%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU417+2 : TPTP v9.2.1. Released v3.4.0.
% 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 : n029.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 05:12:14 PM UTC 2026
% Result : Theorem 5.38s 4.74s
% Output : CNFRefutation 5.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 49 ( 17 unt; 0 def)
% Number of atoms : 119 ( 17 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 124 ( 54 ~; 45 |; 8 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 104 ( 4 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t7_relset_2,conjecture,
! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1)))
=> r1_tarski(k5_subset_1(X1,k8_setfam_1(X1,X2),k8_setfam_1(X1,X3)),k8_setfam_1(X1,k1_relset_2(X1,X2,X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_relset_2) ).
fof(t8_mssubfam,axiom,
! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1)))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(k1_zfmisc_1(X1)))
=> ( X2 = k4_subset_1(k1_zfmisc_1(X1),X3,X4)
=> k8_setfam_1(X1,X2) = k5_subset_1(X1,k8_setfam_1(X1,X3),k8_setfam_1(X1,X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+188.ax',t8_mssubfam) ).
fof(dt_k4_subset_1,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X2,k1_zfmisc_1(X1))
& m1_subset_1(X3,k1_zfmisc_1(X1)) )
=> m1_subset_1(k4_subset_1(X1,X2,X3),k1_zfmisc_1(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+7.ax',dt_k4_subset_1) ).
fof(redefinition_k4_subset_1,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X2,k1_zfmisc_1(X1))
& m1_subset_1(X3,k1_zfmisc_1(X1)) )
=> k4_subset_1(X1,X2,X3) = k2_xboole_0(X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+7.ax',redefinition_k4_subset_1) ).
fof(t59_setfam_1,axiom,
! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1)))
=> ( r1_tarski(X2,X3)
=> r1_tarski(k8_setfam_1(X1,X3),k8_setfam_1(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+8.ax',t59_setfam_1) ).
fof(dt_k1_relset_2,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))
& m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1))) )
=> m1_subset_1(k1_relset_2(X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relset_2) ).
fof(redefinition_k1_relset_2,axiom,
! [X1,X2,X3] :
( ( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))
& m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1))) )
=> k1_relset_2(X1,X2,X3) = k3_xboole_0(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_relset_2) ).
fof(t48_xboole_1,axiom,
! [X1,X2] : k4_xboole_0(X1,k4_xboole_0(X1,X2)) = k3_xboole_0(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t48_xboole_1) ).
fof(t29_xboole_1,axiom,
! [X1,X2,X3] : r1_tarski(k3_xboole_0(X1,X2),k2_xboole_0(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t29_xboole_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( m1_subset_1(X1,k1_zfmisc_1(X2))
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+9.ax',t3_subset) ).
fof(t8_xboole_1,axiom,
! [X1,X2,X3] :
( ( r1_tarski(X1,X2)
& r1_tarski(X3,X2) )
=> r1_tarski(k2_xboole_0(X1,X3),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t8_xboole_1) ).
fof(c_0_11,negated_conjecture,
~ ! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1)))
=> r1_tarski(k5_subset_1(X1,k8_setfam_1(X1,X2),k8_setfam_1(X1,X3)),k8_setfam_1(X1,k1_relset_2(X1,X2,X3))) ) ),
inference(assume_negation,[status(cth)],[t7_relset_2]) ).
fof(c_0_12,plain,
! [X1466,X1467,X1468,X1469] :
( ~ m1_subset_1(X1467,k1_zfmisc_1(k1_zfmisc_1(X1466)))
| ~ m1_subset_1(X1468,k1_zfmisc_1(k1_zfmisc_1(X1466)))
| ~ m1_subset_1(X1469,k1_zfmisc_1(k1_zfmisc_1(X1466)))
| X1467 != k4_subset_1(k1_zfmisc_1(X1466),X1468,X1469)
| k8_setfam_1(X1466,X1467) = k5_subset_1(X1466,k8_setfam_1(X1466,X1468),k8_setfam_1(X1466,X1469)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_mssubfam])])]) ).
fof(c_0_13,plain,
! [X1810,X1811,X1812] :
( ~ m1_subset_1(X1811,k1_zfmisc_1(X1810))
| ~ m1_subset_1(X1812,k1_zfmisc_1(X1810))
| m1_subset_1(k4_subset_1(X1810,X1811,X1812),k1_zfmisc_1(X1810)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_subset_1])]) ).
