%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG218+4 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 61.64s 16.98s
% Output : CNFRefutation 61.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 83 ( 32 unt; 0 def)
% Number of atoms : 439 ( 65 equ)
% Maximal formula atoms : 38 ( 5 avg)
% Number of connectives : 531 ( 175 ~; 151 |; 171 &)
% ( 4 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 96 ( 0 sgn 68 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t12_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)
& 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 != k7_rlvect_2(X2,k1_rlvect_1(X2))
& X3 != k1_xboole_0
& k1_rmod_5(X1,X2,X3) = k1_rmod_2(X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_rmod_5) ).
fof(t10_rmod_5,axiom,
! [X1,X2] :
( ( l3_vectsp_1(X2)
& v2_vectsp_2(X2)
& ~ v10_vectsp_1(X2)
& v8_vectsp_1(X2)
& v7_vectsp_1(X2)
& v6_vectsp_1(X2)
& v7_group_1(X2)
& v4_group_1(X2)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( ( l1_vectsp_2(X3,X2)
& v5_vectsp_2(X3,X2)
& v6_rlvect_1(X3)
& v5_rlvect_1(X3)
& v4_rlvect_1(X3)
& v3_rlvect_1(X3)
& ~ v3_struct_0(X3) )
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X3)))
=> ( r2_hidden(X1,X4)
=> r1_rlvect_1(k1_rmod_5(X2,X3,X4),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_rmod_5) ).
fof(t46_rmod_2,axiom,
! [X1,X2] :
( ( l3_vectsp_1(X2)
& v8_vectsp_1(X2)
& v7_vectsp_1(X2)
& v6_vectsp_1(X2)
& v4_group_1(X2)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( ( l1_vectsp_2(X3,X2)
& v5_vectsp_2(X3,X2)
& v6_rlvect_1(X3)
& v5_rlvect_1(X3)
& v4_rlvect_1(X3)
& v3_rlvect_1(X3)
& ~ v3_struct_0(X3) )
=> ( r1_rlvect_1(k1_rmod_2(X2,X3),X1)
<=> X1 = k1_rlvect_1(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+278.ax',t46_rmod_2) ).
fof(t2_collsp,axiom,
! [X1] :
~ ( ! [X2] :
( ! [X3,X4] :
~ ( r2_hidden(X4,X1)
& r2_hidden(X3,X1)
& X3 != X4 )
& k1_tarski(X2) != X1 )
& X1 != k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+232.ax',t2_collsp) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = k1_tarski(X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+1.ax',d1_tarski) ).
fof(redefinition_k7_rlvect_2,axiom,
! [X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X1))
& l1_struct_0(X1)
& ~ v3_struct_0(X1) )
=> k7_rlvect_2(X1,X2) = k1_tarski(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+224.ax',redefinition_k7_rlvect_2) ).
fof(dt_l2_struct_0,axiom,
! [X1] :
( l2_struct_0(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+200.ax',dt_l2_struct_0) ).
fof(dt_l2_vectsp_1,axiom,
! [X1] :
( l2_vectsp_1(X1)
=> ( l2_struct_0(X1)
& l1_vectsp_1(X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+213.ax',dt_l2_vectsp_1) ).
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/sandbox/benchmark/Axioms/SET007/SET007+210.ax',dt_k1_rlvect_1) ).
fof(dt_l1_vectsp_2,axiom,
! [X1] :
( l1_struct_0(X1)
=> ! [X2] :
( l1_vectsp_2(X2,X1)
=> l1_rlvect_1(X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+241.ax',dt_l1_vectsp_2) ).
fof(dt_l3_vectsp_1,axiom,
! [X1] :
( l3_vectsp_1(X1)
=> ( l2_vectsp_1(X1)
& l1_rlvect_1(X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+213.ax',dt_l3_vectsp_1) ).
fof(dt_l1_rlvect_1,axiom,
! [X1] :
( l1_rlvect_1(X1)
=> l2_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+210.ax',dt_l1_rlvect_1) ).
fof(c_0_12,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)
& 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 != k7_rlvect_2(X2,k1_rlvect_1(X2))
& X3 != k1_xboole_0
& k1_rmod_5(X1,X2,X3) = k1_rmod_2(X1,X2) ) ) ) ),
inference(assume_negation,[status(cth)],[t12_rmod_5]) ).
