TSTP Solution File: SET996+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET996+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n023.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 14:36:34 EDT 2023
% Result : Theorem 0.54s 1.05s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 48
% Syntax : Number of formulae : 148 ( 33 unt; 28 typ; 0 def)
% Number of atoms : 324 ( 65 equ)
% Maximal formula atoms : 32 ( 2 avg)
% Number of connectives : 373 ( 169 ~; 148 |; 38 &)
% ( 4 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 19 >; 11 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-3 aty)
% Number of variables : 193 ( 25 sgn; 73 !; 6 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
function: $i > $o ).
tff(decl_25,type,
relation: $i > $o ).
tff(decl_26,type,
subset: ( $i * $i ) > $o ).
tff(decl_27,type,
relation_rng: $i > $i ).
tff(decl_28,type,
relation_dom: $i > $i ).
tff(decl_29,type,
apply: ( $i * $i ) > $i ).
tff(decl_30,type,
element: ( $i * $i ) > $o ).
tff(decl_31,type,
empty_set: $i ).
tff(decl_32,type,
relation_empty_yielding: $i > $o ).
tff(decl_33,type,
powerset: $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_0: $i ).
tff(decl_41,type,
esk8_1: $i > $i ).
tff(decl_42,type,
esk9_0: $i ).
tff(decl_43,type,
esk10_0: $i ).
tff(decl_44,type,
esk11_1: $i > $i ).
tff(decl_45,type,
esk12_0: $i ).
tff(decl_46,type,
esk13_0: $i ).
tff(decl_47,type,
esk14_3: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
esk15_0: $i ).
tff(decl_49,type,
esk16_0: $i ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(rc1_relat_1,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(fc5_relat_1,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(s3_funct_1__e4_16_2__funct_1,axiom,
! [X1,X2,X3] :
( element(X3,X1)
=> ? [X4] :
( relation(X4)
& function(X4)
& relation_dom(X4) = X2
& ! [X5] :
( in(X5,X2)
=> apply(X4,X5) = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e4_16_2__funct_1) ).
fof(d5_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(t18_funct_1,conjecture,
! [X1,X2] :
~ ( ~ ( X1 = empty_set
& X2 != empty_set )
& ! [X3] :
( ( relation(X3)
& function(X3) )
=> ~ ( X2 = relation_dom(X3)
& subset(relation_rng(X3),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_funct_1) ).
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(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(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
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(fc8_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_rng(X1))
& relation(relation_rng(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(cc1_funct_1,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(cc1_relat_1,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(t2_xboole_1,axiom,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(fc7_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(c_0_20,plain,
! [X65] :
( ~ empty(X65)
| X65 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_21,plain,
empty(esk9_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(c_0_22,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,plain,
empty(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_24,plain,
empty_set = esk9_0,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_25,plain,
( empty(esk7_0)
& relation(esk7_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).
cnf(c_0_26,plain,
( X1 = esk9_0
| ~ empty(X1) ),
inference(rw,[status(thm)],[c_0_22,c_0_24]) ).
cnf(c_0_27,plain,
empty(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_28,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
inference(fof_simplification,[status(thm)],[fc5_relat_1]) ).
cnf(c_0_29,plain,
esk9_0 = esk7_0,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_30,plain,
! [X39] :
( element(esk11_1(X39),powerset(X39))
& empty(esk11_1(X39)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(c_0_31,plain,
! [X29] :
( empty(X29)
| ~ relation(X29)
| ~ empty(relation_dom(X29)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])]) ).
fof(c_0_32,plain,
! [X44,X45,X46,X48] :
( ( relation(esk14_3(X44,X45,X46))
| ~ element(X46,X44) )
& ( function(esk14_3(X44,X45,X46))
| ~ element(X46,X44) )
& ( relation_dom(esk14_3(X44,X45,X46)) = X45
| ~ element(X46,X44) )
& ( ~ in(X48,X45)
| apply(esk14_3(X44,X45,X46),X48) = X46
| ~ element(X46,X44) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s3_funct_1__e4_16_2__funct_1])])])])]) ).
