TSTP Solution File: SEU411+2 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SEU411+2 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n025.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 : 600s
% DateTime : Tue Jul 19 09:19:49 EDT 2022
% Result : Theorem 0.51s 9.70s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 22
% Syntax : Number of formulae : 122 ( 79 unt; 0 def)
% Number of atoms : 319 ( 67 equ)
% Maximal formula atoms : 28 ( 2 avg)
% Number of connectives : 308 ( 111 ~; 105 |; 71 &)
% ( 4 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 251 ( 33 sgn 109 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t51_xboole_1,axiom,
! [X1,X2] : k2_xboole_0(k3_xboole_0(X1,X2),k4_xboole_0(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t51_xboole_1) ).
fof(t48_xboole_1,axiom,
! [X1,X2] : k4_xboole_0(X1,k4_xboole_0(X1,X2)) = k3_xboole_0(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t48_xboole_1) ).
fof(t54_xboole_1,axiom,
! [X1,X2,X3] : k4_xboole_0(X1,k3_xboole_0(X2,X3)) = k2_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t54_xboole_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : k3_xboole_0(X1,X2) = k3_xboole_0(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+2.ax',commutativity_k3_xboole_0) ).
fof(t52_xboole_1,axiom,
! [X1,X2,X3] : k4_xboole_0(X1,k4_xboole_0(X2,X3)) = k2_xboole_0(k4_xboole_0(X1,X2),k3_xboole_0(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t52_xboole_1) ).
fof(t2_boole,axiom,
! [X1] : k3_xboole_0(X1,k1_xboole_0) = k1_xboole_0,
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+3.ax',t2_boole) ).
fof(t47_xboole_1,axiom,
! [X1,X2] : k4_xboole_0(X1,k3_xboole_0(X1,X2)) = k4_xboole_0(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t47_xboole_1) ).
fof(t49_xboole_1,axiom,
! [X1,X2,X3] : k3_xboole_0(X1,k4_xboole_0(X2,X3)) = k4_xboole_0(k3_xboole_0(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t49_xboole_1) ).
fof(t20_latsum_1,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& v2_orders_2(X1)
& v3_orders_2(X1)
& v4_orders_2(X1)
& v1_yellow_0(X1)
& v1_lattice3(X1)
& l1_orders_2(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v2_orders_2(X2)
& v3_orders_2(X2)
& v4_orders_2(X2)
& v1_yellow_0(X2)
& v1_lattice3(X2)
& l1_orders_2(X2) )
=> ( ( ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)))
& v1_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
& v12_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
& m1_subset_1(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),k1_zfmisc_1(u1_struct_0(X2))) )
=> r2_hidden(k3_yellow_0(X2),u1_struct_0(X1)) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t20_latsum_1) ).
fof(t17_xboole_1,axiom,
! [X1,X2] : r1_tarski(k3_xboole_0(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t17_xboole_1) ).
fof(d19_waybel_0,axiom,
! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
=> ( v12_waybel_0(X2,X1)
<=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(X1))
=> ( ( r2_hidden(X3,X2)
& r1_orders_2(X1,X4,X3) )
=> r2_hidden(X4,X2) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+481.ax',d19_waybel_0) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(X3)) )
=> m1_subset_1(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+9.ax',t4_subset) ).
fof(t31_xboole_1,axiom,
! [X1,X2,X3] : r1_tarski(k2_xboole_0(k3_xboole_0(X1,X2),k3_xboole_0(X1,X3)),k2_xboole_0(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t31_xboole_1) ).
fof(t53_xboole_1,axiom,
! [X1,X2,X3] : k4_xboole_0(X1,k2_xboole_0(X2,X3)) = k3_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t53_xboole_1) ).
fof(t44_yellow_0,axiom,
! [X1] :
( ( ~ v3_struct_0(X1)
& v4_orders_2(X1)
& v1_yellow_0(X1)
& l1_orders_2(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> r1_orders_2(X1,k3_yellow_0(X1),X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+480.ax',t44_yellow_0) ).