fof(c_0_13,plain,
! [X1,X2] :
( ( l3_vectsp_1(X2)
& v2_vectsp_2(X2)
& ~ v10_vectsp_1(X2)
& v8_vectsp_1(X2)
& v7_vectsp_1(X2)
& v6_vectsp_1(X2)
& v7_group_1(X2)
& v4_group_1(X2)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( ( l1_vectsp_2(X3,X2)
& v5_vectsp_2(X3,X2)
& v6_rlvect_1(X3)
& v5_rlvect_1(X3)
& v4_rlvect_1(X3)
& v3_rlvect_1(X3)
& ~ v3_struct_0(X3) )
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X3)))
=> ( r2_hidden(X1,X4)
=> r1_rlvect_1(k1_rmod_5(X2,X3,X4),X1) ) ) ) ),
inference(fof_simplification,[status(thm)],[t10_rmod_5]) ).
fof(c_0_14,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)
& 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 != k7_rlvect_2(X2,k1_rlvect_1(X2))
& X3 != k1_xboole_0
& k1_rmod_5(X1,X2,X3) = k1_rmod_2(X1,X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X1,X2] :
( ( l3_vectsp_1(X2)
& v8_vectsp_1(X2)
& v7_vectsp_1(X2)
& v6_vectsp_1(X2)
& v4_group_1(X2)
& v6_rlvect_1(X2)
& v5_rlvect_1(X2)
& v4_rlvect_1(X2)
& v3_rlvect_1(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( ( l1_vectsp_2(X3,X2)
& v5_vectsp_2(X3,X2)
& v6_rlvect_1(X3)
& v5_rlvect_1(X3)
& v4_rlvect_1(X3)
& v3_rlvect_1(X3)
& ~ v3_struct_0(X3) )
=> ( r1_rlvect_1(k1_rmod_2(X2,X3),X1)
<=> X1 = k1_rlvect_1(X3) ) ) ),
inference(fof_simplification,[status(thm)],[t46_rmod_2]) ).
fof(c_0_16,plain,
! [X202,X203,X204,X205] :
( r1_rlvect_1(k1_rmod_5(X203,X204,X205),X202)
| ~ r2_hidden(X202,X205)
| ~ m1_subset_1(X205,k1_zfmisc_1(u1_struct_0(X204)))
| ~ l1_vectsp_2(X204,X203)
| ~ v5_vectsp_2(X204,X203)
| ~ v6_rlvect_1(X204)
| ~ v5_rlvect_1(X204)
| ~ v4_rlvect_1(X204)
| ~ v3_rlvect_1(X204)
| v3_struct_0(X204)
| ~ l3_vectsp_1(X203)
| ~ v2_vectsp_2(X203)
| v10_vectsp_1(X203)
| ~ v8_vectsp_1(X203)
| ~ v7_vectsp_1(X203)
| ~ v6_vectsp_1(X203)
| ~ v7_group_1(X203)
| ~ v4_group_1(X203)
| ~ v6_rlvect_1(X203)
| ~ v5_rlvect_1(X203)
| ~ v4_rlvect_1(X203)
| ~ v3_rlvect_1(X203)
| v3_struct_0(X203) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
fof(c_0_17,negated_conjecture,
( esk3_0 != k7_rlvect_2(esk2_0,k1_rlvect_1(esk2_0))
& esk3_0 != k1_xboole_0
& k1_rmod_5(esk1_0,esk2_0,esk3_0) = k1_rmod_2(esk1_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)
& 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_14])])])]) ).
