%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU214+3 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:11:05 PM UTC 2026
% Result : Theorem 79.49s 50.60s
% Output : CNFRefutation 79.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 73 ( 15 unt; 0 def)
% Number of atoms : 421 ( 96 equ)
% Maximal formula atoms : 38 ( 5 avg)
% Number of connectives : 639 ( 291 ~; 291 |; 31 &)
% ( 8 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 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 : 221 ( 6 sgn 55 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(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(X4,X6),X1)
& in(ordered_pair(X6,X5),X2) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t22_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
=> apply(relation_composition(X3,X2),X1) = apply(X2,apply(X3,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_1) ).
fof(dt_k5_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(fc1_funct_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& relation(X2)
& function(X2) )
=> ( relation(relation_composition(X1,X2))
& function(relation_composition(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(c_0_8,plain,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
inference(fof_simplification,[status(thm)],[d4_funct_1]) ).
fof(c_0_9,plain,
! [X87,X88,X89,X91,X92,X93,X95] :
( ( ~ in(X89,X88)
| in(ordered_pair(X89,esk1_3(X87,X88,X89)),X87)
| X88 != relation_dom(X87)
| ~ relation(X87) )
& ( ~ in(ordered_pair(X91,X92),X87)
| in(X91,X88)
| X88 != relation_dom(X87)
| ~ relation(X87) )
& ( ~ in(esk2_2(X87,X93),X93)
| ~ in(ordered_pair(esk2_2(X87,X93),X95),X87)
| X93 = relation_dom(X87)
| ~ relation(X87) )
& ( in(esk2_2(X87,X93),X93)
| in(ordered_pair(esk2_2(X87,X93),esk3_2(X87,X93)),X87)
| X93 = relation_dom(X87)
| ~ relation(X87) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_relat_1])])])])])]) ).
fof(c_0_10,plain,
! [X97,X98] : ordered_pair(X97,X98) = unordered_pair(unordered_pair(X97,X98),singleton(X97)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_11,plain,
! [X99,X100,X101,X102,X103,X105,X106,X107,X110] :
( ( in(ordered_pair(X102,esk4_5(X99,X100,X101,X102,X103)),X99)
| ~ in(ordered_pair(X102,X103),X101)
| X101 != relation_composition(X99,X100)
| ~ relation(X101)
| ~ relation(X100)
| ~ relation(X99) )
& ( in(ordered_pair(esk4_5(X99,X100,X101,X102,X103),X103),X100)
| ~ in(ordered_pair(X102,X103),X101)
| X101 != relation_composition(X99,X100)
| ~ relation(X101)
| ~ relation(X100)
| ~ relation(X99) )
& ( ~ in(ordered_pair(X105,X107),X99)
| ~ in(ordered_pair(X107,X106),X100)
| in(ordered_pair(X105,X106),X101)
| X101 != relation_composition(X99,X100)
| ~ relation(X101)
| ~ relation(X100)
| ~ relation(X99) )
& ( ~ in(ordered_pair(esk5_3(X99,X100,X101),esk6_3(X99,X100,X101)),X101)
| ~ in(ordered_pair(esk5_3(X99,X100,X101),X110),X99)
| ~ in(ordered_pair(X110,esk6_3(X99,X100,X101)),X100)
| X101 = relation_composition(X99,X100)
| ~ relation(X101)
| ~ relation(X100)
| ~ relation(X99) )
& ( in(ordered_pair(esk5_3(X99,X100,X101),esk7_3(X99,X100,X101)),X99)
| in(ordered_pair(esk5_3(X99,X100,X101),esk6_3(X99,X100,X101)),X101)
| X101 = relation_composition(X99,X100)
| ~ relation(X101)
| ~ relation(X100)
| ~ relation(X99) )
& ( in(ordered_pair(esk7_3(X99,X100,X101),esk6_3(X99,X100,X101)),X100)
| in(ordered_pair(esk5_3(X99,X100,X101),esk6_3(X99,X100,X101)),X101)
| X101 = relation_composition(X99,X100)
| ~ relation(X101)
| ~ relation(X100)
| ~ relation(X99) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_relat_1])])])])])]) ).
