%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU297+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:24:36 PM UTC 2026
% Result : Theorem 0.68s 0.66s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of formulae : 51 ( 9 unt; 0 def)
% Number of atoms : 352 ( 70 equ)
% Maximal formula atoms : 130 ( 6 avg)
% Number of connectives : 509 ( 208 ~; 256 |; 37 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-4 aty)
% Number of variables : 114 ( 0 sgn 22 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_tarski__e6_27__finset_1__1,axiom,
! [X1,X2,X3] :
( ( function(X3)
& relation(X3)
& element(X2,powerset(powerset(X1))) )
=> ( ! [X4,X5,X6] :
( ( in(relation_image(X3,X6),X2)
& X4 = X6
& in(relation_image(X3,X5),X2)
& X4 = X5 )
=> X5 = X6 )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( in(relation_image(X3,X5),X2)
& X6 = X5
& in(X6,powerset(relation_dom(X3))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_27__finset_1__1) ).
fof(s1_xboole_0__e6_27__finset_1,conjecture,
! [X1,X2,X3] :
( ( function(X3)
& relation(X3)
& element(X2,powerset(powerset(X1))) )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ( in(relation_image(X3,X5),X2)
& in(X5,powerset(relation_dom(X3))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_27__finset_1) ).
fof(c_0_2,plain,
! [X14,X15,X16,X21,X23,X24] :
( ( ~ function(X16)
| ~ relation(X16)
| ~ element(X15,powerset(powerset(X14)))
| esk6_3(X14,X15,X16) != esk7_3(X14,X15,X16)
| in(X23,esk8_3(X14,X15,X16))
| ~ in(relation_image(X16,X23),X15)
| X24 != X23
| ~ in(X24,powerset(relation_dom(X16))) )
& ( ~ function(X16)
| ~ relation(X16)
| ~ element(X15,powerset(powerset(X14)))
| esk6_3(X14,X15,X16) != esk7_3(X14,X15,X16)
| ~ in(X21,esk8_3(X14,X15,X16))
| in(relation_image(X16,X21),X15) )
& ( ~ function(X16)
| ~ relation(X16)
| ~ element(X15,powerset(powerset(X14)))
| esk6_3(X14,X15,X16) != esk7_3(X14,X15,X16)
| ~ in(X21,esk8_3(X14,X15,X16))
| esk9_4(X14,X15,X16,X21) = X21 )
& ( ~ function(X16)
| ~ relation(X16)
| ~ element(X15,powerset(powerset(X14)))
| esk6_3(X14,X15,X16) != esk7_3(X14,X15,X16)
| ~ in(X21,esk8_3(X14,X15,X16))
| in(esk9_4(X14,X15,X16,X21),powerset(relation_dom(X16))) )
& ( ~ function(X16)
| ~ relation(X16)
| ~ element(X15,powerset(powerset(X14)))
| in(relation_image(X16,esk7_3(X14,X15,X16)),X15)
| in(X23,esk8_3(X14,X15,X16))
| ~ in(relation_image(X16,X23),X15)
| X24 != X23
| ~ in(X24,powerset(relation_dom(X16))) )
& ( ~ function(X16)
| ~ relation(X16)
| ~ element(X15,powerset(powerset(X14)))
| in(relation_image(X16,esk7_3(X14,X15,X16)),X15)
| ~ in(X21,esk8_3(X14,X15,X16))
| in(relation_image(X16,X21),X15) )
& ( ~ function(X16)
| ~ relation(X16)
| ~ element(X15,powerset(powerset(X14)))
| in(relation_image(X16,esk7_3(X14,X15,X16)),X15)
| ~ in(X21,esk8_3(X14,X15,X16))
| esk9_4(X14,X15,X16,X21) = X21 )
& ( ~ function(X16)
| ~ relation(X16)
| ~ element(X15,powerset(powerset(X14)))
| in(relation_image(X16,esk7_3(X14,X15,X16)),X15)
| ~ in(X21,esk8_3(X14,X15,X16))
