%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU208+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n004.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 05:11:03 PM UTC 2026
% Result : Theorem 1.34s 1.75s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 46 ( 13 unt; 0 def)
% Number of atoms : 170 ( 26 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 212 ( 88 ~; 97 |; 17 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-4 aty)
% Number of variables : 101 ( 1 sgn 38 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d14_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(ordered_pair(X4,X5),X1)
& in(X5,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(t166_relat_1,conjecture,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_inverse_image(X3,X2))
<=> ? [X4] :
( in(X4,relation_rng(X3))
& in(ordered_pair(X1,X4),X3)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).
fof(d5_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(c_0_5,plain,
! [X53,X54,X55,X56,X58,X59,X60,X61,X63] :
( ( in(ordered_pair(X56,esk1_4(X53,X54,X55,X56)),X53)
| ~ in(X56,X55)
| X55 != relation_inverse_image(X53,X54)
| ~ relation(X53) )
& ( in(esk1_4(X53,X54,X55,X56),X54)
| ~ in(X56,X55)
| X55 != relation_inverse_image(X53,X54)
| ~ relation(X53) )
& ( ~ in(ordered_pair(X58,X59),X53)
| ~ in(X59,X54)
| in(X58,X55)
| X55 != relation_inverse_image(X53,X54)
| ~ relation(X53) )
& ( ~ in(esk2_3(X53,X60,X61),X61)
| ~ in(ordered_pair(esk2_3(X53,X60,X61),X63),X53)
| ~ in(X63,X60)
| X61 = relation_inverse_image(X53,X60)
| ~ relation(X53) )
& ( in(ordered_pair(esk2_3(X53,X60,X61),esk3_3(X53,X60,X61)),X53)
| in(esk2_3(X53,X60,X61),X61)
| X61 = relation_inverse_image(X53,X60)
| ~ relation(X53) )
& ( in(esk3_3(X53,X60,X61),X60)
| in(esk2_3(X53,X60,X61),X61)
| X61 = relation_inverse_image(X53,X60)
| ~ relation(X53) ) ),
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)],[d14_relat_1])])])])])]) ).
fof(c_0_6,plain,
! [X75,X76] : ordered_pair(X75,X76) = unordered_pair(unordered_pair(X75,X76),singleton(X75)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_inverse_image(X3,X2))
<=> ? [X4] :
( in(X4,relation_rng(X3))
& in(ordered_pair(X1,X4),X3)
& in(X4,X2) ) ) ),
inference(assume_negation,[status(cth)],[t166_relat_1]) ).
fof(c_0_8,plain,
! [X65,X66,X67,X69,X70,X71,X73] :
( ( ~ in(X67,X66)
| in(ordered_pair(esk4_3(X65,X66,X67),X67),X65)
| X66 != relation_rng(X65)
| ~ relation(X65) )
& ( ~ in(ordered_pair(X70,X69),X65)
| in(X69,X66)
| X66 != relation_rng(X65)
| ~ relation(X65) )
& ( ~ in(esk5_2(X65,X71),X71)
| ~ in(ordered_pair(X73,esk5_2(X65,X71)),X65)
| X71 = relation_rng(X65)
| ~ relation(X65) )
& ( in(esk5_2(X65,X71),X71)
| in(ordered_pair(esk6_2(X65,X71),esk5_2(X65,X71)),X65)
| X71 = relation_rng(X65)
| ~ relation(X65) ) ),
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)],[d5_relat_1])])])])])]) ).
cnf(c_0_9,plain,
( in(ordered_pair(X1,esk1_4(X2,X3,X4,X1)),X2)
| ~ in(X1,X4)
| X4 != relation_inverse_image(X2,X3)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,plain,
! [X51,X52] : unordered_pair(X51,X52) = unordered_pair(X52,X51),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_12,negated_conjecture,
! [X93] :
( relation(esk14_0)
& ( ~ in(esk12_0,relation_inverse_image(esk14_0,esk13_0))
| ~ in(X93,relation_rng(esk14_0))
| ~ in(ordered_pair(esk12_0,X93),esk14_0)
| ~ in(X93,esk13_0) )
& ( in(esk15_0,relation_rng(esk14_0))
| in(esk12_0,relation_inverse_image(esk14_0,esk13_0)) )
& ( in(ordered_pair(esk12_0,esk15_0),esk14_0)
| in(esk12_0,relation_inverse_image(esk14_0,esk13_0)) )
& ( in(esk15_0,esk13_0)
| in(esk12_0,relation_inverse_image(esk14_0,esk13_0)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
cnf(c_0_13,plain,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( in(unordered_pair(unordered_pair(X1,esk1_4(X2,X3,X4,X1)),singleton(X1)),X2)
| X4 != relation_inverse_image(X2,X3)
| ~ relation(X2)
| ~ in(X1,X4) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
( ~ in(esk12_0,relation_inverse_image(esk14_0,esk13_0))
| ~ in(X1,relation_rng(esk14_0))
| ~ in(ordered_pair(esk12_0,X1),esk14_0)
| ~ in(X1,esk13_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( in(esk1_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != relation_inverse_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,plain,
( in(X2,X4)
| X4 != relation_rng(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_19,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk1_4(X2,X3,X4,X1))),X2)
| X4 != relation_inverse_image(X2,X3)
| ~ relation(X2)
| ~ in(X1,X4) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( in(X1,X5)
| ~ in(ordered_pair(X1,X2),X3)
| ~ in(X2,X4)
| X5 != relation_inverse_image(X3,X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_21,negated_conjecture,
( ~ in(X1,esk13_0)
| ~ in(X1,relation_rng(esk14_0))
| ~ in(esk12_0,relation_inverse_image(esk14_0,esk13_0))
| ~ in(unordered_pair(unordered_pair(esk12_0,X1),singleton(esk12_0)),esk14_0) ),
inference(rw,[status(thm)],[c_0_16,c_0_10]) ).
