%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU283+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 : n017.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 05:11:21 PM UTC 2026
% Result : Theorem 8.24s 5.64s
% Output : CNFRefutation 8.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 7
% Syntax : Number of formulae : 115 ( 15 unt; 0 def)
% Number of atoms : 502 ( 214 equ)
% Maximal formula atoms : 70 ( 4 avg)
% Number of connectives : 569 ( 182 ~; 295 |; 65 &)
% ( 9 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 2 con; 0-3 aty)
% Number of variables : 241 ( 16 sgn 68 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_funct_1__e16_22__wellord2__1,axiom,
! [X1] :
( ! [X2,X3,X4] :
( ( in(X2,X1)
& X3 = singleton(X2)
& in(X2,X1)
& X4 = singleton(X2) )
=> X3 = X4 )
=> ? [X2] :
( relation(X2)
& function(X2)
& ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& in(X3,X1)
& X4 = singleton(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_funct_1__e16_22__wellord2__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_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(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(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(s2_funct_1__e16_22__wellord2__1,conjecture,
! [X1] :
( ( ! [X2,X3,X4] :
( ( in(X2,X1)
& X3 = singleton(X2)
& X4 = singleton(X2) )
=> X3 = X4 )
& ! [X2] :
~ ( in(X2,X1)
& ! [X3] : X3 != singleton(X2) ) )
=> ? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = singleton(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_funct_1__e16_22__wellord2__1) ).
fof(c_0_7,plain,
! [X1] :
( ! [X2,X3,X4] :
( ( in(X2,X1)
& X3 = singleton(X2)
& in(X2,X1)
& X4 = singleton(X2) )
=> X3 = X4 )
=> ? [X2] :
( relation(X2)
& function(X2)
& ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& X4 = singleton(X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[s1_funct_1__e16_22__wellord2__1]) ).
fof(c_0_8,plain,
! [X73,X78,X79,X80,X81] :
( ( relation(esk8_1(X73))
| in(esk5_1(X73),X73) )
& ( function(esk8_1(X73))
| in(esk5_1(X73),X73) )
& ( in(X78,X73)
| ~ in(ordered_pair(X78,X79),esk8_1(X73))
| in(esk5_1(X73),X73) )
& ( X79 = singleton(X78)
| ~ in(ordered_pair(X78,X79),esk8_1(X73))
| in(esk5_1(X73),X73) )
& ( ~ in(X80,X73)
| X81 != singleton(X80)
| in(ordered_pair(X80,X81),esk8_1(X73))
| in(esk5_1(X73),X73) )
& ( relation(esk8_1(X73))
| esk6_1(X73) = singleton(esk5_1(X73)) )
& ( function(esk8_1(X73))
| esk6_1(X73) = singleton(esk5_1(X73)) )
& ( in(X78,X73)
| ~ in(ordered_pair(X78,X79),esk8_1(X73))
| esk6_1(X73) = singleton(esk5_1(X73)) )
& ( X79 = singleton(X78)
| ~ in(ordered_pair(X78,X79),esk8_1(X73))
| esk6_1(X73) = singleton(esk5_1(X73)) )
& ( ~ in(X80,X73)
| X81 != singleton(X80)
| in(ordered_pair(X80,X81),esk8_1(X73))
| esk6_1(X73) = singleton(esk5_1(X73)) )
& ( relation(esk8_1(X73))
| in(esk5_1(X73),X73) )
& ( function(esk8_1(X73))
| in(esk5_1(X73),X73) )
& ( in(X78,X73)
| ~ in(ordered_pair(X78,X79),esk8_1(X73))
| in(esk5_1(X73),X73) )
& ( X79 = singleton(X78)
| ~ in(ordered_pair(X78,X79),esk8_1(X73))
| in(esk5_1(X73),X73) )
& ( ~ in(X80,X73)
| X81 != singleton(X80)
| in(ordered_pair(X80,X81),esk8_1(X73))
