%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU407+2 : 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 : n013.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 02:29:16 PM UTC 2026
% Result : Theorem 263.48s 39.27s
% Output : CNFRefutation 263.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 81 ( 16 unt; 0 def)
% Number of atoms : 415 ( 60 equ)
% Maximal formula atoms : 96 ( 5 avg)
% Number of connectives : 521 ( 187 ~; 217 |; 83 &)
% ( 12 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-6 aty)
% Number of variables : 143 ( 3 sgn 89 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t7_latsum_1,conjecture,
! [X1] :
( ( l1_orders_2(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_orders_2(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k1_latsum_1(X1,X2)))
=> ( r2_hidden(X3,k4_xboole_0(u1_struct_0(X2),u1_struct_0(X1)))
| r2_hidden(X3,u1_struct_0(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_latsum_1) ).
fof(d2_subset_1,axiom,
! [X1,X2] :
( ( v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> v1_xboole_0(X2) ) )
& ( ~ v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> r2_hidden(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+7.ax',d2_subset_1) ).
fof(t91_orders_1,axiom,
! [X1] :
( ~ ( ! [X2] :
~ ( r2_hidden(X2,X1)
& X2 != k1_xboole_0 )
& k3_tarski(X1) != k1_xboole_0 )
& ~ ( k3_tarski(X1) = k1_xboole_0
& ? [X2] :
( r2_hidden(X2,X1)
& X2 != k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+59.ax',t91_orders_1) ).
fof(d5_xboole_0,axiom,
! [X1] :
( v1_xboole_0(X1)
<=> X1 = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',d5_xboole_0) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( v1_xboole_0(X2)
& r2_hidden(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+3.ax',t7_boole) ).
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = k4_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( ~ r2_hidden(X4,X2)
& r2_hidden(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',d4_xboole_0) ).
fof(d2_latsum_1,axiom,
! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( l1_orders_2(X2)
=> ! [X3] :
( ( l1_orders_2(X3)
& v1_orders_2(X3) )
=> ( X3 = k1_latsum_1(X1,X2)
<=> ( u1_orders_2(X3) = k2_xboole_0(k2_xboole_0(u1_orders_2(X1),u1_orders_2(X2)),k7_relset_1(u1_struct_0(X1),u1_struct_0(X1),u1_struct_0(X2),u1_struct_0(X2),u1_orders_2(X1),u1_orders_2(X2)))
& u1_struct_0(X3) = k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_latsum_1) ).
fof(dt_k1_latsum_1,axiom,
! [X1,X2] :
( ( l1_orders_2(X2)
& l1_orders_2(X1) )
=> ( l1_orders_2(k1_latsum_1(X1,X2))
& v1_orders_2(k1_latsum_1(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_latsum_1) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( l1_struct_0(X1)
& ~ v3_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+200.ax',fc1_struct_0) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = k2_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( r2_hidden(X4,X2)
| r2_hidden(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',d2_xboole_0) ).
fof(dt_l1_orders_2,axiom,
! [X1] :
( l1_orders_2(X1)
=> l1_struct_0(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+218.ax',dt_l1_orders_2) ).
fof(t1_latsum_1,axiom,
! [X1,X2,X3,X4] :
~ ( ~ ( r2_hidden(X2,k4_xboole_0(X3,X4))
& r2_hidden(X1,X4) )
& ~ ( r2_hidden(X2,X4)
& r2_hidden(X1,k4_xboole_0(X3,X4)) )
& ~ ( r2_hidden(X2,X4)
& r2_hidden(X1,X4) )
& ~ ( r2_hidden(X2,k4_xboole_0(X3,X4))
& r2_hidden(X1,k4_xboole_0(X3,X4)) )
& r2_hidden(X2,k2_xboole_0(X3,X4))
& r2_hidden(X1,k2_xboole_0(X3,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_latsum_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',commutativity_k2_xboole_0) ).
fof(fc2_latsum_1,axiom,
! [X1,X2] :
( ( l1_orders_2(X2)
& l1_orders_2(X1)
& ~ v3_struct_0(X1) )
=> ( v1_orders_2(k1_latsum_1(X1,X2))
& ~ v3_struct_0(k1_latsum_1(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_latsum_1) ).