cnf(c_0_33,plain,
( X1 = esk7_0
| ~ empty(X1) ),
inference(rw,[status(thm)],[c_0_26,c_0_29]) ).
cnf(c_0_34,plain,
empty(esk11_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,plain,
( empty(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,plain,
( relation_dom(esk14_3(X1,X2,X3)) = X2
| ~ element(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
( relation(esk14_3(X1,X2,X3))
| ~ element(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
element(esk11_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,plain,
esk11_1(X1) = esk7_0,
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
fof(c_0_40,plain,
! [X16,X17,X18,X20,X21,X22,X24] :
( ( in(esk2_3(X16,X17,X18),relation_dom(X16))
| ~ in(X18,X17)
| X17 != relation_rng(X16)
| ~ relation(X16)
| ~ function(X16) )
& ( X18 = apply(X16,esk2_3(X16,X17,X18))
| ~ in(X18,X17)
| X17 != relation_rng(X16)
| ~ relation(X16)
| ~ function(X16) )
& ( ~ in(X21,relation_dom(X16))
| X20 != apply(X16,X21)
| in(X20,X17)
| X17 != relation_rng(X16)
| ~ relation(X16)
| ~ function(X16) )
& ( ~ in(esk3_2(X16,X22),X22)
| ~ in(X24,relation_dom(X16))
| esk3_2(X16,X22) != apply(X16,X24)
| X22 = relation_rng(X16)
| ~ relation(X16)
| ~ function(X16) )
& ( in(esk4_2(X16,X22),relation_dom(X16))
| in(esk3_2(X16,X22),X22)
| X22 = relation_rng(X16)
| ~ relation(X16)
| ~ function(X16) )
& ( esk3_2(X16,X22) = apply(X16,esk4_2(X16,X22))
| in(esk3_2(X16,X22),X22)
| X22 = relation_rng(X16)
| ~ relation(X16)
| ~ function(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_funct_1])])])])])]) ).
fof(c_0_41,negated_conjecture,
~ ! [X1,X2] :
~ ( ~ ( X1 = empty_set
& X2 != empty_set )
& ! [X3] :
( ( relation(X3)
& function(X3) )
=> ~ ( X2 = relation_dom(X3)
& subset(relation_rng(X3),X1) ) ) ),
inference(assume_negation,[status(cth)],[t18_funct_1]) ).
cnf(c_0_42,plain,
( empty(esk14_3(X1,X2,X3))
| ~ element(X3,X1)
| ~ empty(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_43,plain,
element(esk7_0,powerset(X1)),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
fof(c_0_44,plain,
! [X62,X63,X64] :
( ~ in(X62,X63)
| ~ element(X63,powerset(X64))
| ~ empty(X64) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_45,plain,
( X1 = apply(X2,esk2_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,plain,
( in(esk2_3(X1,X2,X3),relation_dom(X1))
| ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_47,negated_conjecture,
! [X51] :
( ( esk15_0 != empty_set
| esk16_0 = empty_set )
& ( ~ relation(X51)
| ~ function(X51)
| esk16_0 != relation_dom(X51)
| ~ subset(relation_rng(X51),esk15_0) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])]) ).
fof(c_0_48,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])])])])])]) ).
fof(c_0_49,plain,
! [X66,X67] :
( ~ in(X66,X67)
| ~ empty(X67) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(c_0_50,plain,
! [X54,X55] :
( ~ element(X54,X55)
| empty(X55)
| in(X54,X55) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_51,plain,
! [X26] : element(esk5_1(X26),X26),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_52,plain,
( empty(esk14_3(powerset(X1),X2,esk7_0))
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_53,plain,
! [X32] :
( ( empty(relation_rng(X32))
| ~ empty(X32) )
& ( relation(relation_rng(X32))
| ~ empty(X32) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc8_relat_1])])]) ).
cnf(c_0_54,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_55,plain,
( apply(esk14_3(X3,X2,X4),X1) = X4
| ~ in(X1,X2)
| ~ element(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_56,plain,
( apply(X1,esk2_3(X1,relation_rng(X1),X2)) = X2
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_45]) ).