fof(c_0_14,negated_conjecture,
( m1_subset_1(esk2_0,k1_zfmisc_1(k1_zfmisc_1(esk1_0)))
& m1_subset_1(esk3_0,k1_zfmisc_1(k1_zfmisc_1(esk1_0)))
& ~ r1_tarski(k5_subset_1(esk1_0,k8_setfam_1(esk1_0,esk2_0),k8_setfam_1(esk1_0,esk3_0)),k8_setfam_1(esk1_0,k1_relset_2(esk1_0,esk2_0,esk3_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
cnf(c_0_15,plain,
( k8_setfam_1(X2,X1) = k5_subset_1(X2,k8_setfam_1(X2,X3),k8_setfam_1(X2,X4))
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X2)))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X2)))
| ~ m1_subset_1(X4,k1_zfmisc_1(k1_zfmisc_1(X2)))
| X1 != k4_subset_1(k1_zfmisc_1(X2),X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( m1_subset_1(k4_subset_1(X2,X1,X3),k1_zfmisc_1(X2))
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ m1_subset_1(X3,k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
~ r1_tarski(k5_subset_1(esk1_0,k8_setfam_1(esk1_0,esk2_0),k8_setfam_1(esk1_0,esk3_0)),k8_setfam_1(esk1_0,k1_relset_2(esk1_0,esk2_0,esk3_0))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( k5_subset_1(X1,k8_setfam_1(X1,X2),k8_setfam_1(X1,X3)) = k8_setfam_1(X1,k4_subset_1(k1_zfmisc_1(X1),X2,X3))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1))) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_15]),c_0_16]) ).
cnf(c_0_19,negated_conjecture,
m1_subset_1(esk3_0,k1_zfmisc_1(k1_zfmisc_1(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
m1_subset_1(esk2_0,k1_zfmisc_1(k1_zfmisc_1(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_21,plain,
! [X1819,X1820,X1821] :
( ~ m1_subset_1(X1820,k1_zfmisc_1(X1819))
| ~ m1_subset_1(X1821,k1_zfmisc_1(X1819))
| k4_subset_1(X1819,X1820,X1821) = k2_xboole_0(X1820,X1821) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_subset_1])]) ).
cnf(c_0_22,negated_conjecture,
~ r1_tarski(k8_setfam_1(esk1_0,k4_subset_1(k1_zfmisc_1(esk1_0),esk2_0,esk3_0)),k8_setfam_1(esk1_0,k1_relset_2(esk1_0,esk2_0,esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]) ).
cnf(c_0_23,plain,
( k4_subset_1(X2,X1,X3) = k2_xboole_0(X1,X3)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ m1_subset_1(X3,k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_24,plain,
! [X1440,X1441,X1442] :
( ~ m1_subset_1(X1441,k1_zfmisc_1(k1_zfmisc_1(X1440)))
| ~ m1_subset_1(X1442,k1_zfmisc_1(k1_zfmisc_1(X1440)))
| ~ r1_tarski(X1441,X1442)
| r1_tarski(k8_setfam_1(X1440,X1442),k8_setfam_1(X1440,X1441)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t59_setfam_1])])]) ).
cnf(c_0_25,negated_conjecture,
~ r1_tarski(k8_setfam_1(esk1_0,k2_xboole_0(esk2_0,esk3_0)),k8_setfam_1(esk1_0,k1_relset_2(esk1_0,esk2_0,esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_19]),c_0_20])]) ).
cnf(c_0_26,plain,
( r1_tarski(k8_setfam_1(X2,X3),k8_setfam_1(X2,X1))
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X2)))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X2)))
| ~ r1_tarski(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_27,plain,
! [X1477,X1478,X1479] :
( ~ m1_subset_1(X1478,k1_zfmisc_1(k1_zfmisc_1(X1477)))
| ~ m1_subset_1(X1479,k1_zfmisc_1(k1_zfmisc_1(X1477)))
| m1_subset_1(k1_relset_2(X1477,X1478,X1479),k1_zfmisc_1(k1_zfmisc_1(X1477))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_relset_2])]) ).
fof(c_0_28,plain,
! [X1486,X1487,X1488] :
( ~ m1_subset_1(X1487,k1_zfmisc_1(k1_zfmisc_1(X1486)))
| ~ m1_subset_1(X1488,k1_zfmisc_1(k1_zfmisc_1(X1486)))
| k1_relset_2(X1486,X1487,X1488) = k3_xboole_0(X1487,X1488) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k1_relset_2])]) ).
