%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU181+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 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 : Tue May 5 05:10:58 PM UTC 2026
% Result : Theorem 79.19s 47.87s
% Output : CNFRefutation 79.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 93 ( 12 unt; 0 def)
% Number of atoms : 393 ( 142 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 531 ( 231 ~; 274 |; 12 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 1 con; 0-3 aty)
% Number of variables : 226 ( 8 sgn 44 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(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_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(t37_relat_1,conjecture,
! [X1] :
( relation(X1)
=> ( relation_rng(X1) = relation_dom(relation_inverse(X1))
& relation_dom(X1) = relation_rng(relation_inverse(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
fof(involutiveness_k4_relat_1,axiom,
! [X1] :
( relation(X1)
=> relation_inverse(relation_inverse(X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_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(c_0_8,plain,
! [X77,X78,X79,X81,X82,X83,X85] :
( ( ~ in(X79,X78)
| in(ordered_pair(X79,esk2_3(X77,X78,X79)),X77)
| X78 != relation_dom(X77)
| ~ relation(X77) )
& ( ~ in(ordered_pair(X81,X82),X77)
| in(X81,X78)
| X78 != relation_dom(X77)
| ~ relation(X77) )
& ( ~ in(esk3_2(X77,X83),X83)
| ~ in(ordered_pair(esk3_2(X77,X83),X85),X77)
| X83 = relation_dom(X77)
| ~ relation(X77) )
& ( in(esk3_2(X77,X83),X83)
| in(ordered_pair(esk3_2(X77,X83),esk4_2(X77,X83)),X77)
| X83 = relation_dom(X77)
| ~ relation(X77) ) ),
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_9,plain,
! [X97,X98] : ordered_pair(X97,X98) = unordered_pair(unordered_pair(X97,X98),singleton(X97)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_10,plain,
! [X99,X100,X101,X102,X103,X104] :
( ( ~ in(ordered_pair(X101,X102),X100)
| in(ordered_pair(X102,X101),X99)
| X100 != relation_inverse(X99)
| ~ relation(X100)
| ~ relation(X99) )
& ( ~ in(ordered_pair(X104,X103),X99)
| in(ordered_pair(X103,X104),X100)
| X100 != relation_inverse(X99)
| ~ relation(X100)
| ~ relation(X99) )
& ( ~ in(ordered_pair(esk8_2(X99,X100),esk9_2(X99,X100)),X100)
| ~ in(ordered_pair(esk9_2(X99,X100),esk8_2(X99,X100)),X99)
| X100 = relation_inverse(X99)
| ~ relation(X100)
| ~ relation(X99) )
& ( in(ordered_pair(esk8_2(X99,X100),esk9_2(X99,X100)),X100)
| in(ordered_pair(esk9_2(X99,X100),esk8_2(X99,X100)),X99)
| X100 = relation_inverse(X99)
| ~ relation(X100)
| ~ relation(X99) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_relat_1])])])])])]) ).
fof(c_0_11,plain,
! [X87,X88,X89,X91,X92,X93,X95] :
( ( ~ in(X89,X88)
| in(ordered_pair(esk5_3(X87,X88,X89),X89),X87)
| X88 != relation_rng(X87)
| ~ relation(X87) )
& ( ~ in(ordered_pair(X92,X91),X87)
| in(X91,X88)
| X88 != relation_rng(X87)
| ~ relation(X87) )
& ( ~ in(esk6_2(X87,X93),X93)
| ~ in(ordered_pair(X95,esk6_2(X87,X93)),X87)
| X93 = relation_rng(X87)
| ~ relation(X87) )
& ( in(esk6_2(X87,X93),X93)
| in(ordered_pair(esk7_2(X87,X93),esk6_2(X87,X93)),X87)
| X93 = relation_rng(X87)
| ~ relation(X87) ) ),
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])])])])])]) ).
cnf(c_0_12,plain,
( in(esk3_2(X1,X2),X2)
| in(ordered_pair(esk3_2(X1,X2),esk4_2(X1,X2)),X1)
| X2 = relation_dom(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X67,X68] : unordered_pair(X67,X68) = unordered_pair(X68,X67),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ( relation_rng(X1) = relation_dom(relation_inverse(X1))
& relation_dom(X1) = relation_rng(relation_inverse(X1)) ) ),
inference(assume_negation,[status(cth)],[t37_relat_1]) ).