cnf(c_0_57,plain,
( function(esk14_3(X1,X2,X3))
| ~ element(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_58,plain,
( in(esk2_3(X1,relation_rng(X1),X2),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_46]) ).
cnf(c_0_59,negated_conjecture,
( ~ relation(X1)
| ~ function(X1)
| esk16_0 != relation_dom(X1)
| ~ subset(relation_rng(X1),esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_60,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_61,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_62,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_63,plain,
element(esk5_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_64,plain,
( esk14_3(powerset(X1),X2,esk7_0) = esk7_0
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_52]) ).
cnf(c_0_65,plain,
( in(X3,X4)
| ~ in(X1,relation_dom(X2))
| X3 != apply(X2,X1)
| X4 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_66,plain,
( empty(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_67,plain,
! [X8] :
( ~ empty(X8)
| function(X8) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).
fof(c_0_68,plain,
! [X9] :
( ~ empty(X9)
| relation(X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
cnf(c_0_69,plain,
( ~ empty(X1)
| ~ in(X2,esk11_1(X1)) ),
inference(spm,[status(thm)],[c_0_54,c_0_38]) ).
fof(c_0_70,plain,
! [X56] : subset(empty_set,X56),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
cnf(c_0_71,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_72,plain,
( X1 = X2
| ~ element(X2,X3)
| ~ in(esk2_3(esk14_3(X3,X4,X2),relation_rng(esk14_3(X3,X4,X2)),X1),X4)
| ~ in(X1,relation_rng(esk14_3(X3,X4,X2))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_37]) ).
cnf(c_0_73,plain,
( in(esk2_3(esk14_3(X1,X2,X3),relation_rng(esk14_3(X1,X2,X3)),X4),X2)
| ~ element(X3,X1)
| ~ in(X4,relation_rng(esk14_3(X1,X2,X3))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_36]),c_0_57]),c_0_37]) ).
cnf(c_0_74,negated_conjecture,
( in(esk1_2(relation_rng(X1),esk15_0),relation_rng(X1))
| relation_dom(X1) != esk16_0
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_75,plain,
( ~ relation(X1)
| ~ function(X1)
| ~ empty(relation_dom(X1))
| ~ in(X2,relation_rng(X1)) ),
inference(spm,[status(thm)],[c_0_61,c_0_58]) ).
cnf(c_0_76,plain,
( empty(X1)
| in(esk5_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_77,plain,
esk14_3(powerset(X1),esk7_0,esk7_0) = esk7_0,
inference(spm,[status(thm)],[c_0_64,c_0_27]) ).
cnf(c_0_78,plain,
( in(apply(X1,X2),relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_65])]) ).
cnf(c_0_79,plain,
( relation_rng(X1) = esk7_0
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_66]) ).
cnf(c_0_80,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_81,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_82,plain,
( ~ empty(X1)
| ~ in(X2,esk7_0) ),
inference(rw,[status(thm)],[c_0_69,c_0_39]) ).
cnf(c_0_83,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_84,negated_conjecture,
( relation_dom(X1) != esk16_0
| ~ relation(X1)
| ~ function(X1)
| ~ in(esk1_2(relation_rng(X1),esk15_0),esk15_0) ),
inference(spm,[status(thm)],[c_0_59,c_0_71]) ).
cnf(c_0_85,plain,
( X1 = X2
| ~ element(X2,X3)
| ~ in(X1,relation_rng(esk14_3(X3,X4,X2))) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_86,negated_conjecture,
( in(esk1_2(relation_rng(esk14_3(X1,esk16_0,X2)),esk15_0),relation_rng(esk14_3(X1,esk16_0,X2)))
| ~ element(X2,X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_36])]),c_0_57]),c_0_37]) ).
fof(c_0_87,plain,
! [X57,X58] :
( ( ~ element(X57,powerset(X58))
| subset(X57,X58) )
& ( ~ subset(X57,X58)
| element(X57,powerset(X58)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_88,plain,
! [X43] : subset(X43,X43),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_89,plain,
( empty(relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ empty(relation_dom(X1)) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_90,plain,
relation_dom(esk7_0) = esk7_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_77]),c_0_43])]) ).
