%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU438+3 : TPTP v9.2.1. Released v3.4.0.
% 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 : n013.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 05:12:21 PM UTC 2026
% Result : Theorem 18.59s 17.45s
% Output : CNFRefutation 18.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 13 unt; 0 def)
% Number of atoms : 99 ( 6 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 113 ( 51 ~; 41 |; 7 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 78 ( 2 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t41_relset_2,conjecture,
! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
=> ! [X5] :
( m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
=> r1_tarski(k4_subset_1(X2,k8_relset_2(X1,X2,X3,X4),k8_relset_2(X1,X2,X3,X5)),k8_relset_2(X1,X2,X3,k4_subset_1(k2_zfmisc_1(X1,X2),X4,X5))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_relset_2) ).
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/sandbox2/benchmark/Axioms/SET007/SET007+7.ax',redefinition_k4_subset_1) ).
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/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t8_xboole_1) ).
fof(t40_relset_2,axiom,
! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
=> ! [X5] :
( m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
=> ( r1_tarski(X4,X5)
=> r1_tarski(k8_relset_2(X1,X2,X3,X4),k8_relset_2(X1,X2,X3,X5)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_relset_2) ).
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/sandbox2/benchmark/Axioms/SET007/SET007+7.ax',dt_k4_subset_1) ).
fof(t7_xboole_1,axiom,
! [X1,X2] : r1_tarski(X1,k2_xboole_0(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+4.ax',t7_xboole_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+2.ax',commutativity_k2_xboole_0) ).
fof(dt_k8_relset_2,axiom,
! [X1,X2,X3,X4] :
( ( m1_subset_1(X3,k1_zfmisc_1(X1))
& m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) )
=> m1_subset_1(k8_relset_2(X1,X2,X3,X4),k1_zfmisc_1(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relset_2) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
=> ! [X5] :
( m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
=> r1_tarski(k4_subset_1(X2,k8_relset_2(X1,X2,X3,X4),k8_relset_2(X1,X2,X3,X5)),k8_relset_2(X1,X2,X3,k4_subset_1(k2_zfmisc_1(X1,X2),X4,X5))) ) ) ),
inference(assume_negation,[status(cth)],[t41_relset_2]) ).
fof(c_0_9,negated_conjecture,
( m1_subset_1(esk3_0,k1_zfmisc_1(esk1_0))
& m1_subset_1(esk4_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0)))
& m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0)))
& ~ r1_tarski(k4_subset_1(esk2_0,k8_relset_2(esk1_0,esk2_0,esk3_0,esk4_0),k8_relset_2(esk1_0,esk2_0,esk3_0,esk5_0)),k8_relset_2(esk1_0,esk2_0,esk3_0,k4_subset_1(k2_zfmisc_1(esk1_0,esk2_0),esk4_0,esk5_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_10,plain,
! [X1608,X1609,X1610] :
( ~ m1_subset_1(X1609,k1_zfmisc_1(X1608))
| ~ m1_subset_1(X1610,k1_zfmisc_1(X1608))
| k4_subset_1(X1608,X1609,X1610) = k2_xboole_0(X1609,X1610) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_subset_1])]) ).
cnf(c_0_11,negated_conjecture,
~ r1_tarski(k4_subset_1(esk2_0,k8_relset_2(esk1_0,esk2_0,esk3_0,esk4_0),k8_relset_2(esk1_0,esk2_0,esk3_0,esk5_0)),k8_relset_2(esk1_0,esk2_0,esk3_0,k4_subset_1(k2_zfmisc_1(esk1_0,esk2_0),esk4_0,esk5_0))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,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_10]) ).
fof(c_0_13,plain,
! [X2210,X2211,X2212] :
( ~ r1_tarski(X2210,X2211)
| ~ r1_tarski(X2212,X2211)
| r1_tarski(k2_xboole_0(X2210,X2212),X2211) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])]) ).
