%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU430+1 : 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 : n023.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 05:12:18 PM UTC 2026
% Result : Theorem 1.36s 1.76s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 10 unt; 0 def)
% Number of atoms : 128 ( 53 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 135 ( 54 ~; 56 |; 13 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 69 ( 6 sgn 35 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t30_relset_2,conjecture,
! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))
=> ( k5_setfam_1(X1,X2) = k1_xboole_0
<=> ! [X3] :
( r2_hidden(X3,X2)
=> X3 = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relset_2) ).
fof(redefinition_k5_setfam_1,axiom,
! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))
=> k5_setfam_1(X1,X2) = k3_tarski(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = k1_xboole_0
<=> ! [X2] : ~ r2_hidden(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(d4_tarski,axiom,
! [X1,X2] :
( X2 = k3_tarski(X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ? [X4] :
( r2_hidden(X3,X4)
& r2_hidden(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( r2_hidden(X1,X2)
& v1_xboole_0(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(t6_boole,axiom,
! [X1] :
( v1_xboole_0(X1)
=> X1 = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(fc12_relat_1,axiom,
( v1_xboole_0(k1_xboole_0)
& v1_relat_1(k1_xboole_0)
& v3_relat_1(k1_xboole_0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))
=> ( k5_setfam_1(X1,X2) = k1_xboole_0
<=> ! [X3] :
( r2_hidden(X3,X2)
=> X3 = k1_xboole_0 ) ) ),
inference(assume_negation,[status(cth)],[t30_relset_2]) ).
fof(c_0_8,plain,
! [X84,X85] :
( ~ m1_subset_1(X85,k1_zfmisc_1(k1_zfmisc_1(X84)))
| k5_setfam_1(X84,X85) = k3_tarski(X85) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1])]) ).
fof(c_0_9,negated_conjecture,
! [X53] :
( m1_subset_1(esk2_0,k1_zfmisc_1(k1_zfmisc_1(esk1_0)))
& ( r2_hidden(esk3_0,esk2_0)
| k5_setfam_1(esk1_0,esk2_0) != k1_xboole_0 )
& ( esk3_0 != k1_xboole_0
| k5_setfam_1(esk1_0,esk2_0) != k1_xboole_0 )
& ( k5_setfam_1(esk1_0,esk2_0) = k1_xboole_0
| ~ r2_hidden(X53,esk2_0)
| X53 = k1_xboole_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
fof(c_0_10,plain,
! [X1] :
( X1 = k1_xboole_0
<=> ! [X2] : ~ r2_hidden(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
cnf(c_0_11,plain,
( k5_setfam_1(X2,X1) = k3_tarski(X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
m1_subset_1(esk2_0,k1_zfmisc_1(k1_zfmisc_1(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X61,X62,X63,X65,X66,X67,X68,X70] :
( ( r2_hidden(X63,esk5_3(X61,X62,X63))
| ~ r2_hidden(X63,X62)
| X62 != k3_tarski(X61) )
& ( r2_hidden(esk5_3(X61,X62,X63),X61)
| ~ r2_hidden(X63,X62)
| X62 != k3_tarski(X61) )
& ( ~ r2_hidden(X65,X66)
| ~ r2_hidden(X66,X61)
| r2_hidden(X65,X62)
| X62 != k3_tarski(X61) )
& ( ~ r2_hidden(esk6_2(X67,X68),X68)
| ~ r2_hidden(esk6_2(X67,X68),X70)
| ~ r2_hidden(X70,X67)
| X68 = k3_tarski(X67) )
& ( r2_hidden(esk6_2(X67,X68),esk7_2(X67,X68))
| r2_hidden(esk6_2(X67,X68),X68)
| X68 = k3_tarski(X67) )
& ( r2_hidden(esk7_2(X67,X68),X67)
| r2_hidden(esk6_2(X67,X68),X68)
| X68 = k3_tarski(X67) ) ),
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)],[d4_tarski])])])])])]) ).
fof(c_0_14,plain,
! [X57,X58,X59] :
( ( X57 != k1_xboole_0
| ~ r2_hidden(X58,X57) )
& ( r2_hidden(esk4_1(X59),X59)
| X59 = k1_xboole_0 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])]) ).
