%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU422+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 : n031.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 05:12:16 PM UTC 2026
% Result : Theorem 15.12s 9.75s
% Output : CNFRefutation 15.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 72 ( 32 unt; 0 def)
% Number of atoms : 149 ( 35 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 134 ( 57 ~; 47 |; 12 &)
% ( 5 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 119 ( 4 sgn 71 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t16_relset_2,conjecture,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> m1_subset_1(a_2_0_relset_2(X1,X2),k1_zfmisc_1(k1_zfmisc_1(X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_relset_2) ).
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(t69_xboole_1,axiom,
! [X1,X2] :
( ~ v1_xboole_0(X2)
=> ~ ( r1_tarski(X2,X1)
& r1_xboole_0(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t69_xboole_1) ).
fof(t1_xboole_1,axiom,
! [X1,X2,X3] :
( ( r1_tarski(X1,X2)
& r1_tarski(X2,X3) )
=> r1_tarski(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t1_xboole_1) ).
fof(t79_xboole_1,axiom,
! [X1,X2] : r1_xboole_0(k4_xboole_0(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t79_xboole_1) ).
fof(t36_xboole_1,axiom,
! [X1,X2] : r1_tarski(k4_xboole_0(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t36_xboole_1) ).
fof(t83_zfmisc_1,axiom,
! [X1,X2] : k1_zfmisc_1(k3_xboole_0(X1,X2)) = k3_xboole_0(k1_zfmisc_1(X1),k1_zfmisc_1(X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+6.ax',t83_zfmisc_1) ).
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(t38_xboole_1,axiom,
! [X1,X2] :
( r1_tarski(X1,k4_xboole_0(X2,X1))
=> X1 = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t38_xboole_1) ).
fof(d5_xboole_0,axiom,
! [X1] :
( v1_xboole_0(X1)
<=> X1 = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+2.ax',d5_xboole_0) ).
fof(t3_boole,axiom,
! [X1] : k4_xboole_0(X1,k1_xboole_0) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+3.ax',t3_boole) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( r2_hidden(X1,X2)
& m1_subset_1(X2,k1_zfmisc_1(X3)) )
=> m1_subset_1(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+9.ax',t4_subset) ).
fof(t37_xboole_1,axiom,
! [X1,X2] :
( k4_xboole_0(X1,X2) = k1_xboole_0
<=> r1_tarski(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+4.ax',t37_xboole_1) ).
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = k1_zfmisc_1(X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> r1_tarski(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+6.ax',d1_zfmisc_1) ).
fof(t15_relset_2,axiom,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> X2 = k3_tarski(a_2_0_relset_2(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_relset_2) ).
fof(t100_zfmisc_1,axiom,
! [X1] : r1_tarski(X1,k1_zfmisc_1(k3_tarski(X1))),
file('/export/starexec/sandbox/benchmark/Axioms/SET007/SET007+6.ax',t100_zfmisc_1) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> m1_subset_1(a_2_0_relset_2(X1,X2),k1_zfmisc_1(k1_zfmisc_1(X1))) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t16_relset_2])]) ).
fof(c_0_17,plain,
! [X1411,X1412] :
( ( ~ m1_subset_1(X1411,k1_zfmisc_1(X1412))
| r1_tarski(X1411,X1412) )
& ( ~ r1_tarski(X1411,X1412)
| m1_subset_1(X1411,k1_zfmisc_1(X1412)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_18,negated_conjecture,
( ~ v1_xboole_0(esk1_0)
& m1_subset_1(esk2_0,k1_zfmisc_1(esk1_0))
& ~ m1_subset_1(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(k1_zfmisc_1(esk1_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_19,plain,
! [X1,X2] :
( ~ v1_xboole_0(X2)
=> ~ ( r1_tarski(X2,X1)
& r1_xboole_0(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[t69_xboole_1]) ).
fof(c_0_20,plain,
! [X1464,X1465,X1466] :
( ~ r1_tarski(X1464,X1465)
| ~ r1_tarski(X1465,X1466)
| r1_tarski(X1464,X1466) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
cnf(c_0_21,plain,
( r1_tarski(X1,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
m1_subset_1(esk2_0,k1_zfmisc_1(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_23,plain,
! [X2499,X2500] :
( v1_xboole_0(X2500)
| ~ r1_tarski(X2500,X2499)
| ~ r1_xboole_0(X2500,X2499) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])]) ).
