%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT359+1 : TPTP v9.2.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n002.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 04:38:19 PM UTC 2026
% Result : Theorem 2.14s 1.94s
% Output : CNFRefutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 19
% Syntax : Number of formulae : 103 ( 27 unt; 0 def)
% Number of atoms : 302 ( 54 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 341 ( 142 ~; 131 |; 38 &)
% ( 6 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-3 aty)
% Number of variables : 181 ( 20 sgn 81 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_funct_1,axiom,
! [X1] :
( ( v1_relat_1(X1)
& v1_funct_1(X1) )
=> ! [X2,X3] :
( ( r2_hidden(X2,k1_relat_1(X1))
=> ( X3 = k1_funct_1(X1,X2)
<=> r2_hidden(k4_tarski(X2,X3),X1) ) )
& ( ~ r2_hidden(X2,k1_relat_1(X1))
=> ( X3 = k1_funct_1(X1,X2)
<=> X3 = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : k4_tarski(X1,X2) = k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : k2_tarski(X1,X2) = k2_tarski(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( r2_hidden(X1,X2)
& v1_xboole_0(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(cc1_funct_1,axiom,
! [X1] :
( v1_xboole_0(X1)
=> v1_funct_1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,X2)
=> ( v1_xboole_0(X2)
| r2_hidden(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : m1_subset_1(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t6_boole,axiom,
! [X1] :
( v1_xboole_0(X1)
=> X1 = k1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_funct_1,axiom,
? [X1] :
( v1_relat_1(X1)
& v1_xboole_0(X1)
& v1_funct_1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(d3_pboole,axiom,
! [X1,X2] :
( ( v1_relat_1(X2)
& v1_funct_1(X2) )
=> ( m1_pboole(X2,X1)
<=> k1_relat_1(X2) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pboole) ).
fof(dt_m1_pboole,axiom,
! [X1,X2] :
( m1_pboole(X2,X1)
=> ( v1_relat_1(X2)
& v1_funct_1(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_pboole) ).
fof(t106_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( r2_hidden(k4_tarski(X1,X2),k2_zfmisc_1(X3,X4))
<=> ( r2_hidden(X1,X3)
& r2_hidden(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(dt_u1_altcat_1,axiom,
! [X1] :
( l1_altcat_1(X1)
=> m1_pboole(u1_altcat_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_altcat_1) ).
fof(d1_binop_1,axiom,
! [X1] :
( ( v1_relat_1(X1)
& v1_funct_1(X1) )
=> ! [X2,X3] : k1_binop_1(X1,X2,X3) = k1_funct_1(X1,k4_tarski(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_binop_1) ).
fof(t12_waybel34,conjecture,
! [X1] :
( ( ~ v3_struct_0(X1)
& l2_altcat_1(X1) )
=> ! [X2,X3,X4] :
~ ( r2_hidden(X4,k1_binop_1(u1_altcat_1(X1),X2,X3))
& ! [X5] :
( m1_subset_1(X5,u1_struct_0(X1))
=> ! [X6] :
( m1_subset_1(X6,u1_struct_0(X1))
=> ~ ( X5 = X2
& X6 = X3
& r2_hidden(X4,k1_altcat_1(X1,X5,X6))
& m1_subset_1(X4,k1_altcat_1(X1,X5,X6)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_waybel34) ).
fof(fc6_membered,axiom,
( v1_xboole_0(k1_xboole_0)
& v1_membered(k1_xboole_0)
& v2_membered(k1_xboole_0)
& v3_membered(k1_xboole_0)
& v4_membered(k1_xboole_0)
& v5_membered(k1_xboole_0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_membered) ).
fof(dt_l2_altcat_1,axiom,
! [X1] :
( l2_altcat_1(X1)
=> l1_altcat_1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_altcat_1) ).
fof(t1_subset,axiom,
! [X1,X2] :
( r2_hidden(X1,X2)
=> m1_subset_1(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(d2_altcat_1,axiom,
! [X1] :
( l1_altcat_1(X1)
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> k1_altcat_1(X1,X2,X3) = k1_binop_1(u1_altcat_1(X1),X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_altcat_1) ).
fof(c_0_19,plain,
! [X1] :
( ( v1_relat_1(X1)
& v1_funct_1(X1) )
=> ! [X2,X3] :
( ( r2_hidden(X2,k1_relat_1(X1))
=> ( X3 = k1_funct_1(X1,X2)
<=> r2_hidden(k4_tarski(X2,X3),X1) ) )
& ( ~ r2_hidden(X2,k1_relat_1(X1))
=> ( X3 = k1_funct_1(X1,X2)
<=> X3 = k1_xboole_0 ) ) ) ),
inference(fof_simplification,[status(thm)],[d4_funct_1]) ).
