%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU446+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 : n008.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 05:12:23 PM UTC 2026
% Result : Theorem 21.69s 18.98s
% Output : CNFRefutation 21.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 21 unt; 0 def)
% Number of atoms : 100 ( 36 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 78 ( 32 ~; 26 |; 7 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-5 aty)
% Number of variables : 91 ( 2 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t58_relset_2,conjecture,
! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
=> k10_relset_1(X1,X2,X3,X1) = k10_relset_1(X2,X2,k9_relset_2(X2,X1,X2,k6_relset_1(X1,X2,X3),X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t58_relset_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/sandbox2/benchmark/Axioms/SET007/SET007+16.ax',redefinition_m2_relset_1) ).
fof(d1_relset_1,axiom,
! [X1,X2,X3] :
( m1_relset_1(X3,X1,X2)
<=> r1_tarski(X3,k2_zfmisc_1(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+16.ax',d1_relset_1) ).
fof(t3_relat_1,axiom,
! [X1,X2] :
( v1_relat_1(X2)
=> ( r1_tarski(X1,X2)
=> v1_relat_1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+10.ax',t3_relat_1) ).
fof(t6_relat_1,axiom,
! [X1,X2] : v1_relat_1(k2_zfmisc_1(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+10.ax',t6_relat_1) ).
fof(redefinition_k6_relset_1,axiom,
! [X1,X2,X3] :
( m1_relset_1(X3,X1,X2)
=> k6_relset_1(X1,X2,X3) = k4_relat_1(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+16.ax',redefinition_k6_relset_1) ).
fof(t21_funct_5,axiom,
! [X1] :
( v1_relat_1(X1)
=> ( k1_funct_5(X1) = k1_relat_1(X1)
& k2_funct_5(X1) = k2_relat_1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+61.ax',t21_funct_5) ).
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/sandbox2/benchmark/Axioms/SET007/SET007+16.ax',dt_k6_relset_1) ).
fof(t51_relset_2,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X2,X1)
=> ( k1_funct_5(X3) = k10_relset_1(X1,X2,k6_relset_1(X2,X1,X3),X1)
& k2_funct_5(X3) = k10_relset_1(X2,X1,X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_relset_2) ).
fof(redefinition_k10_relset_1,axiom,
! [X1,X2,X3,X4] :
( m1_relset_1(X3,X1,X2)
=> k10_relset_1(X1,X2,X3,X4) = k9_relat_1(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+16.ax',redefinition_k10_relset_1) ).
fof(involutiveness_k4_relat_1,axiom,
! [X1] :
( v1_relat_1(X1)
=> k4_relat_1(k4_relat_1(X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+10.ax',involutiveness_k4_relat_1) ).
fof(t57_relset_2,axiom,
! [X1,X2,X3] :
( m2_relset_1(X3,X2,X1)
=> k10_relset_1(X1,X2,k6_relset_1(X2,X1,X3),X1) = k10_relset_1(X2,X2,k9_relset_2(X2,X1,X2,X3,k6_relset_1(X2,X1,X3)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_relset_2) ).
fof(c_0_12,negated_conjecture,
~ ! [X1,X2,X3] :
( m2_relset_1(X3,X1,X2)
=> k10_relset_1(X1,X2,X3,X1) = k10_relset_1(X2,X2,k9_relset_2(X2,X1,X2,k6_relset_1(X1,X2,X3),X3),X2) ),
inference(assume_negation,[status(cth)],[t58_relset_2]) ).
fof(c_0_13,plain,
! [X1891,X1892,X1893] :
( ( ~ m2_relset_1(X1893,X1891,X1892)
| m1_relset_1(X1893,X1891,X1892) )
& ( ~ m1_relset_1(X1893,X1891,X1892)
| m2_relset_1(X1893,X1891,X1892) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_14,negated_conjecture,
( m2_relset_1(esk3_0,esk1_0,esk2_0)
& k10_relset_1(esk1_0,esk2_0,esk3_0,esk1_0) != k10_relset_1(esk2_0,esk2_0,k9_relset_2(esk2_0,esk1_0,esk2_0,k6_relset_1(esk1_0,esk2_0,esk3_0),esk3_0),esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_15,plain,
! [X1885,X1886,X1887] :
( ( ~ m1_relset_1(X1887,X1885,X1886)
| r1_tarski(X1887,k2_zfmisc_1(X1885,X1886)) )
& ( ~ r1_tarski(X1887,k2_zfmisc_1(X1885,X1886))
| m1_relset_1(X1887,X1885,X1886) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_relset_1])]) ).