fof(dt_k3_yellow_0,axiom,
! [X1] :
( l1_orders_2(X1)
=> m1_subset_1(k3_yellow_0(X1),u1_struct_0(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+480.ax',dt_k3_yellow_0) ).
fof(t3_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,k1_zfmisc_1(X2))
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+9.ax',t3_subset) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(X3))
& v1_xboole_0(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+9.ax',t5_subset) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
& v1_xboole_0(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+7.ax',rc2_subset_1) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = k3_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( r2_hidden(X4,X1)
& r2_hidden(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+2.ax',d3_xboole_0) ).
fof(t10_subset_1,axiom,
! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> ~ ( X2 != k1_xboole_0
& ! [X3] :
( m1_subset_1(X3,X1)
=> ~ r2_hidden(X3,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+7.ax',t10_subset_1) ).
fof(t4_subset_1,axiom,
! [X1] : m1_subset_1(k1_xboole_0,k1_zfmisc_1(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+7.ax',t4_subset_1) ).
fof(c_0_22,plain,
! [X3,X4] : k2_xboole_0(k3_xboole_0(X3,X4),k4_xboole_0(X3,X4)) = X3,
inference(variable_rename,[status(thm)],[t51_xboole_1]) ).
fof(c_0_23,plain,
! [X3,X4] : k4_xboole_0(X3,k4_xboole_0(X3,X4)) = k3_xboole_0(X3,X4),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(c_0_24,plain,
! [X4,X5,X6] : k4_xboole_0(X4,k3_xboole_0(X5,X6)) = k2_xboole_0(k4_xboole_0(X4,X5),k4_xboole_0(X4,X6)),
inference(variable_rename,[status(thm)],[t54_xboole_1]) ).
fof(c_0_25,plain,
! [X3,X4] : k3_xboole_0(X3,X4) = k3_xboole_0(X4,X3),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_26,plain,
! [X4,X5,X6] : k4_xboole_0(X4,k4_xboole_0(X5,X6)) = k2_xboole_0(k4_xboole_0(X4,X5),k3_xboole_0(X4,X6)),
inference(variable_rename,[status(thm)],[t52_xboole_1]) ).
fof(c_0_27,plain,
! [X2] : k3_xboole_0(X2,k1_xboole_0) = k1_xboole_0,
inference(variable_rename,[status(thm)],[t2_boole]) ).
cnf(c_0_28,plain,
k2_xboole_0(k3_xboole_0(X1,X2),k4_xboole_0(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
k4_xboole_0(X1,k4_xboole_0(X1,X2)) = k3_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
k4_xboole_0(X1,k3_xboole_0(X2,X3)) = k2_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
k3_xboole_0(X1,X2) = k3_xboole_0(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
k4_xboole_0(X1,k4_xboole_0(X2,X3)) = k2_xboole_0(k4_xboole_0(X1,X2),k3_xboole_0(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_33,plain,
! [X3,X4] : k4_xboole_0(X3,k3_xboole_0(X3,X4)) = k4_xboole_0(X3,X4),
inference(variable_rename,[status(thm)],[t47_xboole_1]) ).
cnf(c_0_34,plain,
k3_xboole_0(X1,k1_xboole_0) = k1_xboole_0,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,plain,
k2_xboole_0(k4_xboole_0(X1,k4_xboole_0(X1,X2)),k4_xboole_0(X1,X2)) = X1,
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
k4_xboole_0(X1,k4_xboole_0(X2,k4_xboole_0(X2,X3))) = k2_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(X1,X3)),
inference(rw,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_37,plain,
k4_xboole_0(X1,k4_xboole_0(X1,X2)) = k4_xboole_0(X2,k4_xboole_0(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_29]),c_0_29]) ).
