%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU243+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 : n007.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 05:11:14 PM UTC 2026
% Result : Theorem 133.29s 92.69s
% Output : CNFRefutation 133.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 4 unt; 0 def)
% Number of atoms : 125 ( 14 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 168 ( 70 ~; 74 |; 16 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 44 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_wellord1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_well_founded_in(X1,X2)
<=> ! [X3] :
~ ( subset(X3,X2)
& X3 != empty_set
& ! [X4] :
~ ( in(X4,X3)
& disjoint(fiber(X1,X4),X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_wellord1) ).
fof(d2_wellord1,axiom,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> ! [X2] :
~ ( subset(X2,relation_field(X1))
& X2 != empty_set
& ! [X3] :
~ ( in(X3,X2)
& disjoint(fiber(X1,X3),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_wellord1) ).
fof(t5_wellord1,conjecture,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> is_well_founded_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord1) ).
fof(c_0_3,plain,
! [X856,X857,X858,X860,X862] :
( ( in(esk45_3(X856,X857,X858),X858)
| ~ subset(X858,X857)
| X858 = empty_set
| ~ is_well_founded_in(X856,X857)
| ~ relation(X856) )
& ( disjoint(fiber(X856,esk45_3(X856,X857,X858)),X858)
| ~ subset(X858,X857)
| X858 = empty_set
| ~ is_well_founded_in(X856,X857)
| ~ relation(X856) )
& ( subset(esk46_2(X856,X860),X860)
| is_well_founded_in(X856,X860)
| ~ relation(X856) )
& ( esk46_2(X856,X860) != empty_set
| is_well_founded_in(X856,X860)
| ~ relation(X856) )
& ( ~ in(X862,esk46_2(X856,X860))
| ~ disjoint(fiber(X856,X862),esk46_2(X856,X860))
| is_well_founded_in(X856,X860)
| ~ relation(X856) ) ),
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_wellord1])])])])])]) ).
fof(c_0_4,plain,
! [X807,X808,X811] :
( ( in(esk32_2(X807,X808),X808)
| ~ subset(X808,relation_field(X807))
| X808 = empty_set
| ~ well_founded_relation(X807)
| ~ relation(X807) )
& ( disjoint(fiber(X807,esk32_2(X807,X808)),X808)
| ~ subset(X808,relation_field(X807))
| X808 = empty_set
| ~ well_founded_relation(X807)
| ~ relation(X807) )
& ( subset(esk33_1(X807),relation_field(X807))
| well_founded_relation(X807)
| ~ relation(X807) )
& ( esk33_1(X807) != empty_set
| well_founded_relation(X807)
| ~ relation(X807) )
& ( ~ in(X811,esk33_1(X807))
| ~ disjoint(fiber(X807,X811),esk33_1(X807))
| well_founded_relation(X807)
| ~ relation(X807) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_wellord1])])])])]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> is_well_founded_in(X1,relation_field(X1)) ) ),
inference(assume_negation,[status(cth)],[t5_wellord1]) ).
cnf(c_0_6,plain,
( is_well_founded_in(X2,X3)
| ~ in(X1,esk46_2(X2,X3))
| ~ disjoint(fiber(X2,X1),esk46_2(X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_7,plain,
( disjoint(fiber(X1,esk32_2(X1,X2)),X2)
| X2 = empty_set
| ~ subset(X2,relation_field(X1))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( in(esk32_2(X1,X2),X2)
| X2 = empty_set
| ~ subset(X2,relation_field(X1))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,plain,
( is_well_founded_in(X1,X2)
| esk46_2(X1,X2) != empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_10,negated_conjecture,
( relation(esk118_0)
& ( ~ well_founded_relation(esk118_0)
| ~ is_well_founded_in(esk118_0,relation_field(esk118_0)) )
& ( well_founded_relation(esk118_0)
| is_well_founded_in(esk118_0,relation_field(esk118_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_11,plain,
( is_well_founded_in(X1,X2)
| ~ well_founded_relation(X1)
| ~ subset(esk46_2(X1,X2),relation_field(X1))
| ~ relation(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]),c_0_9]) ).
cnf(c_0_12,plain,
( subset(esk46_2(X1,X2),X2)
| is_well_founded_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_13,plain,
( well_founded_relation(X2)
| ~ in(X1,esk33_1(X2))
| ~ disjoint(fiber(X2,X1),esk33_1(X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_14,plain,
( disjoint(fiber(X1,esk45_3(X1,X2,X3)),X3)
| X3 = empty_set
| ~ subset(X3,X2)
| ~ is_well_founded_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_15,plain,
( in(esk45_3(X1,X2,X3),X3)
| X3 = empty_set
| ~ subset(X3,X2)
| ~ is_well_founded_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_16,plain,
( well_founded_relation(X1)
| esk33_1(X1) != empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_17,negated_conjecture,
( ~ well_founded_relation(esk118_0)
| ~ is_well_founded_in(esk118_0,relation_field(esk118_0)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( is_well_founded_in(X1,relation_field(X1))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_19,negated_conjecture,
relation(esk118_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20,plain,
( well_founded_relation(X1)
| ~ is_well_founded_in(X1,X2)
| ~ subset(esk33_1(X1),X2)
| ~ relation(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16]) ).
cnf(c_0_21,plain,
( subset(esk33_1(X1),relation_field(X1))
| well_founded_relation(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_22,negated_conjecture,
( well_founded_relation(esk118_0)
| is_well_founded_in(esk118_0,relation_field(esk118_0)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,negated_conjecture,
~ well_founded_relation(esk118_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_24,plain,
( well_founded_relation(X1)
| ~ is_well_founded_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
is_well_founded_in(esk118_0,relation_field(esk118_0)),
inference(sr,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_19])]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU243+2 : 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 : n007.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 02:51:24 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 133.29/92.69 % Version : CSE_E---1.7
% 133.29/92.69 % Problem : theBenchmark.p
% 133.29/92.69 % SZS status Theorem for theBenchmark.p
% 133.29/92.69 % SZS output start CNFRefutation
% See solution above
% 133.71/93.03 % Total time : 79.701s
%------------------------------------------------------------------------------