%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU181+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:24:09 PM UTC 2026
% Result : Theorem 272.29s 35.51s
% Output : CNFRefutation 272.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 93 ( 14 unt; 0 def)
% Number of atoms : 321 ( 64 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 399 ( 171 ~; 199 |; 14 &)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 1 con; 0-3 aty)
% Number of variables : 212 ( 9 sgn 50 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d7_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_inverse(X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> in(ordered_pair(X4,X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_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(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(dt_k4_relat_1,axiom,
! [X1] :
( relation(X1)
=> relation(relation_inverse(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
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(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(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(t37_relat_1,conjecture,
! [X1] :
( relation(X1)
=> ( relation_dom(X1) = relation_rng(relation_inverse(X1))
& relation_rng(X1) = relation_dom(relation_inverse(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
fof(c_0_8,plain,
! [X39,X40,X41,X42,X43,X44] :
( ( ~ relation(X39)
| ~ relation(X40)
| X40 = relation_inverse(X39)
| in(ordered_pair(esk9_2(X39,X40),esk8_2(X39,X40)),X39)
| in(ordered_pair(esk8_2(X39,X40),esk9_2(X39,X40)),X40) )
& ( ~ relation(X39)
| ~ relation(X40)
| X40 = relation_inverse(X39)
| ~ in(ordered_pair(esk9_2(X39,X40),esk8_2(X39,X40)),X39)
| ~ in(ordered_pair(esk8_2(X39,X40),esk9_2(X39,X40)),X40) )
& ( ~ relation(X39)
| ~ relation(X40)
| X40 != relation_inverse(X39)
| in(ordered_pair(X43,X44),X40)
| ~ in(ordered_pair(X44,X43),X39) )
& ( ~ relation(X39)
| ~ relation(X40)
| X40 != relation_inverse(X39)
| in(ordered_pair(X42,X41),X39)
| ~ in(ordered_pair(X41,X42),X40) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[d7_relat_1])])])])])])]) ).
fof(c_0_9,plain,
! [X37,X38] : ordered_pair(X37,X38) = unordered_pair(unordered_pair(X37,X38),singleton(X37)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_10,plain,
! [X17,X18,X19,X21,X22,X23,X25] :
( ( ~ relation(X17)
| X23 = relation_dom(X17)
| in(ordered_pair(esk3_2(X17,X23),esk4_2(X17,X23)),X17)
| in(esk3_2(X17,X23),X23) )
& ( ~ relation(X17)
| X23 = relation_dom(X17)
| ~ in(ordered_pair(esk3_2(X17,X23),X25),X17)
| ~ in(esk3_2(X17,X23),X23) )
& ( ~ relation(X17)
| X18 != relation_dom(X17)
| in(X21,X18)
| ~ in(ordered_pair(X21,X22),X17) )
& ( ~ relation(X17)
| X18 != relation_dom(X17)
| in(ordered_pair(X19,esk2_3(X17,X18,X19)),X17)
| ~ in(X19,X18) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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])])])])])])]) ).
cnf(c_0_11,plain,
( ~ relation(X4)
| ~ relation(X3)
| X3 != relation_inverse(X4)
| ~ in(ordered_pair(X1,X2),X3)
| in(ordered_pair(X2,X1),X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X47] :
( relation(relation_inverse(X47))
| ~ relation(X47) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_relat_1])])]) ).
fof(c_0_14,plain,
! [X27,X28,X29,X31,X32,X33,X35] :
( ( ~ relation(X27)
| X33 = relation_rng(X27)
| in(ordered_pair(esk7_2(X27,X33),esk6_2(X27,X33)),X27)
| in(esk6_2(X27,X33),X33) )
& ( ~ relation(X27)
| X33 = relation_rng(X27)
| ~ in(ordered_pair(X35,esk6_2(X27,X33)),X27)
| ~ in(esk6_2(X27,X33),X33) )
& ( ~ relation(X27)
| X28 != relation_rng(X27)
| in(X31,X28)
| ~ in(ordered_pair(X32,X31),X27) )
& ( ~ relation(X27)
| X28 != relation_rng(X27)
| in(ordered_pair(esk5_3(X27,X28,X29),X29),X27)
| ~ in(X29,X28) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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])])])])])])]) ).
cnf(c_0_15,plain,
( ~ relation(X3)
| X4 != relation_dom(X3)
| ~ in(ordered_pair(X1,X2),X3)
| in(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| ~ relation(X3)
| ~ relation(X4)
| X3 != relation_inverse(X4)
| in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_12]) ).
