%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU249+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n005.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 05:11:15 PM UTC 2026
% Result : Theorem 8.39s 5.66s
% Output : CNFRefutation 8.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 23
% Syntax : Number of formulae : 145 ( 22 unt; 0 def)
% Number of atoms : 376 ( 51 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 425 ( 194 ~; 189 |; 20 &)
% ( 5 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-3 aty)
% Number of variables : 250 ( 32 sgn 102 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(t99_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_dom_restriction(X2,X1)),relation_rng(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_relat_1) ).
fof(d6_relat_1,axiom,
! [X1] :
( relation(X1)
=> relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
fof(t19_wellord1,conjecture,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_field(relation_restriction(X3,X2)))
=> ( in(X1,relation_field(X3))
& in(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_wellord1) ).
fof(l29_wellord1,axiom,
! [X1,X2] :
( relation(X2)
=> subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l29_wellord1) ).
fof(t17_wellord1,axiom,
! [X1,X2] :
( relation(X2)
=> relation_restriction(X2,X1) = relation_dom_restriction(relation_rng_restriction(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_wellord1) ).
fof(dt_k8_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> relation(relation_rng_restriction(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(t119_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> relation_rng(relation_rng_restriction(X1,X2)) = set_intersection2(relation_rng(X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_relat_1) ).
fof(t18_wellord1,axiom,
! [X1,X2] :
( relation(X2)
=> relation_restriction(X2,X1) = relation_rng_restriction(X1,relation_dom_restriction(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_wellord1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(dt_k7_relat_1,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(t90_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> relation_dom(relation_dom_restriction(X2,X1)) = set_intersection2(relation_dom(X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_relat_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(t2_boole,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(dt_k2_wellord1,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_restriction(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(c_0_23,plain,
! [X160,X161,X162] :
( ~ in(X160,X161)
| ~ element(X161,powerset(X162))
| ~ empty(X162) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(c_0_24,plain,
! [X155,X156] :
( ( ~ element(X155,powerset(X156))
| subset(X155,X156) )
& ( ~ subset(X155,X156)
| element(X155,powerset(X156)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_25,plain,
! [X93,X94,X95,X96,X97,X98,X99,X100] :
( ( ~ in(X96,X95)
| in(X96,X93)
| in(X96,X94)
| X95 != set_union2(X93,X94) )
& ( ~ in(X97,X93)
| in(X97,X95)
| X95 != set_union2(X93,X94) )
& ( ~ in(X97,X94)
| in(X97,X95)
| X95 != set_union2(X93,X94) )
& ( ~ in(esk1_3(X98,X99,X100),X98)
| ~ in(esk1_3(X98,X99,X100),X100)
| X100 = set_union2(X98,X99) )
& ( ~ in(esk1_3(X98,X99,X100),X99)
| ~ in(esk1_3(X98,X99,X100),X100)
| X100 = set_union2(X98,X99) )
& ( in(esk1_3(X98,X99,X100),X100)
| in(esk1_3(X98,X99,X100),X98)
| in(esk1_3(X98,X99,X100),X99)
| X100 = set_union2(X98,X99) ) ),
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)],[d2_xboole_0])])])])])]) ).
cnf(c_0_26,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_28,plain,
! [X170,X171] :
( ~ relation(X171)
| subset(relation_rng(relation_dom_restriction(X171,X170)),relation_rng(X171)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t99_relat_1])]) ).
cnf(c_0_29,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_30,plain,
! [X111] :
( ~ relation(X111)
| relation_field(X111) = set_union2(relation_dom(X111),relation_rng(X111)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_relat_1])]) ).
fof(c_0_31,negated_conjecture,
~ ! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_field(relation_restriction(X3,X2)))
=> ( in(X1,relation_field(X3))
& in(X1,X2) ) ) ),
inference(assume_negation,[status(cth)],[t19_wellord1]) ).