fof(c_0_18,plain,
! [X155,X156,X157] :
( ( ~ l3_vectsp_1(X156)
| ~ v8_vectsp_1(X156)
| ~ v7_vectsp_1(X156)
| ~ v6_vectsp_1(X156)
| ~ v4_group_1(X156)
| ~ v6_rlvect_1(X156)
| ~ v5_rlvect_1(X156)
| ~ v4_rlvect_1(X156)
| ~ v3_rlvect_1(X156)
| v3_struct_0(X156)
| ~ l1_vectsp_2(X157,X156)
| ~ v5_vectsp_2(X157,X156)
| ~ v6_rlvect_1(X157)
| ~ v5_rlvect_1(X157)
| ~ v4_rlvect_1(X157)
| ~ v3_rlvect_1(X157)
| v3_struct_0(X157)
| r1_rlvect_1(k1_rmod_2(X156,X157),X155)
| X155 != k1_rlvect_1(X157) )
& ( ~ l3_vectsp_1(X156)
| ~ v8_vectsp_1(X156)
| ~ v7_vectsp_1(X156)
| ~ v6_vectsp_1(X156)
| ~ v4_group_1(X156)
| ~ v6_rlvect_1(X156)
| ~ v5_rlvect_1(X156)
| ~ v4_rlvect_1(X156)
| ~ v3_rlvect_1(X156)
| v3_struct_0(X156)
| ~ l1_vectsp_2(X157,X156)
| ~ v5_vectsp_2(X157,X156)
| ~ v6_rlvect_1(X157)
| ~ v5_rlvect_1(X157)
| ~ v4_rlvect_1(X157)
| ~ v3_rlvect_1(X157)
| v3_struct_0(X157)
| X155 = k1_rlvect_1(X157)
| ~ r1_rlvect_1(k1_rmod_2(X156,X157),X155) ) ),
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_15])])])])]) ).
cnf(c_0_19,plain,
( ~ r2_hidden(X4,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| ~ l3_vectsp_1(X1)
| ~ 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)
| r1_rlvect_1(k1_rmod_5(X1,X2,X3),X4)
| v3_struct_0(X2)
| v10_vectsp_1(X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
k1_rmod_5(esk1_0,esk2_0,esk3_0) = k1_rmod_2(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
v5_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
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,
v2_vectsp_2(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
v8_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
v7_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,negated_conjecture,
v6_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,negated_conjecture,
l3_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,negated_conjecture,
v7_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_29,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_30,negated_conjecture,
v6_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_31,negated_conjecture,
v6_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_32,negated_conjecture,
v5_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_33,negated_conjecture,
v5_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_34,negated_conjecture,
v4_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_35,negated_conjecture,
v4_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_36,negated_conjecture,
v3_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_37,negated_conjecture,
v3_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_38,negated_conjecture,
m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_39,negated_conjecture,
~ v10_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_40,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_41,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_42,plain,
! [X1] :
~ ( ! [X2] :
( ! [X3,X4] :
~ ( r2_hidden(X4,X1)
& r2_hidden(X3,X1)
& X3 != X4 )
& k1_tarski(X2) != X1 )
& X1 != k1_xboole_0 ),
inference(fof_simplification,[status(thm)],[t2_collsp]) ).
cnf(c_0_43,plain,
( ~ l3_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v4_group_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| ~ l1_vectsp_2(X2,X1)
| ~ v5_vectsp_2(X2,X1)
| ~ v6_rlvect_1(X2)
| ~ v5_rlvect_1(X2)
| ~ v4_rlvect_1(X2)
| ~ v3_rlvect_1(X2)
| ~ r1_rlvect_1(k1_rmod_2(X1,X2),X3)
| v3_struct_0(X1)
| v3_struct_0(X2)
| X3 = k1_rlvect_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_44,negated_conjecture,
( ~ r2_hidden(X1,esk3_0)
| r1_rlvect_1(k1_rmod_2(esk1_0,esk2_0),X1) ),
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(spm,[status(thm)],[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]),c_0_34]),c_0_35]),c_0_36]),c_0_37]),c_0_38])]),c_0_39]),c_0_40]),c_0_41]) ).
fof(c_0_45,plain,
! [X629] :
( ( X629 = k1_xboole_0
| k1_tarski(esk88_1(X629)) = X629
| r2_hidden(esk90_1(X629),X629) )
& ( X629 = k1_xboole_0
| k1_tarski(esk88_1(X629)) = X629
| r2_hidden(esk89_1(X629),X629) )
& ( X629 = k1_xboole_0
| k1_tarski(esk88_1(X629)) = X629
| esk89_1(X629) != esk90_1(X629) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])])])]) ).