fof(c_0_29,plain,
! [X2084,X2085] : k4_xboole_0(X2084,k4_xboole_0(X2084,X2085)) = k3_xboole_0(X2084,X2085),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(c_0_30,plain,
! [X2073,X2074,X2075] : r1_tarski(k3_xboole_0(X2073,X2074),k2_xboole_0(X2073,X2075)),
inference(variable_rename,[status(thm)],[t29_xboole_1]) ).
cnf(c_0_31,negated_conjecture,
( ~ m1_subset_1(k1_relset_2(esk1_0,esk2_0,esk3_0),k1_zfmisc_1(k1_zfmisc_1(esk1_0)))
| ~ m1_subset_1(k2_xboole_0(esk2_0,esk3_0),k1_zfmisc_1(k1_zfmisc_1(esk1_0)))
| ~ r1_tarski(k1_relset_2(esk1_0,esk2_0,esk3_0),k2_xboole_0(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
( m1_subset_1(k1_relset_2(X2,X1,X3),k1_zfmisc_1(k1_zfmisc_1(X2)))
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X2)))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
( k1_relset_2(X2,X1,X3) = k3_xboole_0(X1,X3)
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X2)))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
k4_xboole_0(X1,k4_xboole_0(X1,X2)) = k3_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
r1_tarski(k3_xboole_0(X1,X2),k2_xboole_0(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( ~ m1_subset_1(k2_xboole_0(esk2_0,esk3_0),k1_zfmisc_1(k1_zfmisc_1(esk1_0)))
| ~ r1_tarski(k1_relset_2(esk1_0,esk2_0,esk3_0),k2_xboole_0(esk2_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_19]),c_0_20])]) ).
cnf(c_0_37,plain,
( k1_relset_2(X2,X1,X3) = k4_xboole_0(X1,k4_xboole_0(X1,X3))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X2)))
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X2))) ),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
r1_tarski(k4_xboole_0(X1,k4_xboole_0(X1,X2)),k2_xboole_0(X1,X3)),
inference(rw,[status(thm)],[c_0_35,c_0_34]) ).
fof(c_0_39,plain,
! [X1558,X1559] :
( ( ~ m1_subset_1(X1558,k1_zfmisc_1(X1559))
| r1_tarski(X1558,X1559) )
& ( ~ r1_tarski(X1558,X1559)
| m1_subset_1(X1558,k1_zfmisc_1(X1559)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
cnf(c_0_40,negated_conjecture,
~ m1_subset_1(k2_xboole_0(esk2_0,esk3_0),k1_zfmisc_1(k1_zfmisc_1(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_19]),c_0_20])]) ).
cnf(c_0_41,plain,
( m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_42,plain,
! [X2407,X2408,X2409] :
( ~ r1_tarski(X2407,X2408)
| ~ r1_tarski(X2409,X2408)
| r1_tarski(k2_xboole_0(X2407,X2409),X2408) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])]) ).
cnf(c_0_43,plain,
( r1_tarski(X1,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_44,negated_conjecture,
~ r1_tarski(k2_xboole_0(esk2_0,esk3_0),k1_zfmisc_1(esk1_0)),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,plain,
( r1_tarski(k2_xboole_0(X1,X3),X2)
| ~ r1_tarski(X1,X2)
| ~ r1_tarski(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_46,negated_conjecture,
r1_tarski(esk3_0,k1_zfmisc_1(esk1_0)),
inference(spm,[status(thm)],[c_0_43,c_0_19]) ).
cnf(c_0_47,negated_conjecture,
r1_tarski(esk2_0,k1_zfmisc_1(esk1_0)),
inference(spm,[status(thm)],[c_0_43,c_0_20]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU417+2 : TPTP v9.2.1. Released v3.4.0.
% 0.12/0.13 % 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
% 0.17/0.35 % Computer : n029.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue May 5 03:08:30 EDT 2026
% 0.17/0.35 % CPUTime :
% 0.21/0.36 % start to proof: theBenchmark
% 5.38/4.74 % Version : CSE_E---1.7
% 5.38/4.74 % Problem : theBenchmark.p
% 5.38/4.74 % SZS status Theorem for theBenchmark.p
% 5.38/4.74 % SZS output start CNFRefutation
% See solution above
% 5.38/4.75 % Total time : 4.018s
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