%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU411+1 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n007.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 : Tue May 5 05:12:13 PM UTC 2026
% Result : Theorem 27.58s 16.55s
% Output : CNFRefutation 27.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 76 ( 28 unt; 0 def)
% Number of atoms : 281 ( 33 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 316 ( 111 ~; 112 |; 70 &)
% ( 5 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 125 ( 10 sgn 64 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',t20_latsum_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : k3_xboole_0(X1,X2) = k3_xboole_0(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = k1_xboole_0
<=> ! [X2] : ~ r2_hidden(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
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/sandbox/benchmark/theBenchmark.p',t5_subset) ).
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/sandbox/benchmark/theBenchmark.p',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/sandbox/benchmark/theBenchmark.p',t4_subset) ).
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/sandbox/benchmark/theBenchmark.p',t44_yellow_0) ).
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/sandbox/benchmark/theBenchmark.p',d3_xboole_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/sandbox/benchmark/theBenchmark.p',dt_k3_yellow_0) ).
fof(t2_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( v1_xboole_0(X2)
| r2_hidden(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : m1_subset_1(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(fc1_xboole_0,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(idempotence_k3_xboole_0,axiom,
! [X1,X2] : k3_xboole_0(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(c_0_13,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(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t20_latsum_1])]) ).
fof(c_0_14,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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_15,plain,
! [X72,X73] : k3_xboole_0(X72,X73) = k3_xboole_0(X73,X72),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_16,plain,
! [X1] :
( X1 = k1_xboole_0
<=> ! [X2] : ~ r2_hidden(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_17,plain,
! [X130,X131,X132] :
( ~ r2_hidden(X130,X131)
| ~ m1_subset_1(X131,k1_zfmisc_1(X132))
| ~ v1_xboole_0(X132) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_18,negated_conjecture,
m1_subset_1(k3_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0)),k1_zfmisc_1(u1_struct_0(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
k3_xboole_0(X1,X2) = k3_xboole_0(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,plain,
! [X74,X75,X76,X77] :
( ( ~ v12_waybel_0(X75,X74)
| ~ m1_subset_1(X76,u1_struct_0(X74))
| ~ m1_subset_1(X77,u1_struct_0(X74))
| ~ r2_hidden(X76,X75)
| ~ r1_orders_2(X74,X77,X76)
| r2_hidden(X77,X75)
| ~ m1_subset_1(X75,k1_zfmisc_1(u1_struct_0(X74)))
| ~ l1_orders_2(X74) )
& ( m1_subset_1(esk3_2(X74,X75),u1_struct_0(X74))
| v12_waybel_0(X75,X74)
| ~ m1_subset_1(X75,k1_zfmisc_1(u1_struct_0(X74)))
| ~ l1_orders_2(X74) )
& ( m1_subset_1(esk4_2(X74,X75),u1_struct_0(X74))
| v12_waybel_0(X75,X74)
| ~ m1_subset_1(X75,k1_zfmisc_1(u1_struct_0(X74)))
| ~ l1_orders_2(X74) )
& ( r2_hidden(esk3_2(X74,X75),X75)
| v12_waybel_0(X75,X74)
| ~ m1_subset_1(X75,k1_zfmisc_1(u1_struct_0(X74)))
| ~ l1_orders_2(X74) )
& ( r1_orders_2(X74,esk4_2(X74,X75),esk3_2(X74,X75))
| v12_waybel_0(X75,X74)
| ~ m1_subset_1(X75,k1_zfmisc_1(u1_struct_0(X74)))
| ~ l1_orders_2(X74) )
& ( ~ r2_hidden(esk4_2(X74,X75),X75)
| v12_waybel_0(X75,X74)
| ~ m1_subset_1(X75,k1_zfmisc_1(u1_struct_0(X74)))
| ~ l1_orders_2(X74) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d19_waybel_0])])])])]) ).
fof(c_0_21,plain,
! [X127,X128,X129] :
( ~ r2_hidden(X127,X128)
| ~ m1_subset_1(X128,k1_zfmisc_1(X129))
| m1_subset_1(X127,X129) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(c_0_22,plain,
! [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) ) ),
inference(fof_simplification,[status(thm)],[t44_yellow_0]) ).
fof(c_0_23,plain,
! [X80,X81,X82] :
( ( X80 != k1_xboole_0
| ~ r2_hidden(X81,X80) )
& ( r2_hidden(esk5_1(X82),X82)
| X82 = k1_xboole_0 ) ),
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_16])])])])]) ).
