%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU214+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 134.18s 20.38s
% Output : CNFRefutation 134.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 75 ( 15 unt; 0 def)
% Number of atoms : 445 ( 100 equ)
% Maximal formula atoms : 38 ( 5 avg)
% Number of connectives : 681 ( 311 ~; 313 |; 31 &)
% ( 8 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Maximal term depth : 4 ( 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 : 261 ( 6 sgn 55 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(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(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(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(t22_funct_1,conjecture,
! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ! [X3] :
( ( function(X3)
& relation(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(fc1_funct_1,axiom,
! [X1,X2] :
( ( function(X2)
& relation(X2)
& function(X1)
& relation(X1) )
=> ( function(relation_composition(X1,X2))
& relation(relation_composition(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(c_0_8,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]) ).
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])])])])])])]) ).
fof(c_0_10,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_11,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_8])])])])]) ).
fof(c_0_12,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])])])])])])]) ).
cnf(c_0_13,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_14,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,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_11]) ).
cnf(c_0_16,plain,
( ~ relation(X3)
| X4 != relation_dom(X3)
| ~ in(ordered_pair(X1,X2),X3)
| in(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X11,X12] : unordered_pair(X11,X12) = unordered_pair(X12,X11),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_18,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_19,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_13,c_0_14]),c_0_14]),c_0_14]) ).
cnf(c_0_20,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_15,c_0_14]) ).
cnf(c_0_21,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_16,c_0_14]) ).
cnf(c_0_22,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,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_18,c_0_14]),c_0_14]) ).
cnf(c_0_24,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_25,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_11]) ).
cnf(c_0_26,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_19,c_0_20]) ).
fof(c_0_27,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_28,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_21,c_0_22]) ).
cnf(c_0_29,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_23,c_0_22]) ).
cnf(c_0_30,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_12]) ).
cnf(c_0_31,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_24,c_0_14]),c_0_14]) ).
cnf(c_0_32,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_25,c_0_14]) ).
cnf(c_0_33,plain,
( ~ in(X1,relation_dom(X4))
| ~ in(X6,relation_dom(X5))
| ~ function(X4)
| ~ function(X5)
| ~ relation(X4)
| ~ relation(X5)
| ~ relation(X3)
| X6 != apply(X4,X1)
| 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_26,c_0_20]) ).
cnf(c_0_34,plain,
( ~ relation(X2)
| ~ relation(X1)
| relation(relation_composition(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,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_28,c_0_29]) ).
cnf(c_0_36,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_30,c_0_14]) ).
cnf(c_0_37,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_21,c_0_22]) ).
cnf(c_0_38,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_31,c_0_22]) ).
cnf(c_0_39,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_32,c_0_22]) ).
cnf(c_0_40,plain,
( ~ in(X1,relation_dom(X3))
| ~ in(X5,relation_dom(X4))
| ~ function(X3)
| ~ function(X4)
| ~ relation(X3)
| ~ relation(X4)
| X5 != apply(X3,X1)
| X2 != apply(X4,X5)
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),relation_composition(X3,X4)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_33]),c_0_34]) ).
cnf(c_0_41,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_35,c_0_22]) ).
cnf(c_0_42,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_36,c_0_22]) ).
cnf(c_0_43,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_37,c_0_38]) ).
cnf(c_0_44,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_39,c_0_29]) ).
cnf(c_0_45,plain,
( ~ in(X1,relation_dom(X4))
| ~ in(X3,relation_dom(X2))
| ~ function(X4)
| ~ function(X2)
| ~ relation(X4)
| ~ relation(X2)
| X3 != apply(X4,X1)
| in(unordered_pair(singleton(X1),unordered_pair(X1,apply(X2,X3))),relation_composition(X4,X2)) ),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_40]),c_0_22]) ).
cnf(c_0_46,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_41,c_0_42]) ).
fof(c_0_47,negated_conjecture,
~ ! [X1,X2] :
( ( function(X2)
& relation(X2) )
=> ! [X3] :
( ( function(X3)
& relation(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_48,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_43,c_0_22]) ).
cnf(c_0_49,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_44,c_0_22]) ).
cnf(c_0_50,plain,
( ~ in(X1,relation_dom(X3))
| ~ in(X5,relation_dom(X4))
| ~ function(X3)
| ~ function(X4)
| ~ relation(X3)
| ~ relation(X4)
| X5 != apply(X3,X1)
| X2 != relation_dom(relation_composition(X3,X4))
| in(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_45]),c_0_34]) ).
fof(c_0_51,plain,
! [X47,X48] :
( ( ~ function(X48)
| ~ relation(X48)
| ~ function(X47)
| ~ relation(X47)
| function(relation_composition(X47,X48)) )
& ( ~ function(X48)
| ~ relation(X48)
| ~ function(X47)
| ~ relation(X47)
| relation(relation_composition(X47,X48)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_funct_1])])])]) ).
cnf(c_0_52,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_46]),c_0_34]) ).
