TSTP Solution File: SEU213+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU213+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 : n004.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 16:23:23 EDT 2023
% Result : Theorem 239.99s 240.12s
% Output : CNFRefutation 239.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 37
% Syntax : Number of formulae : 104 ( 14 unt; 30 typ; 0 def)
% Number of atoms : 431 ( 94 equ)
% Maximal formula atoms : 38 ( 5 avg)
% Number of connectives : 653 ( 296 ~; 303 |; 29 &)
% ( 10 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 20 >; 20 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 10 con; 0-5 aty)
% Number of variables : 250 ( 6 sgn; 51 !; 2 ?; 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,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_27,type,
relation_dom: $i > $i ).
tff(decl_28,type,
apply: ( $i * $i ) > $i ).
tff(decl_29,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_30,type,
empty_set: $i ).
tff(decl_31,type,
singleton: $i > $i ).
tff(decl_32,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_33,type,
element: ( $i * $i ) > $o ).
tff(decl_34,type,
relation_empty_yielding: $i > $o ).
tff(decl_35,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk4_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_39,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
esk8_1: $i > $i ).
tff(decl_43,type,
esk9_0: $i ).
tff(decl_44,type,
esk10_0: $i ).
tff(decl_45,type,
esk11_0: $i ).
tff(decl_46,type,
esk12_0: $i ).
tff(decl_47,type,
esk13_0: $i ).
tff(decl_48,type,
esk14_0: $i ).
tff(decl_49,type,
esk15_0: $i ).
tff(decl_50,type,
esk16_0: $i ).
tff(decl_51,type,
esk17_0: $i ).
fof(d4_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_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(d8_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ! [X3] :
( relation(X3)
=> ( X3 = relation_composition(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ? [X6] :
( in(ordered_pair(X4,X6),X1)
& in(ordered_pair(X6,X5),X2) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
fof(d4_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
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(dt_k5_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(t21_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
<=> ( in(X1,relation_dom(X3))
& in(apply(X3,X1),relation_dom(X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
fof(c_0_7,plain,
! [X16,X17,X18,X20,X21,X22,X24] :
( ( ~ in(X18,X17)
| in(ordered_pair(X18,esk1_3(X16,X17,X18)),X16)
| X17 != relation_dom(X16)
| ~ relation(X16) )
& ( ~ in(ordered_pair(X20,X21),X16)
| in(X20,X17)
| X17 != relation_dom(X16)
| ~ relation(X16) )
& ( ~ in(esk2_2(X16,X22),X22)
| ~ in(ordered_pair(esk2_2(X16,X22),X24),X16)
| X22 = relation_dom(X16)
| ~ relation(X16) )
& ( in(esk2_2(X16,X22),X22)
| in(ordered_pair(esk2_2(X16,X22),esk3_2(X16,X22)),X16)
| X22 = relation_dom(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)],[d4_relat_1])])])])])]) ).