fof(c_0_24,plain,
! [X84,X85,X86,X87,X88,X89,X90,X91] :
( ( r2_hidden(X87,X84)
| ~ r2_hidden(X87,X86)
| X86 != k3_xboole_0(X84,X85) )
& ( r2_hidden(X87,X85)
| ~ r2_hidden(X87,X86)
| X86 != k3_xboole_0(X84,X85) )
& ( ~ r2_hidden(X88,X84)
| ~ r2_hidden(X88,X85)
| r2_hidden(X88,X86)
| X86 != k3_xboole_0(X84,X85) )
& ( ~ r2_hidden(esk6_3(X89,X90,X91),X91)
| ~ r2_hidden(esk6_3(X89,X90,X91),X89)
| ~ r2_hidden(esk6_3(X89,X90,X91),X90)
| X91 = k3_xboole_0(X89,X90) )
& ( r2_hidden(esk6_3(X89,X90,X91),X89)
| r2_hidden(esk6_3(X89,X90,X91),X91)
| X91 = k3_xboole_0(X89,X90) )
& ( r2_hidden(esk6_3(X89,X90,X91),X90)
| r2_hidden(esk6_3(X89,X90,X91),X91)
| X91 = k3_xboole_0(X89,X90) ) ),
inference(distribute,[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)],[d3_xboole_0])])])])])]) ).
cnf(c_0_25,plain,
( ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3))
| ~ v1_xboole_0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,negated_conjecture,
m1_subset_1(k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0)),k1_zfmisc_1(u1_struct_0(esk2_0))),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,plain,
( r2_hidden(X4,X1)
| ~ v12_waybel_0(X1,X2)
| ~ m1_subset_1(X3,u1_struct_0(X2))
| ~ m1_subset_1(X4,u1_struct_0(X2))
| ~ r2_hidden(X3,X1)
| ~ r1_orders_2(X2,X4,X3)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| ~ l1_orders_2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
( m1_subset_1(X1,X3)
| ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_29,plain,
! [X125,X126] :
( v3_struct_0(X125)
| ~ v4_orders_2(X125)
| ~ v1_yellow_0(X125)
| ~ l1_orders_2(X125)
| ~ m1_subset_1(X126,u1_struct_0(X125))
| r1_orders_2(X125,k3_yellow_0(X125),X126) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
fof(c_0_30,plain,
! [X93] :
( ~ l1_orders_2(X93)
| m1_subset_1(k3_yellow_0(X93),u1_struct_0(X93)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_yellow_0])]) ).
cnf(c_0_31,plain,
( X1 != k1_xboole_0
| ~ r2_hidden(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
( r2_hidden(esk6_3(X1,X2,X3),X2)
| r2_hidden(esk6_3(X1,X2,X3),X3)
| X3 = k3_xboole_0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,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_14]) ).
cnf(c_0_34,negated_conjecture,
( ~ r2_hidden(X1,k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0)))
| ~ v1_xboole_0(u1_struct_0(esk2_0)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_35,plain,
( r2_hidden(esk5_1(X1),X1)
| X1 = k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_36,plain,
( r2_hidden(X1,X2)
| ~ r1_orders_2(X3,X1,X4)
| ~ r2_hidden(X4,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X3)))
| ~ m1_subset_1(X1,u1_struct_0(X3))
| ~ v12_waybel_0(X2,X3)
| ~ l1_orders_2(X3) ),
inference(csr,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_37,plain,
( v3_struct_0(X1)
| r1_orders_2(X1,k3_yellow_0(X1),X2)
| ~ v4_orders_2(X1)
| ~ v1_yellow_0(X1)
| ~ l1_orders_2(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
( m1_subset_1(k3_yellow_0(X1),u1_struct_0(X1))
| ~ l1_orders_2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,plain,
~ r2_hidden(X1,k1_xboole_0),
inference(er,[status(thm)],[c_0_31]) ).
fof(c_0_40,plain,
! [X121,X122] :
( ~ m1_subset_1(X121,X122)
| v1_xboole_0(X122)
| r2_hidden(X121,X122) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_41,plain,
! [X97] : m1_subset_1(esk9_1(X97),X97),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_42,negated_conjecture,
( m1_subset_1(X1,u1_struct_0(esk2_0))
| ~ r2_hidden(X1,k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))) ),
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_43,plain,
( k3_xboole_0(X1,X2) = X2
| r2_hidden(esk6_3(X1,X2,X2),X2) ),
inference(ef,[status(thm)],[c_0_32]) ).
cnf(c_0_44,negated_conjecture,
~ v1_xboole_0(k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))),
inference(rw,[status(thm)],[c_0_33,c_0_19]) ).