fof(c_0_46,plain,
! [X557,X558,X559,X560,X561,X562] :
( ( X562 = k1_tarski(X561)
| esk84_2(X561,X562) = X561
| r2_hidden(esk84_2(X561,X562),X562) )
& ( X562 = k1_tarski(X561)
| esk84_2(X561,X562) != X561
| ~ r2_hidden(esk84_2(X561,X562),X562) )
& ( X558 != k1_tarski(X557)
| r2_hidden(X560,X558)
| X560 != X557 )
& ( X558 != k1_tarski(X557)
| X559 = X557
| ~ r2_hidden(X559,X558) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tarski])])])])])])]) ).
cnf(c_0_47,negated_conjecture,
( ~ r2_hidden(X1,esk3_0)
| X1 = 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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_21]),c_0_22]),c_0_24]),c_0_25]),c_0_26]),c_0_27]),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_40]),c_0_41]) ).
cnf(c_0_48,plain,
( X1 = k1_xboole_0
| k1_tarski(esk88_1(X1)) = X1
| r2_hidden(esk90_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_49,negated_conjecture,
esk3_0 != k1_xboole_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_50,plain,
( X1 = k1_xboole_0
| k1_tarski(esk88_1(X1)) = X1
| r2_hidden(esk89_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,plain,
( X3 != k1_tarski(X2)
| X1 != X2
| r2_hidden(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_52,plain,
( esk89_1(X1) != esk90_1(X1)
| X1 = k1_xboole_0
| k1_tarski(esk88_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_53,negated_conjecture,
( esk90_1(esk3_0) = k1_rlvect_1(esk2_0)
| k1_tarski(esk88_1(esk3_0)) = esk3_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_54,negated_conjecture,
( esk89_1(esk3_0) = k1_rlvect_1(esk2_0)
| k1_tarski(esk88_1(esk3_0)) = esk3_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_50]),c_0_49]) ).
fof(c_0_55,plain,
! [X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X1))
& l1_struct_0(X1)
& ~ v3_struct_0(X1) )
=> k7_rlvect_2(X1,X2) = k1_tarski(X2) ),
inference(fof_simplification,[status(thm)],[redefinition_k7_rlvect_2]) ).
cnf(c_0_56,plain,
r2_hidden(X1,k1_tarski(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_51])]) ).
cnf(c_0_57,negated_conjecture,
k1_tarski(esk88_1(esk3_0)) = esk3_0,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_49]),c_0_54]) ).
fof(c_0_58,plain,
! [X2950] :
( l1_struct_0(X2950)
| ~ l2_struct_0(X2950) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_struct_0])])]) ).
fof(c_0_59,plain,
! [X1793] :
( ( ~ l2_vectsp_1(X1793)
| l2_struct_0(X1793) )
& ( ~ l2_vectsp_1(X1793)
| l1_vectsp_1(X1793) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_vectsp_1])])])]) ).
fof(c_0_60,plain,
! [X65,X66] :
( k7_rlvect_2(X65,X66) = k1_tarski(X66)
| ~ m1_subset_1(X66,u1_struct_0(X65))
| ~ l1_struct_0(X65)
| v3_struct_0(X65) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])]) ).
fof(c_0_61,plain,
! [X2955] :
( m1_subset_1(k1_rlvect_1(X2955),u1_struct_0(X2955))
| ~ l2_struct_0(X2955) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_rlvect_1])])]) ).
cnf(c_0_62,negated_conjecture,
r2_hidden(esk88_1(esk3_0),esk3_0),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
fof(c_0_63,plain,
! [X531,X532] :
( l1_rlvect_1(X532)
| ~ l1_vectsp_2(X532,X531)
| ~ l1_struct_0(X531) ),
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_64,plain,
( ~ l2_struct_0(X1)
| l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_65,plain,
( ~ l2_vectsp_1(X1)
| l2_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
fof(c_0_66,plain,
! [X1795] :
( ( ~ l3_vectsp_1(X1795)
| l2_vectsp_1(X1795) )
& ( ~ l3_vectsp_1(X1795)
| l1_rlvect_1(X1795) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_vectsp_1])])])]) ).
cnf(c_0_67,plain,
( ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_struct_0(X1)
| k7_rlvect_2(X1,X2) = k1_tarski(X2)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_68,plain,
( ~ l2_struct_0(X1)
| m1_subset_1(k1_rlvect_1(X1),u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_69,negated_conjecture,
esk88_1(esk3_0) = k1_rlvect_1(esk2_0),
inference(spm,[status(thm)],[c_0_47,c_0_62]) ).