fof(c_0_12,plain,
! [X84,X85,X86] :
( ( X86 != apply(X84,X85)
| in(ordered_pair(X85,X86),X84)
| ~ in(X85,relation_dom(X84))
| ~ relation(X84)
| ~ function(X84) )
& ( ~ in(ordered_pair(X85,X86),X84)
| X86 = apply(X84,X85)
| ~ in(X85,relation_dom(X84))
| ~ relation(X84)
| ~ function(X84) )
& ( X86 != apply(X84,X85)
| X86 = empty_set
| in(X85,relation_dom(X84))
| ~ relation(X84)
| ~ function(X84) )
& ( X86 != empty_set
| X86 = apply(X84,X85)
| in(X85,relation_dom(X84))
| ~ relation(X84)
| ~ function(X84) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_13,plain,
( in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_dom(X3)
| ~ relation(X3) ),
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]) ).
fof(c_0_15,plain,
! [X82,X83] : unordered_pair(X82,X83) = unordered_pair(X83,X82),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_16,plain,
( in(ordered_pair(X1,esk4_5(X2,X3,X4,X1,X5)),X2)
| ~ in(ordered_pair(X1,X5),X4)
| X4 != relation_composition(X2,X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( 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_12]) ).
cnf(c_0_18,plain,
( in(ordered_pair(X1,esk1_3(X3,X2,X1)),X3)
| ~ in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,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_13,c_0_14]) ).
cnf(c_0_20,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( in(unordered_pair(unordered_pair(X1,esk4_5(X2,X3,X4,X1,X5)),singleton(X1)),X2)
| X4 != relation_composition(X2,X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X5),singleton(X1)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_14]),c_0_14]) ).
cnf(c_0_22,plain,
( X2 = apply(X3,X1)
| ~ function(X3)
| ~ relation(X3)
| ~ in(X1,relation_dom(X3))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_23,plain,
( in(unordered_pair(unordered_pair(X1,esk1_3(X3,X2,X1)),singleton(X1)),X3)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_24,plain,
( in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X4)),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk4_5(X2,X3,X4,X1,X5))),X2)
| X4 != relation_composition(X2,X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X5),singleton(X1)),X4) ),
inference(rw,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_26,plain,
( in(ordered_pair(esk4_5(X1,X2,X3,X4,X5),X5),X2)
| ~ in(ordered_pair(X4,X5),X3)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_27,plain,
( X1 = apply(X2,X3)
| ~ relation(X2)
| ~ function(X2)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),X2)
| ~ in(X3,relation_dom(X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_28,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk1_3(X2,X3,X1))),X2)
| X3 != relation_dom(X2)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_23,c_0_20]) ).
fof(c_0_29,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
=> apply(relation_composition(X3,X2),X1) = apply(X2,apply(X3,X1)) ) ) ),
inference(assume_negation,[status(cth)],[t22_funct_1]) ).
cnf(c_0_30,plain,
( in(X1,X2)
| X3 != relation_composition(X4,X5)
| X2 != relation_dom(X4)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X5)
| ~ in(unordered_pair(unordered_pair(X1,X6),singleton(X1)),X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( in(unordered_pair(unordered_pair(esk4_5(X1,X2,X3,X4,X5),X5),singleton(esk4_5(X1,X2,X3,X4,X5))),X2)
| X3 != relation_composition(X1,X2)
| ~ relation(X3)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_14]),c_0_14]) ).
cnf(c_0_32,plain,
( esk1_3(X1,X2,X3) = apply(X1,X3)
| X2 != relation_dom(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X3,relation_dom(X1))
| ~ in(X3,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_33,negated_conjecture,
( relation(esk18_0)
& function(esk18_0)
& relation(esk19_0)
& function(esk19_0)
& in(esk17_0,relation_dom(relation_composition(esk19_0,esk18_0)))
& apply(relation_composition(esk19_0,esk18_0),esk17_0) != apply(esk18_0,apply(esk19_0,esk17_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
cnf(c_0_34,plain,
( in(X1,X2)
| X3 != relation_composition(X4,X5)
| X2 != relation_dom(X4)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X5)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X6)),X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_20]) ).
fof(c_0_35,plain,
! [X112,X113] :
( ~ relation(X112)
| ~ relation(X113)
| relation(relation_composition(X112,X113)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])]) ).
cnf(c_0_36,plain,
( X1 = apply(X2,X3)
| ~ relation(X2)
| ~ function(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X3)),X2)
| ~ in(X3,relation_dom(X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_37,plain,
( in(unordered_pair(unordered_pair(X1,esk4_5(X2,X3,X4,X5,X1)),singleton(esk4_5(X2,X3,X4,X5,X1))),X3)
| X4 != relation_composition(X2,X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X5,X1),singleton(X5)),X4) ),
inference(rw,[status(thm)],[c_0_31,c_0_20]) ).
cnf(c_0_38,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_12]) ).