| in(esk9_4(X14,X15,X16,X21),powerset(relation_dom(X16))) )
& ( ~ function(X16)
| ~ relation(X16)
| ~ element(X15,powerset(powerset(X14)))
| esk5_3(X14,X15,X16) = esk7_3(X14,X15,X16)
| in(X23,esk8_3(X14,X15,X16))
| ~ in(relation_image(X16,X23),X15)
| X24 != X23
| ~ in(X24,powerset(relation_dom(X16))) )
& ( ~ function(X16)
| ~ relation(X16)
| ~ element(X15,powerset(powerset(X14)))
| esk5_3(X14,X15,X16) = esk7_3(X14,X15,X16)
| ~ in(X21,esk8_3(X14,X15,X16))
| in(relation_image(X16,X21),X15) )
& ( ~ function(X16)
| ~ relation(X16)
| ~ element(X15,powerset(powerset(X14)))
| esk5_3(X14,X15,X16) = esk7_3(X14,X15,X16)
| ~ in(X21,esk8_3(X14,X15,X16))
| esk9_4(X14,X15,X16,X21) = X21 )
& ( ~ function(X16)
| ~ relation(X16)
| ~ element(X15,powerset(powerset(X14)))
| esk5_3(X14,X15,X16) = esk7_3(X14,X15,X16)
| ~ in(X21,esk8_3(X14,X15,X16))
| in(esk9_4(X14,X15,X16,X21),powerset(relation_dom(X16))) )
& ( ~ function(X16)
| ~ relation(X16)
| ~ element(X15,powerset(powerset(X14)))
| in(relation_image(X16,esk6_3(X14,X15,X16)),X15)
| in(X23,esk8_3(X14,X15,X16))
| ~ in(relation_image(X16,X23),X15)
| X24 != X23
| ~ in(X24,powerset(relation_dom(X16))) )
& ( ~ function(X16)
| ~ relation(X16)
| ~ element(X15,powerset(powerset(X14)))
| in(relation_image(X16,esk6_3(X14,X15,X16)),X15)
| ~ in(X21,esk8_3(X14,X15,X16))
| in(relation_image(X16,X21),X15) )
& ( ~ function(X16)
| ~ relation(X16)
| ~ element(X15,powerset(powerset(X14)))
| in(relation_image(X16,esk6_3(X14,X15,X16)),X15)
| ~ in(X21,esk8_3(X14,X15,X16))
| esk9_4(X14,X15,X16,X21) = X21 )
& ( ~ function(X16)
| ~ relation(X16)
| ~ element(X15,powerset(powerset(X14)))
| in(relation_image(X16,esk6_3(X14,X15,X16)),X15)
| ~ in(X21,esk8_3(X14,X15,X16))
| in(esk9_4(X14,X15,X16,X21),powerset(relation_dom(X16))) )
& ( ~ function(X16)
| ~ relation(X16)
| ~ element(X15,powerset(powerset(X14)))
| esk5_3(X14,X15,X16) = esk6_3(X14,X15,X16)
| in(X23,esk8_3(X14,X15,X16))
| ~ in(relation_image(X16,X23),X15)
| X24 != X23
| ~ in(X24,powerset(relation_dom(X16))) )
& ( ~ function(X16)
| ~ relation(X16)
| ~ element(X15,powerset(powerset(X14)))
| esk5_3(X14,X15,X16) = esk6_3(X14,X15,X16)
| ~ in(X21,esk8_3(X14,X15,X16))
| in(relation_image(X16,X21),X15) )
& ( ~ function(X16)
| ~ relation(X16)
| ~ element(X15,powerset(powerset(X14)))
| esk5_3(X14,X15,X16) = esk6_3(X14,X15,X16)
| ~ in(X21,esk8_3(X14,X15,X16))
| esk9_4(X14,X15,X16,X21) = X21 )
& ( ~ function(X16)
| ~ relation(X16)
| ~ element(X15,powerset(powerset(X14)))
| esk5_3(X14,X15,X16) = esk6_3(X14,X15,X16)
| ~ in(X21,esk8_3(X14,X15,X16))
| in(esk9_4(X14,X15,X16,X21),powerset(relation_dom(X16))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[s1_tarski__e6_27__finset_1__1])])])])])])]) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3] :
( ( function(X3)
& relation(X3)
& element(X2,powerset(powerset(X1))) )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ( in(relation_image(X3,X5),X2)
& in(X5,powerset(relation_dom(X3))) ) ) ),
inference(assume_negation,[status(cth)],[s1_xboole_0__e6_27__finset_1]) ).