fof(c_0_14,negated_conjecture,
~ ! [X1] :
( ( l1_orders_2(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_orders_2(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k1_latsum_1(X1,X2)))
=> ( r2_hidden(X3,k4_xboole_0(u1_struct_0(X2),u1_struct_0(X1)))
| r2_hidden(X3,u1_struct_0(X1)) ) ) ) ),
inference(assume_negation,[status(cth)],[t7_latsum_1]) ).
fof(c_0_15,plain,
! [X1,X2] :
( ( v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> v1_xboole_0(X2) ) )
& ( ~ v1_xboole_0(X1)
=> ( m1_subset_1(X2,X1)
<=> r2_hidden(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d2_subset_1]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ( l1_orders_2(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( ( l1_orders_2(X2)
& ~ v3_struct_0(X2) )
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k1_latsum_1(X1,X2)))
=> ( r2_hidden(X3,k4_xboole_0(u1_struct_0(X2),u1_struct_0(X1)))
| r2_hidden(X3,u1_struct_0(X1)) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_17,plain,
! [X87,X88] :
( ( ~ v1_xboole_0(X87)
| m1_subset_1(X88,X87)
| ~ v1_xboole_0(X88) )
& ( ~ v1_xboole_0(X87)
| v1_xboole_0(X88)
| ~ m1_subset_1(X88,X87) )
& ( v1_xboole_0(X87)
| m1_subset_1(X88,X87)
| ~ r2_hidden(X88,X87) )
& ( v1_xboole_0(X87)
| r2_hidden(X88,X87)
| ~ m1_subset_1(X88,X87) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
fof(c_0_18,negated_conjecture,
( ~ r2_hidden(esk3_0,k4_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0)))
& ~ r2_hidden(esk3_0,u1_struct_0(esk1_0))
& m1_subset_1(esk3_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0)))
& l1_orders_2(esk2_0)
& ~ v3_struct_0(esk2_0)
& l1_orders_2(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_16])])])]) ).
fof(c_0_19,plain,
! [X1] :
( ~ ( ! [X2] :
~ ( r2_hidden(X2,X1)
& X2 != k1_xboole_0 )
& k3_tarski(X1) != k1_xboole_0 )
& ~ ( k3_tarski(X1) = k1_xboole_0
& ? [X2] :
( r2_hidden(X2,X1)
& X2 != k1_xboole_0 ) ) ),
inference(fof_simplification,[status(thm)],[t91_orders_1]) ).
cnf(c_0_20,plain,
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,X2)
| v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
( ~ m1_subset_1(X1,X2)
| v1_xboole_0(X2)
| r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,plain,
! [X3736,X3737,X3738] :
( ( k3_tarski(X3738) = k1_xboole_0
| r2_hidden(esk306_1(X3738),X3738) )
& ( k3_tarski(X3738) = k1_xboole_0
| esk306_1(X3738) != k1_xboole_0 )
& ( k3_tarski(X3736) != k1_xboole_0
| ~ r2_hidden(X3737,X3736)
| X3737 = k1_xboole_0 ) ),
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)],[c_0_19])])])])])])]) ).
cnf(c_0_24,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(k1_latsum_1(esk1_0,esk2_0)))
| v1_xboole_0(esk3_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( r2_hidden(esk3_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0)))
| v1_xboole_0(u1_struct_0(k1_latsum_1(esk1_0,esk2_0))) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
fof(c_0_26,plain,
! [X1040] :
( ( v1_xboole_0(X1040)
| X1040 != k1_xboole_0 )
& ( X1040 = k1_xboole_0
| ~ v1_xboole_0(X1040) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_xboole_0])])]) ).
fof(c_0_27,plain,
! [X60,X61] :
( ~ v1_xboole_0(X61)
| ~ r2_hidden(X60,X61) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])]) ).