cnf(c_0_45,negated_conjecture,
( k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0)) = k1_xboole_0
| ~ v1_xboole_0(u1_struct_0(esk2_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_46,plain,
v1_xboole_0(k1_xboole_0),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_47,plain,
( r2_hidden(k3_yellow_0(X1),X2)
| v3_struct_0(X1)
| ~ r2_hidden(X3,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ v12_waybel_0(X2,X1)
| ~ l1_orders_2(X1)
| ~ v1_yellow_0(X1)
| ~ v4_orders_2(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_28]),c_0_38]) ).
cnf(c_0_48,plain,
( k1_xboole_0 = k3_xboole_0(X1,X2)
| r2_hidden(esk6_3(X1,X2,k1_xboole_0),X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_32]) ).
cnf(c_0_49,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_14]) ).
cnf(c_0_50,plain,
( r2_hidden(X1,X2)
| ~ r2_hidden(X1,X3)
| X3 != k3_xboole_0(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_51,plain,
( v1_xboole_0(X2)
| r2_hidden(X1,X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_52,plain,
m1_subset_1(esk9_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_53,plain,
( X3 = k3_xboole_0(X1,X2)
| ~ r2_hidden(esk6_3(X1,X2,X3),X3)
| ~ r2_hidden(esk6_3(X1,X2,X3),X1)
| ~ r2_hidden(esk6_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_54,negated_conjecture,
( k3_xboole_0(X1,k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))) = k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))
| m1_subset_1(esk6_3(X1,k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0)),k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))),u1_struct_0(esk2_0)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_55,negated_conjecture,
~ v1_xboole_0(u1_struct_0(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]) ).
fof(c_0_56,plain,
! [X100] : k3_xboole_0(X100,X100) = X100,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
cnf(c_0_57,plain,
( k1_xboole_0 = k3_xboole_0(X1,X2)
| r2_hidden(k3_yellow_0(X3),X2)
| v3_struct_0(X3)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X3)))
| ~ v12_waybel_0(X2,X3)
| ~ l1_orders_2(X3)
| ~ v1_yellow_0(X3)
| ~ v4_orders_2(X3) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_58,negated_conjecture,
v12_waybel_0(k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0)),esk2_0),
inference(rw,[status(thm)],[c_0_49,c_0_19]) ).
cnf(c_0_59,negated_conjecture,
l1_orders_2(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_60,negated_conjecture,
v1_yellow_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_61,negated_conjecture,
v4_orders_2(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_62,negated_conjecture,
~ v3_struct_0(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_63,plain,
( r2_hidden(X1,X2)
| ~ r2_hidden(X1,k3_xboole_0(X3,X2)) ),
inference(er,[status(thm)],[c_0_50]) ).
cnf(c_0_64,plain,
( r2_hidden(esk9_1(X1),X1)
| v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_65,plain,
( k3_xboole_0(X1,X2) = X2
| ~ r2_hidden(esk6_3(X1,X2,X2),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_43]),c_0_43]) ).
cnf(c_0_66,negated_conjecture,
( k3_xboole_0(X1,k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))) = k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))
| r2_hidden(esk6_3(X1,k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0)),k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))),u1_struct_0(esk2_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_54]),c_0_55]) ).
cnf(c_0_67,plain,
k3_xboole_0(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_68,negated_conjecture,
( k3_xboole_0(X1,k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))) = k1_xboole_0
| r2_hidden(k3_yellow_0(esk2_0),k3_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_57,c_0_26]),c_0_58]),c_0_59]),c_0_60]),c_0_61])]),c_0_62]) ).
cnf(c_0_69,plain,
( r2_hidden(esk9_1(k3_xboole_0(X1,X2)),X2)
| v1_xboole_0(k3_xboole_0(X1,X2)) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_70,negated_conjecture,
k3_xboole_0(u1_struct_0(esk2_0),k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))) = k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_71,negated_conjecture,
( k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0)) = k1_xboole_0
| r2_hidden(k3_yellow_0(esk2_0),k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_72,negated_conjecture,
~ r2_hidden(k3_yellow_0(esk2_0),u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_73,negated_conjecture,
r2_hidden(esk9_1(k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))),k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk1_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_44]) ).
cnf(c_0_74,negated_conjecture,
k3_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_63,c_0_71]),c_0_72]) ).
cnf(c_0_75,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74]),c_0_74]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU411+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n007.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 03:03:38 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 27.58/16.55 % Version : CSE_E---1.7
% 27.58/16.55 % Problem : theBenchmark.p
% 27.58/16.55 % SZS status Theorem for theBenchmark.p
% 27.58/16.55 % SZS output start CNFRefutation
% See solution above
% 27.68/16.66 % Total time : 12.395s
%------------------------------------------------------------------------------