%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU451+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 : n010.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 05:12:25 PM UTC 2026
% Result : Theorem 1.34s 1.75s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 7 unt; 0 def)
% Number of atoms : 82 ( 27 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 79 ( 34 ~; 30 |; 8 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-6 aty)
% Number of variables : 103 ( 6 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(redefinition_k7_relset_1,axiom,
! [X1,X2,X3,X4,X5,X6] :
( ( m1_relset_1(X5,X1,X2)
& m1_relset_1(X6,X3,X4) )
=> k7_relset_1(X1,X2,X3,X4,X5,X6) = k5_relat_1(X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_relset_1) ).
fof(t23_funct_2,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
=> ( k7_relset_1(X1,X1,X1,X2,k6_partfun1(X1),X3) = X3
& k7_relset_1(X1,X2,X2,X2,X3,k6_partfun1(X2)) = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_2) ).
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(dt_k6_partfun1,axiom,
! [X1] :
( v1_partfun1(k6_partfun1(X1),X1,X1)
& m2_relset_1(k6_partfun1(X1),X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_partfun1) ).
fof(redefinition_k9_relset_2,axiom,
! [X1,X2,X3,X4,X5] :
( ( m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
& m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X2,X3))) )
=> k9_relset_2(X1,X2,X3,X4,X5) = k5_relat_1(X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k9_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(t65_relset_2,conjecture,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
=> k9_relset_2(X1,X1,X2,k6_partfun1(X1),X3) = k9_relset_2(X1,X2,X2,X3,k6_partfun1(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relset_2) ).
fof(c_0_7,plain,
! [X161,X162,X163,X164,X165,X166] :
( ~ m1_relset_1(X165,X161,X162)
| ~ m1_relset_1(X166,X163,X164)
| k7_relset_1(X161,X162,X163,X164,X165,X166) = k5_relat_1(X165,X166) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k7_relset_1])]) ).
fof(c_0_8,plain,
! [X178,X179,X180] :
( ( k7_relset_1(X178,X178,X178,X179,k6_partfun1(X178),X180) = X180
| ~ m2_relset_1(X180,X178,X179) )
& ( k7_relset_1(X178,X179,X179,X179,X180,k6_partfun1(X179)) = X180
| ~ m2_relset_1(X180,X178,X179) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_2])])]) ).
fof(c_0_9,plain,
! [X172,X173,X174] :
( ( ~ m2_relset_1(X174,X172,X173)
| m1_relset_1(X174,X172,X173) )
& ( ~ m1_relset_1(X174,X172,X173)
| m2_relset_1(X174,X172,X173) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
cnf(c_0_10,plain,
( k7_relset_1(X2,X3,X5,X6,X1,X4) = k5_relat_1(X1,X4)
| ~ m1_relset_1(X1,X2,X3)
| ~ m1_relset_1(X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( k7_relset_1(X1,X2,X2,X2,X3,k6_partfun1(X2)) = X3
| ~ m2_relset_1(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( m2_relset_1(X1,X2,X3)
| ~ m1_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X114] :
( v1_partfun1(k6_partfun1(X114),X114,X114)
& m2_relset_1(k6_partfun1(X114),X114,X114) ),
inference(variable_rename,[status(thm)],[dt_k6_partfun1]) ).
fof(c_0_14,plain,
! [X167,X168,X169,X170,X171] :
( ~ m1_subset_1(X170,k1_zfmisc_1(k2_zfmisc_1(X167,X168)))
| ~ m1_subset_1(X171,k1_zfmisc_1(k2_zfmisc_1(X168,X169)))
| k9_relset_2(X167,X168,X169,X170,X171) = k5_relat_1(X170,X171) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k9_relset_2])]) ).
fof(c_0_15,plain,
! [X127,X128,X129] :
( ~ m2_relset_1(X129,X127,X128)
| m1_subset_1(X129,k1_zfmisc_1(k2_zfmisc_1(X127,X128))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).