cnf(c_0_17,plain,
( ~ relation(X1)
| relation(relation_inverse(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X7,X8] : unordered_pair(X7,X8) = unordered_pair(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_19,plain,
( ~ relation(X3)
| X2 != relation_rng(X3)
| ~ in(X1,X2)
| in(ordered_pair(esk5_3(X3,X2,X1),X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| ~ relation(X3)
| X4 != relation_dom(X3)
| in(X1,X4) ),
inference(rw,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_21,plain,
( ~ in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),relation_inverse(X3))
| ~ relation(X3)
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_16]),c_0_17]) ).
cnf(c_0_22,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( ~ in(X1,X2)
| ~ relation(X3)
| X2 != relation_rng(X3)
| in(unordered_pair(unordered_pair(esk5_3(X3,X2,X1),X1),singleton(esk5_3(X3,X2,X1))),X3) ),
inference(rw,[status(thm)],[c_0_19,c_0_12]) ).
cnf(c_0_24,plain,
( ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X2)
| ~ relation(X2)
| in(X1,relation_dom(X2)) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X2)),relation_inverse(X3))
| ~ relation(X3)
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( ~ in(X1,relation_rng(X2))
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X1,esk5_3(X2,relation_rng(X2),X1)),singleton(esk5_3(X2,relation_rng(X2),X1))),X2) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_22])]) ).
cnf(c_0_27,plain,
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X2)
| ~ relation(X2)
| in(X1,relation_dom(X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_28,plain,
( ~ in(X1,relation_rng(relation_inverse(X2)))
| ~ relation(X2)
| in(unordered_pair(singleton(X1),unordered_pair(X1,esk5_3(relation_inverse(X2),relation_rng(relation_inverse(X2)),X1))),X2) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_22]),c_0_17]) ).
fof(c_0_29,plain,
! [X11,X12,X13,X14,X15] :
( ( subset(X14,X15)
| ~ in(esk1_2(X14,X15),X15) )
& ( subset(X14,X15)
| in(esk1_2(X14,X15),X14) )
& ( in(X13,X12)
| ~ in(X13,X11)
| ~ subset(X11,X12) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_30,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ( relation_dom(X1) = relation_rng(relation_inverse(X1))
& relation_rng(X1) = relation_dom(relation_inverse(X1)) ) ),
inference(assume_negation,[status(cth)],[t37_relat_1]) ).
cnf(c_0_31,plain,
( ~ relation(X3)
| X4 != relation_rng(X3)
| ~ in(ordered_pair(X1,X2),X3)
| in(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_32,plain,
( ~ relation(X3)
| X2 != relation_dom(X3)
| ~ in(X1,X2)
| in(ordered_pair(X1,esk2_3(X3,X2,X1)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_33,plain,
( ~ in(X1,relation_rng(relation_inverse(X2)))
| ~ relation(X2)
| in(X1,relation_dom(X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
( subset(X1,X2)
| in(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_35,negated_conjecture,
( ( relation_dom(esk16_0) != relation_rng(relation_inverse(esk16_0))
| relation_rng(esk16_0) != relation_dom(relation_inverse(esk16_0)) )
& relation(esk16_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])]) ).
cnf(c_0_36,plain,
( ~ relation(X1)
| X2 = relation_dom(X1)
| in(ordered_pair(esk3_2(X1,X2),esk4_2(X1,X2)),X1)
| in(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_37,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| ~ relation(X3)
| X4 != relation_rng(X3)
| in(X2,X4) ),
inference(rw,[status(thm)],[c_0_31,c_0_12]) ).
cnf(c_0_38,plain,
( ~ in(X1,X2)
| ~ relation(X3)
| X2 != relation_dom(X3)
| in(unordered_pair(unordered_pair(X1,esk2_3(X3,X2,X1)),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_32,c_0_12]) ).
cnf(c_0_39,plain,
( ~ relation(X1)
| in(esk1_2(relation_rng(relation_inverse(X1)),X2),relation_dom(X1))
| subset(relation_rng(relation_inverse(X1)),X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,plain,
( ~ relation(X1)
| in(unordered_pair(unordered_pair(esk3_2(X1,X2),esk4_2(X1,X2)),singleton(esk3_2(X1,X2))),X1)
| in(esk3_2(X1,X2),X2)
| X2 = relation_dom(X1) ),
inference(rw,[status(thm)],[c_0_36,c_0_12]) ).