cnf(c_0_28,plain,
( k3_tarski(X2) != k1_xboole_0
| ~ r2_hidden(X1,X2)
| X1 = k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
( r2_hidden(esk3_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0)))
| v1_xboole_0(esk3_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
( ~ v1_xboole_0(X1)
| X1 = k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
( ~ v1_xboole_0(X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
( k3_tarski(X1) = k1_xboole_0
| r2_hidden(esk306_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_33,plain,
! [X1,X2,X3] :
( X3 = k4_xboole_0(X1,X2)
<=> ! [X4] :
( r2_hidden(X4,X3)
<=> ( ~ r2_hidden(X4,X2)
& r2_hidden(X4,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
cnf(c_0_34,negated_conjecture,
( k3_tarski(u1_struct_0(k1_latsum_1(esk1_0,esk2_0))) != k1_xboole_0
| esk3_0 = k1_xboole_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_35,plain,
( ~ v1_xboole_0(X1)
| k3_tarski(X1) = k1_xboole_0 ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
fof(c_0_36,plain,
! [X512,X513,X514] :
( ( ~ l1_orders_2(X512)
| ~ l1_orders_2(X513)
| ~ l1_orders_2(X514)
| ~ v1_orders_2(X514)
| X514 = k1_latsum_1(X512,X513)
| u1_orders_2(X514) != k2_xboole_0(k2_xboole_0(u1_orders_2(X512),u1_orders_2(X513)),k7_relset_1(u1_struct_0(X512),u1_struct_0(X512),u1_struct_0(X513),u1_struct_0(X513),u1_orders_2(X512),u1_orders_2(X513)))
| u1_struct_0(X514) != k2_xboole_0(u1_struct_0(X512),u1_struct_0(X513)) )
& ( ~ l1_orders_2(X512)
| ~ l1_orders_2(X513)
| ~ l1_orders_2(X514)
| ~ v1_orders_2(X514)
| X514 != k1_latsum_1(X512,X513)
| u1_orders_2(X514) = k2_xboole_0(k2_xboole_0(u1_orders_2(X512),u1_orders_2(X513)),k7_relset_1(u1_struct_0(X512),u1_struct_0(X512),u1_struct_0(X513),u1_struct_0(X513),u1_orders_2(X512),u1_orders_2(X513))) )
& ( ~ l1_orders_2(X512)
| ~ l1_orders_2(X513)
| ~ l1_orders_2(X514)
| ~ v1_orders_2(X514)
| X514 != k1_latsum_1(X512,X513)
| u1_struct_0(X514) = k2_xboole_0(u1_struct_0(X512),u1_struct_0(X513)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_latsum_1])])])])]) ).
fof(c_0_37,plain,
! [X510,X511] :
( ( ~ l1_orders_2(X511)
| ~ l1_orders_2(X510)
| l1_orders_2(k1_latsum_1(X510,X511)) )
& ( ~ l1_orders_2(X511)
| ~ l1_orders_2(X510)
| v1_orders_2(k1_latsum_1(X510,X511)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_latsum_1])])])]) ).
fof(c_0_38,plain,
! [X238,X239,X240,X241,X242,X243,X244,X245] :
( ( X245 = k4_xboole_0(X243,X244)
| r2_hidden(esk40_3(X243,X244,X245),X245)
| ~ r2_hidden(esk40_3(X243,X244,X245),X244) )
& ( X245 = k4_xboole_0(X243,X244)
| r2_hidden(esk40_3(X243,X244,X245),X245)
| r2_hidden(esk40_3(X243,X244,X245),X243) )
& ( X245 = k4_xboole_0(X243,X244)
| r2_hidden(esk40_3(X243,X244,X245),X244)
| ~ r2_hidden(esk40_3(X243,X244,X245),X243)
| ~ r2_hidden(esk40_3(X243,X244,X245),X245) )
& ( X240 != k4_xboole_0(X238,X239)
| r2_hidden(X242,X240)
| r2_hidden(X242,X239)
| ~ r2_hidden(X242,X238) )
& ( X240 != k4_xboole_0(X238,X239)
| ~ r2_hidden(X241,X240)
| ~ r2_hidden(X241,X239) )
& ( X240 != k4_xboole_0(X238,X239)
| ~ r2_hidden(X241,X240)
| r2_hidden(X241,X238) ) ),
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)],[c_0_33])])])])])])]) ).
