%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU213+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 02:24:16 PM UTC 2026
% Result : Theorem 27.65s 5.00s
% Output : CNFRefutation 30.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 7
% Syntax : Number of formulae : 85 ( 14 unt; 0 def)
% Number of atoms : 491 ( 115 equ)
% Maximal formula atoms : 38 ( 5 avg)
% Number of connectives : 751 ( 345 ~; 352 |; 29 &)
% ( 10 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 5 ( 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 : 265 ( 6 sgn 51 !; 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/sandbox2/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/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(X6,X5),X2)
& in(ordered_pair(X4,X6),X1) ) ) ) ) ) ),
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(d4_funct_1,axiom,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2,X3] :
( ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) )
& ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(dt_k5_relat_1,axiom,
! [X1,X2] :
( ( relation(X2)
& relation(X1) )
=> relation(relation_composition(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(t21_funct_1,conjecture,
! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
<=> ( in(apply(X3,X1),relation_dom(X2))
& in(X1,relation_dom(X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
fof(c_0_7,plain,
! [X16,X17,X18,X20,X21,X22,X24] :
( ( ~ relation(X16)
| X22 = relation_dom(X16)
| in(ordered_pair(esk2_2(X16,X22),esk3_2(X16,X22)),X16)
| in(esk2_2(X16,X22),X22) )
& ( ~ relation(X16)
| X22 = relation_dom(X16)
| ~ in(ordered_pair(esk2_2(X16,X22),X24),X16)
| ~ in(esk2_2(X16,X22),X22) )
& ( ~ relation(X16)
| X17 != relation_dom(X16)
| in(X20,X17)
| ~ in(ordered_pair(X20,X21),X16) )
& ( ~ relation(X16)
| X17 != relation_dom(X16)
| in(ordered_pair(X18,esk1_3(X16,X17,X18)),X16)
| ~ in(X18,X17) ) ),
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])])])])])])]) ).
fof(c_0_8,plain,
! [X26,X27] : ordered_pair(X26,X27) = unordered_pair(unordered_pair(X26,X27),singleton(X26)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_9,plain,
! [X28,X29,X30,X31,X32,X34,X35,X36,X39] :
( ( ~ relation(X28)
| ~ relation(X29)
| ~ relation(X30)
| X30 = relation_composition(X28,X29)
| in(ordered_pair(esk5_3(X28,X29,X30),esk6_3(X28,X29,X30)),X30)
| in(ordered_pair(esk7_3(X28,X29,X30),esk6_3(X28,X29,X30)),X29) )
& ( ~ relation(X28)
| ~ relation(X29)
| ~ relation(X30)
| X30 = relation_composition(X28,X29)
| in(ordered_pair(esk5_3(X28,X29,X30),esk6_3(X28,X29,X30)),X30)
| in(ordered_pair(esk5_3(X28,X29,X30),esk7_3(X28,X29,X30)),X28) )
& ( ~ relation(X28)
| ~ relation(X29)
| ~ relation(X30)
| X30 = relation_composition(X28,X29)
| ~ in(ordered_pair(X39,esk6_3(X28,X29,X30)),X29)
| ~ in(ordered_pair(esk5_3(X28,X29,X30),X39),X28)
| ~ in(ordered_pair(esk5_3(X28,X29,X30),esk6_3(X28,X29,X30)),X30) )
& ( ~ relation(X28)
| ~ relation(X29)
| ~ relation(X30)
| X30 != relation_composition(X28,X29)
| in(ordered_pair(X34,X35),X30)
| ~ in(ordered_pair(X36,X35),X29)
| ~ in(ordered_pair(X34,X36),X28) )
& ( ~ relation(X28)
| ~ relation(X29)
| ~ relation(X30)
| X30 != relation_composition(X28,X29)
| ~ in(ordered_pair(X31,X32),X30)
| in(ordered_pair(esk4_5(X28,X29,X30,X31,X32),X32),X29) )
& ( ~ relation(X28)
| ~ relation(X29)
| ~ relation(X30)
| X30 != relation_composition(X28,X29)
| ~ in(ordered_pair(X31,X32),X30)
| in(ordered_pair(X31,esk4_5(X28,X29,X30,X31,X32)),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)],[d8_relat_1])])])])])])]) ).