cnf(c_0_4,plain,
( ~ function(X2)
| ~ relation(X2)
| ~ element(X4,powerset(powerset(X5)))
| ~ in(relation_image(X2,X3),X4)
| X1 != X3
| ~ in(X1,powerset(relation_dom(X2)))
| esk5_3(X5,X4,X2) = esk6_3(X5,X4,X2)
| in(X3,esk8_3(X5,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
fof(c_0_5,negated_conjecture,
! [X10] :
( ( in(esk4_1(X10),X10)
| in(relation_image(esk3_0,esk4_1(X10)),esk2_0) )
& ( in(esk4_1(X10),X10)
| in(esk4_1(X10),powerset(relation_dom(esk3_0))) )
& ( ~ in(relation_image(esk3_0,esk4_1(X10)),esk2_0)
| ~ in(esk4_1(X10),powerset(relation_dom(esk3_0)))
| ~ in(esk4_1(X10),X10) )
& function(esk3_0)
& relation(esk3_0)
& element(esk2_0,powerset(powerset(esk1_0))) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])])]) ).
cnf(c_0_6,plain,
( ~ element(X2,powerset(powerset(X1)))
| ~ relation(X3)
| ~ function(X3)
| ~ in(relation_image(X3,X4),X2)
| ~ in(X4,powerset(relation_dom(X3)))
| in(X4,esk8_3(X1,X2,X3))
| esk5_3(X1,X2,X3) = esk6_3(X1,X2,X3) ),
inference(er,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
element(esk2_0,powerset(powerset(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( ~ relation(X1)
| ~ function(X1)
| ~ in(relation_image(X1,X2),esk2_0)
| ~ in(X2,powerset(relation_dom(X1)))
| in(X2,esk8_3(esk1_0,esk2_0,X1))
| esk5_3(esk1_0,esk2_0,X1) = esk6_3(esk1_0,esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,negated_conjecture,
( in(esk4_1(X1),X1)
| in(esk4_1(X1),powerset(relation_dom(esk3_0))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
function(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,negated_conjecture,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
( in(esk4_1(X1),X1)
| in(relation_image(esk3_0,esk4_1(X1)),esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,negated_conjecture,
( in(esk4_1(X1),X1)
| in(esk4_1(X1),esk8_3(esk1_0,esk2_0,esk3_0))
| esk5_3(esk1_0,esk2_0,esk3_0) = esk6_3(esk1_0,esk2_0,esk3_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]),c_0_11])]),c_0_12]) ).
cnf(c_0_14,plain,
( ~ function(X3)
| ~ relation(X3)
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X4,esk8_3(X1,X2,X3))
| esk5_3(X1,X2,X3) = esk6_3(X1,X2,X3)
| esk9_4(X1,X2,X3,X4) = X4 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_15,negated_conjecture,
( in(esk4_1(esk8_3(esk1_0,esk2_0,esk3_0)),esk8_3(esk1_0,esk2_0,esk3_0))
| esk5_3(esk1_0,esk2_0,esk3_0) = esk6_3(esk1_0,esk2_0,esk3_0) ),
inference(ef,[status(thm)],[c_0_13]) ).
cnf(c_0_16,plain,
( ~ function(X2)
| ~ relation(X2)
| ~ element(X4,powerset(powerset(X5)))
| ~ in(relation_image(X2,X3),X4)
| X1 != X3
| ~ in(X1,powerset(relation_dom(X2)))
| esk5_3(X5,X4,X2) = esk7_3(X5,X4,X2)
| in(X3,esk8_3(X5,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_17,plain,
( ~ function(X3)
| ~ relation(X3)
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X4,esk8_3(X1,X2,X3))
| esk5_3(X1,X2,X3) = esk6_3(X1,X2,X3)
| in(esk9_4(X1,X2,X3,X4),powerset(relation_dom(X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_18,negated_conjecture,
( esk5_3(esk1_0,esk2_0,esk3_0) = esk6_3(esk1_0,esk2_0,esk3_0)
| esk9_4(esk1_0,esk2_0,esk3_0,esk4_1(esk8_3(esk1_0,esk2_0,esk3_0))) = esk4_1(esk8_3(esk1_0,esk2_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_14,c_0_15]),c_0_10]),c_0_11]),c_0_7])]) ).