cnf(c_0_42,plain,
( ~ relation(X3)
| ~ relation(X4)
| X4 != relation_inverse(X3)
| ~ in(ordered_pair(X1,X2),X3)
| in(ordered_pair(X2,X1),X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_43,plain,
( ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2)
| ~ relation(X2)
| in(X1,relation_rng(X2)) ),
inference(er,[status(thm)],[c_0_37]) ).
cnf(c_0_44,plain,
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X1)),relation_inverse(X3))
| ~ relation(X3)
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_45,plain,
( ~ in(X1,relation_dom(X2))
| ~ relation(X2)
| in(unordered_pair(singleton(X1),unordered_pair(X1,esk2_3(X2,relation_dom(X2),X1))),X2) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_22])]) ).
cnf(c_0_46,plain,
( ~ relation(X1)
| ~ in(ordered_pair(esk3_2(X1,X2),X3),X1)
| ~ in(esk3_2(X1,X2),X2)
| X2 = relation_dom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_47,plain,
( ~ in(esk1_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_48,negated_conjecture,
( in(esk1_2(relation_rng(relation_inverse(esk16_0)),X1),relation_dom(esk16_0))
| subset(relation_rng(relation_inverse(esk16_0)),X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_49,plain,
( ~ relation(X2)
| in(esk3_2(X2,X1),X1)
| in(unordered_pair(singleton(esk3_2(X2,X1)),unordered_pair(esk3_2(X2,X1),esk4_2(X2,X1))),X2)
| X1 = relation_dom(X2) ),
inference(rw,[status(thm)],[c_0_41,c_0_22]) ).
cnf(c_0_50,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| ~ relation(X3)
| ~ relation(X4)
| X4 != relation_inverse(X3)
| in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_12]),c_0_12]) ).
cnf(c_0_51,plain,
( ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X3)),X2)
| ~ relation(X2)
| in(X1,relation_rng(X2)) ),
inference(spm,[status(thm)],[c_0_43,c_0_22]) ).
cnf(c_0_52,plain,
( ~ in(X1,relation_dom(relation_inverse(X2)))
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X1,esk2_3(relation_inverse(X2),relation_dom(relation_inverse(X2)),X1)),singleton(esk2_3(relation_inverse(X2),relation_dom(relation_inverse(X2)),X1))),X2) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_22]),c_0_17]) ).
cnf(c_0_53,plain,
( ~ in(unordered_pair(unordered_pair(esk3_2(X1,X2),X3),singleton(esk3_2(X1,X2))),X1)
| ~ in(esk3_2(X1,X2),X2)
| ~ relation(X1)
| X2 = relation_dom(X1) ),
inference(rw,[status(thm)],[c_0_46,c_0_12]) ).
cnf(c_0_54,plain,
( ~ in(X3,X1)
| ~ subset(X1,X2)
| in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_55,negated_conjecture,
subset(relation_rng(relation_inverse(esk16_0)),relation_dom(esk16_0)),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_56,negated_conjecture,
( in(esk3_2(esk16_0,X1),X1)
| in(unordered_pair(singleton(esk3_2(esk16_0,X1)),unordered_pair(esk3_2(esk16_0,X1),esk4_2(esk16_0,X1))),esk16_0)
| X1 = relation_dom(esk16_0) ),
inference(spm,[status(thm)],[c_0_49,c_0_40]) ).
cnf(c_0_57,plain,
( ~ in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),X3)
| ~ relation(X3)
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),relation_inverse(X3)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_50]),c_0_17]) ).
cnf(c_0_58,plain,
( ~ in(X1,relation_dom(relation_inverse(X2)))
| ~ relation(X2)
| in(X1,relation_rng(X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,plain,
( ~ relation(X1)
| X2 = relation_rng(X1)
| in(ordered_pair(esk7_2(X1,X2),esk6_2(X1,X2)),X1)
| in(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_60,plain,
( ~ in(esk3_2(X2,X1),X1)
| ~ in(unordered_pair(singleton(esk3_2(X2,X1)),unordered_pair(esk3_2(X2,X1),X3)),X2)
| ~ relation(X2)
| X1 = relation_dom(X2) ),
inference(spm,[status(thm)],[c_0_53,c_0_22]) ).
cnf(c_0_61,negated_conjecture,
( ~ in(X1,relation_rng(relation_inverse(esk16_0)))
| in(X1,relation_dom(esk16_0)) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_62,negated_conjecture,
( in(esk3_2(esk16_0,X1),X1)
| in(esk3_2(esk16_0,X1),relation_dom(esk16_0))
| X1 = relation_dom(esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_56]),c_0_40])]) ).