cnf(c_0_14,negated_conjecture,
( ~ m1_subset_1(k8_relset_2(esk1_0,esk2_0,esk3_0,esk5_0),k1_zfmisc_1(esk2_0))
| ~ m1_subset_1(k8_relset_2(esk1_0,esk2_0,esk3_0,esk4_0),k1_zfmisc_1(esk2_0))
| ~ r1_tarski(k2_xboole_0(k8_relset_2(esk1_0,esk2_0,esk3_0,esk4_0),k8_relset_2(esk1_0,esk2_0,esk3_0,esk5_0)),k8_relset_2(esk1_0,esk2_0,esk3_0,k4_subset_1(k2_zfmisc_1(esk1_0,esk2_0),esk4_0,esk5_0))) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( r1_tarski(k2_xboole_0(X1,X3),X2)
| ~ r1_tarski(X1,X2)
| ~ r1_tarski(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X1580,X1581,X1582,X1583,X1584] :
( ~ m1_subset_1(X1582,k1_zfmisc_1(X1580))
| ~ m1_subset_1(X1583,k1_zfmisc_1(k2_zfmisc_1(X1580,X1581)))
| ~ m1_subset_1(X1584,k1_zfmisc_1(k2_zfmisc_1(X1580,X1581)))
| ~ r1_tarski(X1583,X1584)
| r1_tarski(k8_relset_2(X1580,X1581,X1582,X1583),k8_relset_2(X1580,X1581,X1582,X1584)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t40_relset_2])])]) ).
cnf(c_0_17,negated_conjecture,
( ~ m1_subset_1(k8_relset_2(esk1_0,esk2_0,esk3_0,esk5_0),k1_zfmisc_1(esk2_0))
| ~ m1_subset_1(k8_relset_2(esk1_0,esk2_0,esk3_0,esk4_0),k1_zfmisc_1(esk2_0))
| ~ r1_tarski(k8_relset_2(esk1_0,esk2_0,esk3_0,esk5_0),k8_relset_2(esk1_0,esk2_0,esk3_0,k4_subset_1(k2_zfmisc_1(esk1_0,esk2_0),esk4_0,esk5_0)))
| ~ r1_tarski(k8_relset_2(esk1_0,esk2_0,esk3_0,esk4_0),k8_relset_2(esk1_0,esk2_0,esk3_0,k4_subset_1(k2_zfmisc_1(esk1_0,esk2_0),esk4_0,esk5_0))) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( r1_tarski(k8_relset_2(X2,X4,X1,X3),k8_relset_2(X2,X4,X1,X5))
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,X4)))
| ~ m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X2,X4)))
| ~ r1_tarski(X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,negated_conjecture,
m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,negated_conjecture,
m1_subset_1(esk3_0,k1_zfmisc_1(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,negated_conjecture,
( ~ m1_subset_1(k4_subset_1(k2_zfmisc_1(esk1_0,esk2_0),esk4_0,esk5_0),k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0)))
| ~ m1_subset_1(k8_relset_2(esk1_0,esk2_0,esk3_0,esk5_0),k1_zfmisc_1(esk2_0))
| ~ m1_subset_1(k8_relset_2(esk1_0,esk2_0,esk3_0,esk4_0),k1_zfmisc_1(esk2_0))
| ~ r1_tarski(k8_relset_2(esk1_0,esk2_0,esk3_0,esk4_0),k8_relset_2(esk1_0,esk2_0,esk3_0,k4_subset_1(k2_zfmisc_1(esk1_0,esk2_0),esk4_0,esk5_0)))
| ~ r1_tarski(esk5_0,k4_subset_1(k2_zfmisc_1(esk1_0,esk2_0),esk4_0,esk5_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_22,negated_conjecture,
m1_subset_1(esk4_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_23,plain,
! [X1599,X1600,X1601] :
( ~ m1_subset_1(X1600,k1_zfmisc_1(X1599))
| ~ m1_subset_1(X1601,k1_zfmisc_1(X1599))
| m1_subset_1(k4_subset_1(X1599,X1600,X1601),k1_zfmisc_1(X1599)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_subset_1])]) ).
