%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU263+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 : n026.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 05:11:17 PM UTC 2026
% Result : Theorem 1.48s 1.78s
% Output : CNFRefutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 9 unt; 0 def)
% Number of atoms : 108 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 103 ( 43 ~; 40 |; 8 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 112 ( 6 sgn 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
<=> subset(X3,cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
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(t1_xboole_1,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(t14_relset_1,conjecture,
! [X1,X2,X3,X4] :
( relation_of2_as_subset(X4,X3,X1)
=> ( subset(relation_rng(X4),X2)
=> relation_of2_as_subset(X4,X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
fof(t119_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(cc1_relset_1,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(dt_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> element(X3,powerset(cartesian_product2(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(t21_relat_1,axiom,
! [X1] :
( relation(X1)
=> subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
fof(t12_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( subset(relation_dom(X3),X1)
& subset(relation_rng(X3),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(c_0_10,plain,
! [X47,X48,X49] :
( ( ~ relation_of2(X49,X47,X48)
| subset(X49,cartesian_product2(X47,X48)) )
& ( ~ subset(X49,cartesian_product2(X47,X48))
| relation_of2(X49,X47,X48) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_relset_1])]) ).
fof(c_0_11,plain,
! [X61,X62,X63] :
( ( ~ relation_of2_as_subset(X63,X61,X62)
| relation_of2(X63,X61,X62) )
& ( ~ relation_of2(X63,X61,X62)
| relation_of2_as_subset(X63,X61,X62) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_12,plain,
! [X76,X77,X78] :
( ~ subset(X76,X77)
| ~ subset(X77,X78)
| subset(X76,X78) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
cnf(c_0_13,plain,
( subset(X1,cartesian_product2(X2,X3))
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( relation_of2_as_subset(X4,X3,X1)
=> ( subset(relation_rng(X4),X2)
=> relation_of2_as_subset(X4,X3,X2) ) ),
inference(assume_negation,[status(cth)],[t14_relset_1]) ).
fof(c_0_16,plain,
! [X65,X66,X67,X68] :
( ~ subset(X65,X66)
| ~ subset(X67,X68)
| subset(cartesian_product2(X65,X67),cartesian_product2(X66,X68)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t119_zfmisc_1])]) ).
fof(c_0_17,plain,
! [X44,X45,X46] :
( ~ element(X46,powerset(cartesian_product2(X44,X45)))
| relation(X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
fof(c_0_18,plain,
! [X50,X51,X52] :
( ~ relation_of2_as_subset(X52,X50,X51)
| element(X52,powerset(cartesian_product2(X50,X51))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).
cnf(c_0_19,plain,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( subset(X1,cartesian_product2(X2,X3))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_21,negated_conjecture,
( relation_of2_as_subset(esk7_0,esk6_0,esk4_0)
& subset(relation_rng(esk7_0),esk5_0)
& ~ relation_of2_as_subset(esk7_0,esk6_0,esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
cnf(c_0_22,plain,
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4))
| ~ subset(X1,X2)
| ~ subset(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_23,plain,
! [X79] :
( ~ relation(X79)
| subset(X79,cartesian_product2(relation_dom(X79),relation_rng(X79))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_relat_1])]) ).
cnf(c_0_24,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( relation_of2_as_subset(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_27,plain,
( relation_of2(X1,X2,X3)
| ~ subset(X1,cartesian_product2(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_28,plain,
( subset(X1,cartesian_product2(X2,X3))
| ~ relation_of2_as_subset(X4,X2,X3)
| ~ subset(X1,X4) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_29,negated_conjecture,
relation_of2_as_subset(esk7_0,esk6_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
( subset(X1,cartesian_product2(X2,X3))
| ~ subset(X1,cartesian_product2(X4,X5))
| ~ subset(X5,X3)
| ~ subset(X4,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_22]) ).
cnf(c_0_31,plain,
( subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1)))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
( relation(X1)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_33,plain,
! [X69,X70,X71] :
( ( subset(relation_dom(X71),X69)
| ~ relation_of2_as_subset(X71,X69,X70) )
& ( subset(relation_rng(X71),X70)
| ~ relation_of2_as_subset(X71,X69,X70) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_relset_1])])]) ).
cnf(c_0_34,plain,
( relation_of2_as_subset(X1,X2,X3)
| ~ subset(X1,cartesian_product2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( subset(X1,cartesian_product2(esk6_0,esk4_0))
| ~ subset(X1,esk7_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
( subset(X1,cartesian_product2(X2,X3))
| ~ subset(relation_rng(X1),X3)
| ~ subset(relation_dom(X1),X2)
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,negated_conjecture,
subset(relation_rng(esk7_0),esk5_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_38,negated_conjecture,
relation(esk7_0),
inference(spm,[status(thm)],[c_0_32,c_0_29]) ).
cnf(c_0_39,plain,
( subset(relation_dom(X1),X2)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,negated_conjecture,
( relation_of2_as_subset(X1,esk6_0,esk4_0)
| ~ subset(X1,esk7_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_41,plain,
! [X64] : subset(X64,X64),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_42,negated_conjecture,
( subset(esk7_0,cartesian_product2(X1,esk5_0))
| ~ subset(relation_dom(esk7_0),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_43,negated_conjecture,
( subset(relation_dom(X1),esk6_0)
| ~ subset(X1,esk7_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_45,negated_conjecture,
subset(esk7_0,cartesian_product2(esk6_0,esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_46,negated_conjecture,
~ relation_of2_as_subset(esk7_0,esk6_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_45]),c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU263+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
% 0.16/0.33 % Computer : n026.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:53:38 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.48/1.78 % Version : CSE_E---1.7
% 1.48/1.78 % Problem : theBenchmark.p
% 1.48/1.78 % SZS status Theorem for theBenchmark.p
% 1.48/1.78 % SZS output start CNFRefutation
% See solution above
% 1.48/1.79 % Total time : 1.372s
%------------------------------------------------------------------------------