cnf(c_0_39,plain,
( esk4_5(X1,X2,X3,X4,X5) = apply(X1,X4)
| X3 != relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ function(X1)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X3)
| ~ in(X4,relation_dom(X1)) ),
inference(spm,[status(thm)],[c_0_27,c_0_25]) ).
cnf(c_0_40,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,apply(X2,X1))),X2)
| X3 != relation_dom(X2)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X1,relation_dom(X2))
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_28,c_0_32]) ).
cnf(c_0_41,negated_conjecture,
in(esk17_0,relation_dom(relation_composition(esk19_0,esk18_0))),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,plain,
( in(X1,X2)
| X3 != relation_composition(X4,X5)
| X2 != relation_dom(X4)
| X6 != relation_dom(X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X5)
| ~ in(X1,X6) ),
inference(spm,[status(thm)],[c_0_34,c_0_28]) ).
cnf(c_0_43,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,plain,
( in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X4,X1),singleton(X1)),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_45,plain,
( apply(X1,esk4_5(X2,X1,X3,X4,X5)) = X5
| X3 != relation_composition(X2,X1)
| ~ relation(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ function(X1)
| ~ in(esk4_5(X2,X1,X3,X4,X5),relation_dom(X1))
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X3) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_46,plain,
( in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2)
| X1 != apply(X2,X3)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(X2)) ),
inference(rw,[status(thm)],[c_0_38,c_0_14]) ).
cnf(c_0_47,plain,
( esk4_5(X1,X2,X3,X4,X5) = apply(X1,X4)
| X3 != relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ function(X1)
| ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),X3)
| ~ in(X4,relation_dom(X1)) ),
inference(spm,[status(thm)],[c_0_39,c_0_20]) ).
cnf(c_0_48,negated_conjecture,
( in(unordered_pair(singleton(esk17_0),unordered_pair(esk17_0,apply(X1,esk17_0))),X1)
| relation_dom(relation_composition(esk19_0,esk18_0)) != relation_dom(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(esk17_0,relation_dom(X1)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,plain,
( in(X1,X2)
| X3 != relation_dom(relation_composition(X4,X5))
| X2 != relation_dom(X4)
| ~ relation(X4)
| ~ relation(X5)
| ~ in(X1,X3) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_42]),c_0_43]) ).
cnf(c_0_50,plain,
( in(esk4_5(X1,X2,X3,X4,X5),X6)
| X3 != relation_composition(X1,X2)
| X6 != relation_dom(X2)
| ~ relation(X2)
| ~ relation(X3)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X3) ),
inference(spm,[status(thm)],[c_0_44,c_0_37]) ).
cnf(c_0_51,plain,
( apply(X1,esk4_5(X2,X1,X3,X4,X5)) = X5
| X3 != relation_composition(X2,X1)
| X5 != apply(X3,X4)
| ~ relation(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ function(X1)
| ~ function(X3)
| ~ in(esk4_5(X2,X1,X3,X4,X5),relation_dom(X1))
| ~ in(X4,relation_dom(X3)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,negated_conjecture,
( esk4_5(X1,X2,X3,esk17_0,apply(X3,esk17_0)) = apply(X1,esk17_0)
| relation_dom(relation_composition(esk19_0,esk18_0)) != relation_dom(X3)
| X3 != relation_composition(X1,X2)
| ~ relation(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ function(X1)
| ~ function(X3)
| ~ in(esk17_0,relation_dom(X1))
| ~ in(esk17_0,relation_dom(X3)) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,plain,
( in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ relation(X4)
| ~ in(X1,relation_dom(relation_composition(X3,X4))) ),
inference(er,[status(thm)],[c_0_49]) ).
cnf(c_0_54,negated_conjecture,
relation(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_55,negated_conjecture,
relation(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_56,plain,
( in(esk4_5(X1,X2,X3,X4,X5),X6)
| X3 != relation_composition(X1,X2)
| X5 != apply(X3,X4)
| X6 != relation_dom(X2)
| ~ relation(X2)
| ~ relation(X3)
| ~ relation(X1)
| ~ function(X3)
| ~ in(X4,relation_dom(X3)) ),
inference(spm,[status(thm)],[c_0_50,c_0_46]) ).