fof(c_0_20,plain,
! [X144,X145,X146] :
( ( X146 != k1_funct_1(X144,X145)
| r2_hidden(k4_tarski(X145,X146),X144)
| ~ r2_hidden(X145,k1_relat_1(X144))
| ~ v1_relat_1(X144)
| ~ v1_funct_1(X144) )
& ( ~ r2_hidden(k4_tarski(X145,X146),X144)
| X146 = k1_funct_1(X144,X145)
| ~ r2_hidden(X145,k1_relat_1(X144))
| ~ v1_relat_1(X144)
| ~ v1_funct_1(X144) )
& ( X146 != k1_funct_1(X144,X145)
| X146 = k1_xboole_0
| r2_hidden(X145,k1_relat_1(X144))
| ~ v1_relat_1(X144)
| ~ v1_funct_1(X144) )
& ( X146 != k1_xboole_0
| X146 = k1_funct_1(X144,X145)
| r2_hidden(X145,k1_relat_1(X144))
| ~ v1_relat_1(X144)
| ~ v1_funct_1(X144) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
fof(c_0_21,plain,
! [X147,X148] : k4_tarski(X147,X148) = k2_tarski(k2_tarski(X147,X148),k1_tarski(X147)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
cnf(c_0_22,plain,
( r2_hidden(k4_tarski(X3,X1),X2)
| X1 != k1_funct_1(X2,X3)
| ~ r2_hidden(X3,k1_relat_1(X2))
| ~ v1_relat_1(X2)
| ~ v1_funct_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,plain,
k4_tarski(X1,X2) = k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_24,plain,
! [X134,X135] : k2_tarski(X134,X135) = k2_tarski(X135,X134),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_25,plain,
! [X201,X202] :
( ~ r2_hidden(X201,X202)
| ~ v1_xboole_0(X202) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_26,plain,
( r2_hidden(k2_tarski(k2_tarski(X3,X1),k1_tarski(X3)),X2)
| X1 != k1_funct_1(X2,X3)
| ~ v1_funct_1(X2)
| ~ v1_relat_1(X2)
| ~ r2_hidden(X3,k1_relat_1(X2)) ),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
k2_tarski(X1,X2) = k2_tarski(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_28,plain,
! [X126] :
( ~ v1_xboole_0(X126)
| v1_funct_1(X126) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).
cnf(c_0_29,plain,
( ~ r2_hidden(X1,X2)
| ~ v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
( r2_hidden(k2_tarski(k1_tarski(X1),k2_tarski(X1,k1_funct_1(X2,X1))),X2)
| ~ v1_relat_1(X2)
| ~ v1_funct_1(X2)
| ~ r2_hidden(X1,k1_relat_1(X2)) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_26]),c_0_27]) ).
cnf(c_0_31,plain,
( v1_funct_1(X1)
| ~ v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_32,plain,
! [X198,X199] :
( ~ m1_subset_1(X198,X199)
| v1_xboole_0(X199)
| r2_hidden(X198,X199) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_33,plain,
( ~ v1_relat_1(X1)
| ~ v1_xboole_0(X1)
| ~ r2_hidden(X2,k1_relat_1(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_34,plain,
( v1_xboole_0(X2)
| r2_hidden(X1,X2)
| ~ m1_subset_1(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_35,plain,
! [X159] : m1_subset_1(esk9_1(X159),X159),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_36,plain,
! [X200] :
( ~ v1_xboole_0(X200)
| X200 = k1_xboole_0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
cnf(c_0_37,plain,
( v1_xboole_0(k1_relat_1(X1))
| ~ v1_relat_1(X1)
| ~ v1_xboole_0(X1)
| ~ m1_subset_1(X2,k1_relat_1(X1)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
m1_subset_1(esk9_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_39,plain,
( v1_relat_1(esk14_0)
& v1_xboole_0(esk14_0)
& v1_funct_1(esk14_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
cnf(c_0_40,plain,
( X1 = k1_xboole_0
| ~ v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,plain,
( v1_xboole_0(k1_relat_1(X1))
| ~ v1_relat_1(X1)
| ~ v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
v1_xboole_0(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_43,plain,
( k1_relat_1(X1) = k1_xboole_0
| ~ v1_relat_1(X1)
| ~ v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,plain,
v1_relat_1(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,plain,
esk14_0 = k1_xboole_0,
inference(spm,[status(thm)],[c_0_40,c_0_42]) ).
