%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWX212+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 03:14:17 PM UTC 2026
% Result : Theorem 73.82s 11.26s
% Output : CNFRefutation 73.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 30
% Syntax : Number of formulae : 164 ( 100 unt; 0 def)
% Number of atoms : 281 ( 169 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 252 ( 135 ~; 80 |; 8 &)
% ( 5 <=>; 22 =>; 0 <=; 2 <~>)
% 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 : 350 ( 91 sgn 148 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_042,axiom,
! [X5,X10] :
( X10 = X5
=> step(atom(X10),X5) = eps ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_042) ).
fof(axiom_019,axiom,
! [X1,X2] : eps != x(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_019) ).
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/sandbox2/benchmark/theBenchmark.p',axiom_041) ).
fof(axiom_020,axiom,
! [X1,X2] : eps != y(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_020) ).
fof(axiom_018,axiom,
! [X1] : eps != atom(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_018) ).
fof(axiom_021,axiom,
! [X1] : eps != star(X1),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',axiom_045) ).
fof(axiom_038,axiom,
! [X6,X7] :
( eps2(x(X6,X7))
<=> ( eps2(X7)
| eps2(X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_038) ).
fof(axiom_022,axiom,
! [X1,X2,X3] : atom(X1) != x(X2,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_022) ).
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/sandbox2/benchmark/theBenchmark.p',axiom_036) ).
fof(axiom_023,axiom,
! [X1,X2,X3] : atom(X1) != y(X2,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_023) ).
fof(axiom_024,axiom,
! [X1,X2] : atom(X1) != star(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_024) ).
fof(axiom_046,axiom,
! [X5,X8,X9] :
( ~ eps2(X8)
=> step(y(X8,X9),X5) = x(y(step(X8,X5),X9),nil2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_046) ).
fof(axiom_044,axiom,
! [X5,X6,X7] : step(x(X6,X7),X5) = x(step(X6,X5),step(X7,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_044) ).
fof(axiom_037,axiom,
eps2(eps),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_037) ).
fof(axiom_049,axiom,
! [X1,X12,X13] :
( rec(X1,cons(X12,X13))
<=> rec(step(X1,X12),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_049) ).
fof(axiom_048,axiom,
! [X1] :
( rec(X1,nil)
<=> eps2(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_048) ).
fof(goal_050,conjecture,
? [X6,X7,X14] :
( rec(y(X6,X7),X14)
<~> rec(y(X7,X6),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_050) ).
fof(axiom_015,axiom,
! [X1,X2] : nil2 != x(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
fof(axiom_016,axiom,
! [X1,X2] : nil2 != y(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
fof(axiom_014,axiom,
! [X1] : nil2 != atom(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_014) ).
fof(axiom_017,axiom,
! [X1] : nil2 != star(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_017) ).
fof(axiom_009,axiom,
! [X1,X2] : proj2(x(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
fof(axiom_025,axiom,
! [X1,X2,X3,X4] : x(X1,X2) != y(X3,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_025) ).
fof(axiom_026,axiom,
! [X1,X2,X3] : x(X1,X2) != star(X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_026) ).
fof(axiom_043,axiom,
! [X5,X10] :
( X10 != X5
=> step(atom(X10),X5) = nil2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_043) ).
fof(axiom_013,axiom,
nil2 != eps,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
fof(axiom_008,axiom,
! [X1,X2] : proj1(x(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
fof(axiom_039,axiom,
! [X8,X9] :
( eps2(y(X8,X9))
<=> ( eps2(X9)
& eps2(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_039) ).
fof(axiom_004,axiom,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
fof(c_0_30,plain,
! [X79,X80] :
( step(atom(X80),X79) = eps
| X80 != X79 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_042])])]) ).
fof(c_0_31,plain,
! [X1,X2] : eps != x(X1,X2),
inference(fof_simplification,[status(thm)],[axiom_019]) ).
