TSTP Solution File: ALG218+4 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ALG218+4 : TPTP v8.2.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n014.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 18:05:41 EDT 2024
% Result : Theorem 73.77s 11.05s
% Output : CNFRefutation 73.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 82 ( 32 unt; 0 def)
% Number of atoms : 415 ( 62 equ)
% Maximal formula atoms : 38 ( 5 avg)
% Number of connectives : 501 ( 168 ~; 151 |; 151 &)
% ( 4 <=>; 27 =>; 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 : 93 ( 0 sgn 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t10_rmod_5,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v4_group_1(X2)
& v7_group_1(X2)
& v6_vectsp_1(X2)
& v7_vectsp_1(X2)
& v8_vectsp_1(X2)
& ~ v10_vectsp_1(X2)
& v2_vectsp_2(X2)
& l3_vectsp_1(X2) )
=> ! [X3] :
( ( ~ v3_struct_0(X3)
& v3_rlvect_1(X3)
& v4_rlvect_1(X3)
& v5_rlvect_1(X3)
& v6_rlvect_1(X3)
& v5_vectsp_2(X3,X2)
& l1_vectsp_2(X3,X2) )
=> ! [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/sandbox2/benchmark/theBenchmark.p',t10_rmod_5) ).
fof(t12_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)
& v7_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& ~ v10_vectsp_1(X1)
& v2_vectsp_2(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,k1_zfmisc_1(u1_struct_0(X2)))
=> ~ ( k1_rmod_5(X1,X2,X3) = k1_rmod_2(X1,X2)
& X3 != k1_xboole_0
& X3 != k7_rlvect_2(X2,k1_rlvect_1(X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_rmod_5) ).
fof(t46_rmod_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v4_group_1(X2)
& v6_vectsp_1(X2)
& v7_vectsp_1(X2)
& v8_vectsp_1(X2)
& l3_vectsp_1(X2) )
=> ! [X3] :
( ( ~ v3_struct_0(X3)
& v3_rlvect_1(X3)
& v4_rlvect_1(X3)
& v5_rlvect_1(X3)
& v6_rlvect_1(X3)
& v5_vectsp_2(X3,X2)
& l1_vectsp_2(X3,X2) )
=> ( r1_rlvect_1(k1_rmod_2(X2,X3),X1)
<=> X1 = k1_rlvect_1(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+278.ax',t46_rmod_2) ).
fof(t2_collsp,axiom,
! [X1] :
~ ( X1 != k1_xboole_0
& ! [X2] :
( k1_tarski(X2) != X1
& ! [X3,X4] :
~ ( X3 != X4
& r2_hidden(X3,X1)
& r2_hidden(X4,X1) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SET007/SET007+1.ax',d1_tarski) ).
fof(redefinition_k7_rlvect_2,axiom,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> k7_rlvect_2(X1,X2) = k1_tarski(X2) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SET007/SET007+200.ax',dt_l2_struct_0) ).
fof(dt_l2_vectsp_1,axiom,
! [X1] :
( l2_vectsp_1(X1)
=> ( l1_vectsp_1(X1)
& l2_struct_0(X1) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/SET007/SET007+241.ax',dt_l1_vectsp_2) ).
fof(dt_l3_vectsp_1,axiom,
! [X1] :
( l3_vectsp_1(X1)
=> ( l1_rlvect_1(X1)
& l2_vectsp_1(X1) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SET007/SET007+210.ax',dt_l1_rlvect_1) ).
fof(c_0_12,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v4_group_1(X2)
& v7_group_1(X2)
& v6_vectsp_1(X2)
& v7_vectsp_1(X2)
& v8_vectsp_1(X2)
& ~ v10_vectsp_1(X2)
& v2_vectsp_2(X2)
& l3_vectsp_1(X2) )
=> ! [X3] :
( ( ~ v3_struct_0(X3)
& v3_rlvect_1(X3)
& v4_rlvect_1(X3)
& v5_rlvect_1(X3)
& v6_rlvect_1(X3)
& v5_vectsp_2(X3,X2)
& l1_vectsp_2(X3,X2) )
=> ! [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_13,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)
& v7_group_1(X1)
& v6_vectsp_1(X1)
& v7_vectsp_1(X1)
& v8_vectsp_1(X1)
& ~ v10_vectsp_1(X1)
& v2_vectsp_2(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,k1_zfmisc_1(u1_struct_0(X2)))
=> ~ ( k1_rmod_5(X1,X2,X3) = k1_rmod_2(X1,X2)
& X3 != k1_xboole_0
& X3 != k7_rlvect_2(X2,k1_rlvect_1(X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t12_rmod_5])]) ).