fof(c_0_24,plain,
! [X2528,X2529] : r1_xboole_0(k4_xboole_0(X2528,X2529),X2529),
inference(variable_rename,[status(thm)],[t79_xboole_1]) ).
cnf(c_0_25,plain,
( r1_tarski(X1,X3)
| ~ r1_tarski(X1,X2)
| ~ r1_tarski(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
r1_tarski(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_27,plain,
! [X2724,X2725] : r1_tarski(k4_xboole_0(X2724,X2725),X2724),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
fof(c_0_28,plain,
! [X2422,X2423] : k1_zfmisc_1(k3_xboole_0(X2422,X2423)) = k3_xboole_0(k1_zfmisc_1(X2422),k1_zfmisc_1(X2423)),
inference(variable_rename,[status(thm)],[t83_zfmisc_1]) ).
fof(c_0_29,plain,
! [X2402,X2403] : k4_xboole_0(X2402,k4_xboole_0(X2402,X2403)) = k3_xboole_0(X2402,X2403),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
cnf(c_0_30,plain,
( v1_xboole_0(X1)
| ~ r1_tarski(X1,X2)
| ~ r1_xboole_0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
r1_xboole_0(k4_xboole_0(X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,negated_conjecture,
( r1_tarski(X1,esk1_0)
| ~ r1_tarski(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
r1_tarski(k4_xboole_0(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_34,plain,
! [X2728,X2729] :
( ~ r1_tarski(X2728,k4_xboole_0(X2729,X2728))
| X2728 = k1_xboole_0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t38_xboole_1])]) ).
cnf(c_0_35,plain,
k1_zfmisc_1(k3_xboole_0(X1,X2)) = k3_xboole_0(k1_zfmisc_1(X1),k1_zfmisc_1(X2)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
k4_xboole_0(X1,k4_xboole_0(X1,X2)) = k3_xboole_0(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_37,plain,
! [X1538] :
( ( ~ v1_xboole_0(X1538)
| X1538 = k1_xboole_0 )
& ( X1538 != k1_xboole_0
| v1_xboole_0(X1538) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_xboole_0])]) ).
cnf(c_0_38,plain,
( v1_xboole_0(k4_xboole_0(X1,X2))
| ~ r1_tarski(k4_xboole_0(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_39,negated_conjecture,
r1_tarski(k4_xboole_0(esk2_0,X1),esk1_0),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,plain,
( X1 = k1_xboole_0
| ~ r1_tarski(X1,k4_xboole_0(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
k1_zfmisc_1(k4_xboole_0(X1,k4_xboole_0(X1,X2))) = k4_xboole_0(k1_zfmisc_1(X1),k4_xboole_0(k1_zfmisc_1(X1),k1_zfmisc_1(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_36]) ).
cnf(c_0_42,plain,
( X1 = k1_xboole_0
| ~ v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,negated_conjecture,
v1_xboole_0(k4_xboole_0(esk2_0,esk1_0)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
fof(c_0_44,plain,
! [X2710] : k4_xboole_0(X2710,k1_xboole_0) = X2710,
inference(variable_rename,[status(thm)],[t3_boole]) ).
cnf(c_0_45,plain,
( k4_xboole_0(k1_zfmisc_1(X1),k1_zfmisc_1(X2)) = k1_xboole_0
| ~ r1_tarski(k4_xboole_0(k1_zfmisc_1(X1),k1_zfmisc_1(X2)),k1_zfmisc_1(k4_xboole_0(X1,k4_xboole_0(X1,X2)))) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,negated_conjecture,
k4_xboole_0(esk2_0,esk1_0) = k1_xboole_0,
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,plain,
k4_xboole_0(X1,k1_xboole_0) = X1,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_48,plain,
! [X1413,X1414,X1415] :
( ~ r2_hidden(X1413,X1414)
| ~ m1_subset_1(X1414,k1_zfmisc_1(X1415))
| m1_subset_1(X1413,X1415) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(c_0_49,plain,
! [X2726,X2727] :
( ( k4_xboole_0(X2726,X2727) != k1_xboole_0
| r1_tarski(X2726,X2727) )
& ( ~ r1_tarski(X2726,X2727)
| k4_xboole_0(X2726,X2727) = k1_xboole_0 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
cnf(c_0_50,negated_conjecture,
k4_xboole_0(k1_zfmisc_1(esk2_0),k1_zfmisc_1(esk1_0)) = k1_xboole_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_33])]) ).
