%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU182+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n015.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 05:10:58 PM UTC 2026
% Result : Theorem 1.56s 1.77s
% Output : CNFRefutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 10 unt; 0 def)
% Number of atoms : 191 ( 39 equ)
% Maximal formula atoms : 38 ( 4 avg)
% Number of connectives : 267 ( 116 ~; 122 |; 14 &)
% ( 5 <=>; 10 =>; 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 : 15 ( 15 usr; 2 con; 0-5 aty)
% Number of variables : 130 ( 5 sgn 48 !; 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(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(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(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(t44_relat_1,conjecture,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_relat_1) ).
fof(c_0_7,plain,
! [X74,X75,X76,X78,X79,X80,X82] :
( ( ~ in(X76,X75)
| in(ordered_pair(X76,esk2_3(X74,X75,X76)),X74)
| X75 != relation_dom(X74)
| ~ relation(X74) )
& ( ~ in(ordered_pair(X78,X79),X74)
| in(X78,X75)
| X75 != relation_dom(X74)
| ~ relation(X74) )
& ( ~ in(esk3_2(X74,X80),X80)
| ~ in(ordered_pair(esk3_2(X74,X80),X82),X74)
| X80 = relation_dom(X74)
| ~ relation(X74) )
& ( in(esk3_2(X74,X80),X80)
| in(ordered_pair(esk3_2(X74,X80),esk4_2(X74,X80)),X74)
| X80 = relation_dom(X74)
| ~ relation(X74) ) ),
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_8,plain,
! [X84,X85] : ordered_pair(X84,X85) = unordered_pair(unordered_pair(X84,X85),singleton(X84)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_9,plain,
! [X86,X87,X88,X89,X90,X92,X93,X94,X97] :
( ( in(ordered_pair(X89,esk5_5(X86,X87,X88,X89,X90)),X86)
| ~ in(ordered_pair(X89,X90),X88)
| X88 != relation_composition(X86,X87)
| ~ relation(X88)
| ~ relation(X87)
| ~ relation(X86) )
& ( in(ordered_pair(esk5_5(X86,X87,X88,X89,X90),X90),X87)
| ~ in(ordered_pair(X89,X90),X88)
| X88 != relation_composition(X86,X87)
| ~ relation(X88)
| ~ relation(X87)
| ~ relation(X86) )
& ( ~ in(ordered_pair(X92,X94),X86)
| ~ in(ordered_pair(X94,X93),X87)
| in(ordered_pair(X92,X93),X88)
| X88 != relation_composition(X86,X87)
| ~ relation(X88)
| ~ relation(X87)
| ~ relation(X86) )
& ( ~ in(ordered_pair(esk6_3(X86,X87,X88),esk7_3(X86,X87,X88)),X88)
| ~ in(ordered_pair(esk6_3(X86,X87,X88),X97),X86)
| ~ in(ordered_pair(X97,esk7_3(X86,X87,X88)),X87)
| X88 = relation_composition(X86,X87)
| ~ relation(X88)
| ~ relation(X87)
| ~ relation(X86) )
& ( in(ordered_pair(esk6_3(X86,X87,X88),esk8_3(X86,X87,X88)),X86)
| in(ordered_pair(esk6_3(X86,X87,X88),esk7_3(X86,X87,X88)),X88)
| X88 = relation_composition(X86,X87)
| ~ relation(X88)
| ~ relation(X87)
| ~ relation(X86) )
& ( in(ordered_pair(esk8_3(X86,X87,X88),esk7_3(X86,X87,X88)),X87)
| in(ordered_pair(esk6_3(X86,X87,X88),esk7_3(X86,X87,X88)),X88)
| X88 = relation_composition(X86,X87)
| ~ relation(X88)
| ~ relation(X87)
| ~ relation(X86) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_relat_1])])])])])]) ).
cnf(c_0_10,plain,
( in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_dom(X3)
| ~ relation(X3) ),
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,
! [X66,X67] : unordered_pair(X66,X67) = unordered_pair(X67,X66),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_13,plain,
( in(ordered_pair(X1,esk5_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_9]) ).
cnf(c_0_14,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_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,esk5_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_13,c_0_11]),c_0_11]) ).
cnf(c_0_17,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_14,c_0_15]) ).
cnf(c_0_18,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk5_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_16,c_0_15]) ).
cnf(c_0_19,plain,
( in(ordered_pair(X1,esk2_3(X3,X2,X1)),X3)
| ~ in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,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_17,c_0_18]) ).
cnf(c_0_21,plain,
( in(unordered_pair(unordered_pair(X1,esk2_3(X3,X2,X1)),singleton(X1)),X3)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_19,c_0_11]) ).
cnf(c_0_22,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_20,c_0_15]) ).
cnf(c_0_23,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk2_3(X2,X3,X1))),X2)
| X3 != relation_dom(X2)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_21,c_0_15]) ).
fof(c_0_24,plain,
! [X99,X100] :
( ~ relation(X99)
| ~ relation(X100)
| relation(relation_composition(X99,X100)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])]) ).
cnf(c_0_25,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_22,c_0_23]) ).
cnf(c_0_26,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_27,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_25]),c_0_26]) ).
fof(c_0_28,plain,
! [X68,X69,X70,X71,X72] :
( ( ~ subset(X68,X69)
| ~ in(X70,X68)
| in(X70,X69) )
& ( in(esk1_2(X71,X72),X71)
| subset(X71,X72) )
& ( ~ in(esk1_2(X71,X72),X72)
| subset(X71,X72) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])]) ).
fof(c_0_29,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1)) ) ),
inference(assume_negation,[status(cth)],[t44_relat_1]) ).
cnf(c_0_30,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_27]) ).
cnf(c_0_31,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_32,negated_conjecture,
( relation(esk15_0)
& relation(esk16_0)
& ~ subset(relation_dom(relation_composition(esk15_0,esk16_0)),relation_dom(esk15_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
cnf(c_0_33,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
( subset(relation_dom(relation_composition(X1,X2)),X3)
| in(esk1_2(relation_dom(relation_composition(X1,X2)),X3),X4)
| X4 != relation_dom(X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
~ subset(relation_dom(relation_composition(esk15_0,esk16_0)),relation_dom(esk15_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
( subset(relation_dom(relation_composition(X1,X2)),X3)
| X3 != relation_dom(X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,negated_conjecture,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU182+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.09 % 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
% 0.11/0.29 % Computer : n015.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue May 5 02:47:31 EDT 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.30 % start to proof: theBenchmark
% 1.56/1.77 % Version : CSE_E---1.7
% 1.56/1.77 % Problem : theBenchmark.p
% 1.56/1.77 % SZS status Theorem for theBenchmark.p
% 1.56/1.77 % SZS output start CNFRefutation
% See solution above
% 1.56/1.78 % Total time : 1.368s
%------------------------------------------------------------------------------