cnf(c_0_63,plain,
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X1)),X3)
| ~ relation(X3)
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),relation_inverse(X3)) ),
inference(spm,[status(thm)],[c_0_57,c_0_22]) ).
cnf(c_0_64,plain,
( ~ relation(X1)
| ~ in(ordered_pair(X3,esk6_2(X1,X2)),X1)
| ~ in(esk6_2(X1,X2),X2)
| X2 = relation_rng(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_65,plain,
( ~ relation(X1)
| in(esk1_2(relation_dom(relation_inverse(X1)),X2),relation_rng(X1))
| subset(relation_dom(relation_inverse(X1)),X2) ),
inference(spm,[status(thm)],[c_0_58,c_0_34]) ).
cnf(c_0_66,plain,
( ~ relation(X1)
| in(unordered_pair(unordered_pair(esk7_2(X1,X2),esk6_2(X1,X2)),singleton(esk7_2(X1,X2))),X1)
| in(esk6_2(X1,X2),X2)
| X2 = relation_rng(X1) ),
inference(rw,[status(thm)],[c_0_59,c_0_12]) ).
cnf(c_0_67,plain,
( ~ in(esk3_2(X2,X1),X1)
| ~ in(esk3_2(X2,X1),relation_dom(X2))
| ~ relation(X2)
| X1 = relation_dom(X2) ),
inference(spm,[status(thm)],[c_0_60,c_0_45]) ).
cnf(c_0_68,negated_conjecture,
( in(esk3_2(esk16_0,relation_rng(relation_inverse(esk16_0))),relation_dom(esk16_0))
| relation_rng(relation_inverse(esk16_0)) = relation_dom(esk16_0) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_69,plain,
( ~ in(X1,relation_dom(X2))
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X1,esk2_3(X2,relation_dom(X2),X1)),singleton(esk2_3(X2,relation_dom(X2),X1))),relation_inverse(X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_45]),c_0_22]) ).
cnf(c_0_70,plain,
( ~ in(unordered_pair(unordered_pair(X3,esk6_2(X1,X2)),singleton(X3)),X1)
| ~ in(esk6_2(X1,X2),X2)
| ~ relation(X1)
| X2 = relation_rng(X1) ),
inference(rw,[status(thm)],[c_0_64,c_0_12]) ).
cnf(c_0_71,negated_conjecture,
( in(esk1_2(relation_dom(relation_inverse(esk16_0)),X1),relation_rng(esk16_0))
| subset(relation_dom(relation_inverse(esk16_0)),X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_40]) ).
cnf(c_0_72,plain,
( ~ relation(X2)
| in(esk6_2(X2,X1),X1)
| in(unordered_pair(singleton(esk7_2(X2,X1)),unordered_pair(esk6_2(X2,X1),esk7_2(X2,X1))),X2)
| X1 = relation_rng(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_22]),c_0_22]) ).
cnf(c_0_73,negated_conjecture,
( ~ in(esk3_2(esk16_0,relation_rng(relation_inverse(esk16_0))),relation_rng(relation_inverse(esk16_0)))
| relation_rng(relation_inverse(esk16_0)) = relation_dom(esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_40])]) ).
cnf(c_0_74,plain,
( ~ in(X1,relation_dom(X2))
| ~ relation(X2)
| in(X1,relation_rng(relation_inverse(X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_69]),c_0_17]) ).
cnf(c_0_75,plain,
( ~ in(esk6_2(X2,X1),X1)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,esk6_2(X2,X1))),X2)
| ~ relation(X2)
| X1 = relation_rng(X2) ),
inference(rw,[status(thm)],[c_0_70,c_0_22]) ).
cnf(c_0_76,negated_conjecture,
subset(relation_dom(relation_inverse(esk16_0)),relation_rng(esk16_0)),
inference(spm,[status(thm)],[c_0_47,c_0_71]) ).
cnf(c_0_77,plain,
( ~ in(unordered_pair(singleton(X3),unordered_pair(X1,X3)),X2)
| ~ relation(X2)
| in(X1,relation_rng(X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_22]) ).
cnf(c_0_78,negated_conjecture,
( in(esk6_2(esk16_0,X1),X1)
| in(unordered_pair(singleton(esk7_2(esk16_0,X1)),unordered_pair(esk6_2(esk16_0,X1),esk7_2(esk16_0,X1))),esk16_0)
| X1 = relation_rng(esk16_0) ),
inference(spm,[status(thm)],[c_0_72,c_0_40]) ).