fof(c_0_8,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_9,plain,
! [X28,X29,X30,X31,X32,X34,X35,X36,X39] :
( ( in(ordered_pair(X31,esk4_5(X28,X29,X30,X31,X32)),X28)
| ~ in(ordered_pair(X31,X32),X30)
| X30 != relation_composition(X28,X29)
| ~ relation(X30)
| ~ relation(X29)
| ~ relation(X28) )
& ( in(ordered_pair(esk4_5(X28,X29,X30,X31,X32),X32),X29)
| ~ in(ordered_pair(X31,X32),X30)
| X30 != relation_composition(X28,X29)
| ~ relation(X30)
| ~ relation(X29)
| ~ relation(X28) )
& ( ~ in(ordered_pair(X34,X36),X28)
| ~ in(ordered_pair(X36,X35),X29)
| in(ordered_pair(X34,X35),X30)
| X30 != relation_composition(X28,X29)
| ~ relation(X30)
| ~ relation(X29)
| ~ relation(X28) )
& ( ~ in(ordered_pair(esk5_3(X28,X29,X30),esk6_3(X28,X29,X30)),X30)
| ~ in(ordered_pair(esk5_3(X28,X29,X30),X39),X28)
| ~ in(ordered_pair(X39,esk6_3(X28,X29,X30)),X29)
| X30 = relation_composition(X28,X29)
| ~ relation(X30)
| ~ relation(X29)
| ~ relation(X28) )
& ( in(ordered_pair(esk5_3(X28,X29,X30),esk7_3(X28,X29,X30)),X28)
| in(ordered_pair(esk5_3(X28,X29,X30),esk6_3(X28,X29,X30)),X30)
| X30 = relation_composition(X28,X29)
| ~ relation(X30)
| ~ relation(X29)
| ~ relation(X28) )
& ( in(ordered_pair(esk7_3(X28,X29,X30),esk6_3(X28,X29,X30)),X29)
| in(ordered_pair(esk5_3(X28,X29,X30),esk6_3(X28,X29,X30)),X30)
| X30 = relation_composition(X28,X29)
| ~ relation(X30)
| ~ relation(X29)
| ~ relation(X28) ) ),
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)],[d8_relat_1])])])])])]) ).
fof(c_0_10,plain,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
inference(fof_simplification,[status(thm)],[d4_funct_1]) ).
cnf(c_0_11,plain,
( in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X11,X12] : unordered_pair(X11,X12) = unordered_pair(X12,X11),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_14,plain,
( in(ordered_pair(X1,esk4_5(X2,X3,X4,X1,X5)),X2)
| ~ in(ordered_pair(X1,X5),X4)
| X4 != relation_composition(X2,X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,plain,
! [X13,X14,X15] :
( ( X15 != apply(X13,X14)
| in(ordered_pair(X14,X15),X13)
| ~ in(X14,relation_dom(X13))
| ~ relation(X13)
| ~ function(X13) )
& ( ~ in(ordered_pair(X14,X15),X13)
| X15 = apply(X13,X14)
| ~ in(X14,relation_dom(X13))
| ~ relation(X13)
| ~ function(X13) )
& ( X15 != apply(X13,X14)
| X15 = empty_set
| in(X14,relation_dom(X13))
| ~ relation(X13)
| ~ function(X13) )
& ( X15 != empty_set
| X15 = apply(X13,X14)
| in(X14,relation_dom(X13))
| ~ relation(X13)
| ~ function(X13) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
cnf(c_0_16,plain,
( in(X1,X4)
| X4 != relation_dom(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( in(unordered_pair(unordered_pair(X1,esk4_5(X2,X3,X4,X1,X5)),singleton(X1)),X2)
| X4 != relation_composition(X2,X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X5),singleton(X1)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_12]),c_0_12]) ).
cnf(c_0_19,plain,
( in(ordered_pair(X1,X4),X6)
| ~ in(ordered_pair(X1,X2),X3)
| ~ in(ordered_pair(X2,X4),X5)
| X6 != relation_composition(X3,X5)
| ~ relation(X6)
| ~ relation(X5)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,plain,
( in(ordered_pair(X3,X1),X2)
| X1 != apply(X2,X3)
| ~ in(X3,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X4)),X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk4_5(X2,X3,X4,X1,X5))),X2)
| X4 != relation_composition(X2,X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X5),singleton(X1)),X4) ),
inference(rw,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_23,plain,
( in(ordered_pair(X1,esk1_3(X3,X2,X1)),X3)
| ~ in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,plain,
( in(unordered_pair(unordered_pair(X1,X4),singleton(X1)),X6)
| X6 != relation_composition(X3,X5)
| ~ relation(X6)
| ~ relation(X5)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X2,X4),singleton(X2)),X5)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_12]),c_0_12]),c_0_12]) ).
cnf(c_0_25,plain,
( in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2)
| X1 != apply(X2,X3)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(X2)) ),
inference(rw,[status(thm)],[c_0_20,c_0_12]) ).