fof(c_0_14,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X2)
& v3_rlvect_1(X2)
& v4_rlvect_1(X2)
& v5_rlvect_1(X2)
& v6_rlvect_1(X2)
& v4_group_1(X2)
& v6_vectsp_1(X2)
& v7_vectsp_1(X2)
& v8_vectsp_1(X2)
& l3_vectsp_1(X2) )
=> ! [X3] :
( ( ~ v3_struct_0(X3)
& v3_rlvect_1(X3)
& v4_rlvect_1(X3)
& v5_rlvect_1(X3)
& v6_rlvect_1(X3)
& v5_vectsp_2(X3,X2)
& l1_vectsp_2(X3,X2) )
=> ( 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_15,plain,
! [X202,X203,X204,X205] :
( v3_struct_0(X203)
| ~ v3_rlvect_1(X203)
| ~ v4_rlvect_1(X203)
| ~ v5_rlvect_1(X203)
| ~ v6_rlvect_1(X203)
| ~ v4_group_1(X203)
| ~ v7_group_1(X203)
| ~ v6_vectsp_1(X203)
| ~ v7_vectsp_1(X203)
| ~ v8_vectsp_1(X203)
| v10_vectsp_1(X203)
| ~ v2_vectsp_2(X203)
| ~ l3_vectsp_1(X203)
| v3_struct_0(X204)
| ~ v3_rlvect_1(X204)
| ~ v4_rlvect_1(X204)
| ~ v5_rlvect_1(X204)
| ~ v6_rlvect_1(X204)
| ~ v5_vectsp_2(X204,X203)
| ~ l1_vectsp_2(X204,X203)
| ~ m1_subset_1(X205,k1_zfmisc_1(u1_struct_0(X204)))
| ~ r2_hidden(X202,X205)
| r1_rlvect_1(k1_rmod_5(X203,X204,X205),X202) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
fof(c_0_16,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)
& v7_group_1(esk1_0)
& v6_vectsp_1(esk1_0)
& v7_vectsp_1(esk1_0)
& v8_vectsp_1(esk1_0)
& ~ v10_vectsp_1(esk1_0)
& v2_vectsp_2(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,k1_zfmisc_1(u1_struct_0(esk2_0)))
& k1_rmod_5(esk1_0,esk2_0,esk3_0) = k1_rmod_2(esk1_0,esk2_0)
& esk3_0 != k1_xboole_0
& esk3_0 != k7_rlvect_2(esk2_0,k1_rlvect_1(esk2_0)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
fof(c_0_17,plain,
! [X155,X156,X157] :
( ( ~ r1_rlvect_1(k1_rmod_2(X156,X157),X155)
| X155 = k1_rlvect_1(X157)
| v3_struct_0(X157)
| ~ v3_rlvect_1(X157)
| ~ v4_rlvect_1(X157)
| ~ v5_rlvect_1(X157)
| ~ v6_rlvect_1(X157)
| ~ v5_vectsp_2(X157,X156)
| ~ l1_vectsp_2(X157,X156)
| v3_struct_0(X156)
| ~ v3_rlvect_1(X156)
| ~ v4_rlvect_1(X156)
| ~ v5_rlvect_1(X156)
| ~ v6_rlvect_1(X156)
| ~ v4_group_1(X156)
| ~ v6_vectsp_1(X156)
| ~ v7_vectsp_1(X156)
| ~ v8_vectsp_1(X156)
| ~ l3_vectsp_1(X156) )
& ( X155 != k1_rlvect_1(X157)
| r1_rlvect_1(k1_rmod_2(X156,X157),X155)
| v3_struct_0(X157)
| ~ v3_rlvect_1(X157)
| ~ v4_rlvect_1(X157)
| ~ v5_rlvect_1(X157)
| ~ v6_rlvect_1(X157)
| ~ v5_vectsp_2(X157,X156)
| ~ l1_vectsp_2(X157,X156)
| v3_struct_0(X156)
| ~ v3_rlvect_1(X156)
| ~ v4_rlvect_1(X156)
| ~ v5_rlvect_1(X156)
| ~ v6_rlvect_1(X156)
| ~ v4_group_1(X156)
| ~ v6_vectsp_1(X156)
| ~ v7_vectsp_1(X156)
| ~ v8_vectsp_1(X156)
| ~ l3_vectsp_1(X156) ) ),
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_14])])])])]) ).