fof(c_0_32,plain,
! [X132,X133] :
( ~ relation(X133)
| subset(relation_dom(relation_rng_restriction(X132,X133)),relation_dom(X133)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l29_wellord1])]) ).
cnf(c_0_33,plain,
( ~ subset(X1,X2)
| ~ empty(X2)
| ~ in(X3,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
( subset(relation_rng(relation_dom_restriction(X1,X2)),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_35,plain,
! [X142,X143] :
( ~ relation(X143)
| relation_restriction(X143,X142) = relation_dom_restriction(relation_rng_restriction(X142,X143),X142) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t17_wellord1])]) ).
fof(c_0_36,plain,
! [X118,X119] :
( ~ relation(X119)
| relation(relation_rng_restriction(X118,X119)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k8_relat_1])]) ).
cnf(c_0_37,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X3,X2)) ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
( relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_39,negated_conjecture,
( relation(esk11_0)
& in(esk9_0,relation_field(relation_restriction(esk11_0,esk10_0)))
& ( ~ in(esk9_0,relation_field(esk11_0))
| ~ in(esk9_0,esk10_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])]) ).
fof(c_0_40,plain,
! [X102,X103,X104,X105,X106,X107,X108,X109] :
( ( in(X105,X102)
| ~ in(X105,X104)
| X104 != set_intersection2(X102,X103) )
& ( in(X105,X103)
| ~ in(X105,X104)
| X104 != set_intersection2(X102,X103) )
& ( ~ in(X106,X102)
| ~ in(X106,X103)
| in(X106,X104)
| X104 != set_intersection2(X102,X103) )
& ( ~ in(esk2_3(X107,X108,X109),X109)
| ~ in(esk2_3(X107,X108,X109),X107)
| ~ in(esk2_3(X107,X108,X109),X108)
| X109 = set_intersection2(X107,X108) )
& ( in(esk2_3(X107,X108,X109),X107)
| in(esk2_3(X107,X108,X109),X109)
| X109 = set_intersection2(X107,X108) )
& ( in(esk2_3(X107,X108,X109),X108)
| in(esk2_3(X107,X108,X109),X109)
| X109 = set_intersection2(X107,X108) ) ),
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])])])])])]) ).
fof(c_0_41,plain,
! [X140,X141] :
( ~ relation(X141)
| relation_rng(relation_rng_restriction(X140,X141)) = set_intersection2(relation_rng(X141),X140) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t119_relat_1])]) ).
fof(c_0_42,plain,
! [X144,X145] :
( ~ relation(X145)
| relation_restriction(X145,X144) = relation_rng_restriction(X144,relation_dom_restriction(X145,X144)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t18_wellord1])]) ).
fof(c_0_43,plain,
! [X91,X92] : set_intersection2(X91,X92) = set_intersection2(X92,X91),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_44,plain,
! [X116,X117] :
( ~ relation(X116)
| relation(relation_dom_restriction(X116,X117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_relat_1])]) ).
cnf(c_0_45,plain,
( subset(relation_dom(relation_rng_restriction(X2,X1)),relation_dom(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_46,plain,
( ~ relation(X1)
| ~ empty(relation_rng(X1))
| ~ in(X2,relation_rng(relation_dom_restriction(X1,X3))) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_47,plain,
( relation_restriction(X1,X2) = relation_dom_restriction(relation_rng_restriction(X2,X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_48,plain,
( relation(relation_rng_restriction(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_49,plain,
( in(X1,relation_rng(X2))
| in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(X1,relation_field(X2)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_50,negated_conjecture,
in(esk9_0,relation_field(relation_restriction(esk11_0,esk10_0))),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_51,plain,
! [X153,X154] :
( ~ element(X153,X154)
| empty(X154)
| in(X153,X154) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_52,plain,
! [X120] : element(esk3_1(X120),X120),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_53,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_54,plain,
( relation_rng(relation_rng_restriction(X2,X1)) = set_intersection2(relation_rng(X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_55,plain,
( relation_restriction(X1,X2) = relation_rng_restriction(X2,relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_56,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_57,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_58,plain,
( ~ relation(X1)
| ~ empty(relation_dom(X1))
| ~ in(X2,relation_dom(relation_rng_restriction(X3,X1))) ),
inference(spm,[status(thm)],[c_0_33,c_0_45]) ).
