%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG216+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 0.27s 0.55s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 25 unt; 0 def)
% Number of atoms : 306 ( 22 equ)
% Maximal formula atoms : 44 ( 5 avg)
% Number of connectives : 380 ( 131 ~; 111 |; 108 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 60 ( 0 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_l1_rlvect_1,axiom,
! [X1] :
( l1_rlvect_1(X1)
=> l2_struct_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_rlvect_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/theBenchmark.p',dt_l3_vectsp_1) ).
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_l2_struct_0,axiom,
! [X1] :
( l2_struct_0(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_struct_0) ).
fof(dt_l1_vectsp_2,axiom,
! [X1] :
( l1_struct_0(X1)
=> ! [X2] :
( l1_vectsp_2(X2,X1)
=> l1_rlvect_1(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_vectsp_2) ).
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(commutativity_k8_rlvect_2,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X1))
& m1_subset_1(X2,u1_struct_0(X1))
& l1_struct_0(X1)
& ~ v3_struct_0(X1) )
=> k8_rlvect_2(X1,X2,X3) = k8_rlvect_2(X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k8_rlvect_2) ).
fof(dt_k1_rlvect_1,axiom,
! [X1] :
( l2_struct_0(X1)
=> m1_subset_1(k1_rlvect_1(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_rlvect_1) ).
fof(c_0_8,plain,
! [X33] :
( l2_struct_0(X33)
| ~ l1_rlvect_1(X33) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_rlvect_1])])]) ).
fof(c_0_9,plain,
! [X30] :
( ( ~ l3_vectsp_1(X30)
| l2_vectsp_1(X30) )
& ( ~ l3_vectsp_1(X30)
| l1_rlvect_1(X30) ) ),
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_10,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_11,plain,
! [X34] :
( l1_struct_0(X34)
| ~ l2_struct_0(X34) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_struct_0])])]) ).
cnf(c_0_12,plain,
( ~ l1_rlvect_1(X1)
| l2_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( ~ l3_vectsp_1(X1)
| l1_rlvect_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,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_10]) ).
cnf(c_0_15,plain,
( ~ l2_struct_0(X1)
| l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( ~ l3_vectsp_1(X1)
| l2_struct_0(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_17,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_14])])])]) ).
fof(c_0_18,plain,
! [X26,X27] :
( l1_rlvect_1(X27)
| ~ l1_vectsp_2(X27,X26)
| ~ l1_struct_0(X26) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_vectsp_2])])])]) ).
cnf(c_0_19,plain,
( ~ l3_vectsp_1(X1)
| l1_struct_0(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
l3_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
( ~ l1_vectsp_2(X2,X1)
| ~ l1_struct_0(X1)
| l1_rlvect_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
l1_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
l1_struct_0(esk1_0),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_24,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_25,plain,
! [X1,X2,X3] :
( ( m1_subset_1(X3,u1_struct_0(X1))
& m1_subset_1(X2,u1_struct_0(X1))
& l1_struct_0(X1)
& ~ v3_struct_0(X1) )
=> k8_rlvect_2(X1,X2,X3) = k8_rlvect_2(X1,X3,X2) ),
inference(fof_simplification,[status(thm)],[commutativity_k8_rlvect_2]) ).
cnf(c_0_26,negated_conjecture,
l1_rlvect_1(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
fof(c_0_27,plain,
! [X8,X9,X10,X11] :
( ( ~ l3_vectsp_1(X8)
| ~ v8_vectsp_1(X8)
| ~ v7_vectsp_1(X8)
| ~ v6_vectsp_1(X8)
| ~ v4_group_1(X8)
| ~ v6_rlvect_1(X8)
| ~ v5_rlvect_1(X8)
| ~ v4_rlvect_1(X8)
| ~ v3_rlvect_1(X8)
| v3_struct_0(X8)
| ~ l1_vectsp_2(X9,X8)
| ~ v5_vectsp_2(X9,X8)
| ~ v6_rlvect_1(X9)
| ~ v5_rlvect_1(X9)
| ~ v4_rlvect_1(X9)
| ~ v3_rlvect_1(X9)
| v3_struct_0(X9)
| ~ m1_subset_1(X10,u1_struct_0(X9))
| ~ m1_subset_1(X11,u1_struct_0(X9))
| ~ v1_rmod_5(k8_rlvect_2(X9,X10,X11),X8,X9)
| k1_rlvect_1(X8) = k2_group_1(X8)
| X11 != k1_rlvect_1(X9) )
& ( ~ l3_vectsp_1(X8)
| ~ v8_vectsp_1(X8)
| ~ v7_vectsp_1(X8)
| ~ v6_vectsp_1(X8)
| ~ v4_group_1(X8)
| ~ v6_rlvect_1(X8)
| ~ v5_rlvect_1(X8)
| ~ v4_rlvect_1(X8)
| ~ v3_rlvect_1(X8)
| v3_struct_0(X8)
| ~ l1_vectsp_2(X9,X8)
| ~ v5_vectsp_2(X9,X8)
| ~ v6_rlvect_1(X9)
| ~ v5_rlvect_1(X9)
| ~ v4_rlvect_1(X9)
| ~ v3_rlvect_1(X9)
| v3_struct_0(X9)
| ~ m1_subset_1(X10,u1_struct_0(X9))
| ~ m1_subset_1(X11,u1_struct_0(X9))
| ~ v1_rmod_5(k8_rlvect_2(X9,X10,X11),X8,X9)
| k1_rlvect_1(X8) = k2_group_1(X8)
| X10 != k1_rlvect_1(X9) ) ),
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_24])])])])]) ).