| in(esk5_1(X73),X73) )
& ( relation(esk8_1(X73))
| esk7_1(X73) = singleton(esk5_1(X73)) )
& ( function(esk8_1(X73))
| esk7_1(X73) = singleton(esk5_1(X73)) )
& ( in(X78,X73)
| ~ in(ordered_pair(X78,X79),esk8_1(X73))
| esk7_1(X73) = singleton(esk5_1(X73)) )
& ( X79 = singleton(X78)
| ~ in(ordered_pair(X78,X79),esk8_1(X73))
| esk7_1(X73) = singleton(esk5_1(X73)) )
& ( ~ in(X80,X73)
| X81 != singleton(X80)
| in(ordered_pair(X80,X81),esk8_1(X73))
| esk7_1(X73) = singleton(esk5_1(X73)) )
& ( relation(esk8_1(X73))
| esk6_1(X73) != esk7_1(X73) )
& ( function(esk8_1(X73))
| esk6_1(X73) != esk7_1(X73) )
& ( in(X78,X73)
| ~ in(ordered_pair(X78,X79),esk8_1(X73))
| esk6_1(X73) != esk7_1(X73) )
& ( X79 = singleton(X78)
| ~ in(ordered_pair(X78,X79),esk8_1(X73))
| esk6_1(X73) != esk7_1(X73) )
& ( ~ in(X80,X73)
| X81 != singleton(X80)
| in(ordered_pair(X80,X81),esk8_1(X73))
| esk6_1(X73) != esk7_1(X73) ) ),
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)],[c_0_7])])])])])]) ).
fof(c_0_9,plain,
! [X99,X100] : ordered_pair(X99,X100) = unordered_pair(unordered_pair(X99,X100),singleton(X99)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
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(ordered_pair(X1,X3),esk8_1(X2))
| esk6_1(X2) = singleton(esk5_1(X2))
| ~ in(X1,X2)
| X3 != singleton(X1) ),
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,
! [X84,X85] : unordered_pair(X84,X85) = unordered_pair(X85,X84),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_14,plain,
! [X86,X87,X88] :
( ( X88 != apply(X86,X87)
| in(ordered_pair(X87,X88),X86)
| ~ in(X87,relation_dom(X86))
| ~ relation(X86)
| ~ function(X86) )
& ( ~ in(ordered_pair(X87,X88),X86)
| X88 = apply(X86,X87)
| ~ in(X87,relation_dom(X86))
| ~ relation(X86)
| ~ function(X86) )
& ( X88 != apply(X86,X87)
| X88 = empty_set
| in(X87,relation_dom(X86))
| ~ relation(X86)
| ~ function(X86) )
& ( X88 != empty_set
| X88 = apply(X86,X87)
| in(X87,relation_dom(X86))
| ~ relation(X86)
| ~ function(X86) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_15,plain,
! [X89,X90,X91,X93,X94,X95,X97] :
( ( ~ in(X91,X90)
| in(ordered_pair(X91,esk9_3(X89,X90,X91)),X89)
| X90 != relation_dom(X89)
| ~ relation(X89) )
& ( ~ in(ordered_pair(X93,X94),X89)
| in(X93,X90)
| X90 != relation_dom(X89)
| ~ relation(X89) )
& ( ~ in(esk10_2(X89,X95),X95)
| ~ in(ordered_pair(esk10_2(X89,X95),X97),X89)
| X95 = relation_dom(X89)
| ~ relation(X89) )
& ( in(esk10_2(X89,X95),X95)
| in(ordered_pair(esk10_2(X89,X95),esk11_2(X89,X95)),X89)
| X95 = relation_dom(X89)
| ~ relation(X89) ) ),
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_16,plain,
( esk6_1(X2) = singleton(esk5_1(X2))
| in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),esk8_1(X2))
| X3 != singleton(X1)
| ~ in(X1,X2) ),
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]) ).
fof(c_0_18,plain,
! [X119,X120] :
( ( ~ in(esk18_2(X119,X120),X119)
| ~ in(esk18_2(X119,X120),X120)
| X119 = X120 )
& ( in(esk18_2(X119,X120),X119)
| in(esk18_2(X119,X120),X120)
| X119 = X120 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(c_0_19,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_14]) ).