fof(c_0_39,plain,
! [X1] :
( ( l1_struct_0(X1)
& ~ v3_struct_0(X1) )
=> ~ v1_xboole_0(u1_struct_0(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
fof(c_0_40,plain,
! [X42,X43,X44,X45,X46,X47,X48,X49] :
( ( X49 = k2_xboole_0(X47,X48)
| r2_hidden(esk9_3(X47,X48,X49),X48)
| r2_hidden(esk9_3(X47,X48,X49),X47)
| r2_hidden(esk9_3(X47,X48,X49),X49) )
& ( X49 = k2_xboole_0(X47,X48)
| ~ r2_hidden(esk9_3(X47,X48,X49),X49)
| ~ r2_hidden(esk9_3(X47,X48,X49),X48) )
& ( X49 = k2_xboole_0(X47,X48)
| ~ r2_hidden(esk9_3(X47,X48,X49),X49)
| ~ r2_hidden(esk9_3(X47,X48,X49),X47) )
& ( X44 != k2_xboole_0(X42,X43)
| r2_hidden(X46,X44)
| ~ r2_hidden(X46,X43) )
& ( X44 != k2_xboole_0(X42,X43)
| r2_hidden(X46,X44)
| ~ r2_hidden(X46,X42) )
& ( X44 != k2_xboole_0(X42,X43)
| r2_hidden(X45,X43)
| r2_hidden(X45,X42)
| ~ r2_hidden(X45,X44) ) ),
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)],[d2_xboole_0])])])])])])]) ).
cnf(c_0_41,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(k1_latsum_1(esk1_0,esk2_0)))
| esk3_0 = k1_xboole_0 ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,plain,
( ~ l1_orders_2(X2)
| ~ l1_orders_2(X3)
| ~ l1_orders_2(X1)
| ~ v1_orders_2(X1)
| X1 != k1_latsum_1(X2,X3)
| u1_struct_0(X1) = k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,plain,
( ~ l1_orders_2(X2)
| ~ l1_orders_2(X1)
| l1_orders_2(k1_latsum_1(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_44,plain,
( ~ l1_orders_2(X2)
| ~ l1_orders_2(X1)
| v1_orders_2(k1_latsum_1(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,plain,
( X4 != k4_xboole_0(X2,X3)
| ~ r2_hidden(X1,X2)
| r2_hidden(X1,X4)
| r2_hidden(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_46,plain,
! [X5544] :
( ~ v1_xboole_0(u1_struct_0(X5544))
| ~ l1_struct_0(X5544)
| v3_struct_0(X5544) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])]) ).
fof(c_0_47,plain,
! [X5555] :
( l1_struct_0(X5555)
| ~ l1_orders_2(X5555) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_orders_2])])]) ).
cnf(c_0_48,plain,
( X2 != k2_xboole_0(X3,X4)
| ~ r2_hidden(X1,X2)
| r2_hidden(X1,X4)
| r2_hidden(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,negated_conjecture,
( r2_hidden(esk3_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0)))
| esk3_0 = k1_xboole_0 ),
inference(spm,[status(thm)],[c_0_41,c_0_25]) ).
cnf(c_0_50,plain,
( ~ l1_orders_2(X1)
| ~ l1_orders_2(X2)
| u1_struct_0(k1_latsum_1(X1,X2)) = k2_xboole_0(u1_struct_0(X1),u1_struct_0(X2)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_42]),c_0_43]),c_0_44]) ).
cnf(c_0_51,negated_conjecture,
l1_orders_2(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_52,negated_conjecture,
l1_orders_2(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_53,negated_conjecture,
~ r2_hidden(esk3_0,k4_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_54,plain,
( ~ r2_hidden(X1,X2)
| r2_hidden(X1,X3)
| r2_hidden(X1,k4_xboole_0(X2,X3)) ),
inference(er,[status(thm)],[c_0_45]) ).