cnf(c_0_15,negated_conjecture,
( k5_setfam_1(esk1_0,esk2_0) = k1_xboole_0
| X1 = k1_xboole_0
| ~ r2_hidden(X1,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
k5_setfam_1(esk1_0,esk2_0) = k3_tarski(esk2_0),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( r2_hidden(X1,X4)
| ~ r2_hidden(X1,X2)
| ~ r2_hidden(X2,X3)
| X4 != k3_tarski(X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( r2_hidden(esk3_0,esk2_0)
| k5_setfam_1(esk1_0,esk2_0) != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,plain,
( X1 != k1_xboole_0
| ~ r2_hidden(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
( k3_tarski(esk2_0) = k1_xboole_0
| X1 = k1_xboole_0
| ~ r2_hidden(X1,esk2_0) ),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( r2_hidden(esk7_2(X1,X2),X1)
| r2_hidden(esk6_2(X1,X2),X2)
| X2 = k3_tarski(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
( r2_hidden(esk5_3(X1,X2,X3),X1)
| ~ r2_hidden(X3,X2)
| X2 != k3_tarski(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_23,plain,
! [X100,X101] :
( ~ r2_hidden(X100,X101)
| ~ v1_xboole_0(X101) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_24,plain,
( r2_hidden(X1,k3_tarski(X2))
| ~ r2_hidden(X3,X2)
| ~ r2_hidden(X1,X3) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
( r2_hidden(esk3_0,esk2_0)
| k3_tarski(esk2_0) != k1_xboole_0 ),
inference(rw,[status(thm)],[c_0_18,c_0_16]) ).
fof(c_0_26,plain,
! [X99] :
( ~ v1_xboole_0(X99)
| X99 = k1_xboole_0 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
cnf(c_0_27,plain,
~ r2_hidden(X1,k1_xboole_0),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_28,negated_conjecture,
( esk7_2(esk2_0,X1) = k1_xboole_0
| k3_tarski(esk2_0) = k1_xboole_0
| X1 = k3_tarski(esk2_0)
| r2_hidden(esk6_2(esk2_0,X1),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,plain,
( r2_hidden(esk5_3(X1,k3_tarski(X1),X2),X1)
| ~ r2_hidden(X2,k3_tarski(X1)) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( ~ r2_hidden(X1,X2)
| ~ v1_xboole_0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,negated_conjecture,
( r2_hidden(X1,k3_tarski(esk2_0))
| k3_tarski(esk2_0) != k1_xboole_0
| ~ r2_hidden(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
( X1 = k1_xboole_0
| ~ v1_xboole_0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
( r2_hidden(esk6_2(X1,X2),esk7_2(X1,X2))
| r2_hidden(esk6_2(X1,X2),X2)
| X2 = k3_tarski(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_34,negated_conjecture,
( esk7_2(esk2_0,k1_xboole_0) = k1_xboole_0
| k3_tarski(esk2_0) = k1_xboole_0 ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,plain,
~ r2_hidden(X1,k3_tarski(k1_xboole_0)),
inference(spm,[status(thm)],[c_0_27,c_0_29]) ).
cnf(c_0_36,plain,
( r2_hidden(esk4_1(X1),X1)
| X1 = k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_37,negated_conjecture,
( esk3_0 != k1_xboole_0
| k5_setfam_1(esk1_0,esk2_0) != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_38,negated_conjecture,
( ~ v1_xboole_0(k3_tarski(esk2_0))
| ~ r2_hidden(X1,esk3_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_39,negated_conjecture,
k3_tarski(esk2_0) = k1_xboole_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_27]) ).
cnf(c_0_40,plain,
v1_xboole_0(k1_xboole_0),
inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).
cnf(c_0_41,plain,
k3_tarski(k1_xboole_0) = k1_xboole_0,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,negated_conjecture,
( k3_tarski(esk2_0) != k1_xboole_0
| esk3_0 != k1_xboole_0 ),
inference(rw,[status(thm)],[c_0_37,c_0_16]) ).
cnf(c_0_43,negated_conjecture,
~ r2_hidden(X1,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_44,plain,
( X1 = k1_xboole_0
| r2_hidden(esk6_2(k1_xboole_0,X1),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_21]),c_0_41]) ).
cnf(c_0_45,negated_conjecture,
esk3_0 != k1_xboole_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_39])]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU430+1 : TPTP v9.2.1. Released v3.4.0.
% 0.00/0.13 % 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
% 0.17/0.34 % Computer : n023.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 03:13:23 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.36 % start to proof: theBenchmark
% 1.36/1.76 % Version : CSE_E---1.7
% 1.36/1.76 % Problem : theBenchmark.p
% 1.36/1.76 % SZS status Theorem for theBenchmark.p
% 1.36/1.76 % SZS output start CNFRefutation
% See solution above
% 1.36/1.76 % Total time : 1.376s
%------------------------------------------------------------------------------