cnf(c_0_20,plain,
( in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( singleton(esk5_1(X1)) = esk6_1(X1)
| in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),esk8_1(X1))
| X3 != singleton(X2)
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( in(esk18_2(X1,X2),X1)
| in(esk18_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2)
| X1 != apply(X2,X3)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X3,relation_dom(X2)) ),
inference(rw,[status(thm)],[c_0_19,c_0_12]) ).
cnf(c_0_24,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_20,c_0_12]) ).
cnf(c_0_25,plain,
( singleton(esk5_1(X1)) = esk6_1(X1)
| X1 = X2
| in(unordered_pair(singleton(esk18_2(X1,X2)),unordered_pair(esk18_2(X1,X2),X3)),esk8_1(X1))
| in(esk18_2(X1,X2),X2)
| X3 != singleton(esk18_2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( relation(esk8_1(X1))
| esk6_1(X1) = singleton(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,plain,
( relation(esk8_1(X1))
| esk7_1(X1) = singleton(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_28,plain,
( relation(esk8_1(X1))
| esk6_1(X1) != esk7_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_29,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3)
| X2 != apply(X3,X1)
| ~ function(X3)
| ~ relation(X3)
| ~ in(X1,relation_dom(X3)) ),
inference(rw,[status(thm)],[c_0_23,c_0_17]) ).
cnf(c_0_30,plain,
( in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X4)),X3) ),
inference(rw,[status(thm)],[c_0_24,c_0_17]) ).
cnf(c_0_31,plain,
( singleton(esk5_1(X1)) = esk6_1(X1)
| X1 = X2
| in(unordered_pair(singleton(esk18_2(X1,X2)),unordered_pair(esk18_2(X1,X2),singleton(esk18_2(X1,X2)))),esk8_1(X1))
| in(esk18_2(X1,X2),X2) ),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
relation(esk8_1(X1)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_33,plain,
( in(X1,X2)
| esk6_1(X2) = singleton(esk5_1(X2))
| ~ in(ordered_pair(X1,X3),esk8_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_34,plain,
( X1 = relation_dom(X2)
| in(unordered_pair(singleton(esk18_2(X1,relation_dom(X2))),unordered_pair(esk18_2(X1,relation_dom(X2)),X3)),X2)
| in(esk18_2(X1,relation_dom(X2)),X1)
| X3 != apply(X2,esk18_2(X1,relation_dom(X2)))
| ~ function(X2)
| ~ relation(X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_22]) ).
cnf(c_0_35,plain,
( singleton(esk5_1(X1)) = esk6_1(X1)
| X1 = X2
| in(esk18_2(X1,X2),X2)
| in(esk18_2(X1,X2),X3)
| X3 != relation_dom(esk8_1(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_36,plain,
( esk6_1(X2) = singleton(esk5_1(X2))
| in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),esk8_1(X2)) ),
inference(rw,[status(thm)],[c_0_33,c_0_12]) ).
cnf(c_0_37,plain,
( X1 = relation_dom(X2)
| in(unordered_pair(singleton(esk18_2(X1,relation_dom(X2))),unordered_pair(esk18_2(X1,relation_dom(X2)),apply(X2,esk18_2(X1,relation_dom(X2))))),X2)
| in(esk18_2(X1,relation_dom(X2)),X1)
| ~ function(X2)
| ~ relation(X2) ),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_38,plain,
( function(esk8_1(X1))
| esk6_1(X1) = singleton(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_39,plain,
( singleton(esk5_1(X1)) = esk6_1(X1)
| X1 = X2
| in(esk18_2(X1,X2),relation_dom(esk8_1(X1)))
| in(esk18_2(X1,X2),X2) ),
inference(er,[status(thm)],[c_0_35]) ).
cnf(c_0_40,plain,
( in(ordered_pair(X1,X3),esk8_1(X2))
| esk7_1(X2) = singleton(esk5_1(X2))
| ~ in(X1,X2)
| X3 != singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_41,negated_conjecture,
~ ! [X1] :
( ( ! [X2,X3,X4] :
( ( in(X2,X1)
& X3 = singleton(X2)
& X4 = singleton(X2) )
=> X3 = X4 )
& ! [X2] :
~ ( in(X2,X1)
& ! [X3] : X3 != singleton(X2) ) )
=> ? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = singleton(X3) ) ) ),
inference(assume_negation,[status(cth)],[s2_funct_1__e16_22__wellord2__1]) ).
