%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWX209+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 03:14:16 PM UTC 2026
% Result : Theorem 275.71s 41.05s
% Output : CNFRefutation 275.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 25
% Syntax : Number of formulae : 118 ( 75 unt; 0 def)
% Number of atoms : 204 ( 108 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 194 ( 108 ~; 55 |; 7 &)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-2 aty)
% Number of variables : 209 ( 40 sgn 117 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goal_050,conjecture,
? [X6] : rec(X6,cons(a,cons(a,cons(b,cons(b,nil))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_050) ).
fof(axiom_049,axiom,
! [X1,X12,X13] :
( rec(X1,cons(X12,X13))
<=> rec(step(X1,X12),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_049) ).
fof(axiom_015,axiom,
! [X1,X2] : nil2 != x(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
fof(axiom_041,axiom,
! [X1,X5] :
( X1 != atom(proj1Atom(X1))
=> ( X1 != x(proj1(X1),proj2(X1))
=> ( X1 != y(proj12(X1),proj22(X1))
=> ( X1 != star(proj1Star(X1))
=> step(X1,X5) = nil2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_041) ).
fof(axiom_016,axiom,
! [X1,X2] : nil2 != y(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
fof(axiom_014,axiom,
! [X1] : nil2 != atom(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
fof(axiom_017,axiom,
! [X1] : nil2 != star(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
fof(axiom_046,axiom,
! [X5,X8,X9] :
( ~ eps2(X8)
=> step(y(X8,X9),X5) = x(y(step(X8,X5),X9),nil2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_046) ).
fof(axiom_042,axiom,
! [X5,X10] :
( X10 = X5
=> step(atom(X10),X5) = eps ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_042) ).
fof(axiom_048,axiom,
! [X1] :
( rec(X1,nil)
<=> eps2(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_048) ).
fof(axiom_044,axiom,
! [X5,X6,X7] : step(x(X6,X7),X5) = x(step(X6,X5),step(X7,X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_044) ).
fof(axiom_038,axiom,
! [X6,X7] :
( eps2(x(X6,X7))
<=> ( eps2(X7)
| eps2(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_038) ).
fof(axiom_019,axiom,
! [X1,X2] : eps != x(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
fof(axiom_020,axiom,
! [X1,X2] : eps != y(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
fof(axiom_018,axiom,
! [X1] : eps != atom(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
fof(axiom_021,axiom,
! [X1] : eps != star(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
fof(axiom_045,axiom,
! [X5,X8,X9] :
( eps2(X8)
=> step(y(X8,X9),X5) = x(y(step(X8,X5),X9),step(X9,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_045) ).
fof(axiom_047,axiom,
! [X5,X11] : step(star(X11),X5) = y(step(X11,X5),star(X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_047) ).
fof(axiom_039,axiom,
! [X8,X9] :
( eps2(y(X8,X9))
<=> ( eps2(X9)
& eps2(X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_039) ).
fof(axiom_040,axiom,
! [X5] : eps2(star(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_040) ).
fof(axiom_037,axiom,
eps2(eps),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_037) ).
fof(axiom_036,axiom,
! [X1] :
( X1 != eps
=> ( X1 != x(proj1(X1),proj2(X1))
=> ( X1 != y(proj12(X1),proj22(X1))
=> ( X1 != star(proj1Star(X1))
=> ~ eps2(X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_036) ).
fof(axiom_022,axiom,
! [X1,X2,X3] : atom(X1) != x(X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_022) ).
fof(axiom_023,axiom,
! [X1,X2,X3] : atom(X1) != y(X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_023) ).
fof(axiom_024,axiom,
! [X1,X2] : atom(X1) != star(X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
fof(c_0_25,negated_conjecture,
~ ? [X6] : rec(X6,cons(a,cons(a,cons(b,cons(b,nil))))),
inference(assume_negation,[status(cth)],[goal_050]) ).