cnf(c_0_79,negated_conjecture,
( relation_dom(esk16_0) != relation_rng(relation_inverse(esk16_0))
| relation_rng(esk16_0) != relation_dom(relation_inverse(esk16_0)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_80,negated_conjecture,
relation_rng(relation_inverse(esk16_0)) = relation_dom(esk16_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_40])]),c_0_68]) ).
cnf(c_0_81,plain,
( ~ in(esk6_2(X2,X1),X1)
| ~ in(unordered_pair(singleton(X3),unordered_pair(esk6_2(X2,X1),X3)),X2)
| ~ relation(X2)
| X1 = relation_rng(X2) ),
inference(spm,[status(thm)],[c_0_75,c_0_22]) ).
cnf(c_0_82,plain,
( ~ in(X2,relation_rng(X1))
| ~ relation(X1)
| in(unordered_pair(singleton(esk5_3(X1,relation_rng(X1),X2)),unordered_pair(X2,esk5_3(X1,relation_rng(X1),X2))),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_83,negated_conjecture,
( ~ in(X1,relation_dom(relation_inverse(esk16_0)))
| in(X1,relation_rng(esk16_0)) ),
inference(spm,[status(thm)],[c_0_54,c_0_76]) ).
cnf(c_0_84,negated_conjecture,
( in(esk6_2(esk16_0,X1),X1)
| in(esk6_2(esk16_0,X1),relation_rng(esk16_0))
| X1 = relation_rng(esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_40])]) ).
cnf(c_0_85,negated_conjecture,
relation_dom(relation_inverse(esk16_0)) != relation_rng(esk16_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])]) ).
cnf(c_0_86,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X2)),X3)
| ~ relation(X3)
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),relation_inverse(X3)) ),
inference(spm,[status(thm)],[c_0_57,c_0_22]) ).
cnf(c_0_87,plain,
( ~ in(esk6_2(X2,X1),X1)
| ~ in(esk6_2(X2,X1),relation_rng(X2))
| ~ relation(X2)
| X1 = relation_rng(X2) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_88,negated_conjecture,
in(esk6_2(esk16_0,relation_dom(relation_inverse(esk16_0))),relation_rng(esk16_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]) ).
cnf(c_0_89,plain,
( ~ in(X1,relation_rng(X2))
| ~ relation(X2)
| in(unordered_pair(singleton(X1),unordered_pair(X1,esk5_3(X2,relation_rng(X2),X1))),relation_inverse(X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_26]),c_0_22]) ).
cnf(c_0_90,negated_conjecture,
~ in(esk6_2(esk16_0,relation_dom(relation_inverse(esk16_0))),relation_dom(relation_inverse(esk16_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_40])]),c_0_85]) ).
cnf(c_0_91,plain,
( ~ in(X1,relation_rng(X2))
| ~ relation(X2)
| in(X1,relation_dom(relation_inverse(X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_89]),c_0_17]) ).
cnf(c_0_92,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_40]),c_0_88])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU181+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 05:55:44 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 272.29/35.51 % Version: 3.5.1
% 272.29/35.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 272.29/35.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 272.29/35.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 272.29/35.51 % Starting new_bool_3 with 300s (1) cores
% 272.29/35.51 % Starting new_bool_1 with 300s (1) cores
% 272.29/35.51 % Starting sh5l with 300s (1) cores
% 272.29/35.51 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2140275 completed with status 0
% 272.29/35.51 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 272.29/35.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 272.29/35.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 272.29/35.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 272.29/35.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 272.29/35.51 % No SInE strategy applied
% 272.29/35.51 % Search class: FGHSM-FFMS31-MFFFFFNN
% 272.29/35.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 272.29/35.51 % Starting SubtermCWHack with 136s (1) cores
% 272.29/35.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 272.29/35.51 % Starting G-E--_107_C37_SOS_F1_PI_AE_Q4_CS_SP_PS_S0Y with 380s (1) cores
% 272.29/35.51 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 272.29/35.51 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AA with 136s (1) cores
% 272.29/35.51 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2140282 completed with status 0
% 272.29/35.51 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 272.29/35.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 272.29/35.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 272.29/35.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 272.29/35.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 272.29/35.51 % No SInE strategy applied
% 272.29/35.51 % Search class: FGHSM-FFMS31-MFFFFFNN
% 272.29/35.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 272.29/35.51 % Starting SubtermCWHack with 136s (1) cores
% 272.29/35.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 272.29/35.51 % Preprocessing time : 0.003 s
% 272.29/35.51 % Presaturation interreduction done
% 272.29/35.51
% 272.29/35.51 % Proof found!