cnf(c_0_42,plain,
( singleton(esk5_1(X1)) = esk6_1(X1)
| in(X2,X1)
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),esk8_1(X1)) ),
inference(rw,[status(thm)],[c_0_36,c_0_17]) ).
cnf(c_0_43,plain,
( singleton(esk5_1(X1)) = esk6_1(X1)
| X2 = relation_dom(esk8_1(X1))
| in(unordered_pair(singleton(esk18_2(X2,relation_dom(esk8_1(X1)))),unordered_pair(esk18_2(X2,relation_dom(esk8_1(X1))),apply(esk8_1(X1),esk18_2(X2,relation_dom(esk8_1(X1)))))),esk8_1(X1))
| in(esk18_2(X2,relation_dom(esk8_1(X1))),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_32])]) ).
cnf(c_0_44,plain,
( X1 = X2
| ~ in(esk18_2(X1,X2),X1)
| ~ in(esk18_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_45,plain,
( singleton(esk5_1(X1)) = esk6_1(X1)
| relation_dom(esk8_1(X1)) = X1
| in(esk18_2(X1,relation_dom(esk8_1(X1))),relation_dom(esk8_1(X1))) ),
inference(ef,[status(thm)],[c_0_39]) ).
cnf(c_0_46,plain,
( esk7_1(X2) = singleton(esk5_1(X2))
| in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),esk8_1(X2))
| X3 != singleton(X1)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_40,c_0_12]) ).
fof(c_0_47,negated_conjecture,
! [X63,X64,X65,X66,X68] :
( ( ~ in(X63,esk1_0)
| X64 != singleton(X63)
| X65 != singleton(X63)
| X64 = X65 )
& ( ~ in(X66,esk1_0)
| esk2_1(X66) = singleton(X66) )
& ( in(esk3_1(X68),esk1_0)
| ~ relation(X68)
| ~ function(X68)
| relation_dom(X68) != esk1_0 )
& ( apply(X68,esk3_1(X68)) != singleton(esk3_1(X68))
| ~ relation(X68)
| ~ function(X68)
| relation_dom(X68) != esk1_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])])]) ).
cnf(c_0_48,plain,
( singleton(esk5_1(X1)) = esk6_1(X1)
| X2 = relation_dom(esk8_1(X1))
| in(esk18_2(X2,relation_dom(esk8_1(X1))),X2)
| in(esk18_2(X2,relation_dom(esk8_1(X1))),X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,plain,
( singleton(esk5_1(X1)) = esk6_1(X1)
| relation_dom(esk8_1(X1)) = X1
| ~ in(esk18_2(X1,relation_dom(esk8_1(X1))),X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
( singleton(esk5_1(X1)) = esk7_1(X1)
| in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),esk8_1(X1))
| X3 != singleton(X2)
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[c_0_46,c_0_17]) ).
cnf(c_0_51,negated_conjecture,
( in(esk3_1(X1),esk1_0)
| ~ relation(X1)
| ~ function(X1)
| relation_dom(X1) != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_52,plain,
( singleton(esk5_1(X1)) = esk6_1(X1)
| relation_dom(esk8_1(X1)) = X1 ),
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_48]),c_0_49]) ).
cnf(c_0_53,plain,
( singleton(esk5_1(X1)) = esk7_1(X1)
| X1 = X2
| in(unordered_pair(singleton(esk18_2(X1,X2)),unordered_pair(esk18_2(X1,X2),X3)),esk8_1(X1))
| in(esk18_2(X1,X2),X2)
| X3 != singleton(esk18_2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_50,c_0_22]) ).
cnf(c_0_54,negated_conjecture,
( singleton(esk5_1(X1)) = esk6_1(X1)
| in(esk3_1(esk8_1(X1)),esk1_0)
| X1 != esk1_0 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_32])]),c_0_38]) ).
