%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU368+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 : n018.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 05:12:05 PM UTC 2026
% Result : Theorem 1.31s 1.72s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 17 unt; 0 def)
% Number of atoms : 84 ( 42 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 73 ( 29 ~; 24 |; 15 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 63 ( 8 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dt_k1_yellow_1) ).
fof(redefinition_k1_yellow_1,axiom,
! [X1] : inclusion_order(X1) = inclusion_relation(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_yellow_1) ).
fof(d1_yellow_1,axiom,
! [X1] : incl_POSet(X1) = rel_str_of(X1,inclusion_order(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_yellow_1) ).
fof(t1_yellow_1,conjecture,
! [X1] :
( the_carrier(incl_POSet(X1)) = X1
& the_InternalRel(incl_POSet(X1)) = inclusion_order(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_yellow_1) ).
fof(dt_k2_yellow_1,axiom,
! [X1] :
( strict_rel_str(incl_POSet(X1))
& rel_str(incl_POSet(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_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/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
fof(c_0_8,plain,
! [X129,X130,X131,X132] :
( ( X129 = X131
| rel_str_of(X129,X130) != rel_str_of(X131,X132)
| ~ relation_of2(X130,X129,X129) )
& ( X130 = X132
| rel_str_of(X129,X130) != rel_str_of(X131,X132)
| ~ relation_of2(X130,X129,X129) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[free_g1_orders_2])])])]) ).
fof(c_0_9,plain,
! [X139,X140,X141] :
( ( ~ relation_of2_as_subset(X141,X139,X140)
| relation_of2(X141,X139,X140) )
& ( ~ relation_of2(X141,X139,X140)
| relation_of2_as_subset(X141,X139,X140) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_10,plain,
! [X152] :
( reflexive(inclusion_order(X152))
& antisymmetric(inclusion_order(X152))
& transitive(inclusion_order(X152))
& v1_partfun1(inclusion_order(X152),X152,X152)
& relation_of2_as_subset(inclusion_order(X152),X152,X152) ),
inference(variable_rename,[status(thm)],[dt_k1_yellow_1]) ).
fof(c_0_11,plain,
! [X151] : inclusion_order(X151) = inclusion_relation(X151),
inference(variable_rename,[status(thm)],[redefinition_k1_yellow_1]) ).
fof(c_0_12,plain,
! [X156] : incl_POSet(X156) = rel_str_of(X156,inclusion_order(X156)),
inference(variable_rename,[status(thm)],[d1_yellow_1]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( the_carrier(incl_POSet(X1)) = X1
& the_InternalRel(incl_POSet(X1)) = inclusion_order(X1) ),
inference(assume_negation,[status(cth)],[t1_yellow_1]) ).
cnf(c_0_14,plain,
( X1 = X2
| rel_str_of(X3,X1) != rel_str_of(X4,X2)
| ~ relation_of2(X1,X3,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
relation_of2_as_subset(inclusion_order(X1),X1,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
inclusion_order(X1) = inclusion_relation(X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_18,plain,
! [X153] :
( strict_rel_str(incl_POSet(X153))
& rel_str(incl_POSet(X153)) ),
inference(variable_rename,[status(thm)],[dt_k2_yellow_1]) ).
cnf(c_0_19,plain,
incl_POSet(X1) = rel_str_of(X1,inclusion_order(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_20,negated_conjecture,
( the_carrier(incl_POSet(esk14_0)) != esk14_0
| the_InternalRel(incl_POSet(esk14_0)) != inclusion_order(esk14_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
cnf(c_0_21,plain,
( X1 = X2
| rel_str_of(X3,X1) != rel_str_of(X4,X2)
| ~ relation_of2_as_subset(X1,X3,X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
relation_of2_as_subset(inclusion_relation(X1),X1,X1),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_23,plain,
! [X133] :
( ~ rel_str(X133)
| ~ strict_rel_str(X133)
| X133 = rel_str_of(the_carrier(X133),the_InternalRel(X133)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v1_orders_2])]) ).
cnf(c_0_24,plain,
strict_rel_str(incl_POSet(X1)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
incl_POSet(X1) = rel_str_of(X1,inclusion_relation(X1)),
inference(rw,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_26,plain,
rel_str(incl_POSet(X1)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,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_8]) ).
cnf(c_0_28,negated_conjecture,
( the_carrier(incl_POSet(esk14_0)) != esk14_0
| the_InternalRel(incl_POSet(esk14_0)) != inclusion_order(esk14_0) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
( inclusion_relation(X1) = X2
| rel_str_of(X1,inclusion_relation(X1)) != rel_str_of(X3,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,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_23]) ).
cnf(c_0_31,plain,
strict_rel_str(rel_str_of(X1,inclusion_relation(X1))),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
rel_str(rel_str_of(X1,inclusion_relation(X1))),
inference(rw,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_33,plain,
( X1 = X2
| rel_str_of(X1,X3) != rel_str_of(X2,X4)
| ~ relation_of2_as_subset(X3,X1,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_15]) ).
cnf(c_0_34,negated_conjecture,
( the_carrier(rel_str_of(esk14_0,inclusion_relation(esk14_0))) != esk14_0
| the_InternalRel(rel_str_of(esk14_0,inclusion_relation(esk14_0))) != inclusion_relation(esk14_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_17]),c_0_25]),c_0_25]) ).
cnf(c_0_35,plain,
the_InternalRel(rel_str_of(X1,inclusion_relation(X1))) = inclusion_relation(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30])]),c_0_31]),c_0_32])]) ).
cnf(c_0_36,plain,
( X1 = X2
| rel_str_of(X1,inclusion_relation(X1)) != rel_str_of(X2,X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_37,negated_conjecture,
the_carrier(rel_str_of(esk14_0,inclusion_relation(esk14_0))) != esk14_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).
cnf(c_0_38,plain,
the_carrier(rel_str_of(X1,inclusion_relation(X1))) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_30])]),c_0_31]),c_0_32])]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU368+1 : 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
% 0.14/0.32 % Computer : n018.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 03:00:47 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.31/1.72 % Version : CSE_E---1.7
% 1.31/1.72 % Problem : theBenchmark.p
% 1.31/1.72 % SZS status Theorem for theBenchmark.p
% 1.31/1.72 % SZS output start CNFRefutation
% See solution above
% 1.31/1.73 % Total time : 1.373s
%------------------------------------------------------------------------------