cnf(c_0_10,plain,
( ~ relation(X3)
| X4 != relation_dom(X3)
| ~ in(ordered_pair(X1,X2),X3)
| in(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X11,X12] : unordered_pair(X11,X12) = unordered_pair(X12,X11),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_13,plain,
( ~ relation(X2)
| ~ relation(X3)
| ~ relation(X4)
| X4 != relation_composition(X2,X3)
| ~ in(ordered_pair(X1,X5),X4)
| in(ordered_pair(X1,esk4_5(X2,X3,X4,X1,X5)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,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_10,c_0_11]) ).
cnf(c_0_15,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( ~ in(unordered_pair(unordered_pair(X1,X5),singleton(X1)),X4)
| ~ relation(X2)
| ~ relation(X3)
| ~ relation(X4)
| X4 != relation_composition(X2,X3)
| in(unordered_pair(unordered_pair(X1,esk4_5(X2,X3,X4,X1,X5)),singleton(X1)),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_11]),c_0_11]) ).
cnf(c_0_17,plain,
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X4)),X3)
| ~ relation(X3)
| X2 != relation_dom(X3)
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( ~ in(unordered_pair(unordered_pair(X1,X5),singleton(X1)),X4)
| ~ relation(X2)
| ~ relation(X3)
| ~ relation(X4)
| X4 != relation_composition(X2,X3)
| in(unordered_pair(singleton(X1),unordered_pair(X1,esk4_5(X2,X3,X4,X1,X5))),X2) ),
inference(rw,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_19,plain,
( ~ relation(X3)
| X2 != relation_dom(X3)
| ~ in(X1,X2)
| in(ordered_pair(X1,esk1_3(X3,X2,X1)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_20,plain,
! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2,X3] :
( ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) )
& ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
inference(fof_simplification,[status(thm)],[d4_funct_1]) ).
cnf(c_0_21,plain,
( ~ in(unordered_pair(unordered_pair(X1,X6),singleton(X1)),X3)
| ~ relation(X5)
| ~ relation(X3)
| ~ relation(X4)
| X2 != relation_dom(X4)
| X3 != relation_composition(X4,X5)
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( ~ in(X1,X2)
| ~ relation(X3)
| X2 != relation_dom(X3)
| in(unordered_pair(unordered_pair(X1,esk1_3(X3,X2,X1)),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_19,c_0_11]) ).
fof(c_0_23,plain,
! [X13,X14,X15] :
( ( ~ function(X13)
| ~ relation(X13)
| in(X14,relation_dom(X13))
| X15 = apply(X13,X14)
| X15 != empty_set )
& ( ~ function(X13)
| ~ relation(X13)
| in(X14,relation_dom(X13))
| X15 = empty_set
| X15 != apply(X13,X14) )
& ( ~ function(X13)
| ~ relation(X13)
| ~ in(X14,relation_dom(X13))
| X15 = apply(X13,X14)
| ~ in(ordered_pair(X14,X15),X13) )
& ( ~ function(X13)
| ~ relation(X13)
| ~ in(X14,relation_dom(X13))
| in(ordered_pair(X14,X15),X13)
| X15 != apply(X13,X14) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])])]) ).
cnf(c_0_24,plain,
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X6)),X3)
| ~ relation(X5)
| ~ relation(X3)
| ~ relation(X4)
| X2 != relation_dom(X4)
| X3 != relation_composition(X4,X5)
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_25,plain,
( ~ in(X1,X3)
| ~ relation(X2)
| X3 != relation_dom(X2)
| in(unordered_pair(singleton(X1),unordered_pair(X1,esk1_3(X2,X3,X1))),X2) ),
inference(rw,[status(thm)],[c_0_22,c_0_15]) ).
fof(c_0_26,plain,
! [X41,X42] :
( relation(relation_composition(X41,X42))
| ~ relation(X42)
| ~ relation(X41) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])])]) ).
cnf(c_0_27,plain,
( ~ function(X3)
| ~ relation(X3)
| ~ in(X1,relation_dom(X3))
| ~ in(ordered_pair(X1,X2),X3)
| X2 = apply(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
( ~ in(X1,X6)
| ~ relation(X5)
| ~ relation(X3)
| ~ relation(X4)
| X6 != relation_dom(X3)
| X2 != relation_dom(X4)
| X3 != relation_composition(X4,X5)
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
( ~ relation(X2)
| ~ relation(X1)
| relation(relation_composition(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_30,negated_conjecture,
~ ! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ! [X3] :
( ( function(X3)
& relation(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
<=> ( in(apply(X3,X1),relation_dom(X2))
& in(X1,relation_dom(X3)) ) ) ) ),
inference(assume_negation,[status(cth)],[t21_funct_1]) ).