cnf(c_0_55,negated_conjecture,
~ r2_hidden(esk3_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_56,plain,
! [X486,X487,X488,X489] :
( ( ~ r2_hidden(X487,k2_xboole_0(X488,X489))
| ~ r2_hidden(X486,k2_xboole_0(X488,X489))
| r2_hidden(X487,k4_xboole_0(X488,X489))
| r2_hidden(X487,X489)
| r2_hidden(X487,X489)
| r2_hidden(X487,k4_xboole_0(X488,X489)) )
& ( ~ r2_hidden(X487,k2_xboole_0(X488,X489))
| ~ r2_hidden(X486,k2_xboole_0(X488,X489))
| r2_hidden(X487,k4_xboole_0(X488,X489))
| r2_hidden(X487,X489)
| r2_hidden(X487,X489)
| r2_hidden(X486,X489) )
& ( ~ r2_hidden(X487,k2_xboole_0(X488,X489))
| ~ r2_hidden(X486,k2_xboole_0(X488,X489))
| r2_hidden(X487,k4_xboole_0(X488,X489))
| r2_hidden(X487,X489)
| r2_hidden(X486,k4_xboole_0(X488,X489))
| r2_hidden(X487,k4_xboole_0(X488,X489)) )
& ( ~ r2_hidden(X487,k2_xboole_0(X488,X489))
| ~ r2_hidden(X486,k2_xboole_0(X488,X489))
| r2_hidden(X487,k4_xboole_0(X488,X489))
| r2_hidden(X487,X489)
| r2_hidden(X486,k4_xboole_0(X488,X489))
| r2_hidden(X486,X489) )
& ( ~ r2_hidden(X487,k2_xboole_0(X488,X489))
| ~ r2_hidden(X486,k2_xboole_0(X488,X489))
| r2_hidden(X487,k4_xboole_0(X488,X489))
| r2_hidden(X486,X489)
| r2_hidden(X487,X489)
| r2_hidden(X487,k4_xboole_0(X488,X489)) )
& ( ~ r2_hidden(X487,k2_xboole_0(X488,X489))
| ~ r2_hidden(X486,k2_xboole_0(X488,X489))
| r2_hidden(X487,k4_xboole_0(X488,X489))
| r2_hidden(X486,X489)
| r2_hidden(X487,X489)
| r2_hidden(X486,X489) )
& ( ~ r2_hidden(X487,k2_xboole_0(X488,X489))
| ~ r2_hidden(X486,k2_xboole_0(X488,X489))
| r2_hidden(X487,k4_xboole_0(X488,X489))
| r2_hidden(X486,X489)
| r2_hidden(X486,k4_xboole_0(X488,X489))
| r2_hidden(X487,k4_xboole_0(X488,X489)) )
& ( ~ r2_hidden(X487,k2_xboole_0(X488,X489))
| ~ r2_hidden(X486,k2_xboole_0(X488,X489))
| r2_hidden(X487,k4_xboole_0(X488,X489))
| r2_hidden(X486,X489)
| r2_hidden(X486,k4_xboole_0(X488,X489))
| r2_hidden(X486,X489) )
& ( ~ r2_hidden(X487,k2_xboole_0(X488,X489))
| ~ r2_hidden(X486,k2_xboole_0(X488,X489))
| r2_hidden(X486,k4_xboole_0(X488,X489))
| r2_hidden(X487,X489)
| r2_hidden(X487,X489)
| r2_hidden(X487,k4_xboole_0(X488,X489)) )
& ( ~ r2_hidden(X487,k2_xboole_0(X488,X489))
| ~ r2_hidden(X486,k2_xboole_0(X488,X489))
| r2_hidden(X486,k4_xboole_0(X488,X489))
| r2_hidden(X487,X489)
| r2_hidden(X487,X489)
| r2_hidden(X486,X489) )
& ( ~ r2_hidden(X487,k2_xboole_0(X488,X489))
| ~ r2_hidden(X486,k2_xboole_0(X488,X489))
| r2_hidden(X486,k4_xboole_0(X488,X489))
| r2_hidden(X487,X489)
| r2_hidden(X486,k4_xboole_0(X488,X489))
| r2_hidden(X487,k4_xboole_0(X488,X489)) )
& ( ~ r2_hidden(X487,k2_xboole_0(X488,X489))
| ~ r2_hidden(X486,k2_xboole_0(X488,X489))
| r2_hidden(X486,k4_xboole_0(X488,X489))
| r2_hidden(X487,X489)
| r2_hidden(X486,k4_xboole_0(X488,X489))
| r2_hidden(X486,X489) )
& ( ~ r2_hidden(X487,k2_xboole_0(X488,X489))
| ~ r2_hidden(X486,k2_xboole_0(X488,X489))
| r2_hidden(X486,k4_xboole_0(X488,X489))
| r2_hidden(X486,X489)
| r2_hidden(X487,X489)
| r2_hidden(X487,k4_xboole_0(X488,X489)) )
& ( ~ r2_hidden(X487,k2_xboole_0(X488,X489))
| ~ r2_hidden(X486,k2_xboole_0(X488,X489))
| r2_hidden(X486,k4_xboole_0(X488,X489))
| r2_hidden(X486,X489)
| r2_hidden(X487,X489)
| r2_hidden(X486,X489) )
& ( ~ r2_hidden(X487,k2_xboole_0(X488,X489))
| ~ r2_hidden(X486,k2_xboole_0(X488,X489))
| r2_hidden(X486,k4_xboole_0(X488,X489))
| r2_hidden(X486,X489)
| r2_hidden(X486,k4_xboole_0(X488,X489))
| r2_hidden(X487,k4_xboole_0(X488,X489)) )
& ( ~ r2_hidden(X487,k2_xboole_0(X488,X489))
| ~ r2_hidden(X486,k2_xboole_0(X488,X489))
| r2_hidden(X486,k4_xboole_0(X488,X489))
| r2_hidden(X486,X489)
| r2_hidden(X486,k4_xboole_0(X488,X489))
| r2_hidden(X486,X489) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_latsum_1])])])]) ).