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] : eps != y(X1,X2),
inference(fof_simplification,[status(thm)],[axiom_020]) ).
fof(c_0_34,plain,
! [X1] : eps != atom(X1),
inference(fof_simplification,[status(thm)],[axiom_018]) ).
fof(c_0_35,plain,
! [X1] : eps != star(X1),
inference(fof_simplification,[status(thm)],[axiom_021]) ).
fof(c_0_36,plain,
! [X86,X87,X88] :
( step(y(X87,X88),X86) = x(y(step(X87,X86),X88),step(X88,X86))
| ~ eps2(X87) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_045])])]) ).
cnf(c_0_37,plain,
( X1 != X2
| step(atom(X1),X2) = eps ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_38,plain,
! [X38,X39] : eps != x(X38,X39),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_31])]) ).
fof(c_0_39,plain,
! [X77,X78] :
( step(X77,X78) = nil2
| X77 = star(proj1Star(X77))
| X77 = y(proj12(X77),proj22(X77))
| X77 = x(proj1(X77),proj2(X77))
| X77 = atom(proj1Atom(X77)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])]) ).
fof(c_0_40,plain,
! [X40,X41] : eps != y(X40,X41),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_33])]) ).
fof(c_0_41,plain,
! [X37] : eps != atom(X37),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_34])]) ).
fof(c_0_42,plain,
! [X42] : eps != star(X42),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_35])]) ).
fof(c_0_43,plain,
! [X72,X73] :
( ( eps2(x(X72,X73))
| ~ eps2(X73) )
& ( eps2(x(X72,X73))
| ~ eps2(X72) )
& ( eps2(X73)
| eps2(X72)
| ~ eps2(x(X72,X73)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_038])])])]) ).
fof(c_0_44,plain,
! [X1,X2,X3] : atom(X1) != x(X2,X3),
inference(fof_simplification,[status(thm)],[axiom_022]) ).
fof(c_0_45,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]) ).
fof(c_0_46,plain,
! [X1,X2,X3] : atom(X1) != y(X2,X3),
inference(fof_simplification,[status(thm)],[axiom_023]) ).
fof(c_0_47,plain,
! [X1,X2] : atom(X1) != star(X2),
inference(fof_simplification,[status(thm)],[axiom_024]) ).
cnf(c_0_48,plain,
( ~ eps2(X1)
| step(y(X1,X2),X3) = x(y(step(X1,X3),X2),step(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_49,plain,
step(atom(X1),X1) = eps,
inference(er,[status(thm)],[c_0_37]) ).
cnf(c_0_50,plain,
eps != x(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_51,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_39]) ).
cnf(c_0_52,plain,
eps != y(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_53,plain,
eps != atom(X1),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_54,plain,
eps != star(X1),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_55,plain,
( ~ eps2(X1)
| eps2(x(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_56,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_57,plain,
! [X43,X44,X45] : atom(X43) != x(X44,X45),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_44])]) ).
fof(c_0_58,plain,
! [X71] :
( ~ eps2(X71)
| X71 = star(proj1Star(X71))
| X71 = y(proj12(X71),proj22(X71))
| X71 = x(proj1(X71),proj2(X71))
| X71 = eps ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])]) ).
fof(c_0_59,plain,
! [X46,X47,X48] : atom(X46) != y(X47,X48),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_46])]) ).
fof(c_0_60,plain,
! [X49,X50] : atom(X49) != star(X50),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_47])]) ).
fof(c_0_61,plain,
! [X83,X84,X85] : step(x(X84,X85),X83) = x(step(X84,X83),step(X85,X83)),
inference(variable_rename,[status(thm)],[axiom_044]) ).
cnf(c_0_62,plain,
( ~ eps2(X1)
| x(y(step(X1,X2),atom(X2)),eps) = step(y(X1,atom(X2)),X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_63,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_50,c_0_51])]),c_0_52]),c_0_53]),c_0_54]) ).
cnf(c_0_64,plain,
eps2(eps),
inference(split_conjunct,[status(thm)],[axiom_037]) ).
cnf(c_0_65,plain,
( ~ eps2(X1)
| ~ eps2(step(X2,X3))
| eps2(step(y(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_55,c_0_48]) ).
fof(c_0_66,plain,
! [X89,X90,X91] :
( step(y(X90,X91),X89) = x(y(step(X90,X89),X91),nil2)
| eps2(X90) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_56])]) ).
cnf(c_0_67,plain,
atom(X1) != x(X2,X3),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_68,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_58]) ).
cnf(c_0_69,plain,
atom(X1) != y(X2,X3),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_70,plain,
atom(X1) != star(X2),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
fof(c_0_71,plain,
! [X95,X96,X97] :
( ( rec(X95,cons(X96,X97))
| ~ rec(step(X95,X96),X97) )
& ( rec(step(X95,X96),X97)
| ~ rec(X95,cons(X96,X97)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_049])])]) ).
fof(c_0_72,plain,
! [X94] :
( ( rec(X94,nil)
| ~ eps2(X94) )
& ( eps2(X94)
| ~ rec(X94,nil) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_048])])]) ).
