TSTP Solution File: SEU210+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU210+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n003.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 : Thu Aug 31 16:23:21 EDT 2023
% Result : Theorem 1.24s 1.37s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 46
% Syntax : Number of formulae : 137 ( 33 unt; 26 typ; 0 def)
% Number of atoms : 278 ( 43 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 287 ( 120 ~; 121 |; 28 &)
% ( 5 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 19 >; 13 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 7 con; 0-3 aty)
% Number of variables : 190 ( 23 sgn; 84 !; 6 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
relation: $i > $o ).
tff(decl_25,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_26,type,
subset: ( $i * $i ) > $o ).
tff(decl_27,type,
relation_rng: $i > $i ).
tff(decl_28,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_29,type,
singleton: $i > $i ).
tff(decl_30,type,
element: ( $i * $i ) > $o ).
tff(decl_31,type,
powerset: $i > $i ).
tff(decl_32,type,
empty_set: $i ).
tff(decl_33,type,
relation_inverse_image: ( $i * $i ) > $i ).
tff(decl_34,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk5_1: $i > $i ).
tff(decl_39,type,
esk6_0: $i ).
tff(decl_40,type,
esk7_1: $i > $i ).
tff(decl_41,type,
esk8_0: $i ).
tff(decl_42,type,
esk9_0: $i ).
tff(decl_43,type,
esk10_1: $i > $i ).
tff(decl_44,type,
esk11_0: $i ).
tff(decl_45,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
esk13_0: $i ).
tff(decl_47,type,
esk14_0: $i ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(rc1_subset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(d5_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(fc3_subset_1,axiom,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(t174_relat_1,conjecture,
! [X1,X2] :
( relation(X2)
=> ~ ( X1 != empty_set
& subset(X1,relation_rng(X2))
& relation_inverse_image(X2,X1) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_relat_1) ).
fof(fc4_relat_1,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(cc1_relat_1,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(t166_relat_1,axiom,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_inverse_image(X3,X2))
<=> ? [X4] :
( in(X4,relation_rng(X3))
& in(ordered_pair(X1,X4),X3)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(c_0_20,plain,
! [X66] :
( ~ empty(X66)
| X66 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_21,plain,
! [X43] :
( element(esk10_1(X43),powerset(X43))
& empty(esk10_1(X43)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
cnf(c_0_22,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,plain,
empty(esk10_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_24,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(c_0_25,plain,
! [X58,X59] :
( ( ~ element(X58,powerset(X59))
| subset(X58,X59) )
& ( ~ subset(X58,X59)
| element(X58,powerset(X59)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
cnf(c_0_26,plain,
element(esk10_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
esk10_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_28,plain,
! [X16,X17,X18,X20,X21,X22,X24] :
( ( ~ in(X18,X17)
| in(ordered_pair(esk2_3(X16,X17,X18),X18),X16)
| X17 != relation_rng(X16)
| ~ relation(X16) )
& ( ~ in(ordered_pair(X21,X20),X16)
| in(X20,X17)
| X17 != relation_rng(X16)
| ~ relation(X16) )
& ( ~ in(esk3_2(X16,X22),X22)
| ~ in(ordered_pair(X24,esk3_2(X16,X22)),X16)
| X22 = relation_rng(X16)
| ~ relation(X16) )
& ( in(esk3_2(X16,X22),X22)
| in(ordered_pair(esk4_2(X16,X22),esk3_2(X16,X22)),X16)
| X22 = relation_rng(X16)
| ~ relation(X16) ) ),
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)],[d5_relat_1])])])])])]) ).