cnf(c_0_26,plain,
( in(ordered_pair(esk4_5(X1,X2,X3,X4,X5),X5),X2)
| ~ in(ordered_pair(X4,X5),X3)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,plain,
( X2 = apply(X3,X1)
| ~ in(ordered_pair(X1,X2),X3)
| ~ in(X1,relation_dom(X3))
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_28,plain,
( in(X1,X2)
| X3 != relation_composition(X4,X5)
| X2 != relation_dom(X4)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X5)
| ~ in(unordered_pair(unordered_pair(X1,X6),singleton(X1)),X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
( in(unordered_pair(unordered_pair(X1,esk1_3(X3,X2,X1)),singleton(X1)),X3)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_23,c_0_12]) ).
cnf(c_0_30,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| X3 != relation_composition(X4,X5)
| X2 != apply(X5,X6)
| ~ relation(X3)
| ~ relation(X5)
| ~ relation(X4)
| ~ function(X5)
| ~ in(unordered_pair(unordered_pair(X1,X6),singleton(X1)),X4)
| ~ in(X6,relation_dom(X5)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_31,plain,
! [X41,X42] :
( ~ relation(X41)
| ~ relation(X42)
| relation(relation_composition(X41,X42)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])]) ).
cnf(c_0_32,plain,
( in(unordered_pair(unordered_pair(esk4_5(X1,X2,X3,X4,X5),X5),singleton(esk4_5(X1,X2,X3,X4,X5))),X2)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_12]),c_0_12]) ).
cnf(c_0_33,plain,
( X2 = apply(X3,X1)
| ~ function(X3)
| ~ relation(X3)
| ~ in(X1,relation_dom(X3))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_27,c_0_12]) ).
cnf(c_0_34,plain,
( in(X1,X2)
| X3 != relation_composition(X4,X5)
| X2 != relation_dom(X4)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X5)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X6)),X3) ),
inference(spm,[status(thm)],[c_0_28,c_0_17]) ).
cnf(c_0_35,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk1_3(X2,X3,X1))),X2)
| X3 != relation_dom(X2)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_29,c_0_17]) ).
cnf(c_0_36,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| X3 != relation_composition(X4,X5)
| X2 != apply(X5,X6)
| X6 != apply(X4,X1)
| ~ relation(X3)
| ~ relation(X5)
| ~ relation(X4)
| ~ function(X5)
| ~ function(X4)
| ~ in(X6,relation_dom(X5))
| ~ in(X1,relation_dom(X4)) ),
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
cnf(c_0_37,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,plain,
( in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X4,X1),singleton(X1)),X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_39,plain,
( in(unordered_pair(unordered_pair(X1,esk4_5(X2,X3,X4,X5,X1)),singleton(esk4_5(X2,X3,X4,X5,X1))),X3)
| X4 != relation_composition(X2,X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X5,X1),singleton(X5)),X4) ),
inference(rw,[status(thm)],[c_0_32,c_0_17]) ).
cnf(c_0_40,plain,
( X1 = apply(X2,X3)
| ~ relation(X2)
| ~ function(X2)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),X2)
| ~ in(X3,relation_dom(X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_17]) ).
cnf(c_0_41,plain,
( in(X1,X2)
| X3 != relation_composition(X4,X5)
| X2 != relation_dom(X4)
| X6 != relation_dom(X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X5)
| ~ in(X1,X6) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_42,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
<=> ( in(X1,relation_dom(X3))
& in(apply(X3,X1),relation_dom(X2)) ) ) ) ),
inference(assume_negation,[status(cth)],[t21_funct_1]) ).
cnf(c_0_43,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),relation_composition(X3,X4))
| X2 != apply(X4,X5)
| X5 != apply(X3,X1)
| ~ relation(X4)
| ~ relation(X3)
| ~ function(X4)
| ~ function(X3)
| ~ in(X5,relation_dom(X4))
| ~ in(X1,relation_dom(X3)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_36]),c_0_37]) ).