cnf(c_0_59,plain,
( ~ relation(X1)
| ~ empty(relation_rng(relation_rng_restriction(X2,X1)))
| ~ in(X3,relation_rng(relation_restriction(X1,X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_60,negated_conjecture,
( in(esk9_0,relation_dom(relation_restriction(esk11_0,esk10_0)))
| in(esk9_0,relation_rng(relation_restriction(esk11_0,esk10_0)))
| ~ relation(relation_restriction(esk11_0,esk10_0)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_61,negated_conjecture,
relation(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_62,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_63,plain,
element(esk3_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_64,plain,
! [X157,X158,X159] :
( ~ in(X157,X158)
| ~ element(X158,powerset(X159))
| element(X157,X159) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
cnf(c_0_65,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[c_0_53]) ).
cnf(c_0_66,plain,
( set_intersection2(X1,relation_rng(relation_dom_restriction(X2,X1))) = relation_rng(relation_restriction(X2,X1))
| ~ relation(X2) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_57]) ).
fof(c_0_67,plain,
! [X168,X169] :
( ~ relation(X169)
| relation_dom(relation_dom_restriction(X169,X168)) = set_intersection2(relation_dom(X169),X168) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t90_relat_1])]) ).
cnf(c_0_68,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_69,plain,
( ~ relation(X1)
| ~ empty(relation_dom(relation_dom_restriction(X1,X2)))
| ~ in(X3,relation_dom(relation_restriction(X1,X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_55]),c_0_57]) ).
cnf(c_0_70,negated_conjecture,
( in(esk9_0,relation_dom(relation_restriction(esk11_0,esk10_0)))
| ~ relation(relation_restriction(esk11_0,esk10_0))
| ~ empty(relation_rng(relation_rng_restriction(esk10_0,esk11_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61])]) ).
fof(c_0_71,plain,
! [X164,X165] :
( ~ in(X164,X165)
| ~ empty(X165) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_72,plain,
( empty(X1)
| in(esk3_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
fof(c_0_73,plain,
! [X152] : set_intersection2(X152,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
cnf(c_0_74,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_75,plain,
( in(X1,relation_rng(relation_dom_restriction(X2,X3)))
| ~ relation(X2)
| ~ in(X1,relation_rng(relation_restriction(X2,X3))) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_76,plain,
( relation_dom(relation_dom_restriction(X1,X2)) = set_intersection2(relation_dom(X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_77,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[c_0_68]) ).
cnf(c_0_78,negated_conjecture,
( ~ relation(relation_restriction(esk11_0,esk10_0))
| ~ empty(relation_dom(relation_dom_restriction(esk11_0,esk10_0)))
| ~ empty(relation_rng(relation_rng_restriction(esk10_0,esk11_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_61])]) ).
fof(c_0_79,plain,
! [X163] :
( ~ empty(X163)
| X163 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
cnf(c_0_80,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_81,plain,
( empty(set_intersection2(X1,X2))
| in(esk3_1(set_intersection2(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_65,c_0_72]) ).
cnf(c_0_82,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_83,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_84,plain,
( element(X1,X2)
| ~ subset(X3,X2)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_74,c_0_27]) ).
cnf(c_0_85,negated_conjecture,
( in(esk9_0,relation_dom(relation_restriction(esk11_0,esk10_0)))
| in(esk9_0,relation_rng(relation_dom_restriction(esk11_0,esk10_0)))
| ~ relation(relation_restriction(esk11_0,esk10_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_60]),c_0_61])]) ).
