%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU214+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n014.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 05:11:05 PM UTC 2026
% Result : Theorem 17.51s 11.89s
% Output : CNFRefutation 17.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 66 ( 21 unt; 0 def)
% Number of atoms : 292 ( 60 equ)
% Maximal formula atoms : 38 ( 4 avg)
% Number of connectives : 389 ( 163 ~; 169 |; 31 &)
% ( 8 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-5 aty)
% Number of variables : 154 ( 4 sgn 55 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t22_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
=> apply(relation_composition(X3,X2),X1) = apply(X2,apply(X3,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_1) ).
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/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(dt_k5_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(fc1_funct_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& relation(X2)
& function(X2) )
=> ( relation(relation_composition(X1,X2))
& function(relation_composition(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(c_0_8,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]) ).
fof(c_0_9,plain,
! [X69,X70,X71] :
( ( X71 != apply(X69,X70)
| in(ordered_pair(X70,X71),X69)
| ~ in(X70,relation_dom(X69))
| ~ relation(X69)
| ~ function(X69) )
& ( ~ in(ordered_pair(X70,X71),X69)
| X71 = apply(X69,X70)
| ~ in(X70,relation_dom(X69))
| ~ relation(X69)
| ~ function(X69) )
& ( X71 != apply(X69,X70)
| X71 = empty_set
| in(X70,relation_dom(X69))
| ~ relation(X69)
| ~ function(X69) )
& ( X71 != empty_set
| X71 = apply(X69,X70)
| in(X70,relation_dom(X69))
| ~ relation(X69)
| ~ function(X69) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_10,plain,
! [X82,X83] : ordered_pair(X82,X83) = unordered_pair(unordered_pair(X82,X83),singleton(X82)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_11,plain,
! [X84,X85,X86,X87,X88,X90,X91,X92,X95] :
( ( in(ordered_pair(X87,esk4_5(X84,X85,X86,X87,X88)),X84)
| ~ in(ordered_pair(X87,X88),X86)
| X86 != relation_composition(X84,X85)
| ~ relation(X86)
| ~ relation(X85)
| ~ relation(X84) )
& ( in(ordered_pair(esk4_5(X84,X85,X86,X87,X88),X88),X85)
| ~ in(ordered_pair(X87,X88),X86)
| X86 != relation_composition(X84,X85)
| ~ relation(X86)
| ~ relation(X85)
| ~ relation(X84) )
& ( ~ in(ordered_pair(X90,X92),X84)
| ~ in(ordered_pair(X92,X91),X85)
| in(ordered_pair(X90,X91),X86)
| X86 != relation_composition(X84,X85)
| ~ relation(X86)
| ~ relation(X85)
| ~ relation(X84) )
& ( ~ in(ordered_pair(esk5_3(X84,X85,X86),esk6_3(X84,X85,X86)),X86)
| ~ in(ordered_pair(esk5_3(X84,X85,X86),X95),X84)
| ~ in(ordered_pair(X95,esk6_3(X84,X85,X86)),X85)
| X86 = relation_composition(X84,X85)
| ~ relation(X86)
| ~ relation(X85)
| ~ relation(X84) )
& ( in(ordered_pair(esk5_3(X84,X85,X86),esk7_3(X84,X85,X86)),X84)
| in(ordered_pair(esk5_3(X84,X85,X86),esk6_3(X84,X85,X86)),X86)
| X86 = relation_composition(X84,X85)
| ~ relation(X86)
| ~ relation(X85)
| ~ relation(X84) )
& ( in(ordered_pair(esk7_3(X84,X85,X86),esk6_3(X84,X85,X86)),X85)
| in(ordered_pair(esk5_3(X84,X85,X86),esk6_3(X84,X85,X86)),X86)
| X86 = relation_composition(X84,X85)
| ~ relation(X86)
| ~ relation(X85)
| ~ relation(X84) ) ),
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])])])])])]) ).
cnf(c_0_12,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_9]) ).
cnf(c_0_13,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
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,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
=> apply(relation_composition(X3,X2),X1) = apply(X2,apply(X3,X1)) ) ) ),
inference(assume_negation,[status(cth)],[t22_funct_1]) ).
cnf(c_0_16,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_11]) ).