cnf(c_0_16,plain,
( in(ordered_pair(X2,X1),X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_inverse(X3)
| ~ relation(X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( in(ordered_pair(esk5_3(X3,X2,X1),X1),X3)
| ~ in(X1,X2)
| X2 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,plain,
( X2 = relation_dom(X1)
| in(esk3_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk3_2(X1,X2),esk4_2(X1,X2)),singleton(esk3_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_20,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_21,negated_conjecture,
( relation(esk16_0)
& ( relation_rng(esk16_0) != relation_dom(relation_inverse(esk16_0))
| relation_dom(esk16_0) != relation_rng(relation_inverse(esk16_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
cnf(c_0_22,plain,
( X2 = relation_dom(X1)
| ~ in(esk3_2(X1,X2),X2)
| ~ in(ordered_pair(esk3_2(X1,X2),X3),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,plain,
( in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),X4)
| X4 != relation_inverse(X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_13]),c_0_13]) ).
cnf(c_0_24,plain,
( in(unordered_pair(unordered_pair(esk5_3(X3,X2,X1),X1),singleton(esk5_3(X3,X2,X1))),X3)
| X2 != relation_rng(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_25,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_18,c_0_13]) ).
cnf(c_0_26,plain,
( X1 = relation_dom(X2)
| in(unordered_pair(singleton(esk3_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)],[c_0_19,c_0_20]) ).
cnf(c_0_27,negated_conjecture,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(esk3_2(X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(esk3_2(X1,X2),X3),singleton(esk3_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[c_0_22,c_0_13]) ).
cnf(c_0_29,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| X3 != relation_inverse(X4)
| ~ relation(X3)
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X2)),X4) ),
inference(spm,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_30,plain,
( in(unordered_pair(unordered_pair(X1,esk5_3(X2,X3,X1)),singleton(esk5_3(X2,X3,X1))),X2)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_31,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_25,c_0_20]) ).
cnf(c_0_32,negated_conjecture,
( X1 = relation_dom(esk16_0)
| in(unordered_pair(singleton(esk3_2(esk16_0,X1)),unordered_pair(esk3_2(esk16_0,X1),esk4_2(esk16_0,X1))),esk16_0)
| in(esk3_2(esk16_0,X1),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
( X1 = relation_dom(X2)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(esk3_2(X2,X1)),unordered_pair(esk3_2(X2,X1),X3)),X2)
| ~ in(esk3_2(X2,X1),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_20]) ).
cnf(c_0_34,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk5_3(X2,X3,X1))),X4)
| X4 != relation_inverse(X2)
| X3 != relation_rng(X2)
| ~ relation(X4)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_20]) ).
cnf(c_0_35,negated_conjecture,
( X1 = relation_dom(esk16_0)
| in(esk3_2(esk16_0,X1),X1)
| in(esk3_2(esk16_0,X1),X2)
| X2 != relation_dom(esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_27])]) ).
cnf(c_0_36,plain,
( X1 = relation_dom(X2)
| X2 != relation_inverse(X3)
| X4 != relation_rng(X3)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(esk3_2(X2,X1),X1)
| ~ in(esk3_2(X2,X1),X4) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( X1 = relation_dom(esk16_0)
| in(esk3_2(esk16_0,X1),relation_dom(esk16_0))
| in(esk3_2(esk16_0,X1),X1) ),
inference(er,[status(thm)],[c_0_35]) ).
cnf(c_0_38,plain,
( in(ordered_pair(X1,esk2_3(X3,X2,X1)),X3)
| ~ in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_39,negated_conjecture,
( X1 = relation_dom(esk16_0)
| in(esk3_2(esk16_0,X1),relation_dom(esk16_0))
| relation_inverse(X2) != esk16_0
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ in(esk3_2(esk16_0,X1),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_27])]) ).
cnf(c_0_40,plain,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_41,plain,
( in(unordered_pair(unordered_pair(X1,esk2_3(X3,X2,X1)),singleton(X1)),X3)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_38,c_0_13]) ).
cnf(c_0_42,negated_conjecture,
( X1 = relation_dom(esk16_0)
| in(esk3_2(esk16_0,X1),relation_dom(esk16_0))
| relation_inverse(X2) != esk16_0
| X1 != relation_rng(X2)
| ~ relation(X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_37]) ).
