%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU449+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 : 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 05:12:24 PM UTC 2026
% Result : Theorem 1.33s 1.74s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 8 unt; 0 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 108 ( 48 ~; 38 |; 8 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 77 ( 1 sgn 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t63_relset_2,conjecture,
! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(X2))
=> ! [X5] :
( m2_relset_1(X5,X1,X2)
=> ( r1_tarski(X3,k8_relset_2(X2,X1,k8_relset_2(X1,X2,X3,X5),k6_relset_1(X1,X2,X5)))
& r1_tarski(X4,k8_relset_2(X1,X2,k8_relset_2(X2,X1,X4,k6_relset_1(X1,X2,X5)),X5)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_relset_2) ).
fof(t61_relset_2,axiom,
! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(X2))
=> ! [X5] :
( m2_relset_1(X5,X1,X2)
=> ( r1_tarski(X3,k8_relset_2(X2,X1,X4,k6_relset_1(X1,X2,X5)))
<=> r1_tarski(X4,k8_relset_2(X1,X2,X3,X5)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_relset_2) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : r1_tarski(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
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/sandbox/benchmark/theBenchmark.p',dt_k8_relset_2) ).
fof(dt_m2_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
=> m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(dt_k6_relset_1,axiom,
! [X1,X2,X3] :
( m1_relset_1(X3,X1,X2)
=> m2_relset_1(k6_relset_1(X1,X2,X3),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relset_1) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
<=> m1_relset_1(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3] :
( m1_subset_1(X3,k1_zfmisc_1(X1))
=> ! [X4] :
( m1_subset_1(X4,k1_zfmisc_1(X2))
=> ! [X5] :
( m2_relset_1(X5,X1,X2)
=> ( r1_tarski(X3,k8_relset_2(X2,X1,k8_relset_2(X1,X2,X3,X5),k6_relset_1(X1,X2,X5)))
& r1_tarski(X4,k8_relset_2(X1,X2,k8_relset_2(X2,X1,X4,k6_relset_1(X1,X2,X5)),X5)) ) ) ) ),
inference(assume_negation,[status(cth)],[t63_relset_2]) ).
fof(c_0_8,plain,
! [X222,X223,X224,X225,X226] :
( ( ~ r1_tarski(X224,k8_relset_2(X223,X222,X225,k6_relset_1(X222,X223,X226)))
| r1_tarski(X225,k8_relset_2(X222,X223,X224,X226))
| ~ m2_relset_1(X226,X222,X223)
| ~ m1_subset_1(X225,k1_zfmisc_1(X223))
| ~ m1_subset_1(X224,k1_zfmisc_1(X222)) )
& ( ~ r1_tarski(X225,k8_relset_2(X222,X223,X224,X226))
| r1_tarski(X224,k8_relset_2(X223,X222,X225,k6_relset_1(X222,X223,X226)))
| ~ m2_relset_1(X226,X222,X223)
| ~ m1_subset_1(X225,k1_zfmisc_1(X223))
| ~ m1_subset_1(X224,k1_zfmisc_1(X222)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t61_relset_2])])])]) ).
fof(c_0_9,plain,
! [X193] : r1_tarski(X193,X193),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(c_0_10,negated_conjecture,
( m1_subset_1(esk3_0,k1_zfmisc_1(esk1_0))
& m1_subset_1(esk4_0,k1_zfmisc_1(esk2_0))
& m2_relset_1(esk5_0,esk1_0,esk2_0)
& ( ~ r1_tarski(esk3_0,k8_relset_2(esk2_0,esk1_0,k8_relset_2(esk1_0,esk2_0,esk3_0,esk5_0),k6_relset_1(esk1_0,esk2_0,esk5_0)))
| ~ r1_tarski(esk4_0,k8_relset_2(esk1_0,esk2_0,k8_relset_2(esk2_0,esk1_0,esk4_0,k6_relset_1(esk1_0,esk2_0,esk5_0)),esk5_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_11,plain,
( r1_tarski(X4,k8_relset_2(X3,X2,X1,X5))
| ~ r1_tarski(X1,k8_relset_2(X2,X3,X4,k6_relset_1(X3,X2,X5)))
| ~ m2_relset_1(X5,X3,X2)
| ~ m1_subset_1(X4,k1_zfmisc_1(X2))
| ~ m1_subset_1(X1,k1_zfmisc_1(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
r1_tarski(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
( ~ r1_tarski(esk3_0,k8_relset_2(esk2_0,esk1_0,k8_relset_2(esk1_0,esk2_0,esk3_0,esk5_0),k6_relset_1(esk1_0,esk2_0,esk5_0)))
| ~ r1_tarski(esk4_0,k8_relset_2(esk1_0,esk2_0,k8_relset_2(esk2_0,esk1_0,esk4_0,k6_relset_1(esk1_0,esk2_0,esk5_0)),esk5_0)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( r1_tarski(X1,k8_relset_2(X2,X3,k8_relset_2(X3,X2,X1,k6_relset_1(X2,X3,X4)),X4))