cnf(c_0_38,plain,
k4_xboole_0(X1,k4_xboole_0(X2,X3)) = k2_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(X1,k4_xboole_0(X1,X3))),
inference(rw,[status(thm)],[c_0_32,c_0_29]) ).
cnf(c_0_39,plain,
k4_xboole_0(X1,k3_xboole_0(X1,X2)) = k4_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,plain,
k4_xboole_0(X1,k4_xboole_0(X1,k1_xboole_0)) = k1_xboole_0,
inference(rw,[status(thm)],[c_0_34,c_0_29]) ).
cnf(c_0_41,plain,
k4_xboole_0(X1,k4_xboole_0(X2,k4_xboole_0(X2,k4_xboole_0(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_42,plain,
k4_xboole_0(X1,k4_xboole_0(X2,k4_xboole_0(X2,k4_xboole_0(X1,X3)))) = k4_xboole_0(X1,k4_xboole_0(X2,X3)),
inference(rw,[status(thm)],[c_0_38,c_0_36]) ).
cnf(c_0_43,plain,
k4_xboole_0(X1,k4_xboole_0(X1,k4_xboole_0(X1,X2))) = k4_xboole_0(X1,X2),
inference(rw,[status(thm)],[c_0_39,c_0_29]) ).
cnf(c_0_44,plain,
k4_xboole_0(k1_xboole_0,k4_xboole_0(k1_xboole_0,X1)) = k1_xboole_0,
inference(spm,[status(thm)],[c_0_40,c_0_37]) ).
fof(c_0_45,plain,
! [X4,X5,X6] : k3_xboole_0(X4,k4_xboole_0(X5,X6)) = k4_xboole_0(k3_xboole_0(X4,X5),X6),
inference(variable_rename,[status(thm)],[t49_xboole_1]) ).
cnf(c_0_46,plain,
k4_xboole_0(X1,k4_xboole_0(X2,X2)) = X1,
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,plain,
k4_xboole_0(k1_xboole_0,X1) = k1_xboole_0,
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
fof(c_0_48,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& v2_orders_2(X1)
& v3_orders_2(X1)
& v4_orders_2(X1)
& v1_yellow_0(X1)
& v1_lattice3(X1)
& l1_orders_2(X1) )
=> ! [X2] :
( ( ~ v3_struct_0(X2)
& v2_orders_2(X2)
& v3_orders_2(X2)
& v4_orders_2(X2)
& v1_yellow_0(X2)
& v1_lattice3(X2)
& l1_orders_2(X2) )
=> ( ( ~ v1_xboole_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)))
& v1_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
& v12_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
& m1_subset_1(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),k1_zfmisc_1(u1_struct_0(X2))) )
=> r2_hidden(k3_yellow_0(X2),u1_struct_0(X1)) ) ) ),
inference(assume_negation,[status(cth)],[t20_latsum_1]) ).
fof(c_0_49,plain,
! [X3,X4] : r1_tarski(k3_xboole_0(X3,X4),X3),
inference(variable_rename,[status(thm)],[t17_xboole_1]) ).
cnf(c_0_50,plain,
k3_xboole_0(X1,k4_xboole_0(X2,X3)) = k4_xboole_0(k3_xboole_0(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,plain,
k4_xboole_0(X1,k1_xboole_0) = X1,
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
fof(c_0_52,plain,
! [X5,X6,X7,X8] :
( ( ~ v12_waybel_0(X6,X5)
| ~ m1_subset_1(X7,u1_struct_0(X5))
| ~ m1_subset_1(X8,u1_struct_0(X5))
| ~ r2_hidden(X7,X6)
| ~ r1_orders_2(X5,X8,X7)
| r2_hidden(X8,X6)
| ~ m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X5)))
| ~ l1_orders_2(X5) )
& ( m1_subset_1(esk24_2(X5,X6),u1_struct_0(X5))
| v12_waybel_0(X6,X5)
| ~ m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X5)))
| ~ l1_orders_2(X5) )
& ( m1_subset_1(esk25_2(X5,X6),u1_struct_0(X5))
| v12_waybel_0(X6,X5)
| ~ m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X5)))
| ~ l1_orders_2(X5) )
& ( r2_hidden(esk24_2(X5,X6),X6)
| v12_waybel_0(X6,X5)
| ~ m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X5)))
| ~ l1_orders_2(X5) )
& ( r1_orders_2(X5,esk25_2(X5,X6),esk24_2(X5,X6))
| v12_waybel_0(X6,X5)
| ~ m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X5)))
| ~ l1_orders_2(X5) )
& ( ~ r2_hidden(esk25_2(X5,X6),X6)
| v12_waybel_0(X6,X5)
| ~ m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X5)))
| ~ l1_orders_2(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d19_waybel_0])])])])])])]) ).