cnf(c_0_46,plain,
v1_funct_1(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_47,plain,
! [X142,X143] :
( ( ~ m1_pboole(X143,X142)
| k1_relat_1(X143) = X142
| ~ v1_relat_1(X143)
| ~ v1_funct_1(X143) )
& ( k1_relat_1(X143) != X142
| m1_pboole(X143,X142)
| ~ v1_relat_1(X143)
| ~ v1_funct_1(X143) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_pboole])])]) ).
fof(c_0_48,plain,
! [X151,X152] :
( ( v1_relat_1(X152)
| ~ m1_pboole(X152,X151) )
& ( v1_funct_1(X152)
| ~ m1_pboole(X152,X151) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m1_pboole])])]) ).
cnf(c_0_49,plain,
( ~ v1_relat_1(X1)
| ~ v1_xboole_0(X1)
| ~ r2_hidden(X2,k1_xboole_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_43]) ).
cnf(c_0_50,plain,
v1_relat_1(k1_xboole_0),
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,plain,
v1_funct_1(k1_xboole_0),
inference(rw,[status(thm)],[c_0_46,c_0_45]) ).
fof(c_0_52,plain,
! [X192,X193,X194,X195] :
( ( r2_hidden(X192,X194)
| ~ r2_hidden(k4_tarski(X192,X193),k2_zfmisc_1(X194,X195)) )
& ( r2_hidden(X193,X195)
| ~ r2_hidden(k4_tarski(X192,X193),k2_zfmisc_1(X194,X195)) )
& ( ~ r2_hidden(X192,X194)
| ~ r2_hidden(X193,X195)
| r2_hidden(k4_tarski(X192,X193),k2_zfmisc_1(X194,X195)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t106_zfmisc_1])])]) ).
cnf(c_0_53,plain,
( k1_relat_1(X1) = X2
| ~ m1_pboole(X1,X2)
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_54,plain,
( v1_funct_1(X1)
| ~ m1_pboole(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_55,plain,
( v1_relat_1(X1)
| ~ m1_pboole(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_56,plain,
! [X153] :
( ~ l1_altcat_1(X153)
| m1_pboole(u1_altcat_1(X153),k2_zfmisc_1(u1_struct_0(X153),u1_struct_0(X153))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_altcat_1])]) ).
cnf(c_0_57,plain,
( ~ v1_relat_1(X1)
| ~ v1_xboole_0(X1)
| ~ r2_hidden(X2,k1_relat_1(k1_xboole_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_30]),c_0_50]),c_0_51])]) ).
cnf(c_0_58,plain,
( r2_hidden(X1,X2)
| ~ r2_hidden(k4_tarski(X1,X3),k2_zfmisc_1(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_59,plain,
( k1_relat_1(X1) = X2
| ~ m1_pboole(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_60,plain,
( m1_pboole(u1_altcat_1(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)))
| ~ l1_altcat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_61,plain,
( v1_xboole_0(k1_relat_1(k1_xboole_0))
| ~ v1_relat_1(X1)
| ~ v1_xboole_0(X1)
| ~ m1_subset_1(X2,k1_relat_1(k1_xboole_0)) ),
inference(spm,[status(thm)],[c_0_57,c_0_34]) ).
fof(c_0_62,plain,
! [X136,X137,X138] :
( ~ v1_relat_1(X136)
| ~ v1_funct_1(X136)
| k1_binop_1(X136,X137,X138) = k1_funct_1(X136,k4_tarski(X137,X138)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_binop_1])])]) ).
cnf(c_0_63,plain,
( r2_hidden(X1,X2)
| ~ r2_hidden(k2_tarski(k2_tarski(X1,X3),k1_tarski(X1)),k2_zfmisc_1(X2,X4)) ),
inference(rw,[status(thm)],[c_0_58,c_0_23]) ).