fof(c_0_26,negated_conjecture,
! [X97] : ~ rec(X97,cons(a,cons(a,cons(b,cons(b,nil))))),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
fof(c_0_27,plain,
! [X94,X95,X96] :
( ( rec(X94,cons(X95,X96))
| ~ rec(step(X94,X95),X96) )
& ( rec(step(X94,X95),X96)
| ~ rec(X94,cons(X95,X96)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_049])])]) ).
cnf(c_0_28,negated_conjecture,
~ rec(X1,cons(a,cons(a,cons(b,cons(b,nil))))),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_29,plain,
( ~ rec(step(X1,X2),X3)
| rec(X1,cons(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_30,negated_conjecture,
~ rec(step(X1,a),cons(a,cons(b,cons(b,nil)))),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_31,plain,
! [X1,X2] : nil2 != x(X1,X2),
inference(fof_simplification,[status(thm)],[axiom_015]) ).
fof(c_0_32,plain,
! [X1,X5] :
( X1 != atom(proj1Atom(X1))
=> ( X1 != x(proj1(X1),proj2(X1))
=> ( X1 != y(proj12(X1),proj22(X1))
=> ( X1 != star(proj1Star(X1))
=> step(X1,X5) = nil2 ) ) ) ),
inference(fof_simplification,[status(thm)],[axiom_041]) ).
fof(c_0_33,plain,
! [X1,X2] : nil2 != y(X1,X2),
inference(fof_simplification,[status(thm)],[axiom_016]) ).
fof(c_0_34,plain,
! [X1] : nil2 != atom(X1),
inference(fof_simplification,[status(thm)],[axiom_014]) ).
fof(c_0_35,plain,
! [X1] : nil2 != star(X1),
inference(fof_simplification,[status(thm)],[axiom_017]) ).
cnf(c_0_36,negated_conjecture,
~ rec(step(step(X1,a),a),cons(b,cons(b,nil))),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
fof(c_0_37,plain,
! [X5,X8,X9] :
( ~ eps2(X8)
=> step(y(X8,X9),X5) = x(y(step(X8,X5),X9),nil2) ),
inference(fof_simplification,[status(thm)],[axiom_046]) ).
fof(c_0_38,plain,
! [X78,X79] :
( step(atom(X79),X78) = eps
| X79 != X78 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_042])])]) ).
fof(c_0_39,plain,
! [X31,X32] : nil2 != x(X31,X32),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_31])]) ).
fof(c_0_40,plain,
! [X76,X77] :
( step(X76,X77) = nil2
| X76 = star(proj1Star(X76))
| X76 = y(proj12(X76),proj22(X76))
| X76 = x(proj1(X76),proj2(X76))
| X76 = atom(proj1Atom(X76)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])]) ).
fof(c_0_41,plain,
! [X33,X34] : nil2 != y(X33,X34),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_33])]) ).
fof(c_0_42,plain,
! [X30] : nil2 != atom(X30),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_34])]) ).
fof(c_0_43,plain,
! [X35] : nil2 != star(X35),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_35])]) ).
cnf(c_0_44,negated_conjecture,
~ rec(step(step(step(X1,a),a),b),cons(b,nil)),
inference(spm,[status(thm)],[c_0_36,c_0_29]) ).
fof(c_0_45,plain,
! [X93] :
( ( rec(X93,nil)
| ~ eps2(X93) )
& ( eps2(X93)
| ~ rec(X93,nil) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_048])])]) ).
fof(c_0_46,plain,
! [X88,X89,X90] :
( step(y(X89,X90),X88) = x(y(step(X89,X88),X90),nil2)
| eps2(X89) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])]) ).
cnf(c_0_47,plain,
( X1 != X2
| step(atom(X1),X2) = eps ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_48,plain,
! [X82,X83,X84] : step(x(X83,X84),X82) = x(step(X83,X82),step(X84,X82)),
inference(variable_rename,[status(thm)],[axiom_044]) ).