cnf(c_0_51,plain,
( m1_subset_1(X1,X3)
| ~ r2_hidden(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_52,plain,
( m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r1_tarski(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_53,plain,
( r1_tarski(X1,X2)
| k4_xboole_0(X1,X2) != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_54,negated_conjecture,
k4_xboole_0(k1_zfmisc_1(k1_zfmisc_1(esk2_0)),k1_zfmisc_1(k1_zfmisc_1(esk1_0))) = k1_xboole_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_50]),c_0_47]),c_0_33])]) ).
cnf(c_0_55,plain,
( m1_subset_1(X1,X2)
| ~ r1_tarski(X3,X2)
| ~ r2_hidden(X1,X3) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
r1_tarski(k1_zfmisc_1(k1_zfmisc_1(esk2_0)),k1_zfmisc_1(k1_zfmisc_1(esk1_0))),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
fof(c_0_57,plain,
! [X1374,X1375,X1376,X1377,X1378,X1379] :
( ( ~ r2_hidden(X1376,X1375)
| r1_tarski(X1376,X1374)
| X1375 != k1_zfmisc_1(X1374) )
& ( ~ r1_tarski(X1377,X1374)
| r2_hidden(X1377,X1375)
| X1375 != k1_zfmisc_1(X1374) )
& ( ~ r2_hidden(esk4_2(X1378,X1379),X1379)
| ~ r1_tarski(esk4_2(X1378,X1379),X1378)
| X1379 = k1_zfmisc_1(X1378) )
& ( r2_hidden(esk4_2(X1378,X1379),X1379)
| r1_tarski(esk4_2(X1378,X1379),X1378)
| X1379 = k1_zfmisc_1(X1378) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_zfmisc_1])])])])])]) ).
fof(c_0_58,plain,
! [X1] :
( ~ v1_xboole_0(X1)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(X1))
=> X2 = k3_tarski(a_2_0_relset_2(X1,X2)) ) ),
inference(fof_simplification,[status(thm)],[t15_relset_2]) ).
cnf(c_0_59,negated_conjecture,
~ m1_subset_1(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(k1_zfmisc_1(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_60,negated_conjecture,
( m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(esk1_0)))
| ~ r2_hidden(X1,k1_zfmisc_1(k1_zfmisc_1(esk2_0))) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_61,plain,
( r2_hidden(X1,X3)
| ~ r1_tarski(X1,X2)
| X3 != k1_zfmisc_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
fof(c_0_62,plain,
! [X1761] : r1_tarski(X1761,k1_zfmisc_1(k3_tarski(X1761))),
inference(variable_rename,[status(thm)],[t100_zfmisc_1]) ).
fof(c_0_63,plain,
! [X1438,X1439] :
( v1_xboole_0(X1438)
| ~ m1_subset_1(X1439,k1_zfmisc_1(X1438))
| X1439 = k3_tarski(a_2_0_relset_2(X1438,X1439)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])]) ).
cnf(c_0_64,negated_conjecture,
~ r2_hidden(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(k1_zfmisc_1(esk2_0))),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_65,plain,
( r2_hidden(X1,k1_zfmisc_1(X2))
| ~ r1_tarski(X1,X2) ),
inference(er,[status(thm)],[c_0_61]) ).
cnf(c_0_66,plain,
r1_tarski(X1,k1_zfmisc_1(k3_tarski(X1))),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_67,plain,
( v1_xboole_0(X1)
| X2 = k3_tarski(a_2_0_relset_2(X1,X2))
| ~ m1_subset_1(X2,k1_zfmisc_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_68,negated_conjecture,
~ r1_tarski(a_2_0_relset_2(esk1_0,esk2_0),k1_zfmisc_1(esk2_0)),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_69,plain,
( v1_xboole_0(X1)
| r1_tarski(a_2_0_relset_2(X1,X2),k1_zfmisc_1(X2))
| ~ m1_subset_1(X2,k1_zfmisc_1(X1)) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_70,negated_conjecture,
~ v1_xboole_0(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_71,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_22])]),c_0_70]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU422+2 : TPTP v9.2.1. Released v3.4.0.
% 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
% 0.16/0.33 % Computer : n031.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 03:10:54 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 15.12/9.75 % Version : CSE_E---1.7
% 15.12/9.75 % Problem : theBenchmark.p
% 15.12/9.75 % SZS status Theorem for theBenchmark.p
% 15.12/9.75 % SZS output start CNFRefutation
% See solution above
% 15.22/9.80 % Total time : 7.571s
%------------------------------------------------------------------------------