cnf(c_0_17,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_12,c_0_13]) ).
cnf(c_0_18,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,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)))
& apply(relation_composition(esk17_0,esk16_0),esk15_0) != apply(esk16_0,apply(esk17_0,esk15_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
fof(c_0_20,plain,
! [X72,X73,X74,X76,X77,X78,X80] :
( ( ~ in(X74,X73)
| in(ordered_pair(X74,esk1_3(X72,X73,X74)),X72)
| X73 != relation_dom(X72)
| ~ relation(X72) )
& ( ~ in(ordered_pair(X76,X77),X72)
| in(X76,X73)
| X73 != relation_dom(X72)
| ~ relation(X72) )
& ( ~ in(esk2_2(X72,X78),X78)
| ~ in(ordered_pair(esk2_2(X72,X78),X80),X72)
| X78 = relation_dom(X72)
| ~ relation(X72) )
& ( in(esk2_2(X72,X78),X78)
| in(ordered_pair(esk2_2(X72,X78),esk3_2(X72,X78)),X72)
| X78 = relation_dom(X72)
| ~ relation(X72) ) ),
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])])])])])]) ).
cnf(c_0_21,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_16,c_0_13]),c_0_13]) ).
fof(c_0_22,plain,
! [X97,X98] :
( ~ relation(X97)
| ~ relation(X98)
| relation(relation_composition(X97,X98)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])]) ).
cnf(c_0_23,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,apply(X2,X1))),X2)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X1,relation_dom(X2)) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_17]),c_0_18]) ).
cnf(c_0_24,negated_conjecture,
in(esk15_0,relation_dom(relation_composition(esk17_0,esk16_0))),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,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_21,c_0_18]) ).
cnf(c_0_27,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0))),relation_composition(esk17_0,esk16_0))
| ~ relation(relation_composition(esk17_0,esk16_0))
| ~ function(relation_composition(esk17_0,esk16_0)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,negated_conjecture,
relation(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_31,plain,
! [X103,X104] :
( ( relation(relation_composition(X103,X104))
| ~ relation(X103)
| ~ function(X103)
| ~ relation(X104)
| ~ function(X104) )
& ( function(relation_composition(X103,X104))
| ~ relation(X103)
| ~ function(X103)
| ~ relation(X104)
| ~ function(X104) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_funct_1])])]) ).
cnf(c_0_32,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_25,c_0_13]) ).
cnf(c_0_33,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk4_5(X2,X3,relation_composition(X2,X3),X1,X4))),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X4),singleton(X1)),relation_composition(X2,X3)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_26]),c_0_27]) ).
cnf(c_0_34,negated_conjecture,
( in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0))),relation_composition(esk17_0,esk16_0))
| ~ function(relation_composition(esk17_0,esk16_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_27]),c_0_29]),c_0_30])]) ).
cnf(c_0_35,plain,
( function(relation_composition(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,negated_conjecture,
function(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_37,negated_conjecture,
function(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_38,plain,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X2) ),
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_39,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk4_5(X2,X3,relation_composition(X2,X3),X1,X4))),X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X4)),relation_composition(X2,X3)) ),
inference(spm,[status(thm)],[c_0_33,c_0_18]) ).
cnf(c_0_40,negated_conjecture,
in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0))),relation_composition(esk17_0,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_34,c_0_35]),c_0_29]),c_0_30]),c_0_36]),c_0_37])]) ).
cnf(c_0_41,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_11]) ).
cnf(c_0_42,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_9]) ).
cnf(c_0_43,plain,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_18]) ).
cnf(c_0_44,negated_conjecture,
in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,esk4_5(esk17_0,esk16_0,relation_composition(esk17_0,esk16_0),esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0)))),esk17_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_29]),c_0_30])]) ).
cnf(c_0_45,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_41,c_0_13]),c_0_13]) ).
cnf(c_0_46,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_42,c_0_13]) ).
cnf(c_0_47,negated_conjecture,
in(esk15_0,relation_dom(esk17_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_30])]) ).
cnf(c_0_48,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_45,c_0_18]) ).
cnf(c_0_49,negated_conjecture,
( X1 = apply(esk17_0,esk15_0)
| ~ in(unordered_pair(unordered_pair(esk15_0,X1),singleton(esk15_0)),esk17_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_30]),c_0_37])]) ).
