%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU180+2 : 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 : n029.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 3.72s 3.17s
% Output : CNFRefutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 27 unt; 0 def)
% Number of atoms : 123 ( 26 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 116 ( 45 ~; 47 |; 13 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 95 ( 7 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(t30_relat_1,conjecture,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
fof(d6_relat_1,axiom,
! [X1] :
( relation(X1)
=> relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t20_relat_1,lemma,
! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_dom(X3))
& in(X2,relation_rng(X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
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(t7_xboole_1,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_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(c_0_10,plain,
! [X474,X475] : ordered_pair(X474,X475) = unordered_pair(unordered_pair(X474,X475),singleton(X474)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_11,lemma,
! [X694] : unordered_pair(X694,X694) = singleton(X694),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X1,X2),X3)
=> ( in(X1,relation_field(X3))
& in(X2,relation_field(X3)) ) ) ),
inference(assume_negation,[status(cth)],[t30_relat_1]) ).
fof(c_0_13,plain,
! [X476] :
( ~ relation(X476)
| relation_field(X476) = set_union2(relation_dom(X476),relation_rng(X476)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_relat_1])]) ).
fof(c_0_14,plain,
! [X334,X335] : set_union2(X334,X335) = set_union2(X335,X334),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_15,lemma,
! [X600,X601,X602] :
( ( in(X600,relation_dom(X602))
| ~ in(ordered_pair(X600,X601),X602)
| ~ relation(X602) )
& ( in(X601,relation_rng(X602))
| ~ in(ordered_pair(X600,X601),X602)
| ~ relation(X602) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_relat_1])])]) ).
cnf(c_0_16,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_18,negated_conjecture,
( relation(esk41_0)
& in(ordered_pair(esk39_0,esk40_0),esk41_0)
& ( ~ in(esk39_0,relation_field(esk41_0))
| ~ in(esk40_0,relation_field(esk41_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_19,plain,
! [X390,X391,X392,X393,X394,X395,X396,X397] :
( ( ~ in(X393,X392)
| in(X393,X390)
| in(X393,X391)
| X392 != set_union2(X390,X391) )
& ( ~ in(X394,X390)
| in(X394,X392)
| X392 != set_union2(X390,X391) )
& ( ~ in(X394,X391)
| in(X394,X392)
| X392 != set_union2(X390,X391) )
& ( ~ in(esk11_3(X395,X396,X397),X395)
| ~ in(esk11_3(X395,X396,X397),X397)
| X397 = set_union2(X395,X396) )
& ( ~ in(esk11_3(X395,X396,X397),X396)
| ~ in(esk11_3(X395,X396,X397),X397)
| X397 = set_union2(X395,X396) )
& ( in(esk11_3(X395,X396,X397),X397)
| in(esk11_3(X395,X396,X397),X395)
| in(esk11_3(X395,X396,X397),X396)
| X397 = set_union2(X395,X396) ) ),
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)],[d2_xboole_0])])])])])]) ).
cnf(c_0_20,plain,
( relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,lemma,
( in(X1,relation_dom(X2))
| ~ in(ordered_pair(X1,X3),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_24,plain,
! [X332,X333] : unordered_pair(X332,X333) = unordered_pair(X333,X332),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_25,negated_conjecture,
in(ordered_pair(esk39_0,esk40_0),esk41_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( set_union2(relation_rng(X1),relation_dom(X1)) = relation_field(X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,negated_conjecture,
relation(esk41_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,lemma,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2) ),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
in(unordered_pair(unordered_pair(esk39_0,esk40_0),unordered_pair(esk39_0,esk39_0)),esk41_0),
inference(rw,[status(thm)],[c_0_25,c_0_23]) ).
fof(c_0_32,lemma,
! [X700,X701] : subset(X700,set_union2(X700,X701)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
cnf(c_0_33,lemma,
( in(X1,relation_rng(X2))
| ~ in(ordered_pair(X3,X1),X2)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_34,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_35,negated_conjecture,
set_union2(relation_rng(esk41_0),relation_dom(esk41_0)) = relation_field(esk41_0),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_36,lemma,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X3)),X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,negated_conjecture,
in(unordered_pair(unordered_pair(esk39_0,esk39_0),unordered_pair(esk39_0,esk40_0)),esk41_0),
inference(rw,[status(thm)],[c_0_31,c_0_30]) ).
fof(c_0_38,plain,
! [X416,X417,X418,X419,X420] :
( ( ~ subset(X416,X417)
| ~ in(X418,X416)
| in(X418,X417) )
& ( in(esk17_2(X419,X420),X419)
| subset(X419,X420) )
& ( ~ in(esk17_2(X419,X420),X420)
| subset(X419,X420) ) ),
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_39,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,lemma,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2) ),
inference(rw,[status(thm)],[c_0_33,c_0_23]) ).
cnf(c_0_41,negated_conjecture,
( in(X1,relation_field(esk41_0))
| ~ in(X1,relation_dom(esk41_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,negated_conjecture,
in(esk39_0,relation_dom(esk41_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_28])]) ).
cnf(c_0_43,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,lemma,
subset(relation_rng(esk41_0),relation_field(esk41_0)),
inference(spm,[status(thm)],[c_0_39,c_0_35]) ).
cnf(c_0_45,lemma,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,X1)),X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_30]) ).
cnf(c_0_46,negated_conjecture,
( ~ in(esk39_0,relation_field(esk41_0))
| ~ in(esk40_0,relation_field(esk41_0)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_47,negated_conjecture,
in(esk39_0,relation_field(esk41_0)),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,lemma,
( in(X1,relation_field(esk41_0))
| ~ in(X1,relation_rng(esk41_0)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,negated_conjecture,
in(esk40_0,relation_rng(esk41_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_37]),c_0_28])]) ).
cnf(c_0_50,negated_conjecture,
~ in(esk40_0,relation_field(esk41_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
cnf(c_0_51,lemma,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU180+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n029.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:47:45 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 3.72/3.17 % Version : CSE_E---1.7
% 3.72/3.17 % Problem : theBenchmark.p
% 3.72/3.17 % SZS status Theorem for theBenchmark.p
% 3.72/3.17 % SZS output start CNFRefutation
% See solution above
% 3.72/3.18 % Total time : 2.425s
%------------------------------------------------------------------------------