fof(c_0_24,plain,
! [X2208,X2209] : r1_tarski(X2208,k2_xboole_0(X2208,X2209)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(c_0_25,plain,
! [X2196,X2197] : k2_xboole_0(X2196,X2197) = k2_xboole_0(X2197,X2196),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_26,negated_conjecture,
( ~ m1_subset_1(k4_subset_1(k2_zfmisc_1(esk1_0,esk2_0),esk4_0,esk5_0),k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0)))
| ~ m1_subset_1(k8_relset_2(esk1_0,esk2_0,esk3_0,esk5_0),k1_zfmisc_1(esk2_0))
| ~ m1_subset_1(k8_relset_2(esk1_0,esk2_0,esk3_0,esk4_0),k1_zfmisc_1(esk2_0))
| ~ r1_tarski(esk5_0,k4_subset_1(k2_zfmisc_1(esk1_0,esk2_0),esk4_0,esk5_0))
| ~ r1_tarski(esk4_0,k4_subset_1(k2_zfmisc_1(esk1_0,esk2_0),esk4_0,esk5_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_18]),c_0_22]),c_0_20])]) ).
cnf(c_0_27,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_23]) ).
cnf(c_0_28,plain,
r1_tarski(X1,k2_xboole_0(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
k2_xboole_0(X1,X2) = k2_xboole_0(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,negated_conjecture,
( ~ m1_subset_1(k8_relset_2(esk1_0,esk2_0,esk3_0,esk5_0),k1_zfmisc_1(esk2_0))
| ~ m1_subset_1(k8_relset_2(esk1_0,esk2_0,esk3_0,esk4_0),k1_zfmisc_1(esk2_0))
| ~ r1_tarski(esk5_0,k4_subset_1(k2_zfmisc_1(esk1_0,esk2_0),esk4_0,esk5_0))
| ~ r1_tarski(esk4_0,k4_subset_1(k2_zfmisc_1(esk1_0,esk2_0),esk4_0,esk5_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_19]),c_0_22])]) ).
cnf(c_0_31,plain,
r1_tarski(X1,k2_xboole_0(X2,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_32,plain,
! [X1531,X1532,X1533,X1534] :
( ~ m1_subset_1(X1533,k1_zfmisc_1(X1531))
| ~ m1_subset_1(X1534,k1_zfmisc_1(k2_zfmisc_1(X1531,X1532)))
| m1_subset_1(k8_relset_2(X1531,X1532,X1533,X1534),k1_zfmisc_1(X1532)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k8_relset_2])]) ).
cnf(c_0_33,negated_conjecture,
( ~ m1_subset_1(k8_relset_2(esk1_0,esk2_0,esk3_0,esk5_0),k1_zfmisc_1(esk2_0))
| ~ m1_subset_1(k8_relset_2(esk1_0,esk2_0,esk3_0,esk4_0),k1_zfmisc_1(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_12]),c_0_31]),c_0_28]),c_0_19]),c_0_22])]) ).
cnf(c_0_34,plain,
( m1_subset_1(k8_relset_2(X2,X4,X1,X3),k1_zfmisc_1(X4))
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_35,negated_conjecture,
~ m1_subset_1(k8_relset_2(esk1_0,esk2_0,esk3_0,esk4_0),k1_zfmisc_1(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_19]),c_0_20])]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_34]),c_0_22]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU438+3 : TPTP v9.2.1. Released v3.4.0.
% 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
% 0.15/0.33 % Computer : n013.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 03:15:29 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 18.59/17.45 % Version : CSE_E---1.7
% 18.59/17.45 % Problem : theBenchmark.p
% 18.59/17.45 % SZS status Theorem for theBenchmark.p
% 18.59/17.45 % SZS output start CNFRefutation
% See solution above
% 18.59/17.46 % Total time : 16.743s
%------------------------------------------------------------------------------