fof(c_0_53,plain,
! [X4,X5,X6] :
( ~ r2_hidden(X4,X5)
| ~ m1_subset_1(X5,k1_zfmisc_1(X6))
| m1_subset_1(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(c_0_54,negated_conjecture,
( ~ v3_struct_0(esk1_0)
& v2_orders_2(esk1_0)
& v3_orders_2(esk1_0)
& v4_orders_2(esk1_0)
& v1_yellow_0(esk1_0)
& v1_lattice3(esk1_0)
& l1_orders_2(esk1_0)
& ~ v3_struct_0(esk2_0)
& v2_orders_2(esk2_0)
& v3_orders_2(esk2_0)
& v4_orders_2(esk2_0)
& v1_yellow_0(esk2_0)
& v1_lattice3(esk2_0)
& l1_orders_2(esk2_0)
& ~ v1_xboole_0(k3_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0)))
& v1_waybel_0(k3_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0)),esk2_0)
& v12_waybel_0(k3_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0)),esk2_0)
& m1_subset_1(k3_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0)),k1_zfmisc_1(u1_struct_0(esk2_0)))
& ~ r2_hidden(k3_yellow_0(esk2_0),u1_struct_0(esk1_0)) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_48])])])])])]) ).
cnf(c_0_55,plain,
r1_tarski(k3_xboole_0(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
fof(c_0_56,plain,
! [X4,X5,X6] : r1_tarski(k2_xboole_0(k3_xboole_0(X4,X5),k3_xboole_0(X4,X6)),k2_xboole_0(X5,X6)),
inference(variable_rename,[status(thm)],[t31_xboole_1]) ).
fof(c_0_57,plain,
! [X4,X5,X6] : k4_xboole_0(X4,k2_xboole_0(X5,X6)) = k3_xboole_0(k4_xboole_0(X4,X5),k4_xboole_0(X4,X6)),
inference(variable_rename,[status(thm)],[t53_xboole_1]) ).
cnf(c_0_58,plain,
k4_xboole_0(X1,k4_xboole_0(X1,k4_xboole_0(X2,X3))) = k4_xboole_0(k4_xboole_0(X1,k4_xboole_0(X1,X2)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_29]),c_0_29]) ).
cnf(c_0_59,plain,
k4_xboole_0(X1,X1) = k1_xboole_0,
inference(rw,[status(thm)],[c_0_40,c_0_51]) ).
cnf(c_0_60,plain,
( r2_hidden(X3,X2)
| ~ l1_orders_2(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ r1_orders_2(X1,X3,X4)
| ~ r2_hidden(X4,X2)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X4,u1_struct_0(X1))
| ~ v12_waybel_0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_61,plain,
( m1_subset_1(X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X2))
| ~ r2_hidden(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_62,plain,
! [X3,X4] :
( v3_struct_0(X3)
| ~ v4_orders_2(X3)
| ~ v1_yellow_0(X3)
| ~ l1_orders_2(X3)
| ~ m1_subset_1(X4,u1_struct_0(X3))
| r1_orders_2(X3,k3_yellow_0(X3),X4) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t44_yellow_0])])])])])]) ).