cnf(c_0_31,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| ~ in(X1,relation_dom(X3))
| ~ relation(X3)
| ~ function(X3)
| X2 = apply(X3,X1) ),
inference(rw,[status(thm)],[c_0_27,c_0_11]) ).
cnf(c_0_32,plain,
( ~ in(X1,X3)
| ~ relation(X5)
| ~ relation(X4)
| X2 != relation_dom(X4)
| X3 != relation_dom(relation_composition(X4,X5))
| in(X1,X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_28]),c_0_29]) ).
fof(c_0_33,negated_conjecture,
( ( in(esk17_0,relation_dom(relation_composition(esk19_0,esk18_0)))
| in(apply(esk19_0,esk17_0),relation_dom(esk18_0)) )
& ( in(esk17_0,relation_dom(relation_composition(esk19_0,esk18_0)))
| in(esk17_0,relation_dom(esk19_0)) )
& ( ~ in(apply(esk19_0,esk17_0),relation_dom(esk18_0))
| ~ in(esk17_0,relation_dom(esk19_0))
| ~ in(esk17_0,relation_dom(relation_composition(esk19_0,esk18_0))) )
& function(esk19_0)
& relation(esk19_0)
& function(esk18_0)
& relation(esk18_0) ),
inference(distribute,[status(thm)],[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_34,plain,
( ~ relation(X3)
| ~ relation(X5)
| ~ relation(X6)
| X6 != relation_composition(X3,X5)
| ~ in(ordered_pair(X2,X4),X5)
| ~ in(ordered_pair(X1,X2),X3)
| in(ordered_pair(X1,X4),X6) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_35,plain,
( ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(X2))
| X1 != apply(X2,X3)
| in(ordered_pair(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_36,plain,
( ~ in(X3,relation_dom(X2))
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),X2)
| ~ function(X2)
| ~ relation(X2)
| X1 = apply(X2,X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_15]) ).
cnf(c_0_37,plain,
( ~ in(X1,relation_dom(relation_composition(X3,X4)))
| ~ relation(X4)
| ~ relation(X3)
| X2 != relation_dom(X3)
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( in(esk17_0,relation_dom(relation_composition(esk19_0,esk18_0)))
| in(esk17_0,relation_dom(esk19_0)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,negated_conjecture,
relation(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,negated_conjecture,
relation(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
( ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| ~ in(ordered_pair(X4,X5),X3)
| in(ordered_pair(esk4_5(X1,X2,X3,X4,X5),X5),X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_42,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| ~ in(unordered_pair(unordered_pair(X2,X4),singleton(X2)),X5)
| ~ relation(X3)
| ~ relation(X5)
| ~ relation(X6)
| X6 != relation_composition(X3,X5)
| in(unordered_pair(unordered_pair(X1,X4),singleton(X1)),X6) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_11]),c_0_11]),c_0_11]) ).
cnf(c_0_43,plain,
( ~ in(X3,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2)
| X1 != apply(X2,X3)
| in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2) ),
inference(rw,[status(thm)],[c_0_35,c_0_11]) ).
cnf(c_0_44,plain,
( ~ in(X3,X2)
| ~ in(X3,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| X2 != relation_dom(X1)
| esk1_3(X1,X2,X3) = apply(X1,X3) ),
inference(spm,[status(thm)],[c_0_36,c_0_25]) ).
cnf(c_0_45,negated_conjecture,
( X1 != relation_dom(esk19_0)
| in(esk17_0,X1)
| in(esk17_0,relation_dom(esk19_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40])]) ).
cnf(c_0_46,plain,
( ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X3)
| ~ relation(X1)
| ~ relation(X2)
| ~ relation(X3)
| X3 != relation_composition(X1,X2)
| in(unordered_pair(unordered_pair(esk4_5(X1,X2,X3,X4,X5),X5),singleton(esk4_5(X1,X2,X3,X4,X5))),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_11]),c_0_11]) ).