cnf(c_0_49,plain,
nil2 != x(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_50,plain,
( step(X1,X2) = nil2
| X1 = star(proj1Star(X1))
| X1 = y(proj12(X1),proj22(X1))
| X1 = x(proj1(X1),proj2(X1))
| X1 = atom(proj1Atom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_51,plain,
nil2 != y(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_52,plain,
nil2 != atom(X1),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_53,plain,
nil2 != star(X1),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_54,plain,
! [X71,X72] :
( ( eps2(x(X71,X72))
| ~ eps2(X72) )
& ( eps2(x(X71,X72))
| ~ eps2(X71) )
& ( eps2(X72)
| eps2(X71)
| ~ eps2(x(X71,X72)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_038])])])]) ).
cnf(c_0_55,negated_conjecture,
~ rec(step(step(step(step(X1,a),a),b),b),nil),
inference(spm,[status(thm)],[c_0_44,c_0_29]) ).
cnf(c_0_56,plain,
( ~ eps2(X1)
| rec(X1,nil) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_57,plain,
( step(y(X1,X2),X3) = x(y(step(X1,X3),X2),nil2)
| eps2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_58,plain,
step(atom(X1),X1) = eps,
inference(er,[status(thm)],[c_0_47]) ).
cnf(c_0_59,plain,
step(x(X1,X2),X3) = x(step(X1,X3),step(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_60,plain,
step(nil2,X1) = nil2,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50])]),c_0_51]),c_0_52]),c_0_53]) ).
cnf(c_0_61,plain,
( ~ eps2(X1)
| eps2(x(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_62,plain,
! [X1,X2] : eps != x(X1,X2),
inference(fof_simplification,[status(thm)],[axiom_019]) ).
fof(c_0_63,plain,
! [X1,X2] : eps != y(X1,X2),
inference(fof_simplification,[status(thm)],[axiom_020]) ).
fof(c_0_64,plain,
! [X1] : eps != atom(X1),
inference(fof_simplification,[status(thm)],[axiom_018]) ).
fof(c_0_65,plain,
! [X1] : eps != star(X1),
inference(fof_simplification,[status(thm)],[axiom_021]) ).
cnf(c_0_66,negated_conjecture,
~ eps2(step(step(step(step(X1,a),a),b),b)),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_67,plain,
( eps2(atom(X1))
| step(y(atom(X1),X2),X1) = x(y(eps,X2),nil2) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_68,plain,
step(x(X1,nil2),X2) = x(step(X1,X2),nil2),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_69,plain,
( ~ eps2(step(X2,X3))
| eps2(step(x(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_61,c_0_59]) ).
fof(c_0_70,plain,
! [X85,X86,X87] :
( step(y(X86,X87),X85) = x(y(step(X86,X85),X87),step(X87,X85))
| ~ eps2(X86) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_045])])]) ).
fof(c_0_71,plain,
! [X37,X38] : eps != x(X37,X38),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_62])]) ).
fof(c_0_72,plain,
! [X39,X40] : eps != y(X39,X40),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_63])]) ).
fof(c_0_73,plain,
! [X36] : eps != atom(X36),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_64])]) ).
fof(c_0_74,plain,
! [X41] : eps != star(X41),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_65])]) ).
cnf(c_0_75,negated_conjecture,
( ~ eps2(x(step(step(step(y(eps,X1),a),b),b),nil2))
| eps2(atom(a)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_68]),c_0_68]) ).
cnf(c_0_76,plain,
( ~ eps2(X1)
| eps2(x(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_77,plain,
( ~ eps2(step(step(X2,X3),X4))
| eps2(step(step(x(X1,X2),X3),X4)) ),
inference(spm,[status(thm)],[c_0_69,c_0_59]) ).
cnf(c_0_78,plain,
( ~ eps2(X1)
| step(y(X1,X2),X3) = x(y(step(X1,X3),X2),step(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
fof(c_0_79,plain,
! [X91,X92] : step(star(X92),X91) = y(step(X92,X91),star(X92)),
inference(variable_rename,[status(thm)],[axiom_047]) ).