fof(c_0_63,plain,
! [X2] :
( ~ l1_orders_2(X2)
| m1_subset_1(k3_yellow_0(X2),u1_struct_0(X2)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_yellow_0])]) ).
cnf(c_0_64,negated_conjecture,
v12_waybel_0(k3_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0)),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_65,plain,
! [X3,X4,X3,X4] :
( ( ~ m1_subset_1(X3,k1_zfmisc_1(X4))
| r1_tarski(X3,X4) )
& ( ~ r1_tarski(X3,X4)
| m1_subset_1(X3,k1_zfmisc_1(X4)) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])])]) ).
cnf(c_0_66,plain,
r1_tarski(k4_xboole_0(X1,k4_xboole_0(X1,X2)),X1),
inference(rw,[status(thm)],[c_0_55,c_0_29]) ).
cnf(c_0_67,plain,
r1_tarski(k2_xboole_0(k3_xboole_0(X1,X2),k3_xboole_0(X1,X3)),k2_xboole_0(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_68,plain,
k4_xboole_0(X1,k2_xboole_0(X2,X3)) = k3_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_69,plain,
k4_xboole_0(X1,k4_xboole_0(X1,k4_xboole_0(k4_xboole_0(X1,X2),X3))) = k4_xboole_0(k4_xboole_0(X1,X2),X3),
inference(spm,[status(thm)],[c_0_58,c_0_43]) ).
cnf(c_0_70,plain,
k4_xboole_0(X1,k4_xboole_0(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_59]),c_0_40]),c_0_51]) ).
cnf(c_0_71,plain,
( r2_hidden(X1,X2)
| ~ v12_waybel_0(X2,X3)
| ~ r1_orders_2(X3,X1,X4)
| ~ l1_orders_2(X3)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X3)))
| ~ m1_subset_1(X1,u1_struct_0(X3))
| ~ r2_hidden(X4,X2) ),
inference(csr,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_72,plain,
( r1_orders_2(X1,k3_yellow_0(X1),X2)
| v3_struct_0(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_orders_2(X1)
| ~ v1_yellow_0(X1)
| ~ v4_orders_2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_73,plain,
( m1_subset_1(k3_yellow_0(X1),u1_struct_0(X1))
| ~ l1_orders_2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_74,negated_conjecture,
v12_waybel_0(k4_xboole_0(u1_struct_0(esk1_0),k4_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0))),esk2_0),
inference(rw,[status(thm)],[c_0_64,c_0_29]) ).
cnf(c_0_75,plain,
( m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_76,plain,
r1_tarski(k4_xboole_0(X1,X2),X1),
inference(spm,[status(thm)],[c_0_66,c_0_43]) ).
cnf(c_0_77,plain,
r1_tarski(k2_xboole_0(k4_xboole_0(X1,k4_xboole_0(X1,X2)),k4_xboole_0(X1,k4_xboole_0(X1,X3))),k2_xboole_0(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_29]),c_0_29]) ).
cnf(c_0_78,plain,
k4_xboole_0(X1,k2_xboole_0(X2,X3)) = k4_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(k4_xboole_0(X1,X2),k4_xboole_0(X1,X3))),
inference(rw,[status(thm)],[c_0_68,c_0_29]) ).
cnf(c_0_79,plain,
k4_xboole_0(k4_xboole_0(X1,X2),X1) = k1_xboole_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_59]) ).