cnf(c_0_18,plain,
( v3_struct_0(X1)
| v10_vectsp_1(X1)
| v3_struct_0(X2)
| r1_rlvect_1(k1_rmod_5(X1,X2,X3),X4)
| ~ v3_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v6_rlvect_1(X1)
| ~ v4_group_1(X1)
| ~ v7_group_1(X1)
| ~ v6_vectsp_1(X1)
| ~ v7_vectsp_1(X1)
| ~ v8_vectsp_1(X1)
| ~ v2_vectsp_2(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_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))
| ~ r2_hidden(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,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_16]) ).
cnf(c_0_20,negated_conjecture,
v5_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
l1_vectsp_2(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
v2_vectsp_2(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
v8_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
v7_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,negated_conjecture,
v6_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,negated_conjecture,
l3_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_27,negated_conjecture,
v7_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_28,negated_conjecture,
v4_group_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_29,negated_conjecture,
v6_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_30,negated_conjecture,
v6_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_31,negated_conjecture,
v5_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_32,negated_conjecture,
v5_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_33,negated_conjecture,
v4_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_34,negated_conjecture,
v4_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_35,negated_conjecture,
v3_rlvect_1(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_36,negated_conjecture,
v3_rlvect_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_37,negated_conjecture,
m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_38,negated_conjecture,
~ v10_vectsp_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_39,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_40,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_41,plain,
! [X1] :
~ ( X1 != k1_xboole_0
& ! [X2] :
( k1_tarski(X2) != X1
& ! [X3,X4] :
~ ( X3 != X4
& r2_hidden(X3,X1)
& r2_hidden(X4,X1) ) ) ),
inference(fof_simplification,[status(thm)],[t2_collsp]) ).
cnf(c_0_42,plain,
( X3 = k1_rlvect_1(X2)
| v3_struct_0(X2)
| v3_struct_0(X1)
| ~ r1_rlvect_1(k1_rmod_2(X1,X2),X3)
| ~ 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)
| ~ 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) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_43,negated_conjecture,
( r1_rlvect_1(k1_rmod_2(esk1_0,esk2_0),X1)
| ~ r2_hidden(X1,esk3_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(rw,[status(thm)],[inference(spm,[status(thm)],[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]),c_0_34]),c_0_35]),c_0_36]),c_0_37])]),c_0_38]),c_0_39]),c_0_40]) ).
fof(c_0_44,plain,
! [X629] :
( ( esk89_1(X629) != esk90_1(X629)
| k1_tarski(esk88_1(X629)) = X629
| X629 = k1_xboole_0 )
& ( r2_hidden(esk89_1(X629),X629)
| k1_tarski(esk88_1(X629)) = X629
| X629 = k1_xboole_0 )
& ( r2_hidden(esk90_1(X629),X629)
| k1_tarski(esk88_1(X629)) = X629
| X629 = k1_xboole_0 ) ),
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_41])])])])])]) ).
fof(c_0_45,plain,
! [X557,X558,X559,X560,X561,X562] :
( ( ~ r2_hidden(X559,X558)
| X559 = X557
| X558 != k1_tarski(X557) )
& ( X560 != X557
| r2_hidden(X560,X558)
| X558 != k1_tarski(X557) )
& ( ~ r2_hidden(esk84_2(X561,X562),X562)
| esk84_2(X561,X562) != X561
| X562 = k1_tarski(X561) )
& ( r2_hidden(esk84_2(X561,X562),X562)
| esk84_2(X561,X562) = X561
| X562 = k1_tarski(X561) ) ),
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_46,negated_conjecture,
( X1 = k1_rlvect_1(esk2_0)
| ~ r2_hidden(X1,esk3_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_42,c_0_43]),c_0_20]),c_0_21]),c_0_23]),c_0_24]),c_0_25]),c_0_26]),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_39]),c_0_40]) ).