fof(c_0_28,plain,
! [X12,X13,X14] :
( k8_rlvect_2(X12,X13,X14) = k8_rlvect_2(X12,X14,X13)
| ~ m1_subset_1(X14,u1_struct_0(X12))
| ~ m1_subset_1(X13,u1_struct_0(X12))
| ~ l1_struct_0(X12)
| v3_struct_0(X12) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
cnf(c_0_29,negated_conjecture,
l2_struct_0(esk2_0),
inference(spm,[status(thm)],[c_0_12,c_0_26]) ).
cnf(c_0_30,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_27]) ).
cnf(c_0_31,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_17]) ).
cnf(c_0_32,plain,
( ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_struct_0(X1)
| k8_rlvect_2(X1,X2,X3) = k8_rlvect_2(X1,X3,X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,negated_conjecture,
l1_struct_0(esk2_0),
inference(spm,[status(thm)],[c_0_15,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_35,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_36,plain,
( ~ 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)
| ~ 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(X3,u1_struct_0(X2))
| ~ m1_subset_1(k1_rlvect_1(X2),u1_struct_0(X2))
| ~ 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_30]) ).
cnf(c_0_37,negated_conjecture,
( ~ m1_subset_1(k1_rlvect_1(esk2_0),u1_struct_0(esk2_0))
| v1_rmod_5(k8_rlvect_2(esk2_0,esk3_0,k1_rlvect_1(esk2_0)),esk1_0,esk2_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34])]),c_0_35]) ).
cnf(c_0_38,negated_conjecture,
v5_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_39,negated_conjecture,
v8_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_40,negated_conjecture,
v7_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_41,negated_conjecture,
v6_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_42,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_43,negated_conjecture,
v6_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_44,negated_conjecture,
v6_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_45,negated_conjecture,
v5_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_46,negated_conjecture,
v5_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_47,negated_conjecture,
v4_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_48,negated_conjecture,
v4_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_49,negated_conjecture,
v3_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_50,negated_conjecture,
v3_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_51,negated_conjecture,
k1_rlvect_1(esk1_0) != k2_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_52,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_53,plain,
! [X15] :
( m1_subset_1(k1_rlvect_1(X15),u1_struct_0(X15))
| ~ l2_struct_0(X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_rlvect_1])])]) ).
cnf(c_0_54,negated_conjecture,
~ m1_subset_1(k1_rlvect_1(esk2_0),u1_struct_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(spm,[status(thm)],[c_0_36,c_0_37]),c_0_34]),c_0_22]),c_0_38]),c_0_20]),c_0_39]),c_0_40]),c_0_41]),c_0_42]),c_0_43]),c_0_44]),c_0_45]),c_0_46]),c_0_47]),c_0_48]),c_0_49]),c_0_50])]),c_0_51]),c_0_52]),c_0_35]) ).
cnf(c_0_55,plain,
( ~ l2_struct_0(X1)
| m1_subset_1(k1_rlvect_1(X1),u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG216+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n026.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 13:05:22 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.50 Running first-order theorem proving
% 0.27/0.50 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
% 0.27/0.55 % Version: 3.5.1
% 0.27/0.55 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.27/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.55 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.27/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.55 % Starting sh5l with 300s (1) cores
% 0.27/0.55 % new_bool_1 with pid 2327252 completed with status 0
% 0.27/0.55 % Result found by new_bool_1
% 0.27/0.55 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.27/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.55 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.27/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.27/0.55 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.27/0.55 % Search class: FGHSS-FFMM31-SFFFFFNN
% 0.27/0.55 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.55 % Starting SubtermCWHack with 28s (1) cores
% 0.27/0.55 % SubtermCWHack with pid 2327258 completed with status 0
% 0.27/0.55 % Result found by SubtermCWHack
% 0.27/0.55 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.27/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.55 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.27/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.55 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.27/0.55 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.27/0.55 % Search class: FGHSS-FFMM31-SFFFFFNN
% 0.27/0.55 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.55 % Starting SubtermCWHack with 28s (1) cores
% 0.27/0.55 % Preprocessing time : 0.002 s
% 0.27/0.55
% 0.27/0.55 % Proof found!