cnf(c_0_47,plain,
( ~ in(X6,relation_dom(X5))
| ~ in(unordered_pair(unordered_pair(X1,X6),singleton(X1)),X4)
| ~ function(X5)
| ~ relation(X4)
| ~ relation(X5)
| ~ relation(X3)
| X2 != apply(X5,X6)
| X3 != relation_composition(X4,X5)
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,plain,
( ~ in(X1,X3)
| ~ in(X1,relation_dom(X2))
| ~ function(X2)
| ~ relation(X2)
| X3 != relation_dom(X2)
| in(unordered_pair(singleton(X1),unordered_pair(X1,apply(X2,X1))),X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_44]) ).
cnf(c_0_49,negated_conjecture,
in(esk17_0,relation_dom(esk19_0)),
inference(er,[status(thm)],[c_0_45]) ).
cnf(c_0_50,plain,
( ~ in(unordered_pair(unordered_pair(X4,X1),singleton(X1)),X3)
| ~ relation(X3)
| X2 != relation_dom(X3)
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_51,plain,
( ~ in(unordered_pair(unordered_pair(X5,X1),singleton(X5)),X4)
| ~ relation(X2)
| ~ relation(X3)
| ~ relation(X4)
| X4 != relation_composition(X2,X3)
| in(unordered_pair(unordered_pair(X1,esk4_5(X2,X3,X4,X5,X1)),singleton(esk4_5(X2,X3,X4,X5,X1))),X3) ),
inference(rw,[status(thm)],[c_0_46,c_0_15]) ).
cnf(c_0_52,plain,
( ~ in(X6,relation_dom(X5))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X6)),X4)
| ~ function(X5)
| ~ relation(X4)
| ~ relation(X5)
| ~ relation(X3)
| X2 != apply(X5,X6)
| X3 != relation_composition(X4,X5)
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(spm,[status(thm)],[c_0_47,c_0_15]) ).
cnf(c_0_53,negated_conjecture,
( ~ in(esk17_0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| relation_dom(esk19_0) != relation_dom(X1)
| in(unordered_pair(singleton(esk17_0),unordered_pair(esk17_0,apply(X1,esk17_0))),X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,plain,
( ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X3)
| ~ relation(X1)
| ~ relation(X3)
| ~ relation(X2)
| X6 != relation_dom(X2)
| X3 != relation_composition(X1,X2)
| in(esk4_5(X1,X2,X3,X4,X5),X6) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,plain,
( ~ in(X4,relation_dom(X1))
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X3)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ relation(X1)
| X3 != relation_composition(X1,X2)
| esk4_5(X1,X2,X3,X4,X5) = apply(X1,X4) ),
inference(spm,[status(thm)],[c_0_36,c_0_18]) ).
cnf(c_0_56,negated_conjecture,
( ~ in(esk17_0,relation_dom(X4))
| ~ in(apply(X4,esk17_0),relation_dom(X3))
| ~ function(X4)
| ~ function(X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| X2 != relation_composition(X4,X3)
| relation_dom(esk19_0) != relation_dom(X4)
| X1 != apply(X3,apply(X4,esk17_0))
| in(unordered_pair(unordered_pair(esk17_0,X1),singleton(esk17_0)),X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,plain,
( ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),X3)
| ~ relation(X1)
| ~ relation(X3)
| ~ relation(X2)
| X6 != relation_dom(X2)
| X3 != relation_composition(X1,X2)
| in(esk4_5(X1,X2,X3,X4,X5),X6) ),
inference(spm,[status(thm)],[c_0_54,c_0_15]) ).
cnf(c_0_58,plain,
( ~ in(X4,relation_dom(X1))
| ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),X3)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ relation(X1)
| X3 != relation_composition(X1,X2)
| esk4_5(X1,X2,X3,X4,X5) = apply(X1,X4) ),
inference(spm,[status(thm)],[c_0_55,c_0_15]) ).
cnf(c_0_59,negated_conjecture,
( ~ in(esk17_0,relation_dom(X2))
| ~ in(apply(X2,esk17_0),relation_dom(X1))
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X3)
| X3 != relation_composition(X2,X1)
| relation_dom(esk19_0) != relation_dom(X2)
| in(unordered_pair(singleton(esk17_0),unordered_pair(esk17_0,apply(X1,apply(X2,esk17_0)))),X3) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_56]),c_0_15]) ).
cnf(c_0_60,plain,
( ~ in(X4,X5)
| ~ relation(X1)
| ~ relation(X3)
| ~ relation(X2)
| X5 != relation_dom(X3)
| X6 != relation_dom(X2)
| X3 != relation_composition(X1,X2)
| in(esk4_5(X1,X2,X3,X4,esk1_3(X3,X5,X4)),X6) ),
inference(spm,[status(thm)],[c_0_57,c_0_25]) ).