| ~ m2_relset_1(X4,X2,X3)
| ~ m1_subset_1(k8_relset_2(X3,X2,X1,k6_relset_1(X2,X3,X4)),k1_zfmisc_1(X2))
| ~ m1_subset_1(X1,k1_zfmisc_1(X3)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
m2_relset_1(esk5_0,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
m1_subset_1(esk4_0,k1_zfmisc_1(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
( ~ r1_tarski(esk3_0,k8_relset_2(esk2_0,esk1_0,k8_relset_2(esk1_0,esk2_0,esk3_0,esk5_0),k6_relset_1(esk1_0,esk2_0,esk5_0)))
| ~ m1_subset_1(k8_relset_2(esk2_0,esk1_0,esk4_0,k6_relset_1(esk1_0,esk2_0,esk5_0)),k1_zfmisc_1(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_18,plain,
( r1_tarski(X4,k8_relset_2(X3,X2,X1,k6_relset_1(X2,X3,X5)))
| ~ r1_tarski(X1,k8_relset_2(X2,X3,X4,X5))
| ~ m2_relset_1(X5,X2,X3)
| ~ m1_subset_1(X1,k1_zfmisc_1(X3))
| ~ m1_subset_1(X4,k1_zfmisc_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,negated_conjecture,
m1_subset_1(esk3_0,k1_zfmisc_1(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_20,plain,
! [X212,X213,X214,X215] :
( ~ m1_subset_1(X214,k1_zfmisc_1(X212))
| ~ m1_subset_1(X215,k1_zfmisc_1(k2_zfmisc_1(X212,X213)))
| m1_subset_1(k8_relset_2(X212,X213,X214,X215),k1_zfmisc_1(X213)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k8_relset_2])]) ).
cnf(c_0_21,negated_conjecture,
( ~ m1_subset_1(k8_relset_2(esk2_0,esk1_0,esk4_0,k6_relset_1(esk1_0,esk2_0,esk5_0)),k1_zfmisc_1(esk1_0))
| ~ m1_subset_1(k8_relset_2(esk1_0,esk2_0,esk3_0,esk5_0),k1_zfmisc_1(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_12]),c_0_15]),c_0_19])]) ).
cnf(c_0_22,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_20]) ).
fof(c_0_23,plain,
! [X216,X217,X218] :
( ~ m2_relset_1(X218,X216,X217)
| m1_subset_1(X218,k1_zfmisc_1(k2_zfmisc_1(X216,X217))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).
cnf(c_0_24,negated_conjecture,
( ~ m1_subset_1(k6_relset_1(esk1_0,esk2_0,esk5_0),k1_zfmisc_1(k2_zfmisc_1(esk2_0,esk1_0)))
| ~ m1_subset_1(k8_relset_2(esk1_0,esk2_0,esk3_0,esk5_0),k1_zfmisc_1(esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_16])]) ).
cnf(c_0_25,plain,
( m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_26,plain,
! [X209,X210,X211] :
( ~ m1_relset_1(X211,X209,X210)
| m2_relset_1(k6_relset_1(X209,X210,X211),X210,X209) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_relset_1])]) ).
cnf(c_0_27,negated_conjecture,
( ~ m2_relset_1(k6_relset_1(esk1_0,esk2_0,esk5_0),esk2_0,esk1_0)
| ~ m1_subset_1(k8_relset_2(esk1_0,esk2_0,esk3_0,esk5_0),k1_zfmisc_1(esk2_0)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
( m2_relset_1(k6_relset_1(X2,X3,X1),X3,X2)
| ~ m1_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_29,negated_conjecture,
( ~ m1_relset_1(esk5_0,esk1_0,esk2_0)
| ~ m1_subset_1(k8_relset_2(esk1_0,esk2_0,esk3_0,esk5_0),k1_zfmisc_1(esk2_0)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_30,plain,
! [X206,X207,X208] :
( ( ~ m2_relset_1(X208,X206,X207)
| m1_relset_1(X208,X206,X207) )
& ( ~ m1_relset_1(X208,X206,X207)
| m2_relset_1(X208,X206,X207) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
cnf(c_0_31,negated_conjecture,
( ~ m1_relset_1(esk5_0,esk1_0,esk2_0)
| ~ m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_22]),c_0_19])]) ).
cnf(c_0_32,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_33,negated_conjecture,
~ m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_15])]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_25]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU449+1 : 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
% 0.15/0.33 % Computer : n026.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 03:20:53 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.33/1.74 % Version : CSE_E---1.7
% 1.33/1.74 % Problem : theBenchmark.p
% 1.33/1.74 % SZS status Theorem for theBenchmark.p
% 1.33/1.74 % SZS output start CNFRefutation
% See solution above
% 1.33/1.74 % Total time : 1.374s
%------------------------------------------------------------------------------