%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU382+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 : n027.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 05:12:07 PM UTC 2026
% Result : Theorem 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 19 unt; 0 def)
% Number of atoms : 65 ( 26 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 50 ( 18 ~; 14 |; 13 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 46 ( 4 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(dt_k1_yellow_1,axiom,
! [X1] :
( reflexive(inclusion_order(X1))
& antisymmetric(inclusion_order(X1))
& transitive(inclusion_order(X1))
& v1_partfun1(inclusion_order(X1),X1,X1)
& relation_of2_as_subset(inclusion_order(X1),X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_yellow_1) ).
fof(t4_waybel_7,conjecture,
! [X1] : the_carrier(boole_POSet(X1)) = powerset(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_waybel_7) ).
fof(free_g1_orders_2,axiom,
! [X1,X2] :
( relation_of2(X2,X1,X1)
=> ! [X3,X4] :
( rel_str_of(X1,X2) = rel_str_of(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_orders_2) ).
fof(dt_k2_yellow_1,axiom,
! [X1] :
( strict_rel_str(incl_POSet(X1))
& rel_str(incl_POSet(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_yellow_1) ).
fof(d1_yellow_1,axiom,
! [X1] : incl_POSet(X1) = rel_str_of(X1,inclusion_order(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_yellow_1) ).
fof(t4_yellow_1,axiom,
! [X1] : boole_POSet(X1) = incl_POSet(powerset(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_yellow_1) ).
fof(abstractness_v1_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> ( strict_rel_str(X1)
=> X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
fof(c_0_8,plain,
! [X207,X208,X209] :
( ( ~ relation_of2_as_subset(X209,X207,X208)
| relation_of2(X209,X207,X208) )
& ( ~ relation_of2(X209,X207,X208)
| relation_of2_as_subset(X209,X207,X208) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_9,plain,
! [X150] :
( reflexive(inclusion_order(X150))
& antisymmetric(inclusion_order(X150))
& transitive(inclusion_order(X150))
& v1_partfun1(inclusion_order(X150),X150,X150)
& relation_of2_as_subset(inclusion_order(X150),X150,X150) ),
inference(variable_rename,[status(thm)],[dt_k1_yellow_1]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] : the_carrier(boole_POSet(X1)) = powerset(X1),
inference(assume_negation,[status(cth)],[t4_waybel_7]) ).
fof(c_0_11,plain,
! [X181,X182,X183,X184] :
( ( X181 = X183
| rel_str_of(X181,X182) != rel_str_of(X183,X184)
| ~ relation_of2(X182,X181,X181) )
& ( X182 = X184
| rel_str_of(X181,X182) != rel_str_of(X183,X184)
| ~ relation_of2(X182,X181,X181) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[free_g1_orders_2])])])]) ).
cnf(c_0_12,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
relation_of2_as_subset(inclusion_order(X1),X1,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X151] :
( strict_rel_str(incl_POSet(X151))
& rel_str(incl_POSet(X151)) ),
inference(variable_rename,[status(thm)],[dt_k2_yellow_1]) ).
fof(c_0_15,plain,
! [X146] : incl_POSet(X146) = rel_str_of(X146,inclusion_order(X146)),
inference(variable_rename,[status(thm)],[d1_yellow_1]) ).
fof(c_0_16,negated_conjecture,
the_carrier(boole_POSet(esk22_0)) != powerset(esk22_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_17,plain,
! [X221] : boole_POSet(X221) = incl_POSet(powerset(X221)),
inference(variable_rename,[status(thm)],[t4_yellow_1]) ).
cnf(c_0_18,plain,
( X1 = X2
| rel_str_of(X1,X3) != rel_str_of(X2,X4)
| ~ relation_of2(X3,X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
relation_of2(inclusion_order(X1),X1,X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_20,plain,
! [X118] :
( ~ rel_str(X118)
| ~ strict_rel_str(X118)
| X118 = rel_str_of(the_carrier(X118),the_InternalRel(X118)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v1_orders_2])]) ).
cnf(c_0_21,plain,
strict_rel_str(incl_POSet(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
incl_POSet(X1) = rel_str_of(X1,inclusion_order(X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
rel_str(incl_POSet(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,negated_conjecture,
the_carrier(boole_POSet(esk22_0)) != powerset(esk22_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
boole_POSet(X1) = incl_POSet(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
( X1 = X2
| rel_str_of(X1,inclusion_order(X1)) != rel_str_of(X2,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,plain,
( X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1))
| ~ rel_str(X1)
| ~ strict_rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
strict_rel_str(rel_str_of(X1,inclusion_order(X1))),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
rel_str(rel_str_of(X1,inclusion_order(X1))),
inference(rw,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_30,negated_conjecture,
the_carrier(rel_str_of(powerset(esk22_0),inclusion_order(powerset(esk22_0)))) != powerset(esk22_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_22]) ).
cnf(c_0_31,plain,
the_carrier(rel_str_of(X1,inclusion_order(X1))) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27])]),c_0_28]),c_0_29])]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU382+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
% 0.14/0.33 % Computer : n027.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 03:02:20 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Theorem for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.370s
%------------------------------------------------------------------------------