cnf(c_0_80,plain,
eps != x(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_81,plain,
eps != y(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_82,plain,
eps != atom(X1),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_83,plain,
eps != star(X1),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
fof(c_0_84,plain,
! [X73,X74] :
( ( eps2(y(X73,X74))
| ~ eps2(X74)
| ~ eps2(X73) )
& ( ~ eps2(y(X73,X74))
| eps2(X74) )
& ( ~ eps2(y(X73,X74))
| eps2(X73) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_039])])])]) ).
fof(c_0_85,plain,
! [X75] : eps2(star(X75)),
inference(variable_rename,[status(thm)],[axiom_040]) ).
cnf(c_0_86,negated_conjecture,
( ~ eps2(step(step(step(y(eps,X1),a),b),b))
| eps2(atom(a)) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_87,plain,
( ~ eps2(X1)
| ~ eps2(step(step(step(X2,X3),X4),X5))
| eps2(step(step(step(y(X1,X2),X3),X4),X5)) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_88,plain,
eps2(eps),
inference(split_conjunct,[status(thm)],[axiom_037]) ).
cnf(c_0_89,plain,
step(star(X1),X2) = y(step(X1,X2),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_90,plain,
step(eps,X1) = nil2,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_50])]),c_0_81]),c_0_82]),c_0_83]) ).
cnf(c_0_91,plain,
( ~ eps2(X2)
| ~ eps2(X1)
| eps2(y(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_92,plain,
eps2(star(X1)),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_93,negated_conjecture,
( ~ eps2(step(step(step(X1,a),b),b))
| eps2(atom(a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88])]) ).
cnf(c_0_94,plain,
step(star(atom(X1)),X1) = y(eps,star(atom(X1))),
inference(spm,[status(thm)],[c_0_89,c_0_58]) ).
cnf(c_0_95,plain,
x(y(nil2,X1),step(X1,X2)) = step(y(eps,X1),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_90]),c_0_88])]) ).
cnf(c_0_96,plain,
( ~ eps2(step(X1,X2))
| eps2(step(star(X1),X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_89]),c_0_92])]) ).
fof(c_0_97,plain,
! [X1] :
( X1 != eps
=> ( X1 != x(proj1(X1),proj2(X1))
=> ( X1 != y(proj12(X1),proj22(X1))
=> ( X1 != star(proj1Star(X1))
=> ~ eps2(X1) ) ) ) ),
inference(fof_simplification,[status(thm)],[axiom_036]) ).
cnf(c_0_98,negated_conjecture,
( ~ eps2(x(step(step(y(eps,X1),b),b),nil2))
| eps2(atom(a)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_67]),c_0_68]),c_0_68]) ).
cnf(c_0_99,plain,
( ~ eps2(X1)
| x(y(step(X1,X2),star(atom(X2))),y(eps,star(atom(X2)))) = step(y(X1,star(atom(X2))),X2) ),
inference(spm,[status(thm)],[c_0_78,c_0_94]) ).
cnf(c_0_100,plain,
x(y(nil2,star(atom(X1))),y(eps,star(atom(X1)))) = step(y(eps,star(atom(X1))),X1),
inference(spm,[status(thm)],[c_0_95,c_0_94]) ).
cnf(c_0_101,plain,
eps2(y(eps,star(atom(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_94]),c_0_58]),c_0_88])]) ).
fof(c_0_102,plain,
! [X1,X2,X3] : atom(X1) != x(X2,X3),
inference(fof_simplification,[status(thm)],[axiom_022]) ).
fof(c_0_103,plain,
! [X1,X2,X3] : atom(X1) != y(X2,X3),
inference(fof_simplification,[status(thm)],[axiom_023]) ).
fof(c_0_104,plain,
! [X1,X2] : atom(X1) != star(X2),
inference(fof_simplification,[status(thm)],[axiom_024]) ).
fof(c_0_105,plain,
! [X70] :
( ~ eps2(X70)
| X70 = star(proj1Star(X70))
| X70 = y(proj12(X70),proj22(X70))
| X70 = x(proj1(X70),proj2(X70))
| X70 = eps ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_97])])]) ).