cnf(c_0_86,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_87,plain,
( set_intersection2(X1,relation_dom(relation_rng_restriction(X1,X2))) = relation_dom(relation_restriction(X2,X1))
| ~ relation(X2) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_47]),c_0_56]),c_0_48]) ).
cnf(c_0_88,plain,
( in(X1,X2)
| ~ relation(X3)
| ~ in(X1,relation_rng(relation_restriction(X3,X2))) ),
inference(spm,[status(thm)],[c_0_77,c_0_66]) ).
cnf(c_0_89,negated_conjecture,
( ~ relation(relation_restriction(esk11_0,esk10_0))
| ~ empty(relation_dom(relation_dom_restriction(esk11_0,esk10_0)))
| ~ empty(set_intersection2(esk10_0,relation_rng(esk11_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_54]),c_0_56]),c_0_61])]) ).
cnf(c_0_90,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_91,plain,
( empty(set_intersection2(X1,X2))
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_92,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_82]) ).
cnf(c_0_93,plain,
set_intersection2(empty_set,X1) = empty_set,
inference(spm,[status(thm)],[c_0_83,c_0_56]) ).
cnf(c_0_94,plain,
( element(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(X1,relation_rng(relation_dom_restriction(X2,X3))) ),
inference(spm,[status(thm)],[c_0_84,c_0_34]) ).
cnf(c_0_95,negated_conjecture,
( in(esk9_0,relation_rng(relation_dom_restriction(esk11_0,esk10_0)))
| ~ relation(relation_restriction(esk11_0,esk10_0))
| ~ empty(relation_dom(relation_dom_restriction(esk11_0,esk10_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_85]),c_0_61])]) ).
cnf(c_0_96,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_86]) ).
cnf(c_0_97,plain,
( in(X1,X2)
| ~ relation(X3)
| ~ in(X1,relation_dom(relation_restriction(X3,X2))) ),
inference(spm,[status(thm)],[c_0_77,c_0_87]) ).
cnf(c_0_98,negated_conjecture,
( in(esk9_0,relation_dom(relation_restriction(esk11_0,esk10_0)))
| in(esk9_0,esk10_0)
| ~ relation(relation_restriction(esk11_0,esk10_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_60]),c_0_61])]) ).
fof(c_0_99,plain,
! [X114,X115] :
( ~ relation(X114)
| relation(relation_restriction(X114,X115)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_wellord1])]) ).
cnf(c_0_100,negated_conjecture,
( ~ relation(relation_restriction(esk11_0,esk10_0))
| ~ empty(set_intersection2(esk10_0,relation_dom(esk11_0)))
| ~ empty(set_intersection2(esk10_0,relation_rng(esk11_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_76]),c_0_56]),c_0_61])]) ).
cnf(c_0_101,plain,
( set_intersection2(X1,X2) = empty_set
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_102,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_103,plain,
( in(X1,relation_dom(relation_rng_restriction(X2,X3)))
| ~ relation(X3)
| ~ in(X1,relation_dom(relation_restriction(X3,X2))) ),
inference(spm,[status(thm)],[c_0_65,c_0_87]) ).
cnf(c_0_104,negated_conjecture,
( in(esk9_0,relation_dom(relation_restriction(esk11_0,esk10_0)))
| ~ relation(relation_restriction(esk11_0,esk10_0))
| ~ empty(relation_rng(relation_restriction(esk11_0,esk10_0))) ),
inference(spm,[status(thm)],[c_0_80,c_0_60]) ).
cnf(c_0_105,plain,
( ~ empty(set_intersection2(X1,X2))
| ~ in(X3,X2)
| ~ in(X3,X1) ),
inference(spm,[status(thm)],[c_0_80,c_0_92]) ).
cnf(c_0_106,plain,
( in(X1,X2)
| ~ in(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_65,c_0_93]) ).