fof(c_0_80,plain,
! [X4,X5,X6] :
( ~ r2_hidden(X4,X5)
| ~ m1_subset_1(X5,k1_zfmisc_1(X6))
| ~ v1_xboole_0(X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(c_0_81,plain,
! [X3] :
( m1_subset_1(esk8_1(X3),k1_zfmisc_1(X3))
& v1_xboole_0(esk8_1(X3)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(c_0_82,plain,
! [X5,X6,X7,X8,X8,X5,X6,X7] :
( ( r2_hidden(X8,X5)
| ~ r2_hidden(X8,X7)
| X7 != k3_xboole_0(X5,X6) )
& ( r2_hidden(X8,X6)
| ~ r2_hidden(X8,X7)
| X7 != k3_xboole_0(X5,X6) )
& ( ~ r2_hidden(X8,X5)
| ~ r2_hidden(X8,X6)
| r2_hidden(X8,X7)
| X7 != k3_xboole_0(X5,X6) )
& ( ~ r2_hidden(esk14_3(X5,X6,X7),X7)
| ~ r2_hidden(esk14_3(X5,X6,X7),X5)
| ~ r2_hidden(esk14_3(X5,X6,X7),X6)
| X7 = k3_xboole_0(X5,X6) )
& ( r2_hidden(esk14_3(X5,X6,X7),X5)
| r2_hidden(esk14_3(X5,X6,X7),X7)
| X7 = k3_xboole_0(X5,X6) )
& ( r2_hidden(esk14_3(X5,X6,X7),X6)
| r2_hidden(esk14_3(X5,X6,X7),X7)
| X7 = k3_xboole_0(X5,X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_xboole_0])])])])])])]) ).
cnf(c_0_83,plain,
( v3_struct_0(X1)
| r2_hidden(k3_yellow_0(X1),X2)
| ~ v12_waybel_0(X2,X1)
| ~ v1_yellow_0(X1)
| ~ v4_orders_2(X1)
| ~ l1_orders_2(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ r2_hidden(X3,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_61]),c_0_73]) ).
cnf(c_0_84,negated_conjecture,
v12_waybel_0(k4_xboole_0(u1_struct_0(esk2_0),k4_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))),esk2_0),
inference(rw,[status(thm)],[c_0_74,c_0_37]) ).
cnf(c_0_85,negated_conjecture,
v1_yellow_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_86,negated_conjecture,
v4_orders_2(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_87,negated_conjecture,
l1_orders_2(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_88,plain,
m1_subset_1(k4_xboole_0(X1,X2),k1_zfmisc_1(X1)),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_89,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_90,plain,
! [X4,X5] :
( ( m1_subset_1(esk11_2(X4,X5),X4)
| X5 = k1_xboole_0
| ~ m1_subset_1(X5,k1_zfmisc_1(X4)) )
& ( r2_hidden(esk11_2(X4,X5),X5)
| X5 = k1_xboole_0
| ~ m1_subset_1(X5,k1_zfmisc_1(X4)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t10_subset_1])])])])])])]) ).
cnf(c_0_91,plain,
r1_tarski(k4_xboole_0(X1,k4_xboole_0(k4_xboole_0(X1,X2),X3)),k2_xboole_0(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_36]),c_0_42]) ).
cnf(c_0_92,plain,
k4_xboole_0(k4_xboole_0(X1,X2),k2_xboole_0(X3,X1)) = k1_xboole_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_51]),c_0_59]) ).
fof(c_0_93,plain,
! [X2] : m1_subset_1(k1_xboole_0,k1_zfmisc_1(X2)),
inference(variable_rename,[status(thm)],[t4_subset_1]) ).
cnf(c_0_94,plain,
( ~ v1_xboole_0(X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ r2_hidden(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_95,plain,
m1_subset_1(esk8_1(X1),k1_zfmisc_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_96,plain,
( X1 = k3_xboole_0(X2,X3)
| r2_hidden(esk14_3(X2,X3,X1),X1)
| r2_hidden(esk14_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_97,plain,
( r2_hidden(X4,X3)
| X1 != k3_xboole_0(X2,X3)
| ~ r2_hidden(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_98,negated_conjecture,
( r2_hidden(k3_yellow_0(esk2_0),k4_xboole_0(u1_struct_0(esk2_0),k4_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))))
| ~ r2_hidden(X1,k4_xboole_0(u1_struct_0(esk2_0),k4_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0)))) ),
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(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]),c_0_86]),c_0_87]),c_0_88])]),c_0_89]) ).