cnf(c_0_91,plain,
relation(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_92,plain,
function(esk7_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_77]),c_0_43])]) ).
cnf(c_0_93,plain,
( ~ empty(X1)
| ~ in(X2,relation_dom(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]),c_0_81]),c_0_82]) ).
cnf(c_0_94,plain,
subset(esk9_0,X1),
inference(rw,[status(thm)],[c_0_83,c_0_24]) ).
fof(c_0_95,plain,
! [X31] :
( ( empty(relation_dom(X31))
| ~ empty(X31) )
& ( relation(relation_dom(X31))
| ~ empty(X31) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_relat_1])])]) ).
cnf(c_0_96,negated_conjecture,
( ~ element(X1,X2)
| ~ in(esk1_2(relation_rng(esk14_3(X2,esk16_0,X1)),esk15_0),esk15_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_36])]),c_0_57]),c_0_37]) ).
cnf(c_0_97,negated_conjecture,
( esk1_2(relation_rng(esk14_3(X1,esk16_0,X2)),esk15_0) = X2
| ~ element(X2,X1) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_98,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_99,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_100,plain,
empty(relation_rng(esk7_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]),c_0_92]),c_0_27])]) ).
cnf(c_0_101,plain,
( ~ element(X1,X2)
| ~ empty(esk14_3(X2,X3,X1))
| ~ in(X4,X3) ),
inference(spm,[status(thm)],[c_0_93,c_0_36]) ).
cnf(c_0_102,plain,
subset(esk7_0,X1),
inference(rw,[status(thm)],[c_0_94,c_0_29]) ).
cnf(c_0_103,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_104,negated_conjecture,
( esk16_0 = empty_set
| esk15_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_105,negated_conjecture,
( ~ element(X1,X2)
| ~ in(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_106,plain,
element(X1,powerset(X1)),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_107,plain,
( in(esk4_2(X1,X2),relation_dom(X1))
| in(esk3_2(X1,X2),X2)
| X2 = relation_rng(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_108,plain,
relation_rng(esk7_0) = esk7_0,
inference(spm,[status(thm)],[c_0_33,c_0_100]) ).
cnf(c_0_109,plain,
~ in(X1,esk7_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_77]),c_0_43]),c_0_27])]) ).
cnf(c_0_110,negated_conjecture,
( relation_dom(X1) != esk16_0
| ~ empty(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_79]),c_0_102])]),c_0_80]),c_0_81]) ).
cnf(c_0_111,plain,
( relation_dom(X1) = esk7_0
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_103]) ).
cnf(c_0_112,negated_conjecture,
( esk9_0 = esk16_0
| esk9_0 != esk15_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_24]),c_0_24]) ).
cnf(c_0_113,negated_conjecture,
~ in(X1,esk15_0),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_114,plain,
( X1 = esk7_0
| in(esk3_2(esk7_0,X1),X1) ),
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_107,c_0_91]),c_0_108]),c_0_90]),c_0_92])]),c_0_109]) ).
cnf(c_0_115,negated_conjecture,
( esk16_0 != esk7_0
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_116,negated_conjecture,
( esk16_0 = esk7_0
| esk15_0 != esk7_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_29]),c_0_29]) ).
cnf(c_0_117,negated_conjecture,
esk15_0 = esk7_0,
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_118,negated_conjecture,
esk16_0 != esk7_0,
inference(spm,[status(thm)],[c_0_115,c_0_27]) ).
cnf(c_0_119,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_117])]),c_0_118]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET996+1 : TPTP v8.1.2. Released v3.2.0.
% 0.04/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 14:20:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.52/0.57 start to proof: theBenchmark
% 0.54/1.05 % Version : CSE_E---1.5
% 0.54/1.05 % Problem : theBenchmark.p
% 0.54/1.05 % Proof found
% 0.54/1.05 % SZS status Theorem for theBenchmark.p
% 0.54/1.05 % SZS output start Proof
% See solution above
% 0.54/1.05 % Total time : 0.471000 s
% 0.54/1.05 % SZS output end Proof
% 0.54/1.05 % Total time : 0.474000 s
%------------------------------------------------------------------------------