cnf(c_0_61,plain,
( ~ in(X4,X5)
| ~ in(X4,relation_dom(X1))
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X3)
| ~ relation(X1)
| X5 != relation_dom(X3)
| X3 != relation_composition(X1,X2)
| esk4_5(X1,X2,X3,X4,esk1_3(X3,X5,X4)) = apply(X1,X4) ),
inference(spm,[status(thm)],[c_0_58,c_0_25]) ).
cnf(c_0_62,negated_conjecture,
( ~ in(esk17_0,relation_dom(X2))
| ~ in(apply(X2,esk17_0),relation_dom(X4))
| ~ function(X2)
| ~ function(X4)
| ~ relation(X2)
| ~ relation(X4)
| ~ relation(X3)
| X1 != relation_dom(X3)
| X3 != relation_composition(X2,X4)
| relation_dom(esk19_0) != relation_dom(X2)
| in(esk17_0,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_59]) ).
cnf(c_0_63,negated_conjecture,
( in(esk17_0,relation_dom(relation_composition(esk19_0,esk18_0)))
| in(apply(esk19_0,esk17_0),relation_dom(esk18_0)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_64,negated_conjecture,
function(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_65,negated_conjecture,
function(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_66,plain,
( ~ in(X2,X6)
| ~ in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X4)
| ~ relation(X5)
| X6 != relation_dom(X4)
| X3 != relation_dom(X5)
| X4 != relation_composition(X1,X5)
| in(apply(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_67,negated_conjecture,
( ~ relation(X2)
| X1 != relation_dom(X2)
| X2 != relation_composition(esk19_0,esk18_0)
| in(esk17_0,X1)
| in(esk17_0,relation_dom(relation_composition(esk19_0,esk18_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_40]),c_0_39]),c_0_64]),c_0_65]),c_0_49])]) ).
cnf(c_0_68,plain,
( ~ in(X2,X4)
| ~ in(X2,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X5)
| X3 != relation_dom(X5)
| X4 != relation_dom(relation_composition(X1,X5))
| in(apply(X1,X2),X3) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_66]),c_0_29]) ).
cnf(c_0_69,negated_conjecture,
( ~ relation(relation_composition(esk19_0,esk18_0))
| X1 != relation_dom(relation_composition(esk19_0,esk18_0))
| in(esk17_0,X1)
| in(esk17_0,relation_dom(relation_composition(esk19_0,esk18_0))) ),
inference(er,[status(thm)],[c_0_67]) ).
cnf(c_0_70,plain,
( ~ in(X2,relation_dom(X1))
| ~ in(X2,relation_dom(relation_composition(X1,X4)))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X4)
| X3 != relation_dom(X4)
| in(apply(X1,X2),X3) ),
inference(er,[status(thm)],[c_0_68]) ).
cnf(c_0_71,negated_conjecture,
( ~ relation(relation_composition(esk19_0,esk18_0))
| in(esk17_0,relation_dom(relation_composition(esk19_0,esk18_0))) ),
inference(er,[status(thm)],[c_0_69]) ).
cnf(c_0_72,negated_conjecture,
( ~ relation(relation_composition(esk19_0,esk18_0))
| X1 != relation_dom(esk18_0)
| in(apply(esk19_0,esk17_0),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_40]),c_0_39]),c_0_65]),c_0_49])]) ).
cnf(c_0_73,negated_conjecture,
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X3)
| ~ relation(relation_composition(esk19_0,esk18_0))
| X1 != relation_dom(X3)
| X3 != relation_composition(esk19_0,X2)
| relation_dom(X2) != relation_dom(esk18_0)
| in(esk17_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_72]),c_0_39]),c_0_65]),c_0_49])]) ).
cnf(c_0_74,negated_conjecture,
( ~ function(X2)
| ~ relation(X2)
| ~ relation(X3)
| X1 != relation_dom(X3)
| X3 != relation_composition(esk19_0,X2)
| relation_dom(X2) != relation_dom(esk18_0)
| in(esk17_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_29]),c_0_40]),c_0_39])]) ).
cnf(c_0_75,negated_conjecture,
( ~ function(X2)
| ~ relation(X2)
| ~ relation(relation_composition(esk19_0,X2))
| relation_dom(X2) != relation_dom(esk18_0)
| X1 != relation_dom(relation_composition(esk19_0,X2))
| in(esk17_0,X1) ),
inference(er,[status(thm)],[c_0_74]) ).