cnf(c_0_50,plain,
( X1 = empty_set
| in(X3,relation_dom(X2))
| X1 != apply(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_51,plain,
( in(unordered_pair(unordered_pair(X1,esk4_5(X2,X3,relation_composition(X2,X3),X4,X1)),singleton(esk4_5(X2,X3,relation_composition(X2,X3),X4,X1))),X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X4,X1),singleton(X4)),relation_composition(X2,X3)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_48]),c_0_27]) ).
cnf(c_0_52,negated_conjecture,
( X1 = apply(esk17_0,esk15_0)
| ~ in(unordered_pair(singleton(esk15_0),unordered_pair(esk15_0,X1)),esk17_0) ),
inference(spm,[status(thm)],[c_0_49,c_0_18]) ).
cnf(c_0_53,plain,
( apply(X1,X2) = empty_set
| in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(er,[status(thm)],[c_0_50]) ).
cnf(c_0_54,plain,
( in(unordered_pair(unordered_pair(X1,esk4_5(X2,X3,relation_composition(X2,X3),X4,X1)),singleton(esk4_5(X2,X3,relation_composition(X2,X3),X4,X1))),X3)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),relation_composition(X2,X3)) ),
inference(spm,[status(thm)],[c_0_51,c_0_18]) ).
cnf(c_0_55,negated_conjecture,
esk4_5(esk17_0,esk16_0,relation_composition(esk17_0,esk16_0),esk15_0,apply(relation_composition(esk17_0,esk16_0),esk15_0)) = apply(esk17_0,esk15_0),
inference(spm,[status(thm)],[c_0_52,c_0_44]) ).
cnf(c_0_56,plain,
( apply(X1,X2) = empty_set
| X3 = apply(X1,X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_53]) ).
cnf(c_0_57,negated_conjecture,
in(unordered_pair(singleton(apply(esk17_0,esk15_0)),unordered_pair(apply(esk17_0,esk15_0),apply(relation_composition(esk17_0,esk16_0),esk15_0))),esk16_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_54,c_0_40]),c_0_55]),c_0_55]),c_0_29]),c_0_30])]),c_0_18]),c_0_18]) ).
cnf(c_0_58,plain,
( apply(X1,X2) = empty_set
| X3 = apply(X1,X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_18]) ).
cnf(c_0_59,negated_conjecture,
apply(relation_composition(esk17_0,esk16_0),esk15_0) != apply(esk16_0,apply(esk17_0,esk15_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_60,negated_conjecture,
in(apply(esk17_0,esk15_0),relation_dom(esk16_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_57]),c_0_29])]) ).
cnf(c_0_61,negated_conjecture,
apply(esk16_0,apply(esk17_0,esk15_0)) = empty_set,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_57]),c_0_29]),c_0_36])]),c_0_59]) ).
cnf(c_0_62,negated_conjecture,
( X1 = empty_set
| ~ in(unordered_pair(unordered_pair(apply(esk17_0,esk15_0),X1),singleton(apply(esk17_0,esk15_0))),esk16_0) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_60]),c_0_29]),c_0_36])]),c_0_61]) ).
cnf(c_0_63,negated_conjecture,
( X1 = empty_set
| ~ in(unordered_pair(singleton(apply(esk17_0,esk15_0)),unordered_pair(apply(esk17_0,esk15_0),X1)),esk16_0) ),
inference(spm,[status(thm)],[c_0_62,c_0_18]) ).
cnf(c_0_64,negated_conjecture,
apply(relation_composition(esk17_0,esk16_0),esk15_0) != empty_set,
inference(rw,[status(thm)],[c_0_59,c_0_61]) ).
cnf(c_0_65,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_57]),c_0_64]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU214+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n014.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:49:06 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 17.51/11.89 % Version : CSE_E---1.7
% 17.51/11.89 % Problem : theBenchmark.p
% 17.51/11.89 % SZS status Theorem for theBenchmark.p
% 17.51/11.89 % SZS output start CNFRefutation
% See solution above
% 17.61/11.95 % Total time : 9.385s
%------------------------------------------------------------------------------