cnf(c_0_57,plain,
( ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_struct_0(X1)
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_58,plain,
( ~ l1_orders_2(X1)
| l1_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_59,plain,
( ~ r2_hidden(X1,k2_xboole_0(X3,X2))
| r2_hidden(X1,X3)
| r2_hidden(X1,X2) ),
inference(er,[status(thm)],[c_0_48]) ).
cnf(c_0_60,negated_conjecture,
( r2_hidden(esk3_0,k2_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0)))
| esk3_0 = k1_xboole_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_52])]) ).
cnf(c_0_61,negated_conjecture,
~ r2_hidden(esk3_0,u1_struct_0(esk2_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_62,plain,
( ~ r2_hidden(X1,k2_xboole_0(X2,X3))
| ~ r2_hidden(X4,k2_xboole_0(X2,X3))
| r2_hidden(X1,k4_xboole_0(X2,X3))
| r2_hidden(X1,X3)
| r2_hidden(X1,X3)
| r2_hidden(X1,k4_xboole_0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_63,plain,
( ~ v1_xboole_0(u1_struct_0(X1))
| ~ l1_orders_2(X1)
| v3_struct_0(X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_64,negated_conjecture,
esk3_0 = k1_xboole_0,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_55]),c_0_61]) ).
cnf(c_0_65,plain,
( ~ r2_hidden(X1,k2_xboole_0(X2,X3))
| ~ r2_hidden(X4,k2_xboole_0(X2,X3))
| r2_hidden(X1,k4_xboole_0(X2,X3))
| r2_hidden(X1,X3) ),
inference(cn,[status(thm)],[c_0_62]) ).
fof(c_0_66,plain,
! [X1159,X1160] : k2_xboole_0(X1159,X1160) = k2_xboole_0(X1160,X1159),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_67,negated_conjecture,
( ~ l1_orders_2(k1_latsum_1(esk1_0,esk2_0))
| r2_hidden(esk3_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0)))
| v3_struct_0(k1_latsum_1(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_63,c_0_25]) ).
cnf(c_0_68,negated_conjecture,
~ r2_hidden(k1_xboole_0,k4_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))),
inference(rw,[status(thm)],[c_0_53,c_0_64]) ).
cnf(c_0_69,plain,
( ~ r2_hidden(X1,k2_xboole_0(X2,X3))
| r2_hidden(X1,X3)
| r2_hidden(X1,k4_xboole_0(X2,X3)) ),
inference(condense,[status(thm)],[c_0_65]) ).
cnf(c_0_70,plain,
k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_71,negated_conjecture,
~ r2_hidden(k1_xboole_0,u1_struct_0(esk1_0)),
inference(rw,[status(thm)],[c_0_55,c_0_64]) ).
fof(c_0_72,plain,
! [X1,X2] :
( ( l1_orders_2(X2)
& l1_orders_2(X1)
& ~ v3_struct_0(X1) )
=> ( v1_orders_2(k1_latsum_1(X1,X2))
& ~ v3_struct_0(k1_latsum_1(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[fc2_latsum_1]) ).
cnf(c_0_73,negated_conjecture,
( ~ l1_orders_2(k1_latsum_1(esk1_0,esk2_0))
| r2_hidden(k1_xboole_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0)))
| v3_struct_0(k1_latsum_1(esk1_0,esk2_0)) ),
inference(rw,[status(thm)],[c_0_67,c_0_64]) ).