cnf(c_0_107,negated_conjecture,
( element(esk9_0,relation_rng(esk11_0))
| ~ relation(relation_restriction(esk11_0,esk10_0))
| ~ empty(relation_dom(relation_dom_restriction(esk11_0,esk10_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_61])]) ).
cnf(c_0_108,negated_conjecture,
( ~ in(esk9_0,relation_field(esk11_0))
| ~ in(esk9_0,esk10_0) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_109,plain,
( in(X1,relation_field(X2))
| ~ relation(X2)
| ~ in(X1,relation_rng(X2)) ),
inference(spm,[status(thm)],[c_0_96,c_0_38]) ).
cnf(c_0_110,negated_conjecture,
( in(esk9_0,esk10_0)
| ~ relation(relation_restriction(esk11_0,esk10_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_61])]) ).
cnf(c_0_111,plain,
( relation(relation_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_112,negated_conjecture,
( ~ relation(relation_restriction(esk11_0,esk10_0))
| ~ empty(set_intersection2(esk10_0,relation_dom(esk11_0)))
| ~ empty(relation_rng(esk11_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102])]) ).
cnf(c_0_113,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_114,plain,
( element(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(X1,relation_dom(relation_rng_restriction(X3,X2))) ),
inference(spm,[status(thm)],[c_0_84,c_0_45]) ).
cnf(c_0_115,negated_conjecture,
( in(esk9_0,relation_dom(relation_rng_restriction(esk10_0,esk11_0)))
| ~ relation(relation_restriction(esk11_0,esk10_0))
| ~ empty(relation_rng(relation_restriction(esk11_0,esk10_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_61])]) ).
cnf(c_0_116,plain,
~ in(X1,empty_set),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_93]),c_0_102])]),c_0_106]) ).
cnf(c_0_117,plain,
( in(esk2_3(X1,X2,X3),X1)
| in(esk2_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_118,negated_conjecture,
( element(esk9_0,relation_rng(esk11_0))
| ~ relation(relation_restriction(esk11_0,esk10_0))
| ~ empty(set_intersection2(esk10_0,relation_dom(esk11_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_76]),c_0_56]),c_0_61])]) ).
cnf(c_0_119,negated_conjecture,
( ~ in(esk9_0,relation_rng(esk11_0))
| ~ in(esk9_0,esk10_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_61])]) ).
cnf(c_0_120,negated_conjecture,
in(esk9_0,esk10_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_61])]) ).
cnf(c_0_121,negated_conjecture,
( ~ relation(relation_restriction(esk11_0,esk10_0))
| ~ empty(relation_rng(esk11_0))
| ~ empty(relation_dom(esk11_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_101]),c_0_102])]) ).
cnf(c_0_122,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_113]) ).
cnf(c_0_123,negated_conjecture,
( element(esk9_0,relation_dom(esk11_0))
| ~ relation(relation_restriction(esk11_0,esk10_0))
| ~ empty(relation_rng(relation_restriction(esk11_0,esk10_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_61])]) ).
cnf(c_0_124,plain,
( empty(relation_rng(relation_restriction(X1,X2)))
| ~ relation(X1)
| ~ empty(relation_rng(relation_dom_restriction(X1,X2))) ),
inference(spm,[status(thm)],[c_0_91,c_0_66]) ).
cnf(c_0_125,plain,
( X1 = empty_set
| in(esk2_3(empty_set,X2,X1),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_93]) ).
cnf(c_0_126,negated_conjecture,
( element(esk9_0,relation_rng(esk11_0))
| ~ relation(relation_restriction(esk11_0,esk10_0))
| ~ empty(relation_dom(esk11_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_101]),c_0_102])]) ).
cnf(c_0_127,negated_conjecture,
~ in(esk9_0,relation_rng(esk11_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_120])]) ).
cnf(c_0_128,negated_conjecture,
( ~ empty(relation_rng(esk11_0))
| ~ empty(relation_dom(esk11_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_111]),c_0_61])]) ).