cnf(c_0_73,plain,
step(x(X1,X2),X3) = x(step(X1,X3),step(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_74,plain,
step(y(eps,atom(X1)),X1) = x(y(nil2,atom(X1)),eps),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64])]) ).
cnf(c_0_75,plain,
( ~ eps2(X1)
| eps2(step(y(X1,atom(X2)),X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_49]),c_0_64])]) ).
fof(c_0_76,negated_conjecture,
~ ? [X6,X7,X14] :
( rec(y(X6,X7),X14)
<~> rec(y(X7,X6),X14) ),
inference(assume_negation,[status(cth)],[goal_050]) ).
cnf(c_0_77,plain,
( step(y(X1,X2),X3) = x(y(step(X1,X3),X2),nil2)
| eps2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_78,plain,
~ eps2(atom(X1)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68])]),c_0_69]),c_0_70]),c_0_53]) ).
cnf(c_0_79,plain,
( ~ rec(step(X1,X2),X3)
| rec(X1,cons(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_80,plain,
( ~ eps2(X1)
| rec(X1,nil) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_81,plain,
( ~ eps2(X1)
| eps2(x(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_82,plain,
x(x(y(nil2,atom(X1)),eps),step(X2,X1)) = step(x(y(eps,atom(X1)),X2),X1),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_83,plain,
eps2(x(y(nil2,atom(X1)),eps)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_74]),c_0_64])]) ).
fof(c_0_84,negated_conjecture,
~ ? [X6,X7,X14] :
~ ( rec(y(X6,X7),X14)
<=> rec(y(X7,X6),X14) ),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
cnf(c_0_85,plain,
step(y(atom(X1),X2),X1) = x(y(eps,X2),nil2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_49]),c_0_78]) ).
cnf(c_0_86,plain,
( ~ eps2(step(X1,X2))
| rec(X1,cons(X2,nil)) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_87,plain,
eps2(step(x(y(eps,atom(X1)),X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83])]) ).
fof(c_0_88,plain,
! [X1,X2] : nil2 != x(X1,X2),
inference(fof_simplification,[status(thm)],[axiom_015]) ).
fof(c_0_89,plain,
! [X1,X2] : nil2 != y(X1,X2),
inference(fof_simplification,[status(thm)],[axiom_016]) ).
fof(c_0_90,plain,
! [X1] : nil2 != atom(X1),
inference(fof_simplification,[status(thm)],[axiom_014]) ).
fof(c_0_91,plain,
! [X1] : nil2 != star(X1),
inference(fof_simplification,[status(thm)],[axiom_017]) ).
fof(c_0_92,negated_conjecture,
! [X98,X99,X100] :
( ( rec(y(X98,X99),X100)
| ~ rec(y(X99,X98),X100) )
& ( rec(y(X99,X98),X100)
| ~ rec(y(X98,X99),X100) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_84])])]) ).
cnf(c_0_93,plain,
( ~ rec(x(y(eps,X2),nil2),X3)
| rec(y(atom(X1),X2),cons(X1,X3)) ),
inference(spm,[status(thm)],[c_0_79,c_0_85]) ).
cnf(c_0_94,plain,
rec(x(y(eps,atom(X1)),X2),cons(X1,nil)),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
fof(c_0_95,plain,
! [X24,X25] : proj2(x(X24,X25)) = X25,
inference(variable_rename,[status(thm)],[axiom_009]) ).
fof(c_0_96,plain,
! [X32,X33] : nil2 != x(X32,X33),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_88])]) ).
fof(c_0_97,plain,
! [X34,X35] : nil2 != y(X34,X35),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_89])]) ).
fof(c_0_98,plain,
! [X31] : nil2 != atom(X31),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_90])]) ).
fof(c_0_99,plain,
! [X36] : nil2 != star(X36),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_91])]) ).
fof(c_0_100,plain,
! [X1,X2,X3,X4] : x(X1,X2) != y(X3,X4),
inference(fof_simplification,[status(thm)],[axiom_025]) ).
fof(c_0_101,plain,
! [X1,X2,X3] : x(X1,X2) != star(X3),
inference(fof_simplification,[status(thm)],[axiom_026]) ).
fof(c_0_102,plain,
! [X5,X10] :
( X10 != X5
=> step(atom(X10),X5) = nil2 ),
inference(fof_simplification,[status(thm)],[axiom_043]) ).
