83/4.29 # ...remaining for further processing : 8078
% 27.83/4.29 # Other redundant clauses eliminated : 253
% 27.83/4.29 # Clauses deleted for lack of memory : 0
% 27.83/4.29 # Backward-subsumed : 138
% 27.83/4.29 # Backward-rewritten : 68
% 27.83/4.29 # Generated clauses : 99910
% 27.83/4.29 # ...of the previous two non-redundant : 95074
% 27.83/4.29 # ...aggressively subsumed : 0
% 27.83/4.29 # Contextual simplify-reflections : 94
% 27.83/4.29 # Paramodulations : 99600
% 27.83/4.29 # Factorizations : 24
% 27.83/4.29 # NegExts : 0
% 27.83/4.29 # Equation resolutions : 299
% 27.83/4.29 # Disequality decompositions : 0
% 27.83/4.29 # Total rewrite steps : 35292
% 27.83/4.29 # ...of those cached : 32494
% 27.83/4.29 # Propositional unsat checks : 1
% 27.83/4.29 # Propositional check models : 0
% 27.83/4.29 # Propositional check unsatisfiable : 0
% 27.83/4.29 # Propositional clauses : 0
% 27.83/4.29 # Propositional clauses after purity: 0
% 27.83/4.29 # Propositional unsat core size : 0
% 27.83/4.29 # Propositional preprocessing time : 0.000
% 27.83/4.29 # Propositional encoding time : 0.028
% 27.83/4.29 # Propositional solver time : 0.023
% 27.83/4.29 # Success case prop preproc time : 0.000
% 27.83/4.29 # Success case prop encoding time : 0.000
% 27.83/4.29 # Success case prop solver time : 0.000
% 27.83/4.29 # Current number of processed clauses : 6097
% 27.83/4.29 # Positive orientable unit clauses : 907
% 27.83/4.29 # Positive unorientable unit clauses: 3
% 27.83/4.29 # Negative unit clauses : 955
% 27.83/4.29 # Non-unit-clauses : 4232
% 27.83/4.29 # Current number of unprocessed clauses: 83219
% 27.83/4.29 # ...number of literals in the above : 250273
% 27.83/4.29 # Current number of archived formulas : 0
% 27.83/4.29 # Current number of archived clauses : 1815
% 27.83/4.29 # Clause-clause subsumption calls (NU) : 6619927
% 27.83/4.29 # Rec. Clause-clause subsumption calls : 1611116
% 27.83/4.29 # Non-unit clause-clause subsumptions : 2264
% 27.83/4.29 # Unit Clause-clause subsumption calls : 497567
% 27.83/4.29 # Rewrite failures with RHS unbound : 0
% 27.83/4.29 # BW rewrite match attempts : 3521
% 27.83/4.29 # BW rewrite match successes : 214
% 27.83/4.29 # Condensation attempts : 0
% 27.83/4.29 # Condensation successes : 0
% 27.83/4.29 # Termbank termtop insertions : 1865429
% 27.83/4.29 # Search garbage collected termcells : 60715
% 27.83/4.29
% 27.83/4.29 # -------------------------------------------------
% 27.83/4.29 # User time : 3.488 s
% 27.83/4.29 # System time : 0.105 s
% 27.83/4.29 # Total time : 3.593 s
% 27.83/4.29 # Maximum resident set size: 12936 pages
% 27.83/4.29
% 27.83/4.29 # -------------------------------------------------
% 27.83/4.29 # User time : 7.024 s
% 27.83/4.29 # System time : 0.120 s
% 27.83/4.29 # Total time : 7.144 s
% 27.83/4.29 # Maximum resident set size: 5780 pages
% 27.83/4.29 % E---3.1 exiting
% 27.83/4.29 % E exiting
%------------------------------------------------------------------------------