cnf(c_0_47,plain,
( r2_hidden(esk90_1(X1),X1)
| k1_tarski(esk88_1(X1)) = X1
| X1 = k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_48,negated_conjecture,
esk3_0 != k1_xboole_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_49,plain,
( r2_hidden(esk89_1(X1),X1)
| k1_tarski(esk88_1(X1)) = X1
| X1 = k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,plain,
( r2_hidden(X1,X3)
| X1 != X2
| X3 != k1_tarski(X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,plain,
( k1_tarski(esk88_1(X1)) = X1
| X1 = k1_xboole_0
| esk89_1(X1) != esk90_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,negated_conjecture,
( k1_tarski(esk88_1(esk3_0)) = esk3_0
| esk90_1(esk3_0) = k1_rlvect_1(esk2_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_53,negated_conjecture,
( k1_tarski(esk88_1(esk3_0)) = esk3_0
| esk89_1(esk3_0) = k1_rlvect_1(esk2_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_49]),c_0_48]) ).
fof(c_0_54,plain,
! [X1,X2] :
( ( ~ v3_struct_0(X1)
& l1_struct_0(X1)
& m1_subset_1(X2,u1_struct_0(X1)) )
=> k7_rlvect_2(X1,X2) = k1_tarski(X2) ),
inference(fof_simplification,[status(thm)],[redefinition_k7_rlvect_2]) ).
cnf(c_0_55,plain,
r2_hidden(X1,k1_tarski(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_50])]) ).
cnf(c_0_56,negated_conjecture,
k1_tarski(esk88_1(esk3_0)) = esk3_0,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_48]),c_0_53]) ).
fof(c_0_57,plain,
! [X2950] :
( ~ l2_struct_0(X2950)
| l1_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_58,plain,
! [X1793] :
( ( l1_vectsp_1(X1793)
| ~ l2_vectsp_1(X1793) )
& ( l2_struct_0(X1793)
| ~ l2_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_59,plain,
! [X65,X66] :
( v3_struct_0(X65)
| ~ l1_struct_0(X65)
| ~ m1_subset_1(X66,u1_struct_0(X65))
| k7_rlvect_2(X65,X66) = k1_tarski(X66) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])])]) ).
fof(c_0_60,plain,
! [X2955] :
( ~ l2_struct_0(X2955)
| m1_subset_1(k1_rlvect_1(X2955),u1_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_61,negated_conjecture,
r2_hidden(esk88_1(esk3_0),esk3_0),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
fof(c_0_62,plain,
! [X531,X532] :
( ~ l1_struct_0(X531)
| ~ l1_vectsp_2(X532,X531)
| l1_rlvect_1(X532) ),
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_63,plain,
( l1_struct_0(X1)
| ~ l2_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_64,plain,
( l2_struct_0(X1)
| ~ l2_vectsp_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_65,plain,
! [X1795] :
( ( l1_rlvect_1(X1795)
| ~ l3_vectsp_1(X1795) )
& ( l2_vectsp_1(X1795)
| ~ l3_vectsp_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_66,plain,
( v3_struct_0(X1)
| k7_rlvect_2(X1,X2) = k1_tarski(X2)
| ~ l1_struct_0(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_67,plain,
( m1_subset_1(k1_rlvect_1(X1),u1_struct_0(X1))
| ~ l2_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_68,negated_conjecture,
esk88_1(esk3_0) = k1_rlvect_1(esk2_0),
inference(spm,[status(thm)],[c_0_46,c_0_61]) ).
cnf(c_0_69,plain,
( l1_rlvect_1(X2)
| ~ l1_struct_0(X1)
| ~ l1_vectsp_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_70,plain,
( l1_struct_0(X1)
| ~ l2_vectsp_1(X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_71,plain,
( l2_vectsp_1(X1)
| ~ l3_vectsp_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_72,negated_conjecture,
esk3_0 != k7_rlvect_2(esk2_0,k1_rlvect_1(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_73,plain,
( k7_rlvect_2(X1,k1_rlvect_1(X1)) = k1_tarski(k1_rlvect_1(X1))
| v3_struct_0(X1)
| ~ l2_struct_0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_63]) ).