cnf(c_0_57,negated_conjecture,
( apply(X1,apply(X2,esk17_0)) = apply(X3,esk17_0)
| relation_dom(relation_composition(esk19_0,esk18_0)) != relation_dom(X3)
| X3 != relation_composition(X2,X1)
| ~ relation(X1)
| ~ relation(X3)
| ~ relation(X2)
| ~ function(X1)
| ~ function(X3)
| ~ function(X2)
| ~ in(apply(X2,esk17_0),relation_dom(X1))
| ~ in(esk17_0,relation_dom(X3))
| ~ in(esk17_0,relation_dom(X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_58,negated_conjecture,
( in(esk17_0,X1)
| X1 != relation_dom(esk19_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_41]),c_0_54]),c_0_55])]) ).
cnf(c_0_59,negated_conjecture,
( in(apply(X1,esk17_0),X2)
| relation_dom(relation_composition(esk19_0,esk18_0)) != relation_dom(X3)
| X3 != relation_composition(X1,X4)
| X2 != relation_dom(X4)
| ~ relation(X4)
| ~ relation(X3)
| ~ relation(X1)
| ~ function(X3)
| ~ function(X1)
| ~ in(esk17_0,relation_dom(X3))
| ~ in(esk17_0,relation_dom(X1)) ),
inference(spm,[status(thm)],[c_0_56,c_0_52]) ).
cnf(c_0_60,negated_conjecture,
apply(relation_composition(esk19_0,esk18_0),esk17_0) != apply(esk18_0,apply(esk19_0,esk17_0)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_61,negated_conjecture,
( apply(X1,apply(X2,esk17_0)) = apply(relation_composition(esk19_0,esk18_0),esk17_0)
| relation_composition(esk19_0,esk18_0) != relation_composition(X2,X1)
| ~ relation(relation_composition(esk19_0,esk18_0))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(relation_composition(esk19_0,esk18_0))
| ~ function(X1)
| ~ function(X2)
| ~ in(apply(X2,esk17_0),relation_dom(X1))
| ~ in(esk17_0,relation_dom(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_57]),c_0_41])]) ).
cnf(c_0_62,negated_conjecture,
function(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_63,negated_conjecture,
function(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_64,negated_conjecture,
in(esk17_0,relation_dom(esk19_0)),
inference(er,[status(thm)],[c_0_58]) ).
cnf(c_0_65,negated_conjecture,
( in(apply(X1,esk17_0),X2)
| relation_composition(esk19_0,esk18_0) != relation_composition(X1,X3)
| X2 != relation_dom(X3)
| ~ relation(relation_composition(esk19_0,esk18_0))
| ~ relation(X3)
| ~ relation(X1)
| ~ function(relation_composition(esk19_0,esk18_0))
| ~ function(X1)
| ~ in(esk17_0,relation_dom(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_59]),c_0_41])]) ).
cnf(c_0_66,negated_conjecture,
( ~ relation(relation_composition(esk19_0,esk18_0))
| ~ function(relation_composition(esk19_0,esk18_0))
| ~ in(apply(esk19_0,esk17_0),relation_dom(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_60,c_0_61]),c_0_55]),c_0_54]),c_0_62]),c_0_63]),c_0_64])]) ).
cnf(c_0_67,negated_conjecture,
( in(apply(esk19_0,esk17_0),X1)
| X1 != relation_dom(esk18_0)
| ~ relation(relation_composition(esk19_0,esk18_0))
| ~ function(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(er,[status(thm)],[c_0_65]),c_0_55]),c_0_54]),c_0_63]),c_0_64])]) ).
fof(c_0_68,plain,
! [X118,X119] :
( ( relation(relation_composition(X118,X119))
| ~ relation(X118)
| ~ function(X118)
| ~ relation(X119)
| ~ function(X119) )
& ( function(relation_composition(X118,X119))
| ~ relation(X118)
| ~ function(X118)
| ~ relation(X119)
| ~ function(X119) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_funct_1])])]) ).
cnf(c_0_69,negated_conjecture,
( ~ relation(relation_composition(esk19_0,esk18_0))
| ~ function(relation_composition(esk19_0,esk18_0)) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_70,plain,
( function(relation_composition(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_71,negated_conjecture,
~ relation(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(spm,[status(thm)],[c_0_69,c_0_70]),c_0_55]),c_0_54]),c_0_62]),c_0_63])]) ).
cnf(c_0_72,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_43]),c_0_55]),c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU214+3 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n022.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:48:51 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 79.49/50.60 % Version : CSE_E---1.7
% 79.49/50.60 % Problem : theBenchmark.p
% 79.49/50.60 % SZS status Theorem for theBenchmark.p
% 79.49/50.60 % SZS output start CNFRefutation
% See solution above
% 79.79/50.97 % Total time : 40.738s
%------------------------------------------------------------------------------