cnf(c_0_19,plain,
( ~ function(X1)
| ~ relation(X1)
| ~ element(X3,powerset(powerset(X4)))
| ~ in(X2,esk8_3(X4,X3,X1))
| esk5_3(X4,X3,X1) = esk6_3(X4,X3,X1)
| in(relation_image(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_20,plain,
( ~ element(X2,powerset(powerset(X1)))
| ~ relation(X3)
| ~ function(X3)
| ~ in(relation_image(X3,X4),X2)
| ~ in(X4,powerset(relation_dom(X3)))
| in(X4,esk8_3(X1,X2,X3))
| esk5_3(X1,X2,X3) = esk7_3(X1,X2,X3) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( ~ in(relation_image(esk3_0,esk4_1(X1)),esk2_0)
| ~ in(esk4_1(X1),powerset(relation_dom(esk3_0)))
| ~ in(esk4_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_22,negated_conjecture,
( in(esk4_1(esk8_3(esk1_0,esk2_0,esk3_0)),powerset(relation_dom(esk3_0)))
| esk5_3(esk1_0,esk2_0,esk3_0) = esk6_3(esk1_0,esk2_0,esk3_0) ),
inference(csr,[status(thm)],[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_10]),c_0_11]),c_0_7])]),c_0_15]) ).
cnf(c_0_23,negated_conjecture,
( in(relation_image(esk3_0,esk4_1(esk8_3(esk1_0,esk2_0,esk3_0))),esk2_0)
| esk5_3(esk1_0,esk2_0,esk3_0) = esk6_3(esk1_0,esk2_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_19,c_0_15]),c_0_10]),c_0_11]),c_0_7])]) ).
cnf(c_0_24,negated_conjecture,
( ~ relation(X1)
| ~ function(X1)
| ~ in(relation_image(X1,X2),esk2_0)
| ~ in(X2,powerset(relation_dom(X1)))
| in(X2,esk8_3(esk1_0,esk2_0,X1))
| esk5_3(esk1_0,esk2_0,X1) = esk7_3(esk1_0,esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_7]) ).
cnf(c_0_25,negated_conjecture,
esk5_3(esk1_0,esk2_0,esk3_0) = esk6_3(esk1_0,esk2_0,esk3_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_15]) ).
cnf(c_0_26,plain,
( ~ function(X1)
| ~ relation(X1)
| ~ element(X3,powerset(powerset(X4)))
| ~ in(X2,esk8_3(X4,X3,X1))
| esk5_3(X4,X3,X1) = esk7_3(X4,X3,X1)
| in(relation_image(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_27,negated_conjecture,
( in(esk4_1(X1),X1)
| in(esk4_1(X1),esk8_3(esk1_0,esk2_0,esk3_0))
| esk7_3(esk1_0,esk2_0,esk3_0) = esk6_3(esk1_0,esk2_0,esk3_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_9]),c_0_25]),c_0_10]),c_0_11])]),c_0_12]) ).
cnf(c_0_28,plain,
( ~ function(X1)
| ~ relation(X1)
| ~ element(X3,powerset(powerset(X4)))
| esk6_3(X4,X3,X1) != esk7_3(X4,X3,X1)
| ~ in(X2,esk8_3(X4,X3,X1))
| in(relation_image(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_29,negated_conjecture,
( ~ element(X2,powerset(powerset(X1)))
| ~ relation(X3)
| ~ function(X3)
| in(relation_image(X3,esk4_1(esk8_3(X1,X2,X3))),X2)
| in(relation_image(esk3_0,esk4_1(esk8_3(X1,X2,X3))),esk2_0)
| esk5_3(X1,X2,X3) = esk7_3(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_12]) ).
