%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU180+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 : n005.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 1.24s 1.72s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 13 unt; 0 def)
% Number of atoms : 145 ( 32 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 175 ( 72 ~; 75 |; 15 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 3 con; 0-3 aty)
% Number of variables : 101 ( 9 sgn 48 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
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(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(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(c_0_7,plain,
! [X63,X64,X65,X66,X67,X68,X69,X70] :
( ( ~ in(X66,X65)
| in(X66,X63)
| in(X66,X64)
| X65 != set_union2(X63,X64) )
& ( ~ in(X67,X63)
| in(X67,X65)
| X65 != set_union2(X63,X64) )
& ( ~ in(X67,X64)
| in(X67,X65)
| X65 != set_union2(X63,X64) )
& ( ~ in(esk1_3(X68,X69,X70),X68)
| ~ in(esk1_3(X68,X69,X70),X70)
| X70 = set_union2(X68,X69) )
& ( ~ in(esk1_3(X68,X69,X70),X69)
| ~ in(esk1_3(X68,X69,X70),X70)
| X70 = set_union2(X68,X69) )
& ( in(esk1_3(X68,X69,X70),X70)
| in(esk1_3(X68,X69,X70),X68)
| in(esk1_3(X68,X69,X70),X69)
| X70 = set_union2(X68,X69) ) ),
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])])])])])]) ).
fof(c_0_8,plain,
! [X82,X83,X84,X86,X87,X88,X90] :
( ( ~ in(X84,X83)
| in(ordered_pair(esk5_3(X82,X83,X84),X84),X82)
| X83 != relation_rng(X82)
| ~ relation(X82) )
& ( ~ in(ordered_pair(X87,X86),X82)
| in(X86,X83)
| X83 != relation_rng(X82)
| ~ relation(X82) )
& ( ~ in(esk6_2(X82,X88),X88)
| ~ in(ordered_pair(X90,esk6_2(X82,X88)),X82)
| X88 = relation_rng(X82)
| ~ relation(X82) )
& ( in(esk6_2(X82,X88),X88)
| in(ordered_pair(esk7_2(X82,X88),esk6_2(X82,X88)),X82)
| X88 = relation_rng(X82)
| ~ relation(X82) ) ),
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,
! [X92,X93] : ordered_pair(X92,X93) = unordered_pair(unordered_pair(X92,X93),singleton(X92)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_10,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]) ).
cnf(c_0_11,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X94] :
( ~ relation(X94)
| relation_field(X94) = set_union2(relation_dom(X94),relation_rng(X94)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_relat_1])]) ).
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,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,negated_conjecture,
( relation(esk14_0)
& in(ordered_pair(esk12_0,esk13_0),esk14_0)
& ( ~ in(esk12_0,relation_field(esk14_0))
| ~ in(esk13_0,relation_field(esk14_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_16,plain,
! [X72,X73,X74,X76,X77,X78,X80] :
( ( ~ in(X74,X73)
| in(ordered_pair(X74,esk2_3(X72,X73,X74)),X72)
| X73 != relation_dom(X72)
| ~ relation(X72) )
& ( ~ in(ordered_pair(X76,X77),X72)
| in(X76,X73)
| X73 != relation_dom(X72)
| ~ relation(X72) )
& ( ~ in(esk3_2(X72,X78),X78)
| ~ in(ordered_pair(esk3_2(X72,X78),X80),X72)
| X78 = relation_dom(X72)
| ~ relation(X72) )
& ( in(esk3_2(X72,X78),X78)
| in(ordered_pair(esk3_2(X72,X78),esk4_2(X72,X78)),X72)
| X78 = relation_dom(X72)
| ~ relation(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)],[d4_relat_1])])])])])]) ).
cnf(c_0_17,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( relation_field(X1) = set_union2(relation_dom(X1),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,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_14]) ).
fof(c_0_21,plain,
! [X59,X60] : unordered_pair(X59,X60) = unordered_pair(X60,X59),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_22,negated_conjecture,
in(ordered_pair(esk12_0,esk13_0),esk14_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
( ~ in(esk12_0,relation_field(esk14_0))
| ~ in(esk13_0,relation_field(esk14_0)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,plain,
( in(X1,relation_field(X2))
| ~ relation(X2)
| ~ in(X1,relation_rng(X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,negated_conjecture,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_27,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,negated_conjecture,
in(unordered_pair(unordered_pair(esk12_0,esk13_0),singleton(esk12_0)),esk14_0),
inference(rw,[status(thm)],[c_0_22,c_0_14]) ).
cnf(c_0_31,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_23,c_0_14]) ).
cnf(c_0_32,negated_conjecture,
( ~ in(esk12_0,relation_field(esk14_0))
| ~ in(esk13_0,relation_rng(esk14_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_33,plain,
( in(X1,relation_field(X2))
| ~ relation(X2)
| ~ in(X1,relation_dom(X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_18]) ).
cnf(c_0_34,plain,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,negated_conjecture,
in(unordered_pair(singleton(esk12_0),unordered_pair(esk12_0,esk13_0)),esk14_0),
inference(rw,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_36,plain,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X2) ),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_37,negated_conjecture,
( ~ in(esk13_0,relation_rng(esk14_0))
| ~ in(esk12_0,relation_dom(esk14_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_26])]) ).
cnf(c_0_38,negated_conjecture,
in(esk13_0,relation_rng(esk14_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_26])]) ).
cnf(c_0_39,plain,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_29]) ).
cnf(c_0_40,negated_conjecture,
~ in(esk12_0,relation_dom(esk14_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_35]),c_0_26])]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU180+1 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.14/0.32 % Computer : n005.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:47:30 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.24/1.72 % Version : CSE_E---1.7
% 1.24/1.72 % Problem : theBenchmark.p
% 1.24/1.72 % SZS status Theorem for theBenchmark.p
% 1.24/1.72 % SZS output start CNFRefutation
% See solution above
% 1.24/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------