fof(c_0_29,plain,
! [X26,X27] : ordered_pair(X26,X27) = unordered_pair(unordered_pair(X26,X27),singleton(X26)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_30,plain,
! [X60,X61,X62] :
( ~ in(X60,X61)
| ~ element(X61,powerset(X62))
| element(X60,X62) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(c_0_31,plain,
! [X39] :
( ( element(esk7_1(X39),powerset(X39))
| empty(X39) )
& ( ~ empty(esk7_1(X39))
| empty(X39) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
fof(c_0_32,plain,
! [X56,X57] :
( ~ element(X56,X57)
| empty(X57)
| in(X56,X57) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_33,plain,
! [X28] : element(esk5_1(X28),X28),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_34,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(c_0_35,plain,
! [X10,X11,X12,X13,X14] :
( ( ~ subset(X10,X11)
| ~ in(X12,X10)
| in(X12,X11) )
& ( in(esk1_2(X13,X14),X13)
| subset(X13,X14) )
& ( ~ in(esk1_2(X13,X14),X14)
| subset(X13,X14) ) ),
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_tarski])])])])])]) ).
cnf(c_0_36,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_37,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_38,plain,
( in(esk3_2(X1,X2),X2)
| in(ordered_pair(esk4_2(X1,X2),esk3_2(X1,X2)),X1)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_39,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_40,plain,
! [X8,X9] : unordered_pair(X8,X9) = unordered_pair(X9,X8),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_41,plain,
! [X63,X64,X65] :
( ~ in(X63,X64)
| ~ element(X64,powerset(X65))
| ~ empty(X65) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_42,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_43,plain,
( element(esk7_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_44,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_45,plain,
element(esk5_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_46,plain,
! [X5,X6] :
( ~ in(X5,X6)
| ~ in(X6,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])]) ).
cnf(c_0_47,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_48,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_49,plain,
( X2 = relation_rng(X1)
| in(esk3_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk4_2(X1,X2),esk3_2(X1,X2)),singleton(esk4_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_50,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_51,plain,
! [X1,X2] : ~ empty(unordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[fc3_subset_1]) ).
cnf(c_0_52,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_53,plain,
( element(X1,X2)
| empty(X2)
| ~ in(X1,esk7_1(X2)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_54,plain,
( empty(X1)
| in(esk5_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_55,plain,
( empty(X1)
| ~ empty(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_56,plain,
subset(esk5_1(powerset(X1)),X1),
inference(spm,[status(thm)],[c_0_36,c_0_45]) ).
fof(c_0_57,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> ~ ( X1 != empty_set
& subset(X1,relation_rng(X2))
& relation_inverse_image(X2,X1) = empty_set ) ),
inference(assume_negation,[status(cth)],[t174_relat_1]) ).
cnf(c_0_58,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_59,plain,
( in(X1,X2)
| ~ in(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_60,plain,
( X1 = relation_rng(X2)
| in(unordered_pair(singleton(esk4_2(X2,X1)),unordered_pair(esk3_2(X2,X1),esk4_2(X2,X1))),X2)
| in(esk3_2(X2,X1),X1)
| ~ relation(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_50]) ).
cnf(c_0_61,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]) ).
fof(c_0_62,plain,
! [X34,X35] : ~ empty(unordered_pair(X34,X35)),
inference(variable_rename,[status(thm)],[c_0_51]) ).
cnf(c_0_63,plain,
( ~ empty(X1)
| ~ in(X2,empty_set) ),
inference(spm,[status(thm)],[c_0_52,c_0_37]) ).
cnf(c_0_64,plain,
( element(esk5_1(esk7_1(X1)),X1)
| empty(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_65,plain,
( in(X1,X2)
| ~ in(X1,esk5_1(powerset(X2))) ),
inference(spm,[status(thm)],[c_0_47,c_0_56]) ).
fof(c_0_66,negated_conjecture,
( relation(esk14_0)
& esk13_0 != empty_set
& subset(esk13_0,relation_rng(esk14_0))
& relation_inverse_image(esk14_0,esk13_0) = empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])]) ).
fof(c_0_67,plain,
! [X67,X68] :
( ~ in(X67,X68)
| ~ empty(X68) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(c_0_68,plain,
! [X7] :
( ~ empty(X7)
| relation(X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
cnf(c_0_69,plain,
( empty(X1)
| ~ in(X1,esk5_1(X1)) ),
inference(spm,[status(thm)],[c_0_58,c_0_54]) ).