fof(c_0_43,plain,
! [X116] :
( ~ relation(X116)
| relation_inverse(relation_inverse(X116)) = X116 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1])]) ).
fof(c_0_44,plain,
! [X107] :
( ~ relation(X107)
| relation(relation_inverse(X107)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_relat_1])]) ).
cnf(c_0_45,plain,
( in(esk6_2(X1,X2),X2)
| in(ordered_pair(esk7_2(X1,X2),esk6_2(X1,X2)),X1)
| X2 = relation_rng(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_46,plain,
( in(X2,X4)
| X4 != relation_rng(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_40,c_0_13]) ).
cnf(c_0_47,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| X3 != relation_inverse(X4)
| ~ relation(X3)
| ~ relation(X4)
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X1)),X4) ),
inference(spm,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_48,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk2_3(X2,X3,X1))),X2)
| X3 != relation_dom(X2)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_41,c_0_20]) ).
cnf(c_0_49,negated_conjecture,
( relation_rng(X1) = relation_dom(esk16_0)
| in(esk3_2(esk16_0,relation_rng(X1)),relation_dom(esk16_0))
| relation_inverse(X1) != esk16_0
| ~ relation(X1) ),
inference(er,[status(thm)],[c_0_42]) ).
cnf(c_0_50,plain,
( relation_inverse(relation_inverse(X1)) = X1
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_51,plain,
( relation(relation_inverse(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,plain,
( X2 = relation_rng(X1)
| in(esk6_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk7_2(X1,X2),esk6_2(X1,X2)),singleton(esk7_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_45,c_0_13]) ).
cnf(c_0_53,plain,
( in(X1,X2)
| X2 != relation_rng(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X4),singleton(X4)),X3) ),
inference(spm,[status(thm)],[c_0_46,c_0_20]) ).
cnf(c_0_54,plain,
( in(unordered_pair(unordered_pair(X1,esk2_3(X2,X3,X1)),singleton(esk2_3(X2,X3,X1))),X4)
| X4 != relation_inverse(X2)
| X3 != relation_dom(X2)
| ~ relation(X4)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_20]) ).
cnf(c_0_55,negated_conjecture,
( relation_rng(relation_inverse(X1)) = relation_dom(esk16_0)
| in(esk3_2(esk16_0,relation_rng(relation_inverse(X1))),relation_dom(esk16_0))
| X1 != esk16_0
| ~ relation(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_56,plain,
( X1 = relation_rng(X2)
| in(unordered_pair(singleton(esk7_2(X2,X1)),unordered_pair(esk6_2(X2,X1),esk7_2(X2,X1))),X2)
| in(esk6_2(X2,X1),X1)
| ~ relation(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_20]),c_0_20]) ).
cnf(c_0_57,plain,
( in(X1,X2)
| X2 != relation_rng(X3)
| X3 != relation_inverse(X4)
| X5 != relation_dom(X4)
| ~ relation(X3)
| ~ relation(X4)
| ~ in(X1,X5) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,negated_conjecture,
( relation_rng(relation_inverse(esk16_0)) = relation_dom(esk16_0)
| in(esk3_2(esk16_0,relation_rng(relation_inverse(esk16_0))),relation_dom(esk16_0)) ),
inference(spm,[status(thm)],[c_0_55,c_0_27]) ).
cnf(c_0_59,plain,
( X2 = relation_rng(X1)
| ~ in(esk6_2(X1,X2),X2)
| ~ in(ordered_pair(X3,esk6_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_60,plain,
( in(X1,X2)
| X2 != relation_rng(X3)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X4),unordered_pair(X1,X4)),X3) ),
inference(spm,[status(thm)],[c_0_53,c_0_20]) ).
cnf(c_0_61,negated_conjecture,
( X1 = relation_rng(esk16_0)
| in(unordered_pair(singleton(esk7_2(esk16_0,X1)),unordered_pair(esk6_2(esk16_0,X1),esk7_2(esk16_0,X1))),esk16_0)
| in(esk6_2(esk16_0,X1),X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_27]) ).