cnf(c_0_44,plain,
( in(esk4_5(X1,X2,X3,X4,X5),X6)
| X3 != relation_composition(X1,X2)
| X6 != relation_dom(X2)
| ~ relation(X2)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X3) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,plain,
( esk4_5(X1,X2,X3,X4,X5) = apply(X1,X4)
| X3 != relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ function(X1)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X3)
| ~ in(X4,relation_dom(X1)) ),
inference(spm,[status(thm)],[c_0_40,c_0_22]) ).
cnf(c_0_46,plain,
( in(X1,X2)
| X3 != relation_dom(relation_composition(X4,X5))
| X2 != relation_dom(X4)
| ~ relation(X4)
| ~ relation(X5)
| ~ in(X1,X3) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_41]),c_0_37]) ).
fof(c_0_47,negated_conjecture,
( relation(esk16_0)
& function(esk16_0)
& relation(esk17_0)
& function(esk17_0)
& ( ~ in(esk15_0,relation_dom(relation_composition(esk17_0,esk16_0)))
| ~ in(esk15_0,relation_dom(esk17_0))
| ~ in(apply(esk17_0,esk15_0),relation_dom(esk16_0)) )
& ( in(esk15_0,relation_dom(esk17_0))
| in(esk15_0,relation_dom(relation_composition(esk17_0,esk16_0))) )
& ( in(apply(esk17_0,esk15_0),relation_dom(esk16_0))
| in(esk15_0,relation_dom(relation_composition(esk17_0,esk16_0))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])]) ).
cnf(c_0_48,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,apply(X2,X3))),relation_composition(X4,X2))
| X3 != apply(X4,X1)
| ~ relation(X2)
| ~ relation(X4)
| ~ function(X2)
| ~ function(X4)
| ~ in(X3,relation_dom(X2))
| ~ in(X1,relation_dom(X4)) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_43]),c_0_17]) ).
cnf(c_0_49,plain,
( in(esk4_5(X1,X2,X3,X4,X5),X6)
| X3 != relation_composition(X1,X2)
| X6 != relation_dom(X2)
| ~ relation(X2)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),X3) ),
inference(spm,[status(thm)],[c_0_44,c_0_17]) ).
cnf(c_0_50,plain,
( esk4_5(X1,X2,X3,X4,X5) = apply(X1,X4)
| X3 != relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ function(X1)
| ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),X3)
| ~ in(X4,relation_dom(X1)) ),
inference(spm,[status(thm)],[c_0_45,c_0_17]) ).
cnf(c_0_51,plain,
( in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ relation(X4)
| ~ in(X1,relation_dom(relation_composition(X3,X4))) ),
inference(er,[status(thm)],[c_0_46]) ).
cnf(c_0_52,negated_conjecture,
( in(esk15_0,relation_dom(esk17_0))
| in(esk15_0,relation_dom(relation_composition(esk17_0,esk16_0))) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_53,negated_conjecture,
relation(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_54,negated_conjecture,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_55,plain,
( in(X1,X2)
| X2 != relation_dom(relation_composition(X3,X4))
| X5 != apply(X3,X1)
| ~ relation(X4)
| ~ relation(X3)
| ~ function(X4)
| ~ function(X3)
| ~ in(X5,relation_dom(X4))
| ~ in(X1,relation_dom(X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_48]),c_0_37]) ).
cnf(c_0_56,plain,
( in(esk4_5(X1,X2,X3,X4,esk1_3(X3,X5,X4)),X6)
| X3 != relation_composition(X1,X2)
| X6 != relation_dom(X2)
| X5 != relation_dom(X3)
| ~ relation(X2)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(X4,X5) ),
inference(spm,[status(thm)],[c_0_49,c_0_35]) ).
cnf(c_0_57,plain,
( esk4_5(X1,X2,X3,X4,esk1_3(X3,X5,X4)) = apply(X1,X4)
| X3 != relation_composition(X1,X2)
| X5 != relation_dom(X3)
| ~ relation(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ function(X1)
| ~ in(X4,relation_dom(X1))
| ~ in(X4,X5) ),
inference(spm,[status(thm)],[c_0_50,c_0_35]) ).