cnf(c_0_70,plain,
( X1 = relation_rng(empty_set)
| in(unordered_pair(singleton(esk4_2(empty_set,X1)),unordered_pair(esk3_2(empty_set,X1),esk4_2(empty_set,X1))),X2)
| in(esk3_2(empty_set,X1),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61])]) ).
cnf(c_0_71,plain,
~ empty(unordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_72,plain,
( X1 = relation_rng(empty_set)
| in(esk3_2(empty_set,X1),X1)
| ~ empty(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_60]),c_0_61])]) ).
cnf(c_0_73,plain,
( empty(X1)
| in(esk5_1(esk7_1(X1)),X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_64]) ).
cnf(c_0_74,plain,
( empty(esk5_1(powerset(X1)))
| in(esk5_1(esk5_1(powerset(X1))),X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_54]) ).
fof(c_0_75,plain,
! [X47,X48,X49,X51] :
( ( in(esk12_3(X47,X48,X49),relation_rng(X49))
| ~ in(X47,relation_inverse_image(X49,X48))
| ~ relation(X49) )
& ( in(ordered_pair(X47,esk12_3(X47,X48,X49)),X49)
| ~ in(X47,relation_inverse_image(X49,X48))
| ~ relation(X49) )
& ( in(esk12_3(X47,X48,X49),X48)
| ~ in(X47,relation_inverse_image(X49,X48))
| ~ relation(X49) )
& ( ~ in(X51,relation_rng(X49))
| ~ in(ordered_pair(X47,X51),X49)
| ~ in(X51,X48)
| in(X47,relation_inverse_image(X49,X48))
| ~ relation(X49) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t166_relat_1])])])])]) ).
cnf(c_0_76,negated_conjecture,
subset(esk13_0,relation_rng(esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_77,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_78,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_79,plain,
( X1 = relation_rng(empty_set)
| in(esk3_2(empty_set,X1),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
cnf(c_0_80,plain,
( relation_rng(empty_set) = empty_set
| in(esk3_2(empty_set,empty_set),X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_72]) ).
cnf(c_0_81,plain,
( relation_rng(empty_set) = empty_set
| ~ empty(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_63,c_0_72]) ).
cnf(c_0_82,plain,
( empty(X1)
| ~ in(X1,esk5_1(esk7_1(X1))) ),
inference(spm,[status(thm)],[c_0_58,c_0_73]) ).
cnf(c_0_83,plain,
( empty(esk5_1(powerset(empty_set)))
| in(esk5_1(esk5_1(powerset(empty_set))),X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_74]) ).
cnf(c_0_84,plain,
( empty(esk5_1(powerset(empty_set)))
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_74]) ).
cnf(c_0_85,plain,
( in(X3,relation_inverse_image(X2,X4))
| ~ in(X1,relation_rng(X2))
| ~ in(ordered_pair(X3,X1),X2)
| ~ in(X1,X4)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_86,negated_conjecture,
( in(X1,relation_rng(esk14_0))
| ~ in(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_76]) ).
cnf(c_0_87,plain,
( X1 = relation_rng(X2)
| in(esk3_2(X2,X1),X1)
| ~ empty(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_60]),c_0_78]) ).
cnf(c_0_88,plain,
( relation_rng(empty_set) = empty_set
| in(esk3_2(empty_set,empty_set),X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_79]) ).
cnf(c_0_89,plain,
( relation_rng(empty_set) = empty_set
| ~ empty(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_80]),c_0_81]) ).
cnf(c_0_90,plain,
empty(esk5_1(powerset(empty_set))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]) ).
cnf(c_0_91,plain,
( in(ordered_pair(esk2_3(X3,X2,X1),X1),X3)
| ~ in(X1,X2)
| X2 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_92,plain,
( in(X3,relation_inverse_image(X2,X4))
| ~ relation(X2)
| ~ in(X1,X4)
| ~ in(X1,relation_rng(X2))
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2) ),
inference(rw,[status(thm)],[c_0_85,c_0_39]) ).