cnf(c_0_62,negated_conjecture,
( relation_rng(relation_inverse(esk16_0)) = relation_dom(esk16_0)
| in(esk3_2(esk16_0,relation_rng(relation_inverse(esk16_0))),X1)
| relation_dom(esk16_0) != relation_dom(X2)
| X1 != relation_rng(X3)
| X3 != relation_inverse(X2)
| ~ relation(X3)
| ~ relation(X2) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,plain,
( X2 = relation_rng(X1)
| ~ relation(X1)
| ~ in(esk6_2(X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(X3,esk6_2(X1,X2)),singleton(X3)),X1) ),
inference(rw,[status(thm)],[c_0_59,c_0_13]) ).
cnf(c_0_64,negated_conjecture,
( X1 = relation_rng(esk16_0)
| in(esk6_2(esk16_0,X1),X1)
| in(esk6_2(esk16_0,X1),X2)
| X2 != relation_rng(esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_27])]) ).
cnf(c_0_65,negated_conjecture,
( relation_rng(relation_inverse(esk16_0)) = relation_dom(esk16_0)
| in(esk3_2(esk16_0,relation_rng(relation_inverse(esk16_0))),relation_rng(X1))
| relation_dom(esk16_0) != relation_dom(X2)
| X1 != relation_inverse(X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(er,[status(thm)],[c_0_62]) ).
cnf(c_0_66,plain,
( X1 = relation_rng(X2)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,esk6_2(X2,X1))),X2)
| ~ in(esk6_2(X2,X1),X1) ),
inference(rw,[status(thm)],[c_0_63,c_0_20]) ).
cnf(c_0_67,plain,
( in(X1,X2)
| X2 != relation_dom(X3)
| X3 != relation_inverse(X4)
| X5 != relation_rng(X4)
| ~ relation(X3)
| ~ relation(X4)
| ~ in(X1,X5) ),
inference(spm,[status(thm)],[c_0_31,c_0_34]) ).
cnf(c_0_68,negated_conjecture,
( X1 = relation_rng(esk16_0)
| in(esk6_2(esk16_0,X1),relation_rng(esk16_0))
| in(esk6_2(esk16_0,X1),X1) ),
inference(er,[status(thm)],[c_0_64]) ).
cnf(c_0_69,negated_conjecture,
( relation_rng(relation_inverse(esk16_0)) = relation_dom(esk16_0)
| in(esk3_2(esk16_0,relation_rng(relation_inverse(esk16_0))),relation_rng(relation_inverse(X1)))
| relation_dom(esk16_0) != relation_dom(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_65]),c_0_51]) ).
cnf(c_0_70,plain,
( X1 = relation_rng(X2)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X3),unordered_pair(esk6_2(X2,X1),X3)),X2)
| ~ in(esk6_2(X2,X1),X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_20]) ).
cnf(c_0_71,plain,
( in(unordered_pair(singleton(esk2_3(X1,X2,X3)),unordered_pair(X3,esk2_3(X1,X2,X3))),X4)
| X4 != relation_inverse(X1)
| X2 != relation_dom(X1)
| ~ relation(X4)
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_20]) ).
cnf(c_0_72,negated_conjecture,
( X1 = relation_rng(esk16_0)
| in(esk6_2(esk16_0,X1),X1)
| in(esk6_2(esk16_0,X1),X2)
| relation_rng(esk16_0) != relation_rng(X3)
| X2 != relation_dom(X4)
| X4 != relation_inverse(X3)
| ~ relation(X4)
| ~ relation(X3) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,plain,
( X1 = relation_dom(X2)
| X3 != relation_dom(X2)
| ~ relation(X2)
| ~ in(esk3_2(X2,X1),X1)
| ~ in(esk3_2(X2,X1),X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_48]) ).
cnf(c_0_74,negated_conjecture,
( relation_rng(relation_inverse(esk16_0)) = relation_dom(esk16_0)
| in(esk3_2(esk16_0,relation_rng(relation_inverse(esk16_0))),relation_rng(relation_inverse(esk16_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_69]),c_0_27])]) ).
cnf(c_0_75,plain,
( X1 = relation_rng(X2)
| X2 != relation_inverse(X3)
| X4 != relation_dom(X3)
| ~ relation(X2)
| ~ relation(X3)
| ~ in(esk6_2(X2,X1),X1)
| ~ in(esk6_2(X2,X1),X4) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_76,negated_conjecture,
( X1 = relation_rng(esk16_0)
| in(esk6_2(esk16_0,X1),X1)
| relation_rng(esk16_0) != relation_rng(X2)
| X1 != relation_dom(X3)
| X3 != relation_inverse(X2)
| ~ relation(X3)
| ~ relation(X2) ),
inference(ef,[status(thm)],[c_0_72]) ).