% 0.27/0.55 % SZS status Theorem
% 0.27/0.55 % SZS output start CNFRefutation
% See solution above
% 0.27/0.55 % Parsed axioms : 53
% 0.27/0.55 % Removed by relevancy pruning/SinE : 15
% 0.27/0.55 % Initial clauses : 66
% 0.27/0.55 % Removed in clause preprocessing : 0
% 0.27/0.55 % Initial clauses in saturation : 66
% 0.27/0.55 % Processed clauses : 188
% 0.27/0.55 % ...of these trivial : 0
% 0.27/0.55 % ...subsumed : 42
% 0.27/0.55 % ...remaining for further processing : 146
% 0.27/0.55 % Other redundant clauses eliminated : 2
% 0.27/0.55 % Clauses deleted for lack of memory : 0
% 0.27/0.55 % Backward-subsumed : 4
% 0.27/0.55 % Backward-rewritten : 2
% 0.27/0.55 % Generated clauses : 221
% 0.27/0.55 % ...of the previous two non-redundant : 198
% 0.27/0.55 % ...aggressively subsumed : 0
% 0.27/0.55 % Contextual simplify-reflections : 6
% 0.27/0.55 % Paramodulations : 219
% 0.27/0.55 % Factorizations : 0
% 0.27/0.55 % NegExts : 0
% 0.27/0.55 % Equation resolutions : 2
% 0.27/0.55 % Disequality decompositions : 0
% 0.27/0.55 % Total rewrite steps : 46
% 0.27/0.55 % ...of those cached : 22
% 0.27/0.55 % Propositional unsat checks : 0
% 0.27/0.55 % Propositional check models : 0
% 0.27/0.55 % Propositional check unsatisfiable : 0
% 0.27/0.55 % Propositional clauses : 0
% 0.27/0.55 % Propositional clauses after purity: 0
% 0.27/0.55 % Propositional unsat core size : 0
% 0.27/0.55 % Propositional preprocessing time : 0.000
% 0.27/0.55 % Propositional encoding time : 0.000
% 0.27/0.55 % Propositional solver time : 0.000
% 0.27/0.55 % Success case prop preproc time : 0.000
% 0.27/0.55 % Success case prop encoding time : 0.000
% 0.27/0.55 % Success case prop solver time : 0.000
% 0.27/0.55 % Current number of processed clauses : 138
% 0.27/0.55 % Positive orientable unit clauses : 44
% 0.27/0.55 % Positive unorientable unit clauses: 0
% 0.27/0.55 % Negative unit clauses : 8
% 0.27/0.55 % Non-unit-clauses : 86
% 0.27/0.55 % Current number of unprocessed clauses: 70
% 0.27/0.55 % ...number of literals in the above : 307
% 0.27/0.55 % Current number of archived formulas : 0
% 0.27/0.55 % Current number of archived clauses : 6
% 0.27/0.55 % Clause-clause subsumption calls (NU) : 4631
% 0.27/0.55 % Rec. Clause-clause subsumption calls : 1849
% 0.27/0.55 % Non-unit clause-clause subsumptions : 51
% 0.27/0.55 % Unit Clause-clause subsumption calls : 29
% 0.27/0.55 % Rewrite failures with RHS unbound : 0
% 0.27/0.55 % BW rewrite match attempts : 1
% 0.27/0.55 % BW rewrite match successes : 1
% 0.27/0.55 % Condensation attempts : 0
% 0.27/0.55 % Condensation successes : 0
% 0.27/0.55 % Termbank termtop insertions : 7566
% 0.27/0.55 % Search garbage collected termcells : 911
% 0.27/0.55
% 0.27/0.55 % -------------------------------------------------
% 0.27/0.55 % User time : 0.016 s
% 0.27/0.55 % System time : 0.006 s
% 0.27/0.55 % Total time : 0.022 s
% 0.27/0.55 % Maximum resident set size: 3680 pages
% 0.27/0.55
% 0.27/0.55 % -------------------------------------------------
% 0.27/0.55 % User time : 0.018 s
% 0.27/0.55 % System time : 0.013 s
% 0.27/0.55 % Total time : 0.031 s
% 0.27/0.55 % Maximum resident set size: 4608 pages
% 0.27/0.55 % E exiting
%------------------------------------------------------------------------------