cnf(c_0_30,plain,
( ~ function(X3)
| ~ relation(X3)
| ~ element(X2,powerset(powerset(X1)))
| esk6_3(X1,X2,X3) != esk7_3(X1,X2,X3)
| ~ in(X4,esk8_3(X1,X2,X3))
| in(esk9_4(X1,X2,X3,X4),powerset(relation_dom(X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_31,plain,
( ~ function(X3)
| ~ relation(X3)
| ~ element(X2,powerset(powerset(X1)))
| esk6_3(X1,X2,X3) != esk7_3(X1,X2,X3)
| ~ in(X4,esk8_3(X1,X2,X3))
| esk9_4(X1,X2,X3,X4) = X4 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_32,plain,
( ~ function(X3)
| ~ relation(X3)
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X4,esk8_3(X1,X2,X3))
| esk5_3(X1,X2,X3) = esk7_3(X1,X2,X3)
| esk9_4(X1,X2,X3,X4) = X4 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_33,negated_conjecture,
( in(esk4_1(esk8_3(esk1_0,esk2_0,esk3_0)),esk8_3(esk1_0,esk2_0,esk3_0))
| esk7_3(esk1_0,esk2_0,esk3_0) = esk6_3(esk1_0,esk2_0,esk3_0) ),
inference(ef,[status(thm)],[c_0_27]) ).
cnf(c_0_34,negated_conjecture,
( ~ element(X2,powerset(powerset(X1)))
| ~ relation(X3)
| ~ function(X3)
| esk7_3(X1,X2,X3) != esk6_3(X1,X2,X3)
| in(relation_image(X3,esk4_1(esk8_3(X1,X2,X3))),X2)
| in(relation_image(esk3_0,esk4_1(esk8_3(X1,X2,X3))),esk2_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_12]) ).
cnf(c_0_35,negated_conjecture,
( ~ relation(X1)
| ~ function(X1)
| in(relation_image(X1,esk4_1(esk8_3(esk1_0,esk2_0,X1))),esk2_0)
| in(relation_image(esk3_0,esk4_1(esk8_3(esk1_0,esk2_0,X1))),esk2_0)
| esk5_3(esk1_0,esk2_0,X1) = esk7_3(esk1_0,esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_7]) ).
cnf(c_0_36,plain,
( ~ element(X4,powerset(powerset(X3)))
| ~ relation(X2)
| ~ function(X2)
| ~ in(X1,esk8_3(X3,X4,X2))
| esk7_3(X3,X4,X2) != esk6_3(X3,X4,X2)
| in(X1,powerset(relation_dom(X2))) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
( ~ function(X3)
| ~ relation(X3)
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X4,esk8_3(X1,X2,X3))
| esk5_3(X1,X2,X3) = esk7_3(X1,X2,X3)
| in(esk9_4(X1,X2,X3,X4),powerset(relation_dom(X3))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_38,negated_conjecture,
( esk7_3(esk1_0,esk2_0,esk3_0) = esk6_3(esk1_0,esk2_0,esk3_0)
| esk9_4(esk1_0,esk2_0,esk3_0,esk4_1(esk8_3(esk1_0,esk2_0,esk3_0))) = esk4_1(esk8_3(esk1_0,esk2_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_25]),c_0_10]),c_0_11]),c_0_7])]) ).
cnf(c_0_39,negated_conjecture,
( ~ relation(X1)
| ~ function(X1)
| esk7_3(esk1_0,esk2_0,X1) != esk6_3(esk1_0,esk2_0,X1)
| in(relation_image(X1,esk4_1(esk8_3(esk1_0,esk2_0,X1))),esk2_0)
| in(relation_image(esk3_0,esk4_1(esk8_3(esk1_0,esk2_0,X1))),esk2_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_7]) ).
cnf(c_0_40,negated_conjecture,
( in(relation_image(esk3_0,esk4_1(esk8_3(esk1_0,esk2_0,esk3_0))),esk2_0)
| esk7_3(esk1_0,esk2_0,esk3_0) = esk6_3(esk1_0,esk2_0,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_10]),c_0_25]),c_0_11])]) ).
cnf(c_0_41,negated_conjecture,
( ~ element(X2,powerset(powerset(X1)))
| ~ relation(X3)
| ~ function(X3)
| esk7_3(X1,X2,X3) != esk6_3(X1,X2,X3)
| in(esk4_1(esk8_3(X1,X2,X3)),powerset(relation_dom(X3)))
| in(esk4_1(esk8_3(X1,X2,X3)),powerset(relation_dom(esk3_0))) ),
inference(spm,[status(thm)],[c_0_36,c_0_9]) ).