cnf(c_0_64,plain,
( k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)) = k1_relat_1(u1_altcat_1(X1))
| ~ l1_altcat_1(X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_65,plain,
( X1 = k1_xboole_0
| r2_hidden(X3,k1_relat_1(X2))
| X1 != k1_funct_1(X2,X3)
| ~ v1_relat_1(X2)
| ~ v1_funct_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_66,negated_conjecture,
~ ! [X1] :
( ( ~ v3_struct_0(X1)
& l2_altcat_1(X1) )
=> ! [X2,X3,X4] :
~ ( r2_hidden(X4,k1_binop_1(u1_altcat_1(X1),X2,X3))
& ! [X5] :
( m1_subset_1(X5,u1_struct_0(X1))
=> ! [X6] :
( m1_subset_1(X6,u1_struct_0(X1))
=> ~ ( X5 = X2
& X6 = X3
& r2_hidden(X4,k1_altcat_1(X1,X5,X6))
& m1_subset_1(X4,k1_altcat_1(X1,X5,X6)) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t12_waybel34])]) ).
cnf(c_0_67,plain,
( v1_xboole_0(k1_relat_1(k1_xboole_0))
| ~ v1_relat_1(X1)
| ~ v1_xboole_0(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_38]) ).
cnf(c_0_68,plain,
v1_xboole_0(k1_xboole_0),
inference(split_conjunct,[status(thm)],[fc6_membered]) ).
cnf(c_0_69,plain,
( r2_hidden(X1,X2)
| ~ r2_hidden(k4_tarski(X3,X1),k2_zfmisc_1(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_70,plain,
( k1_binop_1(X1,X2,X3) = k1_funct_1(X1,k4_tarski(X2,X3))
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_71,plain,
( r2_hidden(X1,u1_struct_0(X2))
| ~ l1_altcat_1(X2)
| ~ r2_hidden(k2_tarski(k2_tarski(X1,X3),k1_tarski(X1)),k1_relat_1(u1_altcat_1(X2))) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_72,plain,
( k1_funct_1(X1,X2) = k1_xboole_0
| r2_hidden(X2,k1_relat_1(X1))
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1) ),
inference(er,[status(thm)],[c_0_65]) ).
cnf(c_0_73,plain,
( v1_funct_1(u1_altcat_1(X1))
| ~ l1_altcat_1(X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_60]) ).
cnf(c_0_74,plain,
( v1_relat_1(u1_altcat_1(X1))
| ~ l1_altcat_1(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_60]) ).
fof(c_0_75,plain,
! [X150] :
( ~ l2_altcat_1(X150)
| l1_altcat_1(X150) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_altcat_1])]) ).
fof(c_0_76,negated_conjecture,
! [X110,X111] :
( ~ v3_struct_0(esk1_0)
& l2_altcat_1(esk1_0)
& r2_hidden(esk4_0,k1_binop_1(u1_altcat_1(esk1_0),esk2_0,esk3_0))
& ( ~ m1_subset_1(X110,u1_struct_0(esk1_0))
| ~ m1_subset_1(X111,u1_struct_0(esk1_0))
| X110 != esk2_0
| X111 != esk3_0
| ~ r2_hidden(esk4_0,k1_altcat_1(esk1_0,X110,X111))
| ~ m1_subset_1(esk4_0,k1_altcat_1(esk1_0,X110,X111)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_66])])])]) ).
cnf(c_0_77,plain,
v1_xboole_0(k1_relat_1(k1_xboole_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_50]),c_0_68])]) ).
cnf(c_0_78,plain,
( r2_hidden(X1,X2)
| ~ r2_hidden(k2_tarski(k2_tarski(X3,X1),k1_tarski(X3)),k2_zfmisc_1(X4,X2)) ),
inference(rw,[status(thm)],[c_0_69,c_0_23]) ).
fof(c_0_79,plain,
! [X196,X197] :
( ~ r2_hidden(X196,X197)
| m1_subset_1(X196,X197) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
cnf(c_0_80,plain,
( k1_binop_1(X1,X2,X3) = k1_funct_1(X1,k2_tarski(k2_tarski(X2,X3),k1_tarski(X2)))
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X1) ),
inference(rw,[status(thm)],[c_0_70,c_0_23]) ).
cnf(c_0_81,plain,
( k1_funct_1(u1_altcat_1(X1),k2_tarski(k2_tarski(X2,X3),k1_tarski(X2))) = k1_xboole_0
| r2_hidden(X2,u1_struct_0(X1))
| ~ l1_altcat_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),c_0_74]) ).
cnf(c_0_82,plain,
( l1_altcat_1(X1)
| ~ l2_altcat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_83,negated_conjecture,
l2_altcat_1(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_84,plain,
k1_relat_1(k1_xboole_0) = k1_xboole_0,
inference(spm,[status(thm)],[c_0_40,c_0_77]) ).