cnf(c_0_74,negated_conjecture,
k1_tarski(k1_rlvect_1(esk2_0)) = esk3_0,
inference(rw,[status(thm)],[c_0_56,c_0_68]) ).
fof(c_0_75,plain,
! [X2954] :
( ~ l1_rlvect_1(X2954)
| l2_struct_0(X2954) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_rlvect_1])])]) ).
cnf(c_0_76,negated_conjecture,
( l1_rlvect_1(esk2_0)
| ~ l1_struct_0(esk1_0) ),
inference(spm,[status(thm)],[c_0_69,c_0_21]) ).
cnf(c_0_77,plain,
( l1_struct_0(X1)
| ~ l3_vectsp_1(X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_78,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_72,c_0_73]),c_0_74])]),c_0_39]) ).
cnf(c_0_79,plain,
( l2_struct_0(X1)
| ~ l1_rlvect_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_80,negated_conjecture,
l1_rlvect_1(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_26])]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : ALG218+4 : TPTP v8.2.0. Released v3.4.0.
% 0.05/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n014.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat May 18 23:52:26 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 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
% 73.77/11.05 # Version: 3.1.0
% 73.77/11.05 # Preprocessing class: FMLLSLLLSSSNFFN.
% 73.77/11.05 # Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 73.77/11.05 # Starting new_ho_10 with 598s (2) cores
% 73.77/11.05 # Starting sh3 with 598s (2) cores
% 73.77/11.05 # Starting ho_unfolding_3 with 598s (2) cores
% 73.77/11.05 # Starting new_ho_10_cnf2 with 598s (2) cores
% 73.77/11.05 # new_ho_10_cnf2 with pid 24674 completed with status 0
% 73.77/11.05 # Result found by new_ho_10_cnf2
% 73.77/11.05 # Preprocessing class: FMLLSLLLSSSNFFN.
% 73.77/11.05 # Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 73.77/11.05 # Starting new_ho_10 with 598s (2) cores
% 73.77/11.05 # Starting sh3 with 598s (2) cores
% 73.77/11.05 # Starting ho_unfolding_3 with 598s (2) cores
% 73.77/11.05 # Starting new_ho_10_cnf2 with 598s (2) cores
% 73.77/11.05 # SinE strategy is gf120_h_gu_RUU_F100_L01000
% 73.77/11.05 # Search class: FGHSM-SMLM32-MFFFFFNN
% 73.77/11.05 # Scheduled 13 strats onto 2 cores with 598 seconds (598 total)
% 73.77/11.05 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 45s (1) cores
% 73.77/11.05 # Starting new_ho_10_cnf2 with 60s (1) cores
% 73.77/11.05 # new_ho_10_cnf2 with pid 24680 completed with status 0
% 73.77/11.05 # Result found by new_ho_10_cnf2
% 73.77/11.05 # Preprocessing class: FMLLSLLLSSSNFFN.
% 73.77/11.05 # Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 73.77/11.05 # Starting new_ho_10 with 598s (2) cores
% 73.77/11.05 # Starting sh3 with 598s (2) cores
% 73.77/11.05 # Starting ho_unfolding_3 with 598s (2) cores
% 73.77/11.05 # Starting new_ho_10_cnf2 with 598s (2) cores
% 73.77/11.05 # SinE strategy is gf120_h_gu_RUU_F100_L01000
% 73.77/11.05 # Search class: FGHSM-SMLM32-MFFFFFNN
% 73.77/11.05 # Scheduled 13 strats onto 2 cores with 598 seconds (598 total)
% 73.77/11.05 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 45s (1) cores
% 73.77/11.05 # Starting new_ho_10_cnf2 with 60s (1) cores
% 73.77/11.05 # Preprocessing time : 0.089 s
% 73.77/11.05 # Presaturation interreduction done
% 73.77/11.05
% 73.77/11.05 # Proof found!