cnf(c_0_22,negated_conjecture,
( in(esk15_0,esk13_0)
| in(esk12_0,relation_inverse_image(esk14_0,esk13_0)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,plain,
( in(esk1_4(X1,X2,relation_inverse_image(X1,X2),X3),X2)
| ~ relation(X1)
| ~ in(X3,relation_inverse_image(X1,X2)) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,plain,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk1_4(X2,X3,relation_inverse_image(X2,X3),X1))),X2)
| ~ relation(X2)
| ~ in(X1,relation_inverse_image(X2,X3)) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( in(X1,X5)
| X5 != relation_inverse_image(X3,X4)
| ~ relation(X3)
| ~ in(X2,X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_20,c_0_10]) ).
cnf(c_0_28,negated_conjecture,
( in(ordered_pair(esk12_0,esk15_0),esk14_0)
| in(esk12_0,relation_inverse_image(esk14_0,esk13_0)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_29,negated_conjecture,
( in(esk15_0,esk13_0)
| ~ in(unordered_pair(unordered_pair(esk12_0,X1),singleton(esk12_0)),esk14_0)
| ~ in(X1,relation_rng(esk14_0))
| ~ in(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,negated_conjecture,
( in(esk1_4(esk14_0,esk13_0,relation_inverse_image(esk14_0,esk13_0),esk12_0),esk13_0)
| in(esk15_0,esk13_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_24])]) ).
cnf(c_0_31,plain,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_15]) ).
cnf(c_0_32,negated_conjecture,
( in(unordered_pair(singleton(esk12_0),unordered_pair(esk12_0,esk1_4(esk14_0,esk13_0,relation_inverse_image(esk14_0,esk13_0),esk12_0))),esk14_0)
| in(esk15_0,esk13_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_22]),c_0_24])]) ).
cnf(c_0_33,plain,
( in(X1,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X4),singleton(X1)),X2)
| ~ in(X4,X3) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_34,negated_conjecture,
( in(esk12_0,relation_inverse_image(esk14_0,esk13_0))
| in(unordered_pair(unordered_pair(esk12_0,esk15_0),singleton(esk12_0)),esk14_0) ),
inference(rw,[status(thm)],[c_0_28,c_0_10]) ).
cnf(c_0_35,negated_conjecture,
( in(esk15_0,esk13_0)
| ~ in(unordered_pair(singleton(esk12_0),unordered_pair(esk12_0,esk1_4(esk14_0,esk13_0,relation_inverse_image(esk14_0,esk13_0),esk12_0))),esk14_0)
| ~ in(esk1_4(esk14_0,esk13_0,relation_inverse_image(esk14_0,esk13_0),esk12_0),relation_rng(esk14_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_15]) ).
cnf(c_0_36,negated_conjecture,
( in(esk1_4(esk14_0,esk13_0,relation_inverse_image(esk14_0,esk13_0),esk12_0),relation_rng(esk14_0))
| in(esk15_0,esk13_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_24])]) ).
cnf(c_0_37,negated_conjecture,
( in(esk12_0,relation_inverse_image(esk14_0,esk13_0))
| in(esk12_0,relation_inverse_image(esk14_0,X1))
| ~ in(esk15_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_24])]) ).
cnf(c_0_38,negated_conjecture,
in(esk15_0,esk13_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_32]) ).
cnf(c_0_39,negated_conjecture,
in(esk12_0,relation_inverse_image(esk14_0,esk13_0)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(esk12_0,X1),singleton(esk12_0)),esk14_0)
| ~ in(X1,relation_rng(esk14_0))
| ~ in(X1,esk13_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_39])]) ).
cnf(c_0_41,negated_conjecture,
in(esk1_4(esk14_0,esk13_0,relation_inverse_image(esk14_0,esk13_0),esk12_0),esk13_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_39]),c_0_24])]) ).
cnf(c_0_42,negated_conjecture,
( ~ in(unordered_pair(singleton(esk12_0),unordered_pair(esk12_0,esk1_4(esk14_0,esk13_0,relation_inverse_image(esk14_0,esk13_0),esk12_0))),esk14_0)
| ~ in(esk1_4(esk14_0,esk13_0,relation_inverse_image(esk14_0,esk13_0),esk12_0),relation_rng(esk14_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_15]) ).
cnf(c_0_43,negated_conjecture,
in(unordered_pair(singleton(esk12_0),unordered_pair(esk12_0,esk1_4(esk14_0,esk13_0,relation_inverse_image(esk14_0,esk13_0),esk12_0))),esk14_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_39]),c_0_24])]) ).
cnf(c_0_44,negated_conjecture,
~ in(esk1_4(esk14_0,esk13_0,relation_inverse_image(esk14_0,esk13_0),esk12_0),relation_rng(esk14_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_43]),c_0_24])]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU208+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n004.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:48:32 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.34/1.75 % Version : CSE_E---1.7
% 1.34/1.75 % Problem : theBenchmark.p
% 1.34/1.75 % SZS status Theorem for theBenchmark.p
% 1.34/1.75 % SZS output start CNFRefutation
% See solution above
% 1.34/1.75 % Total time : 1.372s
%------------------------------------------------------------------------------