%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU178+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 : n012.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 05:10:57 PM UTC 2026
% Result : Theorem 1.98s 1.84s
% Output : CNFRefutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 9 unt; 0 def)
% Number of atoms : 183 ( 34 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 229 ( 95 ~; 107 |; 15 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 1 con; 0-3 aty)
% Number of variables : 142 ( 4 sgn 55 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(d1_relat_1,axiom,
! [X1] :
( relation(X1)
<=> ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_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(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/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(t106_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(t21_relat_1,conjecture,
! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
fof(c_0_8,plain,
! [X95,X96,X97,X99,X100,X101,X103] :
( ( ~ in(X97,X96)
| in(ordered_pair(esk8_3(X95,X96,X97),X97),X95)
| X96 != relation_rng(X95)
| ~ relation(X95) )
& ( ~ in(ordered_pair(X100,X99),X95)
| in(X99,X96)
| X96 != relation_rng(X95)
| ~ relation(X95) )
& ( ~ in(esk9_2(X95,X101),X101)
| ~ in(ordered_pair(X103,esk9_2(X95,X101)),X95)
| X101 = relation_rng(X95)
| ~ relation(X95) )
& ( in(esk9_2(X95,X101),X101)
| in(ordered_pair(esk10_2(X95,X101),esk9_2(X95,X101)),X95)
| X101 = relation_rng(X95)
| ~ relation(X95) ) ),
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])])])])])]) ).
fof(c_0_9,plain,
! [X105,X106] : ordered_pair(X105,X106) = unordered_pair(unordered_pair(X105,X106),singleton(X105)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_10,plain,
! [X71,X72,X75,X77,X78] :
( ( ~ relation(X71)
| ~ in(X72,X71)
| X72 = ordered_pair(esk1_2(X71,X72),esk2_2(X71,X72)) )
& ( in(esk3_1(X75),X75)
| relation(X75) )
& ( esk3_1(X75) != ordered_pair(X77,X78)
| relation(X75) ) ),
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)],[d1_relat_1])])])])])]) ).
cnf(c_0_11,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_12,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X69,X70] : unordered_pair(X69,X70) = unordered_pair(X70,X69),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_14,plain,
( X2 = ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2))
| ~ relation(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X85,X86,X87,X89,X90,X91,X93] :
( ( ~ in(X87,X86)
| in(ordered_pair(X87,esk5_3(X85,X86,X87)),X85)
| X86 != relation_dom(X85)
| ~ relation(X85) )
& ( ~ in(ordered_pair(X89,X90),X85)
| in(X89,X86)
| X86 != relation_dom(X85)
| ~ relation(X85) )
& ( ~ in(esk6_2(X85,X91),X91)
| ~ in(ordered_pair(esk6_2(X85,X91),X93),X85)
| X91 = relation_dom(X85)
| ~ relation(X85) )
& ( in(esk6_2(X85,X91),X91)
| in(ordered_pair(esk6_2(X85,X91),esk7_2(X85,X91)),X85)
| X91 = relation_dom(X85)
| ~ relation(X85) ) ),
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])])])])])]) ).
cnf(c_0_16,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_11,c_0_12]) ).
cnf(c_0_17,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( X2 = unordered_pair(unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),singleton(esk1_2(X1,X2)))
| ~ relation(X1)
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_19,plain,
( in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( in(X1,X2)
| X2 != relation_rng(X3)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X1)),X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( unordered_pair(singleton(esk1_2(X1,X2)),unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2))) = X2
| ~ relation(X1)
| ~ in(X2,X1) ),
inference(rw,[status(thm)],[c_0_18,c_0_17]) ).
fof(c_0_22,plain,
! [X79,X80,X81,X82,X83] :
( ( ~ subset(X79,X80)
| ~ in(X81,X79)
| in(X81,X80) )
& ( in(esk4_2(X82,X83),X82)
| subset(X82,X83) )
& ( ~ in(esk4_2(X82,X83),X83)
| subset(X82,X83) ) ),
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])])])])])]) ).
cnf(c_0_23,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_19,c_0_12]) ).
fof(c_0_24,plain,
! [X125,X126,X127,X128] :
( ( in(X125,X127)
| ~ in(ordered_pair(X125,X126),cartesian_product2(X127,X128)) )
& ( in(X126,X128)
| ~ in(ordered_pair(X125,X126),cartesian_product2(X127,X128)) )
& ( ~ in(X125,X127)
| ~ in(X126,X128)
| in(ordered_pair(X125,X126),cartesian_product2(X127,X128)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t106_zfmisc_1])])]) ).