cnf(c_0_99,plain,
( X1 = k1_xboole_0
| r2_hidden(esk11_2(X2,X1),X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_100,plain,
r1_tarski(X1,k2_xboole_0(X2,k2_xboole_0(X3,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_51]) ).
cnf(c_0_101,plain,
m1_subset_1(k1_xboole_0,k1_zfmisc_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_102,plain,
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X2,esk8_1(X1)) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_103,plain,
( X1 = k4_xboole_0(X2,k4_xboole_0(X2,X3))
| r2_hidden(esk14_3(X2,X3,X1),X3)
| r2_hidden(esk14_3(X2,X3,X1),X1) ),
inference(rw,[status(thm)],[c_0_96,c_0_29]) ).
cnf(c_0_104,negated_conjecture,
~ v1_xboole_0(k3_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_105,plain,
( r2_hidden(X4,X3)
| X1 != k4_xboole_0(X2,k4_xboole_0(X2,X3))
| ~ r2_hidden(X4,X1) ),
inference(rw,[status(thm)],[c_0_97,c_0_29]) ).
cnf(c_0_106,negated_conjecture,
( k4_xboole_0(u1_struct_0(esk2_0),k4_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))) = k1_xboole_0
| r2_hidden(k3_yellow_0(esk2_0),k4_xboole_0(u1_struct_0(esk2_0),k4_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))))
| ~ m1_subset_1(k4_xboole_0(u1_struct_0(esk2_0),k4_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))),k1_zfmisc_1(X1)) ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_107,plain,
m1_subset_1(X1,k1_zfmisc_1(k2_xboole_0(X2,k2_xboole_0(X3,X1)))),
inference(spm,[status(thm)],[c_0_75,c_0_100]) ).
cnf(c_0_108,plain,
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X2,k1_xboole_0) ),
inference(spm,[status(thm)],[c_0_94,c_0_101]) ).
cnf(c_0_109,plain,
( esk8_1(X1) = k4_xboole_0(X2,k4_xboole_0(X2,X3))
| r2_hidden(esk14_3(X2,X3,esk8_1(X1)),X3)
| ~ v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_110,negated_conjecture,
~ v1_xboole_0(k4_xboole_0(u1_struct_0(esk1_0),k4_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0)))),
inference(rw,[status(thm)],[c_0_104,c_0_29]) ).
cnf(c_0_111,plain,
( r2_hidden(X1,X2)
| ~ r2_hidden(X1,k4_xboole_0(X3,k4_xboole_0(X3,X2))) ),
inference(er,[status(thm)],[c_0_105]) ).
cnf(c_0_112,negated_conjecture,
( k4_xboole_0(u1_struct_0(esk2_0),k4_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))) = k1_xboole_0
| r2_hidden(k3_yellow_0(esk2_0),k4_xboole_0(u1_struct_0(esk2_0),k4_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0)))) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_113,negated_conjecture,
~ r2_hidden(k3_yellow_0(esk2_0),u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_114,plain,
( esk8_1(X1) = k1_xboole_0
| ~ v1_xboole_0(X2)
| ~ v1_xboole_0(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_51]),c_0_59]) ).
cnf(c_0_115,plain,
v1_xboole_0(esk8_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_116,negated_conjecture,
~ v1_xboole_0(k4_xboole_0(u1_struct_0(esk2_0),k4_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0)))),
inference(rw,[status(thm)],[c_0_110,c_0_37]) ).
cnf(c_0_117,negated_conjecture,
k4_xboole_0(u1_struct_0(esk2_0),k4_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))) = k1_xboole_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113]) ).
cnf(c_0_118,plain,
( esk8_1(X1) = k1_xboole_0
| ~ v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_119,negated_conjecture,
~ v1_xboole_0(k1_xboole_0),
inference(rw,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_120,plain,
~ v1_xboole_0(X1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_118]),c_0_119]) ).
cnf(c_0_121,plain,
$false,
inference(sr,[status(thm)],[c_0_115,c_0_120]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU411+2 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 16:48:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.51/9.70 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.51/9.70 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.51/9.70 # Preprocessing time : 0.168 s
% 0.51/9.70
% 0.51/9.70 # Proof found!