cnf(c_0_42,negated_conjecture,
( in(esk4_1(esk8_3(esk1_0,esk2_0,esk3_0)),powerset(relation_dom(esk3_0)))
| esk7_3(esk1_0,esk2_0,esk3_0) = esk6_3(esk1_0,esk2_0,esk3_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_25]),c_0_10]),c_0_11]),c_0_7])]),c_0_33]) ).
cnf(c_0_43,negated_conjecture,
in(relation_image(esk3_0,esk4_1(esk8_3(esk1_0,esk2_0,esk3_0))),esk2_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_10]),c_0_11])]),c_0_40]) ).
cnf(c_0_44,negated_conjecture,
( ~ relation(X1)
| ~ function(X1)
| esk7_3(esk1_0,esk2_0,X1) != esk6_3(esk1_0,esk2_0,X1)
| in(esk4_1(esk8_3(esk1_0,esk2_0,X1)),powerset(relation_dom(X1)))
| in(esk4_1(esk8_3(esk1_0,esk2_0,X1)),powerset(relation_dom(esk3_0))) ),
inference(spm,[status(thm)],[c_0_41,c_0_7]) ).
cnf(c_0_45,negated_conjecture,
esk7_3(esk1_0,esk2_0,esk3_0) = esk6_3(esk1_0,esk2_0,esk3_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_42]),c_0_43])]),c_0_33]) ).
cnf(c_0_46,negated_conjecture,
in(esk4_1(esk8_3(esk1_0,esk2_0,esk3_0)),powerset(relation_dom(esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_10]),c_0_45]),c_0_11])]) ).
cnf(c_0_47,plain,
( ~ function(X2)
| ~ relation(X2)
| ~ element(X4,powerset(powerset(X5)))
| esk6_3(X5,X4,X2) != esk7_3(X5,X4,X2)
| ~ in(relation_image(X2,X3),X4)
| X1 != X3
| ~ in(X1,powerset(relation_dom(X2)))
| in(X3,esk8_3(X5,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_48,negated_conjecture,
~ in(esk4_1(esk8_3(esk1_0,esk2_0,esk3_0)),esk8_3(esk1_0,esk2_0,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_46]),c_0_43])]) ).
cnf(c_0_49,plain,
( ~ element(X3,powerset(powerset(X2)))
| ~ relation(X4)
| ~ function(X4)
| ~ in(relation_image(X4,X1),X3)
| ~ in(X1,powerset(relation_dom(X4)))
| esk7_3(X2,X3,X4) != esk6_3(X2,X3,X4)
| in(X1,esk8_3(X2,X3,X4)) ),
inference(er,[status(thm)],[c_0_47]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_45]),c_0_46]),c_0_43]),c_0_10]),c_0_11]),c_0_7])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU297+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.45 % Computer : n008.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 06:09:41 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.52 Running first-order theorem proving
% 0.22/0.52 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.68/0.66 % Version: 3.5.1
% 0.68/0.66 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.68/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.68/0.66 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.68/0.66 % Starting new_bool_3 with 300s (1) cores
% 0.68/0.66 % Starting new_bool_1 with 300s (1) cores
% 0.68/0.66 % Starting sh5l with 300s (1) cores
% 0.68/0.66 % new_bool_3 with pid 310080 completed with status 0
% 0.68/0.66 % Result found by new_bool_3
% 0.68/0.66 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.68/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.68/0.66 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.68/0.66 % Starting new_bool_3 with 300s (1) cores
% 0.68/0.66 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.68/0.66 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.68/0.66 % Search class: FGHSS-FFMM32-SFFFFFNN
% 0.68/0.66 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.68/0.66 % Starting SubtermCWHack with 31s (1) cores
% 0.68/0.66 % SubtermCWHack with pid 310085 completed with status 0
% 0.68/0.66 % Result found by SubtermCWHack
% 0.68/0.66 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.68/0.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.68/0.66 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.68/0.66 % Starting new_bool_3 with 300s (1) cores
% 0.68/0.66 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.68/0.66 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.68/0.66 % Search class: FGHSS-FFMM32-SFFFFFNN
% 0.68/0.66 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.68/0.66 % Starting SubtermCWHack with 31s (1) cores
% 0.68/0.66 % Preprocessing time : 0.003 s
% 0.68/0.66
% 0.68/0.66 % Proof found!