cnf(c_0_93,negated_conjecture,
( relation_rng(X1) = esk13_0
| in(esk3_2(X1,esk13_0),relation_rng(esk14_0))
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_94,negated_conjecture,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_95,plain,
relation_rng(empty_set) = empty_set,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_88]),c_0_89]) ).
cnf(c_0_96,plain,
( ~ empty(X1)
| ~ in(X2,esk5_1(powerset(X1))) ),
inference(spm,[status(thm)],[c_0_52,c_0_45]) ).
cnf(c_0_97,plain,
esk5_1(powerset(empty_set)) = empty_set,
inference(spm,[status(thm)],[c_0_22,c_0_90]) ).
cnf(c_0_98,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_99,plain,
( in(unordered_pair(unordered_pair(esk2_3(X3,X2,X1),X1),singleton(esk2_3(X3,X2,X1))),X3)
| X2 != relation_rng(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_91,c_0_39]) ).
cnf(c_0_100,negated_conjecture,
( relation_rng(X1) = esk13_0
| in(X2,relation_inverse_image(esk14_0,X3))
| ~ empty(X1)
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,esk3_2(X1,esk13_0))),esk14_0)
| ~ in(esk3_2(X1,esk13_0),X3) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94])]),c_0_50]) ).
cnf(c_0_101,plain,
( X1 = empty_set
| in(esk3_2(empty_set,X1),X1) ),
inference(rw,[status(thm)],[c_0_79,c_0_95]) ).
cnf(c_0_102,negated_conjecture,
relation_inverse_image(esk14_0,esk13_0) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_103,negated_conjecture,
esk13_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_104,plain,
~ in(X1,empty_set),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_98])]) ).
cnf(c_0_105,plain,
( in(unordered_pair(unordered_pair(X1,esk2_3(X2,X3,X1)),singleton(esk2_3(X2,X3,X1))),X2)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_99,c_0_50]) ).
cnf(c_0_106,negated_conjecture,
~ in(unordered_pair(singleton(X1),unordered_pair(X1,esk3_2(empty_set,esk13_0))),esk14_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_95]),c_0_102]),c_0_98])]),c_0_103]),c_0_104]) ).
cnf(c_0_107,plain,
( in(unordered_pair(unordered_pair(X1,esk2_3(X2,relation_rng(X2),X1)),singleton(esk2_3(X2,relation_rng(X2),X1))),X2)
| ~ relation(X2)
| ~ in(X1,relation_rng(X2)) ),
inference(er,[status(thm)],[c_0_105]) ).
cnf(c_0_108,negated_conjecture,
~ in(unordered_pair(singleton(X1),unordered_pair(esk3_2(empty_set,esk13_0),X1)),esk14_0),
inference(spm,[status(thm)],[c_0_106,c_0_50]) ).
cnf(c_0_109,negated_conjecture,
( relation_rng(X1) = esk13_0
| in(unordered_pair(singleton(esk2_3(esk14_0,relation_rng(esk14_0),esk3_2(X1,esk13_0))),unordered_pair(esk3_2(X1,esk13_0),esk2_3(esk14_0,relation_rng(esk14_0),esk3_2(X1,esk13_0)))),esk14_0)
| ~ empty(X1) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_93]),c_0_94])]),c_0_50]) ).
cnf(c_0_110,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_108,c_0_109]),c_0_95]),c_0_98])]),c_0_103]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SEU210+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 15:24:22 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 1.24/1.37 % Version : CSE_E---1.5
% 1.24/1.37 % Problem : theBenchmark.p
% 1.24/1.37 % Proof found
% 1.24/1.37 % SZS status Theorem for theBenchmark.p
% 1.24/1.37 % SZS output start Proof
% See solution above
% 1.24/1.38 % Total time : 0.778000 s
% 1.24/1.38 % SZS output end Proof
% 1.24/1.38 % Total time : 0.781000 s
%------------------------------------------------------------------------------