cnf(c_0_55,plain,
( singleton(esk5_1(X1)) = esk7_1(X1)
| X1 = X2
| in(unordered_pair(singleton(esk18_2(X1,X2)),unordered_pair(esk18_2(X1,X2),singleton(esk18_2(X1,X2)))),esk8_1(X1))
| in(esk18_2(X1,X2),X2) ),
inference(er,[status(thm)],[c_0_53]) ).
cnf(c_0_56,negated_conjecture,
( singleton(esk5_1(esk1_0)) = esk6_1(esk1_0)
| in(esk3_1(esk8_1(esk1_0)),esk1_0) ),
inference(er,[status(thm)],[c_0_54]) ).
cnf(c_0_57,plain,
( in(X1,X2)
| esk7_1(X2) = singleton(esk5_1(X2))
| ~ in(ordered_pair(X1,X3),esk8_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_58,plain,
( singleton(esk5_1(X1)) = esk7_1(X1)
| X1 = X2
| in(esk18_2(X1,X2),X2)
| in(esk18_2(X1,X2),X3)
| X3 != relation_dom(esk8_1(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_55]),c_0_32])]) ).
cnf(c_0_59,negated_conjecture,
( singleton(esk5_1(esk1_0)) = esk6_1(esk1_0)
| in(unordered_pair(singleton(esk3_1(esk8_1(esk1_0))),unordered_pair(esk3_1(esk8_1(esk1_0)),X1)),esk8_1(esk1_0))
| X1 != singleton(esk3_1(esk8_1(esk1_0))) ),
inference(spm,[status(thm)],[c_0_21,c_0_56]) ).
cnf(c_0_60,plain,
( esk7_1(X2) = singleton(esk5_1(X2))
| in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),esk8_1(X2)) ),
inference(rw,[status(thm)],[c_0_57,c_0_12]) ).
cnf(c_0_61,plain,
( function(esk8_1(X1))
| esk7_1(X1) = singleton(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_62,plain,
( singleton(esk5_1(X1)) = esk7_1(X1)
| X1 = X2
| in(esk18_2(X1,X2),relation_dom(esk8_1(X1)))
| in(esk18_2(X1,X2),X2) ),
inference(er,[status(thm)],[c_0_58]) ).
cnf(c_0_63,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_14]) ).
cnf(c_0_64,negated_conjecture,
( singleton(esk5_1(esk1_0)) = esk6_1(esk1_0)
| in(unordered_pair(singleton(esk3_1(esk8_1(esk1_0))),unordered_pair(esk3_1(esk8_1(esk1_0)),singleton(esk3_1(esk8_1(esk1_0))))),esk8_1(esk1_0)) ),
inference(er,[status(thm)],[c_0_59]) ).
cnf(c_0_65,plain,
( singleton(esk5_1(X1)) = esk7_1(X1)
| in(X2,X1)
| ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),esk8_1(X1)) ),
inference(rw,[status(thm)],[c_0_60,c_0_17]) ).
cnf(c_0_66,plain,
( singleton(esk5_1(X1)) = esk7_1(X1)
| X2 = relation_dom(esk8_1(X1))
| in(unordered_pair(singleton(esk18_2(X2,relation_dom(esk8_1(X1)))),unordered_pair(esk18_2(X2,relation_dom(esk8_1(X1))),apply(esk8_1(X1),esk18_2(X2,relation_dom(esk8_1(X1)))))),esk8_1(X1))
| in(esk18_2(X2,relation_dom(esk8_1(X1))),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_61]),c_0_32])]) ).
cnf(c_0_67,plain,
( singleton(esk5_1(X1)) = esk7_1(X1)
| relation_dom(esk8_1(X1)) = X1
| in(esk18_2(X1,relation_dom(esk8_1(X1))),relation_dom(esk8_1(X1))) ),
inference(ef,[status(thm)],[c_0_62]) ).
cnf(c_0_68,plain,
( X2 = apply(X3,X1)
| ~ relation(X3)
| ~ function(X3)
| ~ in(X1,relation_dom(X3))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_63,c_0_12]) ).