cnf(c_0_70,plain,
( ~ l1_vectsp_2(X2,X1)
| ~ l1_struct_0(X1)
| l1_rlvect_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_71,plain,
( ~ l2_vectsp_1(X1)
| l1_struct_0(X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_72,plain,
( ~ l3_vectsp_1(X1)
| l2_vectsp_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_73,negated_conjecture,
esk3_0 != k7_rlvect_2(esk2_0,k1_rlvect_1(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_74,plain,
( ~ l2_struct_0(X1)
| v3_struct_0(X1)
| k7_rlvect_2(X1,k1_rlvect_1(X1)) = k1_tarski(k1_rlvect_1(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_64]) ).
cnf(c_0_75,negated_conjecture,
k1_tarski(k1_rlvect_1(esk2_0)) = esk3_0,
inference(rw,[status(thm)],[c_0_57,c_0_69]) ).
fof(c_0_76,plain,
! [X2954] :
( l2_struct_0(X2954)
| ~ l1_rlvect_1(X2954) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_rlvect_1])])]) ).
cnf(c_0_77,negated_conjecture,
( ~ l1_struct_0(esk1_0)
| l1_rlvect_1(esk2_0) ),
inference(spm,[status(thm)],[c_0_70,c_0_22]) ).
cnf(c_0_78,plain,
( ~ l3_vectsp_1(X1)
| l1_struct_0(X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_79,negated_conjecture,
~ l2_struct_0(esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75])]),c_0_40]) ).
cnf(c_0_80,plain,
( ~ l1_rlvect_1(X1)
| l2_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_81,negated_conjecture,
l1_rlvect_1(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_27])]) ).
cnf(c_0_82,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG218+4 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/5.36 % Computer : n005.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Mon Sep 21 13:03:48 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/5.40 Running first-order theorem proving
% 0.12/5.40 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 61.64/16.98 % Version: 3.5.1
% 61.64/16.98 % Preprocessing class: FMLLSLLLSSSNFFN.
% 61.64/16.98 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 61.64/16.98 % Starting new_ho_10 with 598s (2) cores
% 61.64/16.98 % Starting sh3 with 598s (2) cores
% 61.64/16.98 % Starting ho_unfolding_3 with 598s (2) cores
% 61.64/16.98 % Starting new_ho_10_cnf2 with 598s (2) cores
% 61.64/16.98 % new_ho_10 with pid 3540595 completed with status 0
% 61.64/16.98 % Result found by new_ho_10
% 61.64/16.98 % Preprocessing class: FMLLSLLLSSSNFFN.
% 61.64/16.98 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 61.64/16.98 % Starting new_ho_10 with 598s (2) cores
% 61.64/16.98 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 61.64/16.98 % SinE strategy is gf120_h_gu_RUU_F100_L01000
% 61.64/16.98 % Search class: FGHSM-SMLM32-MFFFFFNN
% 61.64/16.98 % Scheduled 13 strats onto 2 cores with 598 seconds (598 total)
% 61.64/16.98 % Starting SubtermCWHack with 54s (1) cores
% 61.64/16.98 % Starting new_ho_10 with 60s (1) cores
% 61.64/16.98 % new_ho_10 with pid 3540600 completed with status 0
% 61.64/16.98 % Result found by new_ho_10
% 61.64/16.98 % Preprocessing class: FMLLSLLLSSSNFFN.
% 61.64/16.98 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 61.64/16.98 % Starting new_ho_10 with 598s (2) cores
% 61.64/16.98 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 61.64/16.98 % SinE strategy is gf120_h_gu_RUU_F100_L01000
% 61.64/16.98 % Search class: FGHSM-SMLM32-MFFFFFNN
% 61.64/16.98 % Scheduled 13 strats onto 2 cores with 598 seconds (598 total)
% 61.64/16.98 % Starting SubtermCWHack with 54s (1) cores
% 61.64/16.98 % Starting new_ho_10 with 60s (1) cores
% 61.64/16.98 % Preprocessing time : 0.115 s
% 61.64/16.98 % Presaturation interreduction done
% 61.64/16.98
% 61.64/16.98 % Proof found!