cnf(c_0_16,plain,
( k5_relat_1(X1,k6_partfun1(X2)) = X1
| ~ m1_relset_1(k6_partfun1(X2),X2,X2)
| ~ m1_relset_1(X1,X3,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_17,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,plain,
m2_relset_1(k6_partfun1(X1),X1,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
=> k9_relset_2(X1,X1,X2,k6_partfun1(X1),X3) = k9_relset_2(X1,X2,X2,X3,k6_partfun1(X2)) ),
inference(assume_negation,[status(cth)],[t65_relset_2]) ).
cnf(c_0_20,plain,
( k7_relset_1(X1,X1,X1,X2,k6_partfun1(X1),X3) = X3
| ~ m2_relset_1(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,plain,
( k9_relset_2(X2,X3,X5,X1,X4) = k5_relat_1(X1,X4)
| ~ m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X3,X5))) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,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_15]) ).
cnf(c_0_23,plain,
( k5_relat_1(X1,k6_partfun1(X2)) = X1
| ~ m1_relset_1(X1,X3,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
fof(c_0_24,negated_conjecture,
( m2_relset_1(esk3_0,esk1_0,esk2_0)
& k9_relset_2(esk1_0,esk1_0,esk2_0,k6_partfun1(esk1_0),esk3_0) != k9_relset_2(esk1_0,esk2_0,esk2_0,esk3_0,k6_partfun1(esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_25,plain,
( k5_relat_1(k6_partfun1(X1),X2) = X2
| ~ m1_relset_1(k6_partfun1(X1),X1,X1)
| ~ m1_relset_1(X2,X1,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_20]),c_0_12]) ).
cnf(c_0_26,plain,
( k9_relset_2(X1,X2,X3,X4,X5) = k5_relat_1(X4,X5)
| ~ m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| ~ m2_relset_1(X5,X2,X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( k5_relat_1(X1,k6_partfun1(X2)) = X1
| ~ m2_relset_1(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_17]) ).
cnf(c_0_28,negated_conjecture,
m2_relset_1(esk3_0,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
( k5_relat_1(k6_partfun1(X1),X2) = X2
| ~ m1_relset_1(X2,X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_17]),c_0_18])]) ).
cnf(c_0_30,negated_conjecture,
k9_relset_2(esk1_0,esk1_0,esk2_0,k6_partfun1(esk1_0),esk3_0) != k9_relset_2(esk1_0,esk2_0,esk2_0,esk3_0,k6_partfun1(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( k9_relset_2(X1,X2,X3,X4,X5) = k5_relat_1(X4,X5)
| ~ m2_relset_1(X5,X2,X3)
| ~ m2_relset_1(X4,X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_32,negated_conjecture,
k5_relat_1(esk3_0,k6_partfun1(esk2_0)) = esk3_0,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
( k5_relat_1(k6_partfun1(X1),X2) = X2
| ~ m2_relset_1(X2,X1,X3) ),
inference(spm,[status(thm)],[c_0_29,c_0_17]) ).
cnf(c_0_34,negated_conjecture,
k9_relset_2(esk1_0,esk1_0,esk2_0,k6_partfun1(esk1_0),esk3_0) != esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_18]),c_0_28])]) ).
cnf(c_0_35,negated_conjecture,
k5_relat_1(k6_partfun1(esk1_0),esk3_0) = esk3_0,
inference(spm,[status(thm)],[c_0_33,c_0_28]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_31]),c_0_35]),c_0_28]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU451+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
% 0.14/0.33 % Computer : n010.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 03:20:51 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.34/1.75 % Version : CSE_E---1.7
% 1.34/1.75 % Problem : theBenchmark.p
% 1.34/1.75 % SZS status Theorem for theBenchmark.p
% 1.34/1.75 % SZS output start CNFRefutation
% See solution above
% 1.34/1.75 % Total time : 1.374s
%------------------------------------------------------------------------------