cnf(c_0_85,plain,
( r2_hidden(X1,u1_struct_0(X2))
| ~ l1_altcat_1(X2)
| ~ r2_hidden(k2_tarski(k2_tarski(X3,X1),k1_tarski(X3)),k1_relat_1(u1_altcat_1(X2))) ),
inference(spm,[status(thm)],[c_0_78,c_0_64]) ).
fof(c_0_86,plain,
! [X139,X140,X141] :
( ~ l1_altcat_1(X139)
| ~ m1_subset_1(X140,u1_struct_0(X139))
| ~ m1_subset_1(X141,u1_struct_0(X139))
| k1_altcat_1(X139,X140,X141) = k1_binop_1(u1_altcat_1(X139),X140,X141) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_altcat_1])])]) ).
cnf(c_0_87,negated_conjecture,
( ~ m1_subset_1(X1,u1_struct_0(esk1_0))
| ~ m1_subset_1(X2,u1_struct_0(esk1_0))
| X1 != esk2_0
| X2 != esk3_0
| ~ r2_hidden(esk4_0,k1_altcat_1(esk1_0,X1,X2))
| ~ m1_subset_1(esk4_0,k1_altcat_1(esk1_0,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_88,plain,
( m1_subset_1(X1,X2)
| ~ r2_hidden(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_89,negated_conjecture,
r2_hidden(esk4_0,k1_binop_1(u1_altcat_1(esk1_0),esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_90,plain,
( k1_binop_1(u1_altcat_1(X1),X2,X3) = k1_xboole_0
| r2_hidden(X2,u1_struct_0(X1))
| ~ l1_altcat_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_73]),c_0_74]) ).
cnf(c_0_91,negated_conjecture,
l1_altcat_1(esk1_0),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_92,plain,
~ r2_hidden(X1,k1_xboole_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_84]),c_0_50]),c_0_68])]) ).
cnf(c_0_93,plain,
( k1_funct_1(u1_altcat_1(X1),k2_tarski(k2_tarski(X2,X3),k1_tarski(X2))) = k1_xboole_0
| r2_hidden(X3,u1_struct_0(X1))
| ~ l1_altcat_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_72]),c_0_73]),c_0_74]) ).
cnf(c_0_94,plain,
( k1_altcat_1(X1,X2,X3) = k1_binop_1(u1_altcat_1(X1),X2,X3)
| ~ l1_altcat_1(X1)
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ m1_subset_1(X3,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_95,negated_conjecture,
( ~ m1_subset_1(esk3_0,u1_struct_0(esk1_0))
| ~ m1_subset_1(esk2_0,u1_struct_0(esk1_0))
| ~ r2_hidden(esk4_0,k1_altcat_1(esk1_0,esk2_0,esk3_0)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(csr,[status(thm)],[c_0_87,c_0_88])])]) ).
cnf(c_0_96,negated_conjecture,
r2_hidden(esk2_0,u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91])]),c_0_92]) ).
cnf(c_0_97,plain,
( k1_binop_1(u1_altcat_1(X1),X2,X3) = k1_xboole_0
| r2_hidden(X3,u1_struct_0(X1))
| ~ l1_altcat_1(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_93]),c_0_73]),c_0_74]) ).
cnf(c_0_98,negated_conjecture,
( ~ m1_subset_1(esk3_0,u1_struct_0(esk1_0))
| ~ m1_subset_1(esk2_0,u1_struct_0(esk1_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_94]),c_0_91])]),c_0_95]) ).
cnf(c_0_99,negated_conjecture,
m1_subset_1(esk2_0,u1_struct_0(esk1_0)),
inference(spm,[status(thm)],[c_0_88,c_0_96]) ).
cnf(c_0_100,negated_conjecture,
r2_hidden(esk3_0,u1_struct_0(esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_97]),c_0_91])]),c_0_92]) ).
cnf(c_0_101,negated_conjecture,
~ m1_subset_1(esk3_0,u1_struct_0(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_99])]) ).
cnf(c_0_102,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_100]),c_0_101]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT359+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n002.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 21:36:01 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.14/1.94 % Version : CSE_E---1.7
% 2.14/1.94 % Problem : theBenchmark.p
% 2.14/1.94 % SZS status Theorem for theBenchmark.p
% 2.14/1.94 % SZS output start CNFRefutation
% See solution above
% 2.14/1.94 % Total time : 1.371s
%------------------------------------------------------------------------------