% 61.64/16.98 % SZS status Theorem
% 61.64/16.98 % SZS output start CNFRefutation
% See solution above
% 61.64/16.98 % Parsed axioms : 24512
% 61.64/16.98 % Removed by relevancy pruning/SinE : 23511
% 61.64/16.98 % Initial clauses : 2879
% 61.64/16.98 % Removed in clause preprocessing : 81
% 61.64/16.98 % Initial clauses in saturation : 2798
% 61.64/16.98 % Processed clauses : 8639
% 61.64/16.98 % ...of these trivial : 117
% 61.64/16.98 % ...subsumed : 1463
% 61.64/16.98 % ...remaining for further processing : 7059
% 61.64/16.98 % Other redundant clauses eliminated : 560
% 61.64/16.98 % Clauses deleted for lack of memory : 0
% 61.64/16.98 % Backward-subsumed : 62
% 61.64/16.98 % Backward-rewritten : 130
% 61.64/16.98 % Generated clauses : 60086
% 61.64/16.98 % ...of the previous two non-redundant : 57168
% 61.64/16.98 % ...aggressively subsumed : 0
% 61.64/16.98 % Contextual simplify-reflections : 190
% 61.64/16.98 % Paramodulations : 59455
% 61.64/16.98 % Factorizations : 2
% 61.64/16.98 % NegExts : 0
% 61.64/16.98 % Equation resolutions : 585
% 61.64/16.98 % Disequality decompositions : 0
% 61.64/16.98 % Total rewrite steps : 10453
% 61.64/16.98 % ...of those cached : 9896
% 61.64/16.98 % Propositional unsat checks : 0
% 61.64/16.98 % Propositional check models : 0
% 61.64/16.98 % Propositional check unsatisfiable : 0
% 61.64/16.98 % Propositional clauses : 0
% 61.64/16.98 % Propositional clauses after purity: 0
% 61.64/16.98 % Propositional unsat core size : 0
% 61.64/16.98 % Propositional preprocessing time : 0.000
% 61.64/16.98 % Propositional encoding time : 0.000
% 61.64/16.98 % Propositional solver time : 0.000
% 61.64/16.98 % Success case prop preproc time : 0.000
% 61.64/16.98 % Success case prop encoding time : 0.000
% 61.64/16.98 % Success case prop solver time : 0.000
% 61.64/16.98 % Current number of processed clauses : 3938
% 61.64/16.98 % Positive orientable unit clauses : 396
% 61.64/16.98 % Positive unorientable unit clauses: 0
% 61.64/16.98 % Negative unit clauses : 185
% 61.64/16.98 % Non-unit-clauses : 3357
% 61.64/16.98 % Current number of unprocessed clauses: 53870
% 61.64/16.98 % ...number of literals in the above : 658980
% 61.64/16.98 % Current number of archived formulas : 0
% 61.64/16.98 % Current number of archived clauses : 2936
% 61.64/16.98 % Clause-clause subsumption calls (NU) : 13722226
% 61.64/16.98 % Rec. Clause-clause subsumption calls : 560829
% 61.64/16.98 % Non-unit clause-clause subsumptions : 845
% 61.64/16.98 % Unit Clause-clause subsumption calls : 281850
% 61.64/16.98 % Rewrite failures with RHS unbound : 0
% 61.64/16.98 % BW rewrite match attempts : 113
% 61.64/16.98 % BW rewrite match successes : 70
% 61.64/16.98 % Condensation attempts : 8641
% 61.64/16.98 % Condensation successes : 41
% 61.64/16.98 % Termbank termtop insertions : 3193701
% 61.64/16.98 % Search garbage collected termcells : 282837
% 61.64/16.98
% 61.64/16.98 % -------------------------------------------------
% 61.64/16.98 % User time : 10.079 s
% 61.64/16.98 % System time : 0.224 s
% 61.64/16.98 % Total time : 10.303 s
% 61.64/16.98 % Maximum resident set size: 50244 pages
% 61.64/16.98
% 61.64/16.98 % -------------------------------------------------
% 61.64/16.98 % User time : 20.755 s
% 61.64/16.98 % System time : 0.471 s
% 61.64/16.98 % Total time : 21.225 s
% 61.64/16.98 % Maximum resident set size: 39680 pages
% 61.64/16.98 % E exiting
%------------------------------------------------------------------------------