cnf(c_0_74,negated_conjecture,
~ r2_hidden(k1_xboole_0,k2_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0))),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_71]) ).
fof(c_0_75,plain,
! [X517,X518] :
( ( ~ l1_orders_2(X518)
| ~ l1_orders_2(X517)
| v3_struct_0(X517)
| v1_orders_2(k1_latsum_1(X517,X518)) )
& ( ~ l1_orders_2(X518)
| ~ l1_orders_2(X517)
| v3_struct_0(X517)
| ~ v3_struct_0(k1_latsum_1(X517,X518)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_72])])])]) ).
cnf(c_0_76,negated_conjecture,
( ~ l1_orders_2(k1_latsum_1(esk1_0,esk2_0))
| v3_struct_0(k1_latsum_1(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_73,c_0_50]),c_0_51]),c_0_52])]),c_0_74]) ).
cnf(c_0_77,plain,
( ~ l1_orders_2(X2)
| ~ l1_orders_2(X1)
| ~ v3_struct_0(k1_latsum_1(X1,X2))
| v3_struct_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_78,negated_conjecture,
v3_struct_0(k1_latsum_1(esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_43]),c_0_51]),c_0_52])]) ).
cnf(c_0_79,negated_conjecture,
~ v3_struct_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_80,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_51]),c_0_52])]),c_0_79]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU407+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n013.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 06:20:51 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.50 Running first-order theorem proving
% 0.16/0.50 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
% 263.48/39.27 % Version: 3.5.1
% 263.48/39.27 % Preprocessing class: FMLMSMLLSSSNFFN.
% 263.48/39.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 263.48/39.27 % Starting new_bool_3 with 900s (3) cores
% 263.48/39.27 % Starting new_bool_1 with 900s (3) cores
% 263.48/39.27 % Starting sh5l with 300s (1) cores
% 263.48/39.27 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2p with 300s (1) cores
% 263.48/39.27 % sh5l with pid 114750 completed with status 0
% 263.48/39.27 % Result found by sh5l
% 263.48/39.27 % Preprocessing class: FMLMSMLLSSSNFFN.
% 263.48/39.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 263.48/39.27 % Starting new_bool_3 with 900s (3) cores
% 263.48/39.27 % Starting new_bool_1 with 900s (3) cores
% 263.48/39.27 % Starting sh5l with 300s (1) cores
% 263.48/39.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 263.48/39.27 % SinE strategy is gf500_gu_R04_F100_L20000
% 263.48/39.27 % Search class: FGHSM-SMLM32-MFFFFFNN
% 263.48/39.27 % Scheduled 13 strats onto 1 cores with 299 seconds (299 total)
% 263.48/39.27 % Starting SubtermCWHack with 27s (1) cores
% 263.48/39.27 % SubtermCWHack with pid 114759 completed with status 8
% 263.48/39.27 % Starting sh5l with 30s (1) cores
% 263.48/39.27 % sh5l with pid 114914 completed with status 0
% 263.48/39.27 % Result found by sh5l
% 263.48/39.27 % Preprocessing class: FMLMSMLLSSSNFFN.
% 263.48/39.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 263.48/39.27 % Starting new_bool_3 with 900s (3) cores
% 263.48/39.27 % Starting new_bool_1 with 900s (3) cores
% 263.48/39.27 % Starting sh5l with 300s (1) cores
% 263.48/39.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 263.48/39.27 % SinE strategy is gf500_gu_R04_F100_L20000
% 263.48/39.27 % Search class: FGHSM-SMLM32-MFFFFFNN
% 263.48/39.27 % Scheduled 13 strats onto 1 cores with 299 seconds (299 total)
% 263.48/39.27 % Starting SubtermCWHack with 27s (1) cores
% 263.48/39.27 % SubtermCWHack with pid 114759 completed with status 8
% 263.48/39.27 % Starting sh5l with 30s (1) cores
% 263.48/39.27 % Preprocessing time : 0.103 s
% 263.48/39.27 % Presaturation interreduction done
% 263.48/39.27
% 263.48/39.27 % Proof found!