cnf(c_0_76,negated_conjecture,
( ~ function(X1)
| ~ relation(X1)
| ~ relation(relation_composition(esk19_0,X1))
| relation_dom(X1) != relation_dom(esk18_0)
| in(esk17_0,relation_dom(relation_composition(esk19_0,X1))) ),
inference(er,[status(thm)],[c_0_75]) ).
cnf(c_0_77,negated_conjecture,
( ~ function(X2)
| ~ relation(X2)
| ~ relation(relation_composition(esk19_0,X2))
| X1 != relation_dom(X2)
| relation_dom(X2) != relation_dom(esk18_0)
| in(apply(esk19_0,esk17_0),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_76]),c_0_39]),c_0_65]),c_0_49])]) ).
cnf(c_0_78,negated_conjecture,
( ~ in(apply(esk19_0,esk17_0),relation_dom(esk18_0))
| ~ in(esk17_0,relation_dom(esk19_0))
| ~ in(esk17_0,relation_dom(relation_composition(esk19_0,esk18_0))) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_79,negated_conjecture,
( ~ function(X2)
| ~ relation(X2)
| X1 != relation_dom(X2)
| relation_dom(X2) != relation_dom(esk18_0)
| in(apply(esk19_0,esk17_0),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_29]),c_0_39])]) ).
cnf(c_0_80,negated_conjecture,
( ~ in(apply(esk19_0,esk17_0),relation_dom(esk18_0))
| ~ in(esk17_0,relation_dom(relation_composition(esk19_0,esk18_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_49])]) ).
cnf(c_0_81,negated_conjecture,
( ~ function(X1)
| ~ relation(X1)
| relation_dom(X1) != relation_dom(esk18_0)
| in(apply(esk19_0,esk17_0),relation_dom(X1)) ),
inference(er,[status(thm)],[c_0_79]) ).
cnf(c_0_82,negated_conjecture,
~ in(esk17_0,relation_dom(relation_composition(esk19_0,esk18_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_40]),c_0_64])]) ).
cnf(c_0_83,negated_conjecture,
~ relation(relation_composition(esk19_0,esk18_0)),
inference(spm,[status(thm)],[c_0_82,c_0_71]) ).
cnf(c_0_84,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_29]),c_0_40]),c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU213+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.45 % Computer : n014.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Mon Sep 21 05:58:50 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.56 Running first-order theorem proving
% 0.27/0.56 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 27.65/5.00 % Version: 3.5.1
% 27.65/5.00 % Preprocessing class: FSMSSMSSSSSNFFN.
% 27.65/5.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.65/5.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 27.65/5.00 % Starting new_bool_3 with 300s (1) cores
% 27.65/5.00 % Starting new_bool_1 with 300s (1) cores
% 27.65/5.00 % Starting sh5l with 300s (1) cores
% 27.65/5.00 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3291235 completed with status 0
% 27.65/5.00 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 27.65/5.00 % Preprocessing class: FSMSSMSSSSSNFFN.
% 27.65/5.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.65/5.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 27.65/5.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 27.65/5.00 % No SInE strategy applied
% 27.65/5.00 % Search class: FGHSM-FFMM32-MFFFFFNN
% 27.65/5.00 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 27.65/5.00 % Starting SubtermCWHack with 136s (1) cores
% 27.65/5.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 27.65/5.00 % Starting G-E--_300_C18_F1_URBAN_S0Y with 369s (1) cores
% 27.65/5.00 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 27.65/5.00 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 136s (1) cores
% 27.65/5.00 % G-E--_300_C18_F1_URBAN_S0Y with pid 3291244 completed with status 0
% 27.65/5.00 % Result found by G-E--_300_C18_F1_URBAN_S0Y
% 27.65/5.00 % Preprocessing class: FSMSSMSSSSSNFFN.
% 27.65/5.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.65/5.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 27.65/5.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 27.65/5.00 % No SInE strategy applied
% 27.65/5.00 % Search class: FGHSM-FFMM32-MFFFFFNN
% 27.65/5.00 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 27.65/5.00 % Starting SubtermCWHack with 136s (1) cores
% 27.65/5.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 27.65/5.00 % Starting G-E--_300_C18_F1_URBAN_S0Y with 369s (1) cores
% 27.65/5.00 % Preprocessing time : 0.005 s
% 27.65/5.00
% 27.65/5.00 % Proof found!