% 73.77/11.05 # SZS status Theorem
% 73.77/11.05 # SZS output start CNFRefutation
% See solution above
% 73.77/11.05 # Parsed axioms : 24512
% 73.77/11.05 # Removed by relevancy pruning/SinE : 23511
% 73.77/11.05 # Initial clauses : 2879
% 73.77/11.05 # Removed in clause preprocessing : 81
% 73.77/11.05 # Initial clauses in saturation : 2798
% 73.77/11.05 # Processed clauses : 8639
% 73.77/11.05 # ...of these trivial : 117
% 73.77/11.05 # ...subsumed : 1461
% 73.77/11.05 # ...remaining for further processing : 7061
% 73.77/11.05 # Other redundant clauses eliminated : 560
% 73.77/11.05 # Clauses deleted for lack of memory : 0
% 73.77/11.05 # Backward-subsumed : 62
% 73.77/11.05 # Backward-rewritten : 131
% 73.77/11.05 # Generated clauses : 60097
% 73.77/11.05 # ...of the previous two non-redundant : 57177
% 73.77/11.05 # ...aggressively subsumed : 0
% 73.77/11.05 # Contextual simplify-reflections : 190
% 73.77/11.05 # Paramodulations : 59466
% 73.77/11.05 # Factorizations : 2
% 73.77/11.05 # NegExts : 0
% 73.77/11.05 # Equation resolutions : 585
% 73.77/11.05 # Disequality decompositions : 0
% 73.77/11.05 # Total rewrite steps : 10464
% 73.77/11.05 # ...of those cached : 9906
% 73.77/11.05 # Propositional unsat checks : 0
% 73.77/11.05 # Propositional check models : 0
% 73.77/11.05 # Propositional check unsatisfiable : 0
% 73.77/11.05 # Propositional clauses : 0
% 73.77/11.05 # Propositional clauses after purity: 0
% 73.77/11.05 # Propositional unsat core size : 0
% 73.77/11.05 # Propositional preprocessing time : 0.000
% 73.77/11.05 # Propositional encoding time : 0.000
% 73.77/11.05 # Propositional solver time : 0.000
% 73.77/11.05 # Success case prop preproc time : 0.000
% 73.77/11.05 # Success case prop encoding time : 0.000
% 73.77/11.05 # Success case prop solver time : 0.000
% 73.77/11.05 # Current number of processed clauses : 3939
% 73.77/11.05 # Positive orientable unit clauses : 397
% 73.77/11.05 # Positive unorientable unit clauses: 0
% 73.77/11.05 # Negative unit clauses : 185
% 73.77/11.05 # Non-unit-clauses : 3357
% 73.77/11.05 # Current number of unprocessed clauses: 53877
% 73.77/11.05 # ...number of literals in the above : 658983
% 73.77/11.05 # Current number of archived formulas : 0
% 73.77/11.05 # Current number of archived clauses : 2937
% 73.77/11.05 # Clause-clause subsumption calls (NU) : 13385438
% 73.77/11.05 # Rec. Clause-clause subsumption calls : 509405
% 73.77/11.05 # Non-unit clause-clause subsumptions : 845
% 73.77/11.05 # Unit Clause-clause subsumption calls : 264271
% 73.77/11.05 # Rewrite failures with RHS unbound : 0
% 73.77/11.05 # BW rewrite match attempts : 114
% 73.77/11.05 # BW rewrite match successes : 71
% 73.77/11.05 # Condensation attempts : 8641
% 73.77/11.05 # Condensation successes : 41
% 73.77/11.05 # Termbank termtop insertions : 3170588
% 73.77/11.05 # Search garbage collected termcells : 282838
% 73.77/11.05
% 73.77/11.05 # -------------------------------------------------
% 73.77/11.05 # User time : 9.090 s
% 73.77/11.05 # System time : 0.179 s
% 73.77/11.05 # Total time : 9.269 s
% 73.77/11.05 # Maximum resident set size: 48152 pages
% 73.77/11.05
% 73.77/11.05 # -------------------------------------------------
% 73.77/11.05 # User time : 18.890 s
% 73.77/11.05 # System time : 0.393 s
% 73.77/11.05 # Total time : 19.283 s
% 73.77/11.05 # Maximum resident set size: 36632 pages
% 73.77/11.05 % E---3.1 exiting
% 73.77/11.05 % E exiting
%------------------------------------------------------------------------------