cnf(c_0_129,plain,
( in(X1,relation_field(X2))
| ~ relation(X2)
| ~ in(X1,relation_dom(X2)) ),
inference(spm,[status(thm)],[c_0_122,c_0_38]) ).
cnf(c_0_130,negated_conjecture,
( element(esk9_0,relation_dom(esk11_0))
| ~ relation(relation_restriction(esk11_0,esk10_0))
| ~ empty(relation_rng(relation_dom_restriction(esk11_0,esk10_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_61])]) ).
cnf(c_0_131,plain,
( relation_rng(relation_dom_restriction(X1,X2)) = empty_set
| ~ relation(X1)
| ~ empty(relation_rng(X1)) ),
inference(spm,[status(thm)],[c_0_46,c_0_125]) ).
cnf(c_0_132,negated_conjecture,
( ~ relation(relation_restriction(esk11_0,esk10_0))
| ~ empty(relation_dom(esk11_0)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_126]),c_0_127]),c_0_128]) ).
cnf(c_0_133,negated_conjecture,
( ~ in(esk9_0,relation_dom(esk11_0))
| ~ in(esk9_0,esk10_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_129]),c_0_61])]) ).
cnf(c_0_134,negated_conjecture,
( in(esk9_0,relation_rng(relation_dom_restriction(esk11_0,esk10_0)))
| in(esk9_0,relation_dom(relation_rng_restriction(esk10_0,esk11_0)))
| ~ relation(relation_restriction(esk11_0,esk10_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_85]),c_0_61])]) ).
cnf(c_0_135,negated_conjecture,
( element(esk9_0,relation_dom(esk11_0))
| ~ relation(relation_restriction(esk11_0,esk10_0))
| ~ empty(relation_rng(esk11_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_102]),c_0_61])]) ).
cnf(c_0_136,negated_conjecture,
~ empty(relation_dom(esk11_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_111]),c_0_61])]) ).
cnf(c_0_137,negated_conjecture,
~ in(esk9_0,relation_dom(esk11_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_120])]) ).
cnf(c_0_138,negated_conjecture,
( element(esk9_0,relation_rng(esk11_0))
| in(esk9_0,relation_dom(relation_rng_restriction(esk10_0,esk11_0)))
| ~ relation(relation_restriction(esk11_0,esk10_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_134]),c_0_61])]) ).
cnf(c_0_139,negated_conjecture,
( ~ relation(relation_restriction(esk11_0,esk10_0))
| ~ empty(relation_rng(esk11_0)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_135]),c_0_136]),c_0_137]) ).
cnf(c_0_140,negated_conjecture,
( element(esk9_0,relation_rng(esk11_0))
| element(esk9_0,relation_dom(esk11_0))
| ~ relation(relation_restriction(esk11_0,esk10_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_138]),c_0_61])]) ).
cnf(c_0_141,negated_conjecture,
~ empty(relation_rng(esk11_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_111]),c_0_61])]) ).
cnf(c_0_142,negated_conjecture,
( element(esk9_0,relation_dom(esk11_0))
| ~ relation(relation_restriction(esk11_0,esk10_0)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_140]),c_0_141]),c_0_127]) ).
cnf(c_0_143,negated_conjecture,
~ relation(relation_restriction(esk11_0,esk10_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_142]),c_0_136]),c_0_137]) ).
cnf(c_0_144,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_111]),c_0_61])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU249+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.09 % 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
% 0.11/0.29 % Computer : n005.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue May 5 02:51:45 EDT 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.30 % start to proof: theBenchmark
% 8.39/5.66 % Version : CSE_E---1.7
% 8.39/5.66 % Problem : theBenchmark.p
% 8.39/5.66 % SZS status Theorem for theBenchmark.p
% 8.39/5.66 % SZS output start CNFRefutation
% See solution above
% 8.39/5.68 % Total time : 4.372s
%------------------------------------------------------------------------------