% 263.48/39.27 % SZS status Theorem
% 263.48/39.27 % SZS output start CNFRefutation
% See solution above
% 263.48/39.27 % Parsed axioms : 4444
% 263.48/39.27 % Removed by relevancy pruning/SinE : 1309
% 263.48/39.27 % Initial clauses : 7228
% 263.48/39.27 % Removed in clause preprocessing : 161
% 263.48/39.27 % Initial clauses in saturation : 7067
% 263.48/39.27 % Processed clauses : 33903
% 263.48/39.27 % ...of these trivial : 406
% 263.48/39.27 % ...subsumed : 17092
% 263.48/39.27 % ...remaining for further processing : 16405
% 263.48/39.27 % Other redundant clauses eliminated : 1892
% 263.48/39.27 % Clauses deleted for lack of memory : 0
% 263.48/39.27 % Backward-subsumed : 321
% 263.48/39.27 % Backward-rewritten : 1157
% 263.48/39.27 % Generated clauses : 127509
% 263.48/39.27 % ...of the previous two non-redundant : 118303
% 263.48/39.27 % ...aggressively subsumed : 0
% 263.48/39.27 % Contextual simplify-reflections : 545
% 263.48/39.27 % Paramodulations : 125633
% 263.48/39.27 % Factorizations : 10
% 263.48/39.27 % NegExts : 0
% 263.48/39.27 % Equation resolutions : 1912
% 263.48/39.27 % Disequality decompositions : 0
% 263.48/39.27 % Total rewrite steps : 34853
% 263.48/39.27 % ...of those cached : 31158
% 263.48/39.27 % Propositional unsat checks : 0
% 263.48/39.27 % Propositional check models : 0
% 263.48/39.27 % Propositional check unsatisfiable : 0
% 263.48/39.27 % Propositional clauses : 0
% 263.48/39.27 % Propositional clauses after purity: 0
% 263.48/39.27 % Propositional unsat core size : 0
% 263.48/39.27 % Propositional preprocessing time : 0.000
% 263.48/39.27 % Propositional encoding time : 0.000
% 263.48/39.27 % Propositional solver time : 0.000
% 263.48/39.27 % Success case prop preproc time : 0.000
% 263.48/39.27 % Success case prop encoding time : 0.000
% 263.48/39.27 % Success case prop solver time : 0.000
% 263.48/39.27 % Current number of processed clauses : 7758
% 263.48/39.27 % Positive orientable unit clauses : 1438
% 263.48/39.27 % Positive unorientable unit clauses: 8
% 263.48/39.27 % Negative unit clauses : 1960
% 263.48/39.27 % Non-unit-clauses : 4352
% 263.48/39.27 % Current number of unprocessed clauses: 97480
% 263.48/39.27 % ...number of literals in the above : 350531
% 263.48/39.27 % Current number of archived formulas : 0
% 263.48/39.27 % Current number of archived clauses : 7960
% 263.48/39.27 % Clause-clause subsumption calls (NU) : 24043231
% 263.48/39.27 % Rec. Clause-clause subsumption calls : 3140885
% 263.48/39.27 % Non-unit clause-clause subsumptions : 5029
% 263.48/39.27 % Unit Clause-clause subsumption calls : 966830
% 263.48/39.27 % Rewrite failures with RHS unbound : 0
% 263.48/39.27 % BW rewrite match attempts : 734
% 263.48/39.27 % BW rewrite match successes : 428
% 263.48/39.27 % Condensation attempts : 33904
% 263.48/39.27 % Condensation successes : 383
% 263.48/39.27 % Termbank termtop insertions : 2383632
% 263.48/39.27 % Search garbage collected termcells : 149896
% 263.48/39.27
% 263.48/39.27 % -------------------------------------------------
% 263.48/39.27 % User time : 36.931 s
% 263.48/39.27 % System time : 0.544 s
% 263.48/39.27 % Total time : 37.475 s
% 263.48/39.27 % Maximum resident set size: 35896 pages
% 263.48/39.27
% 263.48/39.27 % -------------------------------------------------
% 263.48/39.27 % User time : 37.200 s
% 263.48/39.27 % System time : 0.570 s
% 263.48/39.27 % Total time : 37.770 s
% 263.48/39.27 % Maximum resident set size: 10240 pages
% 263.48/39.27 % E exiting
%------------------------------------------------------------------------------