% 272.29/35.51 % SZS status Theorem
% 272.29/35.51 % SZS output start CNFRefutation
% See solution above
% 272.29/35.51 % Parsed axioms : 39
% 272.29/35.51 % Removed by relevancy pruning/SinE : 0
% 272.29/35.51 % Initial clauses : 57
% 272.29/35.51 % Removed in clause preprocessing : 9
% 272.29/35.51 % Initial clauses in saturation : 48
% 272.29/35.51 % Processed clauses : 47127
% 272.29/35.51 % ...of these trivial : 9
% 272.29/35.51 % ...subsumed : 42990
% 272.29/35.51 % ...remaining for further processing : 4128
% 272.29/35.51 % Other redundant clauses eliminated : 8
% 272.29/35.51 % Clauses deleted for lack of memory : 0
% 272.29/35.51 % Backward-subsumed : 489
% 272.29/35.51 % Backward-rewritten : 82
% 272.29/35.51 % Generated clauses : 885611
% 272.29/35.51 % ...of the previous two non-redundant : 732595
% 272.29/35.51 % ...aggressively subsumed : 0
% 272.29/35.51 % Contextual simplify-reflections : 167
% 272.29/35.51 % Paramodulations : 885594
% 272.29/35.51 % Factorizations : 5
% 272.29/35.51 % NegExts : 0
% 272.29/35.51 % Equation resolutions : 8
% 272.29/35.51 % Disequality decompositions : 0
% 272.29/35.51 % Total rewrite steps : 1290569
% 272.29/35.51 % ...of those cached : 1290232
% 272.29/35.51 % Propositional unsat checks : 0
% 272.29/35.51 % Propositional check models : 0
% 272.29/35.51 % Propositional check unsatisfiable : 0
% 272.29/35.51 % Propositional clauses : 0
% 272.29/35.51 % Propositional clauses after purity: 0
% 272.29/35.51 % Propositional unsat core size : 0
% 272.29/35.51 % Propositional preprocessing time : 0.000
% 272.29/35.51 % Propositional encoding time : 0.000
% 272.29/35.51 % Propositional solver time : 0.000
% 272.29/35.51 % Success case prop preproc time : 0.000
% 272.29/35.51 % Success case prop encoding time : 0.000
% 272.29/35.51 % Success case prop solver time : 0.000
% 272.29/35.51 % Current number of processed clauses : 3500
% 272.29/35.51 % Positive orientable unit clauses : 48
% 272.29/35.51 % Positive unorientable unit clauses: 1
% 272.29/35.51 % Negative unit clauses : 30
% 272.29/35.51 % Non-unit-clauses : 3421
% 272.29/35.51 % Current number of unprocessed clauses: 670301
% 272.29/35.51 % ...number of literals in the above : 5039199
% 272.29/35.51 % Current number of archived formulas : 0
% 272.29/35.51 % Current number of archived clauses : 621
% 272.29/35.51 % Clause-clause subsumption calls (NU) : 9414693
% 272.29/35.51 % Rec. Clause-clause subsumption calls : 643001
% 272.29/35.51 % Non-unit clause-clause subsumptions : 22306
% 272.29/35.51 % Unit Clause-clause subsumption calls : 8947
% 272.29/35.51 % Rewrite failures with RHS unbound : 0
% 272.29/35.51 % BW rewrite match attempts : 93
% 272.29/35.51 % BW rewrite match successes : 13
% 272.29/35.51 % Condensation attempts : 0
% 272.29/35.51 % Condensation successes : 0
% 272.29/35.51 % Termbank termtop insertions : 23066331
% 272.29/35.51 % Search garbage collected termcells : 816
% 272.29/35.51
% 272.29/35.51 % -------------------------------------------------
% 272.29/35.51 % User time : 33.513 s
% 272.29/35.51 % System time : 0.955 s
% 272.29/35.51 % Total time : 34.468 s
% 272.29/35.51 % Maximum resident set size: 3660 pages
% 272.29/35.51
% 272.29/35.51 % -------------------------------------------------
% 272.29/35.51 % User time : 166.005 s
% 272.29/35.51 % System time : 4.885 s
% 272.29/35.51 % Total time : 170.890 s
% 272.29/35.51 % Maximum resident set size: 4864 pages
% 272.29/35.51 % E exiting
%------------------------------------------------------------------------------