cnf(c_0_16,plain,
( m1_relset_1(X1,X2,X3)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
m2_relset_1(esk3_0,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_18,plain,
! [X2704,X2705] :
( ~ v1_relat_1(X2705)
| ~ r1_tarski(X2704,X2705)
| v1_relat_1(X2704) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_relat_1])]) ).
cnf(c_0_19,plain,
( r1_tarski(X1,k2_zfmisc_1(X2,X3))
| ~ m1_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
m1_relset_1(esk3_0,esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_21,plain,
! [X2549,X2550] : v1_relat_1(k2_zfmisc_1(X2549,X2550)),
inference(variable_rename,[status(thm)],[t6_relat_1]) ).
fof(c_0_22,plain,
! [X1575,X1576,X1577] :
( ~ m1_relset_1(X1577,X1575,X1576)
| k6_relset_1(X1575,X1576,X1577) = k4_relat_1(X1577) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_relset_1])]) ).
fof(c_0_23,plain,
! [X2787] :
( ( k1_funct_5(X2787) = k1_relat_1(X2787)
| ~ v1_relat_1(X2787) )
& ( k2_funct_5(X2787) = k2_relat_1(X2787)
| ~ v1_relat_1(X2787) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_funct_5])])]) ).
cnf(c_0_24,plain,
( v1_relat_1(X2)
| ~ v1_relat_1(X1)
| ~ r1_tarski(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
r1_tarski(esk3_0,k2_zfmisc_1(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
v1_relat_1(k2_zfmisc_1(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_27,plain,
! [X1569,X1570,X1571] :
( ~ m1_relset_1(X1571,X1569,X1570)
| m2_relset_1(k6_relset_1(X1569,X1570,X1571),X1570,X1569) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_relset_1])]) ).
cnf(c_0_28,plain,
( k6_relset_1(X2,X3,X1) = k4_relat_1(X1)
| ~ m1_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_29,plain,
! [X1579,X1580,X1581] :
( ( k1_funct_5(X1581) = k10_relset_1(X1579,X1580,k6_relset_1(X1580,X1579,X1581),X1579)
| ~ m2_relset_1(X1581,X1580,X1579) )
& ( k2_funct_5(X1581) = k10_relset_1(X1580,X1579,X1581,X1580)
| ~ m2_relset_1(X1581,X1580,X1579) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t51_relset_2])])]) ).
cnf(c_0_30,plain,
( k2_funct_5(X1) = k2_relat_1(X1)
| ~ v1_relat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,negated_conjecture,
v1_relat_1(esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
fof(c_0_32,plain,
! [X1518,X1519,X1520,X1521] :
( ~ m1_relset_1(X1520,X1518,X1519)
| k10_relset_1(X1518,X1519,X1520,X1521) = k9_relat_1(X1520,X1521) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k10_relset_1])]) ).
cnf(c_0_33,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_27]) ).
cnf(c_0_34,negated_conjecture,
k6_relset_1(esk1_0,esk2_0,esk3_0) = k4_relat_1(esk3_0),
inference(spm,[status(thm)],[c_0_28,c_0_20]) ).
fof(c_0_35,plain,
! [X3005] :
( ~ v1_relat_1(X3005)
| k4_relat_1(k4_relat_1(X3005)) = X3005 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k4_relat_1])]) ).