% 0.51/9.70 # SZS status Theorem
% 0.51/9.70 # SZS output start CNFRefutation
% See solution above
% 0.51/9.70 # Proof object total steps : 122
% 0.51/9.70 # Proof object clause steps : 77
% 0.51/9.70 # Proof object formula steps : 45
% 0.51/9.70 # Proof object conjectures : 19
% 0.51/9.70 # Proof object clause conjectures : 16
% 0.51/9.70 # Proof object formula conjectures : 3
% 0.51/9.70 # Proof object initial clauses used : 30
% 0.51/9.70 # Proof object initial formulas used : 22
% 0.51/9.70 # Proof object generating inferences : 23
% 0.51/9.70 # Proof object simplifying inferences : 47
% 0.51/9.70 # Training examples: 0 positive, 0 negative
% 0.51/9.70 # Parsed axioms : 4457
% 0.51/9.70 # Removed by relevancy pruning/SinE : 4356
% 0.51/9.70 # Initial clauses : 184
% 0.51/9.70 # Removed in clause preprocessing : 1
% 0.51/9.70 # Initial clauses in saturation : 183
% 0.51/9.70 # Processed clauses : 6433
% 0.51/9.70 # ...of these trivial : 1171
% 0.51/9.70 # ...subsumed : 3122
% 0.51/9.70 # ...remaining for further processing : 2140
% 0.51/9.70 # Other redundant clauses eliminated : 103
% 0.51/9.70 # Clauses deleted for lack of memory : 50115
% 0.51/9.70 # Backward-subsumed : 34
% 0.51/9.70 # Backward-rewritten : 392
% 0.51/9.70 # Generated clauses : 312667
% 0.51/9.70 # ...of the previous two non-trivial : 219530
% 0.51/9.70 # Contextual simplify-reflections : 99
% 0.51/9.70 # Paramodulations : 312518
% 0.51/9.70 # Factorizations : 6
% 0.51/9.70 # Equation resolutions : 140
% 0.51/9.70 # Current number of processed clauses : 1709
% 0.51/9.70 # Positive orientable unit clauses : 819
% 0.51/9.70 # Positive unorientable unit clauses: 17
% 0.51/9.70 # Negative unit clauses : 133
% 0.51/9.70 # Non-unit-clauses : 740
% 0.51/9.70 # Current number of unprocessed clauses: 110599
% 0.51/9.70 # ...number of literals in the above : 272007
% 0.51/9.70 # Current number of archived formulas : 0
% 0.51/9.70 # Current number of archived clauses : 430
% 0.51/9.70 # Clause-clause subsumption calls (NU) : 152181
% 0.51/9.70 # Rec. Clause-clause subsumption calls : 31658
% 0.51/9.70 # Non-unit clause-clause subsumptions : 1413
% 0.51/9.70 # Unit Clause-clause subsumption calls : 8917
% 0.51/9.70 # Rewrite failures with RHS unbound : 1
% 0.51/9.70 # BW rewrite match attempts : 12863
% 0.51/9.70 # BW rewrite match successes : 1345
% 0.51/9.70 # Condensation attempts : 0
% 0.51/9.70 # Condensation successes : 0
% 0.51/9.70 # Termbank termtop insertions : 8881824
% 0.51/9.70
% 0.51/9.70 # -------------------------------------------------
% 0.51/9.70 # User time : 8.166 s
% 0.51/9.70 # System time : 0.125 s
% 0.51/9.70 # Total time : 8.291 s
% 0.51/9.70 # Maximum resident set size: 148180 pages
%------------------------------------------------------------------------------