fof(c_0_53,negated_conjecture,
( apply(relation_composition(esk17_0,esk16_0),esk15_0) != apply(esk16_0,apply(esk17_0,esk15_0))
& in(esk15_0,relation_dom(relation_composition(esk17_0,esk16_0)))
& function(esk17_0)
& relation(esk17_0)
& function(esk16_0)
& relation(esk16_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])])]) ).
cnf(c_0_54,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_48,c_0_42]) ).
cnf(c_0_55,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_49,c_0_42]) ).
cnf(c_0_56,plain,
( ~ in(X1,relation_dom(X2))
| ~ in(X4,relation_dom(X3))
| ~ function(X2)
| ~ function(X3)
| ~ relation(X2)
| ~ relation(X3)
| X4 != apply(X2,X1)
| in(X1,relation_dom(relation_composition(X2,X3))) ),
inference(er,[status(thm)],[c_0_50]) ).
cnf(c_0_57,plain,
( ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1)
| function(relation_composition(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_58,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_52]) ).
cnf(c_0_59,negated_conjecture,
in(esk15_0,relation_dom(relation_composition(esk17_0,esk16_0))),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,negated_conjecture,
relation(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_61,negated_conjecture,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_62,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_54,c_0_55]) ).
cnf(c_0_63,plain,
( ~ in(X4,relation_dom(X3))
| ~ in(X2,relation_dom(X1))
| ~ function(X3)
| ~ function(X1)
| ~ relation(X3)
| ~ relation(X1)
| X2 != apply(X3,X4)
| apply(X1,X2) = apply(relation_composition(X3,X1),X4) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_45]),c_0_56]),c_0_57]),c_0_34]) ).
cnf(c_0_64,negated_conjecture,
( X1 != relation_dom(esk17_0)
| in(esk15_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_61])]) ).
cnf(c_0_65,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_62]),c_0_34]) ).
cnf(c_0_66,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_53]) ).
cnf(c_0_67,plain,
( ~ in(X3,relation_dom(X2))
| ~ in(apply(X2,X3),relation_dom(X1))
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| apply(X1,apply(X2,X3)) = apply(relation_composition(X2,X1),X3) ),
inference(er,[status(thm)],[c_0_63]) ).
cnf(c_0_68,negated_conjecture,
function(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_69,negated_conjecture,
function(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_70,negated_conjecture,
in(esk15_0,relation_dom(esk17_0)),
inference(er,[status(thm)],[c_0_64]) ).
cnf(c_0_71,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_65]) ).
cnf(c_0_72,negated_conjecture,
~ in(apply(esk17_0,esk15_0),relation_dom(esk16_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_66,c_0_67]),c_0_61]),c_0_60]),c_0_68]),c_0_69]),c_0_70])]) ).
cnf(c_0_73,negated_conjecture,
( X1 != relation_dom(esk16_0)
| in(apply(esk17_0,esk15_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_71,c_0_59]),c_0_61]),c_0_60]),c_0_69]),c_0_70])]) ).
cnf(c_0_74,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_72,c_0_73]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU214+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.42 % Computer : n018.cluster.edu
% 0.19/0.42 % Model : x86_64 x86_64
% 0.19/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.42 % Memory : 8046.5625MB
% 0.19/0.42 % OS : Linux 6.8.0-71-generic
% 0.19/0.42 % CPULimit : 300
% 0.19/0.42 % WCLimit : 300
% 0.19/0.42 % DateTime : Mon Sep 21 06:00:58 UTC 2026
% 0.19/0.43 % CPUTime :
% 0.19/0.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.53 Running first-order theorem proving
% 0.19/0.53 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
% 134.18/20.38 % Version: 3.5.1
% 134.18/20.38 % Preprocessing class: FSMSSMSSSSSNFFN.
% 134.18/20.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 134.18/20.38 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 134.18/20.38 % Starting new_bool_3 with 300s (1) cores
% 134.18/20.38 % Starting new_bool_1 with 300s (1) cores
% 134.18/20.38 % Starting sh5l with 300s (1) cores
% 134.18/20.38 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1125065 completed with status 0
% 134.18/20.38 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 134.18/20.38 % Preprocessing class: FSMSSMSSSSSNFFN.
% 134.18/20.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 134.18/20.38 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 134.18/20.38 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 134.18/20.38 % No SInE strategy applied
% 134.18/20.38 % Search class: FGHSS-FFMM32-MFFFFFNN
% 134.18/20.38 % partial match(1): FGHSM-FFMM32-MFFFFFNN
% 134.18/20.38 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 134.18/20.38 % Starting SubtermCWHack with 136s (1) cores
% 134.18/20.38 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 134.18/20.38 % Starting G-E--_300_C18_F1_URBAN_S0Y with 369s (1) cores
% 134.18/20.38 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 134.18/20.38 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 136s (1) cores
% 134.18/20.38 % G-E--_300_C18_F1_URBAN_S0Y with pid 1125071 completed with status 0
% 134.18/20.38 % Result found by G-E--_300_C18_F1_URBAN_S0Y
% 134.18/20.38 % Preprocessing class: FSMSSMSSSSSNFFN.