fof(c_0_103,plain,
nil2 != eps,
inference(fof_simplification,[status(thm)],[axiom_013]) ).
cnf(c_0_104,negated_conjecture,
( ~ rec(y(X1,X2),X3)
| rec(y(X2,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_105,plain,
rec(y(atom(X1),atom(X2)),cons(X1,cons(X2,nil))),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_106,plain,
proj2(x(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_107,plain,
nil2 != x(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_108,plain,
nil2 != y(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_109,plain,
nil2 != atom(X1),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_110,plain,
nil2 != star(X1),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
fof(c_0_111,plain,
! [X51,X52,X53,X54] : x(X51,X52) != y(X53,X54),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_100])]) ).
fof(c_0_112,plain,
! [X55,X56,X57] : x(X55,X56) != star(X57),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_101])]) ).
fof(c_0_113,plain,
! [X22,X23] : proj1(x(X22,X23)) = X22,
inference(variable_rename,[status(thm)],[axiom_008]) ).
fof(c_0_114,plain,
! [X81,X82] :
( step(atom(X82),X81) = nil2
| X82 = X81 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_102])]) ).
fof(c_0_115,plain,
nil2 != eps,
inference(fof_nnf,[status(thm)],[c_0_103]) ).
cnf(c_0_116,plain,
( ~ rec(X1,cons(X2,X3))
| rec(step(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_117,negated_conjecture,
rec(y(atom(X1),atom(X2)),cons(X2,cons(X1,nil))),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_118,plain,
proj2(step(x(X1,X2),X3)) = step(X2,X3),
inference(spm,[status(thm)],[c_0_106,c_0_73]) ).
cnf(c_0_119,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_107,c_0_51])]),c_0_108]),c_0_109]),c_0_110]) ).
cnf(c_0_120,plain,
x(X1,X2) != y(X3,X4),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_121,plain,
step(x(X1,X2),X3) != nil2,
inference(spm,[status(thm)],[c_0_107,c_0_73]) ).
cnf(c_0_122,plain,
x(X1,X2) != star(X3),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_123,plain,
proj1(x(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_124,plain,
( step(atom(X1),X2) = nil2
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_125,plain,
nil2 != eps,
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_126,plain,
( ~ eps2(x(X1,X2))
| eps2(X2)
| eps2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_127,negated_conjecture,
rec(step(y(atom(X1),atom(X2)),X2),cons(X1,nil)),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_128,plain,
( eps2(X1)
| proj2(step(step(y(X1,X2),X3),X4)) = nil2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_77]),c_0_119]) ).
cnf(c_0_129,plain,
( y(X2,X3) != step(y(X1,X4),X5)
| eps2(X1) ),
inference(spm,[status(thm)],[c_0_120,c_0_77]) ).
cnf(c_0_130,plain,
( step(step(y(X1,X2),X3),X4) != nil2
| eps2(X1) ),
inference(spm,[status(thm)],[c_0_121,c_0_77]) ).
cnf(c_0_131,plain,
( step(y(X1,X2),X3) != star(X4)
| eps2(X1) ),
inference(spm,[status(thm)],[c_0_122,c_0_77]) ).
cnf(c_0_132,plain,
( atom(X2) != step(y(X1,X3),X4)
| eps2(X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_77]) ).
cnf(c_0_133,plain,
( eps2(X1)
| proj1(step(y(X1,X2),X3)) = y(step(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_123,c_0_77]) ).
cnf(c_0_134,plain,
( X1 = X3
| step(y(atom(X1),X2),X3) = x(y(nil2,X2),nil2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_124]),c_0_78]) ).
cnf(c_0_135,plain,
~ eps2(nil2),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_68])]),c_0_108]),c_0_110]),c_0_125]) ).
cnf(c_0_136,plain,
( ~ eps2(step(x(X1,X3),X2))
| eps2(step(X3,X2))
| eps2(step(X1,X2)) ),
inference(spm,[status(thm)],[c_0_126,c_0_73]) ).
cnf(c_0_137,plain,
( ~ rec(X1,nil)
| eps2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_138,negated_conjecture,
rec(step(step(y(atom(X1),atom(X2)),X2),X1),nil),
inference(spm,[status(thm)],[c_0_116,c_0_127]) ).
cnf(c_0_139,plain,
( atom(proj1Atom(X1)) = X1
| star(proj1Star(X1)) = X1
| step(X1,X3) = nil2
| y(proj12(X1),proj22(X1)) = X1
| proj2(step(X1,X2)) = step(proj2(X1),X2) ),
inference(spm,[status(thm)],[c_0_118,c_0_51]) ).