cnf(c_0_69,negated_conjecture,
( singleton(esk5_1(esk1_0)) = esk6_1(esk1_0)
| in(esk3_1(esk8_1(esk1_0)),X1)
| X1 != relation_dom(esk8_1(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_64]),c_0_32])]) ).
cnf(c_0_70,plain,
( singleton(esk5_1(X1)) = esk7_1(X1)
| X2 = relation_dom(esk8_1(X1))
| in(esk18_2(X2,relation_dom(esk8_1(X1))),X2)
| in(esk18_2(X2,relation_dom(esk8_1(X1))),X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_71,plain,
( singleton(esk5_1(X1)) = esk7_1(X1)
| relation_dom(esk8_1(X1)) = X1
| ~ in(esk18_2(X1,relation_dom(esk8_1(X1))),X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_67]) ).
cnf(c_0_72,plain,
( X1 = apply(X2,X3)
| ~ function(X2)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),X2)
| ~ in(X3,relation_dom(X2)) ),
inference(rw,[status(thm)],[c_0_68,c_0_17]) ).
cnf(c_0_73,negated_conjecture,
( singleton(esk5_1(esk1_0)) = esk6_1(esk1_0)
| in(esk3_1(esk8_1(esk1_0)),relation_dom(esk8_1(esk1_0))) ),
inference(er,[status(thm)],[c_0_69]) ).
cnf(c_0_74,plain,
( singleton(esk5_1(X1)) = esk7_1(X1)
| relation_dom(esk8_1(X1)) = X1 ),
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_70]),c_0_71]) ).
cnf(c_0_75,negated_conjecture,
( apply(X1,esk3_1(X1)) != singleton(esk3_1(X1))
| ~ relation(X1)
| ~ function(X1)
| relation_dom(X1) != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_76,negated_conjecture,
( apply(esk8_1(esk1_0),esk3_1(esk8_1(esk1_0))) = singleton(esk3_1(esk8_1(esk1_0)))
| singleton(esk5_1(esk1_0)) = esk6_1(esk1_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_64]),c_0_32])]),c_0_73]),c_0_38]) ).
cnf(c_0_77,negated_conjecture,
( singleton(esk5_1(X1)) = esk7_1(X1)
| in(esk3_1(esk8_1(X1)),esk1_0)
| X1 != esk1_0 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_74]),c_0_32])]),c_0_61]) ).
cnf(c_0_78,negated_conjecture,
singleton(esk5_1(esk1_0)) = esk6_1(esk1_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_32])]),c_0_38]),c_0_52]) ).
cnf(c_0_79,negated_conjecture,
( esk7_1(esk1_0) = esk6_1(esk1_0)
| in(esk3_1(esk8_1(esk1_0)),esk1_0) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_77]),c_0_78]) ).
cnf(c_0_80,negated_conjecture,
( esk7_1(esk1_0) = esk6_1(esk1_0)
| in(unordered_pair(singleton(esk3_1(esk8_1(esk1_0))),unordered_pair(esk3_1(esk8_1(esk1_0)),X1)),esk8_1(esk1_0))
| X1 != singleton(esk3_1(esk8_1(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_79]),c_0_78])]) ).
cnf(c_0_81,negated_conjecture,
( esk7_1(esk1_0) = esk6_1(esk1_0)
| in(unordered_pair(singleton(esk3_1(esk8_1(esk1_0))),unordered_pair(esk3_1(esk8_1(esk1_0)),singleton(esk3_1(esk8_1(esk1_0))))),esk8_1(esk1_0)) ),
inference(er,[status(thm)],[c_0_80]) ).
cnf(c_0_82,negated_conjecture,
( esk7_1(esk1_0) = esk6_1(esk1_0)
| in(esk3_1(esk8_1(esk1_0)),X1)
| X1 != relation_dom(esk8_1(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_81]),c_0_32])]) ).