% 27.65/5.00 % SZS status Theorem
% 27.65/5.00 % SZS output start CNFRefutation
% See solution above
% 30.49/5.00 % Parsed axioms : 40
% 30.49/5.00 % Removed by relevancy pruning/SinE : 0
% 30.49/5.00 % Initial clauses : 71
% 30.49/5.00 % Removed in clause preprocessing : 1
% 30.49/5.00 % Initial clauses in saturation : 70
% 30.49/5.00 % Processed clauses : 6787
% 30.49/5.00 % ...of these trivial : 26
% 30.49/5.00 % ...subsumed : 4501
% 30.49/5.00 % ...remaining for further processing : 2260
% 30.49/5.00 % Other redundant clauses eliminated : 91
% 30.49/5.00 % Clauses deleted for lack of memory : 0
% 30.49/5.00 % Backward-subsumed : 225
% 30.49/5.00 % Backward-rewritten : 57
% 30.49/5.00 % Generated clauses : 80045
% 30.49/5.00 % ...of the previous two non-redundant : 78781
% 30.49/5.00 % ...aggressively subsumed : 0
% 30.49/5.00 % Contextual simplify-reflections : 468
% 30.49/5.00 % Paramodulations : 79395
% 30.49/5.00 % Factorizations : 10
% 30.49/5.00 % NegExts : 0
% 30.49/5.00 % Equation resolutions : 636
% 30.49/5.00 % Disequality decompositions : 0
% 30.49/5.00 % Total rewrite steps : 50936
% 30.49/5.00 % ...of those cached : 50811
% 30.49/5.00 % Propositional unsat checks : 0
% 30.49/5.00 % Propositional check models : 0
% 30.49/5.00 % Propositional check unsatisfiable : 0
% 30.49/5.00 % Propositional clauses : 0
% 30.49/5.00 % Propositional clauses after purity: 0
% 30.49/5.00 % Propositional unsat core size : 0
% 30.49/5.00 % Propositional preprocessing time : 0.000
% 30.49/5.00 % Propositional encoding time : 0.000
% 30.49/5.00 % Propositional solver time : 0.000
% 30.49/5.00 % Success case prop preproc time : 0.000
% 30.49/5.00 % Success case prop encoding time : 0.000
% 30.49/5.00 % Success case prop solver time : 0.000
% 30.49/5.00 % Current number of processed clauses : 1974
% 30.49/5.00 % Positive orientable unit clauses : 34
% 30.49/5.00 % Positive unorientable unit clauses: 1
% 30.49/5.00 % Negative unit clauses : 24
% 30.49/5.00 % Non-unit-clauses : 1915
% 30.49/5.00 % Current number of unprocessed clauses: 70891
% 30.49/5.00 % ...number of literals in the above : 600182
% 30.49/5.00 % Current number of archived formulas : 0
% 30.49/5.00 % Current number of archived clauses : 287
% 30.49/5.00 % Clause-clause subsumption calls (NU) : 1613953
% 30.49/5.00 % Rec. Clause-clause subsumption calls : 71483
% 30.49/5.00 % Non-unit clause-clause subsumptions : 4071
% 30.49/5.00 % Unit Clause-clause subsumption calls : 10303
% 30.49/5.00 % Rewrite failures with RHS unbound : 0
% 30.49/5.00 % BW rewrite match attempts : 70
% 30.49/5.00 % BW rewrite match successes : 24
% 30.49/5.00 % Condensation attempts : 0
% 30.49/5.00 % Condensation successes : 0
% 30.49/5.00 % Termbank termtop insertions : 3394711
% 30.49/5.00 % Search garbage collected termcells : 964
% 30.49/5.00
% 30.49/5.00 % -------------------------------------------------
% 30.49/5.00 % User time : 4.149 s
% 30.49/5.00 % System time : 0.095 s
% 30.49/5.00 % Total time : 4.244 s
% 30.49/5.00 % Maximum resident set size: 3668 pages
% 30.49/5.00
% 30.49/5.00 % -------------------------------------------------
% 30.49/5.00 % User time : 17.311 s
% 30.49/5.00 % System time : 0.563 s
% 30.49/5.00 % Total time : 17.873 s
% 30.49/5.00 % Maximum resident set size: 4864 pages
% 30.49/5.00 % E exiting
%------------------------------------------------------------------------------