cnf(c_0_77,negated_conjecture,
( relation_rng(relation_inverse(esk16_0)) = relation_dom(esk16_0)
| X1 != relation_dom(esk16_0)
| ~ in(esk3_2(esk16_0,relation_rng(relation_inverse(esk16_0))),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_27])]) ).
cnf(c_0_78,negated_conjecture,
( X1 = relation_rng(esk16_0)
| in(esk6_2(esk16_0,X1),relation_rng(esk16_0))
| relation_inverse(X2) != esk16_0
| X3 != relation_dom(X2)
| ~ relation(X2)
| ~ in(esk6_2(esk16_0,X1),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_68]),c_0_27])]) ).
cnf(c_0_79,negated_conjecture,
( relation_dom(X1) = relation_rng(esk16_0)
| in(esk6_2(esk16_0,relation_dom(X1)),relation_dom(X1))
| relation_rng(esk16_0) != relation_rng(X2)
| X1 != relation_inverse(X2)
| ~ relation(X1)
| ~ relation(X2) ),
inference(er,[status(thm)],[c_0_76]) ).
cnf(c_0_80,negated_conjecture,
( relation_rng(esk16_0) != relation_dom(relation_inverse(esk16_0))
| relation_dom(esk16_0) != relation_rng(relation_inverse(esk16_0)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_81,negated_conjecture,
relation_rng(relation_inverse(esk16_0)) = relation_dom(esk16_0),
inference(spm,[status(thm)],[c_0_77,c_0_58]) ).
cnf(c_0_82,negated_conjecture,
( X1 = relation_rng(esk16_0)
| in(esk6_2(esk16_0,X1),relation_rng(esk16_0))
| relation_inverse(X2) != esk16_0
| X1 != relation_dom(X2)
| ~ relation(X2) ),
inference(spm,[status(thm)],[c_0_78,c_0_68]) ).
cnf(c_0_83,plain,
( in(unordered_pair(singleton(esk5_3(X1,X2,X3)),unordered_pair(X3,esk5_3(X1,X2,X3))),X1)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_20]) ).
cnf(c_0_84,negated_conjecture,
( relation_dom(relation_inverse(X1)) = relation_rng(esk16_0)
| in(esk6_2(esk16_0,relation_dom(relation_inverse(X1))),relation_dom(relation_inverse(X1)))
| relation_rng(esk16_0) != relation_rng(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_79]),c_0_51]) ).
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_80,c_0_81])]) ).
cnf(c_0_86,negated_conjecture,
( relation_dom(X1) = relation_rng(esk16_0)
| in(esk6_2(esk16_0,relation_dom(X1)),relation_rng(esk16_0))
| relation_inverse(X1) != esk16_0
| ~ relation(X1) ),
inference(er,[status(thm)],[c_0_82]) ).
cnf(c_0_87,plain,
( X1 = relation_rng(X2)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ in(esk6_2(X2,X1),X1)
| ~ in(esk6_2(X2,X1),X3) ),
inference(spm,[status(thm)],[c_0_70,c_0_83]) ).
cnf(c_0_88,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(er,[status(thm)],[c_0_84]),c_0_27])]),c_0_85]) ).
cnf(c_0_89,negated_conjecture,
( relation_dom(relation_inverse(X1)) = relation_rng(esk16_0)
| in(esk6_2(esk16_0,relation_dom(relation_inverse(X1))),relation_rng(esk16_0))
| X1 != esk16_0
| ~ relation(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_50]),c_0_51]) ).
cnf(c_0_90,negated_conjecture,
( X1 != relation_rng(esk16_0)
| ~ in(esk6_2(esk16_0,relation_dom(relation_inverse(esk16_0))),X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_27])]),c_0_85]) ).
cnf(c_0_91,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_89,c_0_27]),c_0_85]) ).
cnf(c_0_92,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_90,c_0_91]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU181+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n004.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:47:32 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 79.19/47.87 % Version : CSE_E---1.7
% 79.19/47.87 % Problem : theBenchmark.p
% 79.19/47.87 % SZS status Theorem for theBenchmark.p
% 79.19/47.87 % SZS output start CNFRefutation
% See solution above
% 79.42/48.12 % Total time : 38.106s
%------------------------------------------------------------------------------