% 134.18/20.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 134.18/20.38 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 134.18/20.38 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 134.18/20.38 % No SInE strategy applied
% 134.18/20.38 % Search class: FGHSS-FFMM32-MFFFFFNN
% 134.18/20.38 % partial match(1): FGHSM-FFMM32-MFFFFFNN
% 134.18/20.38 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 134.18/20.38 % Starting SubtermCWHack with 136s (1) cores
% 134.18/20.38 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 134.18/20.38 % Starting G-E--_300_C18_F1_URBAN_S0Y with 369s (1) cores
% 134.18/20.38 % Preprocessing time : 0.004 s
% 134.18/20.38
% 134.18/20.38 % Proof found!
% 134.18/20.38 % SZS status Theorem
% 134.18/20.38 % SZS output start CNFRefutation
% See solution above
% 134.18/20.38 % Parsed axioms : 40
% 134.18/20.38 % Removed by relevancy pruning/SinE : 0
% 134.18/20.38 % Initial clauses : 67
% 134.18/20.38 % Removed in clause preprocessing : 8
% 134.18/20.38 % Initial clauses in saturation : 59
% 134.18/20.38 % Processed clauses : 12511
% 134.18/20.38 % ...of these trivial : 39
% 134.18/20.38 % ...subsumed : 8807
% 134.18/20.38 % ...remaining for further processing : 3665
% 134.18/20.38 % Other redundant clauses eliminated : 81
% 134.18/20.38 % Clauses deleted for lack of memory : 0
% 134.18/20.38 % Backward-subsumed : 332
% 134.18/20.38 % Backward-rewritten : 13
% 134.18/20.38 % Generated clauses : 170214
% 134.18/20.38 % ...of the previous two non-redundant : 168201
% 134.18/20.38 % ...aggressively subsumed : 0
% 134.18/20.38 % Contextual simplify-reflections : 939
% 134.18/20.38 % Paramodulations : 168606
% 134.18/20.38 % Factorizations : 102
% 134.18/20.38 % NegExts : 0
% 134.18/20.38 % Equation resolutions : 1504
% 134.18/20.38 % Disequality decompositions : 0
% 134.18/20.38 % Total rewrite steps : 166633
% 134.18/20.38 % ...of those cached : 166494
% 134.18/20.38 % Propositional unsat checks : 0
% 134.18/20.38 % Propositional check models : 0
% 134.18/20.38 % Propositional check unsatisfiable : 0
% 134.18/20.38 % Propositional clauses : 0
% 134.18/20.38 % Propositional clauses after purity: 0
% 134.18/20.38 % Propositional unsat core size : 0
% 134.18/20.38 % Propositional preprocessing time : 0.000
% 134.18/20.38 % Propositional encoding time : 0.000
% 134.18/20.38 % Propositional solver time : 0.000
% 134.18/20.38 % Success case prop preproc time : 0.000
% 134.18/20.38 % Success case prop encoding time : 0.000
% 134.18/20.38 % Success case prop solver time : 0.000
% 134.18/20.38 % Current number of processed clauses : 3318
% 134.18/20.38 % Positive orientable unit clauses : 23
% 134.18/20.38 % Positive unorientable unit clauses: 1
% 134.18/20.38 % Negative unit clauses : 27
% 134.18/20.38 % Non-unit-clauses : 3267
% 134.18/20.38 % Current number of unprocessed clauses: 154540
% 134.18/20.38 % ...number of literals in the above : 1474408
% 134.18/20.38 % Current number of archived formulas : 0
% 134.18/20.38 % Current number of archived clauses : 348
% 134.18/20.38 % Clause-clause subsumption calls (NU) : 4560153
% 134.18/20.38 % Rec. Clause-clause subsumption calls : 226281
% 134.18/20.38 % Non-unit clause-clause subsumptions : 6698
% 134.18/20.38 % Unit Clause-clause subsumption calls : 3760
% 134.18/20.38 % Rewrite failures with RHS unbound : 0
% 134.18/20.38 % BW rewrite match attempts : 13
% 134.18/20.38 % BW rewrite match successes : 13
% 134.18/20.38 % Condensation attempts : 0
% 134.18/20.38 % Condensation successes : 0
% 134.18/20.38 % Termbank termtop insertions : 6646463
% 134.18/20.38 % Search garbage collected termcells : 840
% 134.18/20.38
% 134.18/20.38 % -------------------------------------------------
% 134.18/20.38 % User time : 18.748 s
% 134.18/20.38 % System time : 0.311 s
% 134.18/20.38 % Total time : 19.059 s
% 134.18/20.38 % Maximum resident set size: 3356 pages
% 134.18/20.38
% 134.18/20.38 % -------------------------------------------------
% 134.18/20.38 % User time : 92.244 s
% 134.18/20.38 % System time : 2.640 s
% 134.18/20.38 % Total time : 94.884 s
% 134.18/20.38 % Maximum resident set size: 4864 pages
% 134.18/20.38 % E exiting
%------------------------------------------------------------------------------