cnf(c_0_83,negated_conjecture,
( esk7_1(esk1_0) = esk6_1(esk1_0)
| in(esk3_1(esk8_1(esk1_0)),relation_dom(esk8_1(esk1_0))) ),
inference(er,[status(thm)],[c_0_82]) ).
cnf(c_0_84,plain,
( in(esk10_2(X1,X2),X2)
| in(ordered_pair(esk10_2(X1,X2),esk11_2(X1,X2)),X1)
| X2 = relation_dom(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_85,negated_conjecture,
( apply(esk8_1(esk1_0),esk3_1(esk8_1(esk1_0))) = singleton(esk3_1(esk8_1(esk1_0)))
| esk7_1(esk1_0) = esk6_1(esk1_0)
| ~ function(esk8_1(esk1_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_81]),c_0_32])]),c_0_83]) ).
cnf(c_0_86,plain,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),esk8_1(X2))
| esk6_1(X2) != esk7_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_87,plain,
( X2 = relation_dom(X1)
| in(esk10_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk10_2(X1,X2),esk11_2(X1,X2)),singleton(esk10_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_84,c_0_12]) ).
cnf(c_0_88,negated_conjecture,
( apply(esk8_1(esk1_0),esk3_1(esk8_1(esk1_0))) = singleton(esk3_1(esk8_1(esk1_0)))
| esk7_1(esk1_0) = esk6_1(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_61]),c_0_78])]) ).
cnf(c_0_89,plain,
( in(X1,X2)
| esk7_1(X2) != esk6_1(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),esk8_1(X2)) ),
inference(rw,[status(thm)],[c_0_86,c_0_12]) ).
cnf(c_0_90,plain,
( X1 = relation_dom(X2)
| in(unordered_pair(singleton(esk10_2(X2,X1)),unordered_pair(esk10_2(X2,X1),esk11_2(X2,X1))),X2)
| in(esk10_2(X2,X1),X1)
| ~ relation(X2) ),
inference(rw,[status(thm)],[c_0_87,c_0_17]) ).
cnf(c_0_91,negated_conjecture,
( esk7_1(esk1_0) = esk6_1(esk1_0)
| relation_dom(esk8_1(esk1_0)) != esk1_0
| ~ function(esk8_1(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_88]),c_0_32])]) ).
cnf(c_0_92,plain,
( in(X1,X2)
| esk7_1(X2) != esk6_1(X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),esk8_1(X2)) ),
inference(rw,[status(thm)],[c_0_89,c_0_17]) ).
cnf(c_0_93,plain,
( X1 = relation_dom(esk8_1(X2))
| in(unordered_pair(singleton(esk10_2(esk8_1(X2),X1)),unordered_pair(esk10_2(esk8_1(X2),X1),esk11_2(esk8_1(X2),X1))),esk8_1(X2))
| in(esk10_2(esk8_1(X2),X1),X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_32]) ).
cnf(c_0_94,negated_conjecture,
( esk7_1(esk1_0) = esk6_1(esk1_0)
| ~ function(esk8_1(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_74]),c_0_78])]) ).
cnf(c_0_95,plain,
( in(ordered_pair(X1,X3),esk8_1(X2))
| ~ in(X1,X2)
| X3 != singleton(X1)
| esk6_1(X2) != esk7_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_96,plain,
( X1 = relation_dom(esk8_1(X2))
| in(esk10_2(esk8_1(X2),X1),X1)
| in(esk10_2(esk8_1(X2),X1),X2)
| esk7_1(X2) != esk6_1(X2) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_97,negated_conjecture,
esk7_1(esk1_0) = esk6_1(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_61]),c_0_78])]) ).
cnf(c_0_98,plain,
( in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),esk8_1(X2))
| X3 != singleton(X1)
| esk7_1(X2) != esk6_1(X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_95,c_0_12]) ).
cnf(c_0_99,negated_conjecture,
( X1 = relation_dom(esk8_1(esk1_0))
| in(esk10_2(esk8_1(esk1_0),X1),esk1_0)
| in(esk10_2(esk8_1(esk1_0),X1),X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_100,plain,
( X2 = relation_dom(X1)
| ~ in(esk10_2(X1,X2),X2)
| ~ in(ordered_pair(esk10_2(X1,X2),X3),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_101,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk8_1(X3))
| esk7_1(X3) != esk6_1(X3)
| X2 != singleton(X1)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_98,c_0_17]) ).