cnf(c_0_106,negated_conjecture,
( ~ eps2(step(step(y(eps,X1),b),b))
| eps2(atom(a)) ),
inference(spm,[status(thm)],[c_0_98,c_0_76]) ).
cnf(c_0_107,plain,
( ~ eps2(X1)
| ~ eps2(step(y(eps,star(atom(X2))),X3))
| eps2(step(step(y(X1,star(atom(X2))),X2),X3)) ),
inference(spm,[status(thm)],[c_0_69,c_0_99]) ).
cnf(c_0_108,plain,
eps2(step(y(eps,star(atom(X1))),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_100]),c_0_101])]) ).
fof(c_0_109,plain,
! [X42,X43,X44] : atom(X42) != x(X43,X44),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_102])]) ).
fof(c_0_110,plain,
! [X45,X46,X47] : atom(X45) != y(X46,X47),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_103])]) ).
fof(c_0_111,plain,
! [X48,X49] : atom(X48) != star(X49),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_104])]) ).
cnf(c_0_112,plain,
( ~ eps2(X1)
| X1 = star(proj1Star(X1))
| X1 = y(proj12(X1),proj22(X1))
| X1 = x(proj1(X1),proj2(X1))
| X1 = eps ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_113,negated_conjecture,
eps2(atom(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]),c_0_88])]) ).
cnf(c_0_114,plain,
atom(X1) != x(X2,X3),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_115,plain,
atom(X1) != y(X2,X3),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_116,plain,
atom(X1) != star(X2),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_117,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_114]),c_0_115]),c_0_116]),c_0_82]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX209+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.37 % Computer : n019.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Mon Sep 21 10:33:10 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 275.71/41.05 % Version: 3.5.1
% 275.71/41.05 % Preprocessing class: FSMSSMSSSSSNFFN.
% 275.71/41.05 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 275.71/41.05 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 275.71/41.05 % Starting new_bool_3 with 300s (1) cores
% 275.71/41.05 % Starting new_bool_1 with 300s (1) cores
% 275.71/41.05 % Starting sh5l with 300s (1) cores
% 275.71/41.05 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2340968 completed with status 0
% 275.71/41.05 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 275.71/41.05 % Preprocessing class: FSMSSMSSSSSNFFN.
% 275.71/41.05 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 275.71/41.05 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 275.71/41.05 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 275.71/41.05 % No SInE strategy applied
% 275.71/41.05 % Search class: FGUSM-FFMF21-MFFFFFNN
% 275.71/41.05 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 275.71/41.05 % Starting SubtermCWHack with 136s (1) cores
% 275.71/41.05 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 275.71/41.05 % Starting G-E--_200_B02_F1_AE_CS_SP_PI_S0S with 136s (1) cores
% 275.71/41.05 % Starting new_bool_3 with 136s (1) cores
% 275.71/41.05 % Starting new_bool_1 with 136s (1) cores
% 275.71/41.05 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2340975 completed with status 0
% 275.71/41.05 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 275.71/41.05 % Preprocessing class: FSMSSMSSSSSNFFN.
% 275.71/41.05 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 275.71/41.05 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 275.71/41.05 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 275.71/41.05 % No SInE strategy applied
% 275.71/41.05 % Search class: FGUSM-FFMF21-MFFFFFNN
% 275.71/41.05 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 275.71/41.05 % Starting SubtermCWHack with 136s (1) cores
% 275.71/41.05 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 275.71/41.05 % Preprocessing time : 0.001 s
% 275.71/41.05 % Presaturation interreduction done
% 275.71/41.05
% 275.71/41.05 % Proof found!