cnf(c_0_58,negated_conjecture,
( in(esk15_0,relation_dom(esk17_0))
| in(esk15_0,X1)
| X1 != relation_dom(esk17_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_54])]) ).
cnf(c_0_59,plain,
( in(X1,relation_dom(relation_composition(X2,X3)))
| X4 != apply(X2,X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ function(X3)
| ~ function(X2)
| ~ in(X4,relation_dom(X3))
| ~ in(X1,relation_dom(X2)) ),
inference(er,[status(thm)],[c_0_55]) ).
cnf(c_0_60,negated_conjecture,
( in(apply(esk17_0,esk15_0),relation_dom(esk16_0))
| in(esk15_0,relation_dom(relation_composition(esk17_0,esk16_0))) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_61,negated_conjecture,
function(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_62,plain,
( in(apply(X1,X2),X3)
| X4 != relation_composition(X1,X5)
| X3 != relation_dom(X5)
| X6 != relation_dom(X4)
| ~ relation(X5)
| ~ relation(X4)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X2,X6) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_63,negated_conjecture,
( ~ in(esk15_0,relation_dom(relation_composition(esk17_0,esk16_0)))
| ~ in(esk15_0,relation_dom(esk17_0))
| ~ in(apply(esk17_0,esk15_0),relation_dom(esk16_0)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_64,negated_conjecture,
in(esk15_0,relation_dom(esk17_0)),
inference(er,[status(thm)],[c_0_58]) ).
cnf(c_0_65,negated_conjecture,
( in(esk15_0,relation_dom(relation_composition(esk17_0,esk16_0)))
| in(X1,relation_dom(relation_composition(X2,esk16_0)))
| apply(esk17_0,esk15_0) != apply(X2,X1)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X1,relation_dom(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_54]),c_0_61])]) ).
cnf(c_0_66,negated_conjecture,
function(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_67,plain,
( in(apply(X1,X2),X3)
| X4 != relation_dom(relation_composition(X1,X5))
| X3 != relation_dom(X5)
| ~ relation(X5)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X2,X4) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_62]),c_0_37]) ).
cnf(c_0_68,negated_conjecture,
( ~ in(esk15_0,relation_dom(relation_composition(esk17_0,esk16_0)))
| ~ in(apply(esk17_0,esk15_0),relation_dom(esk16_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]) ).
cnf(c_0_69,negated_conjecture,
in(esk15_0,relation_dom(relation_composition(esk17_0,esk16_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_64]),c_0_53]),c_0_66])]) ).
cnf(c_0_70,plain,
( in(apply(X1,X2),X3)
| X3 != relation_dom(X4)
| ~ relation(X4)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(relation_composition(X1,X4)))
| ~ in(X2,relation_dom(X1)) ),
inference(er,[status(thm)],[c_0_67]) ).
cnf(c_0_71,negated_conjecture,
~ in(apply(esk17_0,esk15_0),relation_dom(esk16_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69])]) ).
cnf(c_0_72,negated_conjecture,
( in(apply(esk17_0,esk15_0),X1)
| X1 != relation_dom(esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_69]),c_0_54]),c_0_53]),c_0_66]),c_0_64])]) ).
cnf(c_0_73,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_71,c_0_72]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU213+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.32 % Computer : n004.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Wed Aug 23 21:41:08 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.18/0.56 start to proof: theBenchmark
% 239.99/240.12 % Version : CSE_E---1.5
% 239.99/240.12 % Problem : theBenchmark.p
% 239.99/240.12 % Proof found
% 239.99/240.12 % SZS status Theorem for theBenchmark.p
% 239.99/240.12 % SZS output start Proof
% See solution above
% 239.99/240.13 % Total time : 239.429000 s
% 239.99/240.13 % SZS output end Proof
% 239.99/240.13 % Total time : 239.442000 s
%------------------------------------------------------------------------------