cnf(c_0_25,plain,
( in(esk2_2(X1,X2),X3)
| X3 != relation_rng(X4)
| ~ relation(X4)
| ~ relation(X1)
| ~ in(X2,X4)
| ~ in(X2,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( in(esk4_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,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_23,c_0_17]) ).
cnf(c_0_28,plain,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
( subset(X1,X2)
| in(esk2_2(X3,esk4_2(X1,X2)),X4)
| X4 != relation_rng(X1)
| ~ relation(X1)
| ~ relation(X3)
| ~ in(esk4_2(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_30,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
inference(assume_negation,[status(cth)],[t21_relat_1]) ).
cnf(c_0_31,plain,
( in(esk1_2(X1,X2),X3)
| X3 != relation_dom(X4)
| ~ relation(X4)
| ~ relation(X1)
| ~ in(X2,X4)
| ~ in(X2,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_21]) ).
cnf(c_0_32,plain,
( in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_28,c_0_12]) ).
cnf(c_0_33,plain,
( subset(X1,X2)
| in(esk2_2(X1,esk4_2(X1,X2)),X3)
| X3 != relation_rng(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_26]) ).
fof(c_0_34,negated_conjecture,
( relation(esk17_0)
& ~ subset(esk17_0,cartesian_product2(relation_dom(esk17_0),relation_rng(esk17_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])]) ).
cnf(c_0_35,plain,
( subset(X1,X2)
| in(esk1_2(X3,esk4_2(X1,X2)),X4)
| X4 != relation_dom(X1)
| ~ relation(X1)
| ~ relation(X3)
| ~ in(esk4_2(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_26]) ).
cnf(c_0_36,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_32,c_0_17]) ).
cnf(c_0_37,plain,
( subset(X1,X2)
| in(esk2_2(X1,esk4_2(X1,X2)),relation_rng(X1))
| ~ relation(X1) ),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
relation(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,plain,
( subset(X1,X2)
| in(esk1_2(X1,esk4_2(X1,X2)),X3)
| X3 != relation_dom(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_26]) ).
cnf(c_0_40,plain,
( in(X1,cartesian_product2(X2,X3))
| ~ relation(X4)
| ~ in(esk2_2(X4,X1),X3)
| ~ in(esk1_2(X4,X1),X2)
| ~ in(X1,X4) ),
inference(spm,[status(thm)],[c_0_36,c_0_21]) ).
cnf(c_0_41,negated_conjecture,
( subset(esk17_0,X1)
| in(esk2_2(esk17_0,esk4_2(esk17_0,X1)),relation_rng(esk17_0)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
( subset(X1,X2)
| in(esk1_2(X1,esk4_2(X1,X2)),relation_dom(X1))
| ~ relation(X1) ),
inference(er,[status(thm)],[c_0_39]) ).
cnf(c_0_43,negated_conjecture,
( subset(esk17_0,X1)
| in(esk4_2(esk17_0,X1),cartesian_product2(X2,relation_rng(esk17_0)))
| ~ in(esk1_2(esk17_0,esk4_2(esk17_0,X1)),X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_38])]),c_0_26]) ).
cnf(c_0_44,negated_conjecture,
( subset(esk17_0,X1)
| in(esk1_2(esk17_0,esk4_2(esk17_0,X1)),relation_dom(esk17_0)) ),
inference(spm,[status(thm)],[c_0_42,c_0_38]) ).
cnf(c_0_45,plain,
( subset(X1,X2)
| ~ in(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_46,negated_conjecture,
( subset(esk17_0,X1)
| in(esk4_2(esk17_0,X1),cartesian_product2(relation_dom(esk17_0),relation_rng(esk17_0))) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,negated_conjecture,
~ subset(esk17_0,cartesian_product2(relation_dom(esk17_0),relation_rng(esk17_0))),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SEU178+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.08 % 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
% 0.07/0.29 % Computer : n012.cluster.edu
% 0.07/0.29 % Model : x86_64 x86_64
% 0.07/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.29 % Memory : 8042.1875MB
% 0.07/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.29 % CPULimit : 300
% 0.07/0.29 % WCLimit : 300
% 0.07/0.29 % DateTime : Tue May 5 02:47:30 EDT 2026
% 0.07/0.29 % CPUTime :
% 0.07/0.29 % start to proof: theBenchmark
% 1.98/1.84 % Version : CSE_E---1.7
% 1.98/1.84 % Problem : theBenchmark.p
% 1.98/1.84 % SZS status Theorem for theBenchmark.p
% 1.98/1.84 % SZS output start CNFRefutation
% See solution above
% 1.98/1.85 % Total time : 1.361s
%------------------------------------------------------------------------------