% 275.71/41.05 % SZS status Theorem
% 275.71/41.05 % SZS output start CNFRefutation
% See solution above
% 275.71/41.06 % Parsed axioms : 50
% 275.71/41.06 % Removed by relevancy pruning/SinE : 0
% 275.71/41.06 % Initial clauses : 56
% 275.71/41.06 % Removed in clause preprocessing : 0
% 275.71/41.06 % Initial clauses in saturation : 56
% 275.71/41.06 % Processed clauses : 30376
% 275.71/41.06 % ...of these trivial : 1120
% 275.71/41.06 % ...subsumed : 24483
% 275.71/41.06 % ...remaining for further processing : 4773
% 275.71/41.06 % Other redundant clauses eliminated : 17949
% 275.71/41.06 % Clauses deleted for lack of memory : 0
% 275.71/41.06 % Backward-subsumed : 542
% 275.71/41.06 % Backward-rewritten : 333
% 275.71/41.06 % Generated clauses : 1795677
% 275.71/41.06 % ...of the previous two non-redundant : 1465322
% 275.71/41.06 % ...aggressively subsumed : 0
% 275.71/41.06 % Contextual simplify-reflections : 78
% 275.71/41.06 % Paramodulations : 1777707
% 275.71/41.06 % Factorizations : 13
% 275.71/41.06 % NegExts : 0
% 275.71/41.06 % Equation resolutions : 17957
% 275.71/41.06 % Disequality decompositions : 0
% 275.71/41.06 % Total rewrite steps : 1157795
% 275.71/41.06 % ...of those cached : 1097953
% 275.71/41.06 % Propositional unsat checks : 0
% 275.71/41.06 % Propositional check models : 0
% 275.71/41.06 % Propositional check unsatisfiable : 0
% 275.71/41.06 % Propositional clauses : 0
% 275.71/41.06 % Propositional clauses after purity: 0
% 275.71/41.06 % Propositional unsat core size : 0
% 275.71/41.06 % Propositional preprocessing time : 0.000
% 275.71/41.06 % Propositional encoding time : 0.000
% 275.71/41.06 % Propositional solver time : 0.000
% 275.71/41.06 % Success case prop preproc time : 0.000
% 275.71/41.06 % Success case prop encoding time : 0.000
% 275.71/41.06 % Success case prop solver time : 0.000
% 275.71/41.06 % Current number of processed clauses : 3841
% 275.71/41.06 % Positive orientable unit clauses : 525
% 275.71/41.06 % Positive unorientable unit clauses: 107
% 275.71/41.06 % Negative unit clauses : 1847
% 275.71/41.06 % Non-unit-clauses : 1362
% 275.71/41.06 % Current number of unprocessed clauses: 1428129
% 275.71/41.06 % ...number of literals in the above : 4690718
% 275.71/41.06 % Current number of archived formulas : 0
% 275.71/41.06 % Current number of archived clauses : 931
% 275.71/41.06 % Clause-clause subsumption calls (NU) : 118268
% 275.71/41.06 % Rec. Clause-clause subsumption calls : 51913
% 275.71/41.06 % Non-unit clause-clause subsumptions : 2690
% 275.71/41.06 % Unit Clause-clause subsumption calls : 80883
% 275.71/41.06 % Rewrite failures with RHS unbound : 0
% 275.71/41.06 % BW rewrite match attempts : 15390
% 275.71/41.06 % BW rewrite match successes : 239
% 275.71/41.06 % Condensation attempts : 0
% 275.71/41.06 % Condensation successes : 0
% 275.71/41.06 % Termbank termtop insertions : 54038523
% 275.71/41.06 % Search garbage collected termcells : 411
% 275.71/41.06
% 275.71/41.06 % -------------------------------------------------
% 275.71/41.06 % User time : 33.284 s
% 275.71/41.06 % System time : 1.067 s
% 275.71/41.06 % Total time : 34.351 s
% 275.71/41.06 % Maximum resident set size: 3680 pages
% 275.71/41.06
% 275.71/41.06 % -------------------------------------------------
% 275.71/41.06 % User time : 167.252 s
% 275.71/41.06 % System time : 6.047 s
% 275.71/41.06 % Total time : 173.298 s
% 275.71/41.06 % Maximum resident set size: 4608 pages
% 275.71/41.06 % E exiting
%------------------------------------------------------------------------------