cnf(c_0_36,negated_conjecture,
k10_relset_1(esk1_0,esk2_0,esk3_0,esk1_0) != k10_relset_1(esk2_0,esk2_0,k9_relset_2(esk2_0,esk1_0,esk2_0,k6_relset_1(esk1_0,esk2_0,esk3_0),esk3_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_37,plain,
( k2_funct_5(X1) = k10_relset_1(X2,X3,X1,X2)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,negated_conjecture,
k2_funct_5(esk3_0) = k2_relat_1(esk3_0),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_39,plain,
( k10_relset_1(X2,X3,X1,X4) = k9_relat_1(X1,X4)
| ~ m1_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,negated_conjecture,
m2_relset_1(k4_relat_1(esk3_0),esk2_0,esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_20]),c_0_34]) ).
cnf(c_0_41,plain,
( k4_relat_1(k4_relat_1(X1)) = X1
| ~ v1_relat_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,negated_conjecture,
k10_relset_1(esk2_0,esk2_0,k9_relset_2(esk2_0,esk1_0,esk2_0,k4_relat_1(esk3_0),esk3_0),esk2_0) != k10_relset_1(esk1_0,esk2_0,esk3_0,esk1_0),
inference(rw,[status(thm)],[c_0_36,c_0_34]) ).
cnf(c_0_43,negated_conjecture,
k10_relset_1(esk1_0,esk2_0,esk3_0,esk1_0) = k2_relat_1(esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_17]),c_0_38]) ).
cnf(c_0_44,negated_conjecture,
k10_relset_1(esk1_0,esk2_0,esk3_0,X1) = k9_relat_1(esk3_0,X1),
inference(spm,[status(thm)],[c_0_39,c_0_20]) ).
fof(c_0_45,plain,
! [X1563,X1564,X1565] :
( ~ m2_relset_1(X1565,X1564,X1563)
| k10_relset_1(X1563,X1564,k6_relset_1(X1564,X1563,X1565),X1563) = k10_relset_1(X1564,X1564,k9_relset_2(X1564,X1563,X1564,X1565,k6_relset_1(X1564,X1563,X1565)),X1564) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t57_relset_2])]) ).
cnf(c_0_46,negated_conjecture,
m1_relset_1(k4_relat_1(esk3_0),esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_16,c_0_40]) ).
cnf(c_0_47,negated_conjecture,
k4_relat_1(k4_relat_1(esk3_0)) = esk3_0,
inference(spm,[status(thm)],[c_0_41,c_0_31]) ).
cnf(c_0_48,negated_conjecture,
k10_relset_1(esk2_0,esk2_0,k9_relset_2(esk2_0,esk1_0,esk2_0,k4_relat_1(esk3_0),esk3_0),esk2_0) != k2_relat_1(esk3_0),
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
k2_relat_1(esk3_0) = k9_relat_1(esk3_0,esk1_0),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,plain,
( k10_relset_1(X3,X2,k6_relset_1(X2,X3,X1),X3) = k10_relset_1(X2,X2,k9_relset_2(X2,X3,X2,X1,k6_relset_1(X2,X3,X1)),X2)
| ~ m2_relset_1(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,negated_conjecture,
k6_relset_1(esk2_0,esk1_0,k4_relat_1(esk3_0)) = esk3_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_46]),c_0_47]) ).
cnf(c_0_52,negated_conjecture,
k10_relset_1(esk2_0,esk2_0,k9_relset_2(esk2_0,esk1_0,esk2_0,k4_relat_1(esk3_0),esk3_0),esk2_0) != k9_relat_1(esk3_0,esk1_0),
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_40]),c_0_51]),c_0_44]),c_0_51]),c_0_52]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SEU446+3 : TPTP v9.2.1. Released v3.4.0.
% 0.10/0.13 % 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
% 0.15/0.35 % Computer : n008.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue May 5 03:19:46 EDT 2026
% 0.15/0.35 % CPUTime :
% 0.19/0.36 % start to proof: theBenchmark
% 21.69/18.98 % Version : CSE_E---1.7
% 21.69/18.98 % Problem : theBenchmark.p
% 21.69/18.98 % SZS status Theorem for theBenchmark.p
% 21.69/18.98 % SZS output start CNFRefutation
% See solution above
% 21.69/19.00 % Total time : 17.739s
%------------------------------------------------------------------------------