cnf(c_0_102,negated_conjecture,
( relation_dom(esk8_1(esk1_0)) = esk1_0
| in(esk10_2(esk8_1(esk1_0),esk1_0),esk1_0) ),
inference(ef,[status(thm)],[c_0_99]) ).
cnf(c_0_103,plain,
( X2 = relation_dom(X1)
| ~ relation(X1)
| ~ in(esk10_2(X1,X2),X2)
| ~ in(unordered_pair(unordered_pair(esk10_2(X1,X2),X3),singleton(esk10_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[c_0_100,c_0_12]) ).
cnf(c_0_104,negated_conjecture,
( relation_dom(esk8_1(esk1_0)) = esk1_0
| in(unordered_pair(singleton(esk10_2(esk8_1(esk1_0),esk1_0)),unordered_pair(esk10_2(esk8_1(esk1_0),esk1_0),X1)),esk8_1(esk1_0))
| X1 != singleton(esk10_2(esk8_1(esk1_0),esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_97])]) ).
cnf(c_0_105,plain,
( X1 = relation_dom(X2)
| ~ relation(X2)
| ~ in(unordered_pair(singleton(esk10_2(X2,X1)),unordered_pair(esk10_2(X2,X1),X3)),X2)
| ~ in(esk10_2(X2,X1),X1) ),
inference(rw,[status(thm)],[c_0_103,c_0_17]) ).
cnf(c_0_106,negated_conjecture,
( relation_dom(esk8_1(esk1_0)) = esk1_0
| in(unordered_pair(singleton(esk10_2(esk8_1(esk1_0),esk1_0)),unordered_pair(esk10_2(esk8_1(esk1_0),esk1_0),singleton(esk10_2(esk8_1(esk1_0),esk1_0)))),esk8_1(esk1_0)) ),
inference(er,[status(thm)],[c_0_104]) ).
cnf(c_0_107,plain,
( function(esk8_1(X1))
| esk6_1(X1) != esk7_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_108,negated_conjecture,
relation_dom(esk8_1(esk1_0)) = esk1_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_32])]),c_0_102]) ).
cnf(c_0_109,negated_conjecture,
function(esk8_1(esk1_0)),
inference(spm,[status(thm)],[c_0_107,c_0_97]) ).
cnf(c_0_110,negated_conjecture,
in(esk3_1(esk8_1(esk1_0)),esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_108]),c_0_109]),c_0_32])]) ).
cnf(c_0_111,negated_conjecture,
( in(unordered_pair(singleton(esk3_1(esk8_1(esk1_0))),unordered_pair(esk3_1(esk8_1(esk1_0)),X1)),esk8_1(esk1_0))
| X1 != singleton(esk3_1(esk8_1(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_110]),c_0_97])]) ).
cnf(c_0_112,negated_conjecture,
in(unordered_pair(singleton(esk3_1(esk8_1(esk1_0))),unordered_pair(esk3_1(esk8_1(esk1_0)),singleton(esk3_1(esk8_1(esk1_0))))),esk8_1(esk1_0)),
inference(er,[status(thm)],[c_0_111]) ).
cnf(c_0_113,negated_conjecture,
apply(esk8_1(esk1_0),esk3_1(esk8_1(esk1_0))) = singleton(esk3_1(esk8_1(esk1_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_72,c_0_112]),c_0_109]),c_0_32]),c_0_108]),c_0_110])]) ).
cnf(c_0_114,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_113]),c_0_108]),c_0_109]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU283+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 : n017.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 02:52:28 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 8.24/5.64 % Version : CSE_E---1.7
% 8.24/5.64 % Problem : theBenchmark.p
% 8.24/5.64 % SZS status Theorem for theBenchmark.p
% 8.24/5.64 % SZS output start CNFRefutation
% See solution above
% 8.24/5.66 % Total time : 4.371s
%------------------------------------------------------------------------------