% 0.68/0.66 % SZS status Theorem
% 0.68/0.66 % SZS output start CNFRefutation
% See solution above
% 0.68/0.66 % Parsed axioms : 37
% 0.68/0.66 % Removed by relevancy pruning/SinE : 10
% 0.68/0.66 % Initial clauses : 72
% 0.68/0.66 % Removed in clause preprocessing : 0
% 0.68/0.66 % Initial clauses in saturation : 72
% 0.68/0.66 % Processed clauses : 476
% 0.68/0.66 % ...of these trivial : 1
% 0.68/0.66 % ...subsumed : 71
% 0.68/0.66 % ...remaining for further processing : 404
% 0.68/0.66 % Other redundant clauses eliminated : 5
% 0.68/0.66 % Clauses deleted for lack of memory : 0
% 0.68/0.66 % Backward-subsumed : 20
% 0.68/0.66 % Backward-rewritten : 44
% 0.68/0.66 % Generated clauses : 1159
% 0.68/0.66 % ...of the previous two non-redundant : 1000
% 0.68/0.66 % ...aggressively subsumed : 0
% 0.68/0.66 % Contextual simplify-reflections : 27
% 0.68/0.66 % Paramodulations : 1144
% 0.68/0.66 % Factorizations : 10
% 0.68/0.66 % NegExts : 0
% 0.68/0.66 % Equation resolutions : 5
% 0.68/0.66 % Disequality decompositions : 0
% 0.68/0.66 % Total rewrite steps : 1160
% 0.68/0.66 % ...of those cached : 1139
% 0.68/0.66 % Propositional unsat checks : 0
% 0.68/0.66 % Propositional check models : 0
% 0.68/0.66 % Propositional check unsatisfiable : 0
% 0.68/0.66 % Propositional clauses : 0
% 0.68/0.66 % Propositional clauses after purity: 0
% 0.68/0.66 % Propositional unsat core size : 0
% 0.68/0.66 % Propositional preprocessing time : 0.000
% 0.68/0.66 % Propositional encoding time : 0.000
% 0.68/0.66 % Propositional solver time : 0.000
% 0.68/0.66 % Success case prop preproc time : 0.000
% 0.68/0.66 % Success case prop encoding time : 0.000
% 0.68/0.66 % Success case prop solver time : 0.000
% 0.68/0.66 % Current number of processed clauses : 335
% 0.68/0.66 % Positive orientable unit clauses : 30
% 0.68/0.66 % Positive unorientable unit clauses: 0
% 0.68/0.66 % Negative unit clauses : 12
% 0.68/0.66 % Non-unit-clauses : 293
% 0.68/0.66 % Current number of unprocessed clauses: 551
% 0.68/0.66 % ...number of literals in the above : 3385
% 0.68/0.66 % Current number of archived formulas : 0
% 0.68/0.66 % Current number of archived clauses : 64
% 0.68/0.66 % Clause-clause subsumption calls (NU) : 22940
% 0.68/0.66 % Rec. Clause-clause subsumption calls : 8923
% 0.68/0.66 % Non-unit clause-clause subsumptions : 105
% 0.68/0.66 % Unit Clause-clause subsumption calls : 901
% 0.68/0.66 % Rewrite failures with RHS unbound : 0
% 0.68/0.66 % BW rewrite match attempts : 33
% 0.68/0.66 % BW rewrite match successes : 5
% 0.68/0.66 % Condensation attempts : 0
% 0.68/0.66 % Condensation successes : 0
% 0.68/0.66 % Termbank termtop insertions : 46623
% 0.68/0.66 % Search garbage collected termcells : 755
% 0.68/0.66
% 0.68/0.66 % -------------------------------------------------
% 0.68/0.66 % User time : 0.097 s
% 0.68/0.66 % System time : 0.013 s
% 0.68/0.66 % Total time : 0.110 s
% 0.68/0.66 % Maximum resident set size: 3664 pages
% 0.68/0.66
% 0.68/0.66 % -------------------------------------------------
% 0.68/0.66 % User time : 0.101 s
% 0.68/0.66 % System time : 0.018 s
% 0.68/0.66 % Total time : 0.120 s
% 0.68/0.66 % Maximum resident set size: 4864 pages
% 0.68/0.66 % E exiting
%------------------------------------------------------------------------------