cnf(c_0_140,plain,
proj2(step(step(y(X1,atom(X2)),X2),X3)) = nil2,
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_62]),c_0_63]),c_0_128]) ).
cnf(c_0_141,plain,
y(X1,X2) != step(y(X3,X4),X5),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_48]),c_0_129]) ).
cnf(c_0_142,plain,
step(step(y(X1,X2),X3),X4) != nil2,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_48]),c_0_130]) ).
cnf(c_0_143,plain,
step(y(X1,X2),X3) != star(X4),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_48]),c_0_131]) ).
cnf(c_0_144,plain,
atom(X1) != step(y(X2,X3),X4),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_48]),c_0_132]) ).
cnf(c_0_145,plain,
proj1(step(y(X1,X2),X3)) = y(step(X1,X3),X2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_48]),c_0_133]) ).
cnf(c_0_146,plain,
( X1 = X2
| y(step(atom(X1),X2),X3) = y(nil2,X3) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_123]),c_0_78]) ).
cnf(c_0_147,plain,
step(y(nil2,X1),X2) = x(y(nil2,X1),nil2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_119]),c_0_135]) ).
cnf(c_0_148,plain,
( ~ eps2(step(X1,X3))
| eps2(step(proj1(X1),X3))
| eps2(step(proj2(X1),X3))
| atom(proj1Atom(X1)) = X1
| star(proj1Star(X1)) = X1
| step(X1,X2) = nil2
| y(proj12(X1),proj22(X1)) = X1 ),
inference(spm,[status(thm)],[c_0_136,c_0_51]) ).
cnf(c_0_149,negated_conjecture,
eps2(step(step(y(atom(X1),atom(X2)),X2),X1)),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_150,plain,
step(proj2(step(y(X1,atom(X2)),X2)),X3) = nil2,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_141]),c_0_142]),c_0_143]),c_0_144]) ).
fof(c_0_151,plain,
! [X74,X75] :
( ( eps2(y(X74,X75))
| ~ eps2(X75)
| ~ eps2(X74) )
& ( ~ eps2(y(X74,X75))
| eps2(X75) )
& ( ~ eps2(y(X74,X75))
| eps2(X74) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_039])])])]) ).
cnf(c_0_152,plain,
( ~ eps2(X1)
| proj2(step(y(X1,atom(X2)),X2)) = eps ),
inference(spm,[status(thm)],[c_0_106,c_0_62]) ).
cnf(c_0_153,plain,
( X1 = X2
| y(step(step(atom(X1),X2),X3),X4) = y(nil2,X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_147]),c_0_123]) ).
fof(c_0_154,plain,
a != b,
inference(fof_simplification,[status(thm)],[axiom_004]) ).
cnf(c_0_155,negated_conjecture,
eps2(step(y(step(atom(X1),X2),atom(X2)),X1)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_150]),c_0_145]),c_0_141]),c_0_142]),c_0_143]),c_0_144]),c_0_135]) ).
cnf(c_0_156,plain,
( ~ eps2(y(X1,X2))
| eps2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_151]) ).
cnf(c_0_157,plain,
( ~ eps2(step(step(atom(X1),X2),X3))
| X1 = X2 ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_147]),c_0_106]),c_0_125]) ).
fof(c_0_158,plain,
a != b,
inference(fof_nnf,[status(thm)],[c_0_154]) ).
cnf(c_0_159,negated_conjecture,
( eps2(x(y(nil2,atom(X2)),nil2))
| X1 = X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_124]),c_0_147]) ).
cnf(c_0_160,plain,
( ~ eps2(y(nil2,X3))
| X1 = X2 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_153]),c_0_157]) ).
cnf(c_0_161,plain,
a != b,
inference(split_conjunct,[status(thm)],[c_0_158]) ).
cnf(c_0_162,negated_conjecture,
X1 = X2,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_159]),c_0_135]),c_0_160]) ).
cnf(c_0_163,plain,
$false,
inference(sr,[status(thm)],[c_0_161,c_0_162]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX212+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n002.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 21 10:37:01 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 73.82/11.26 % Version: 3.5.1
% 73.82/11.26 % Preprocessing class: FSMSSMSSSSSNFFN.
% 73.82/11.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 73.82/11.26 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 73.82/11.26 % Starting new_bool_3 with 300s (1) cores
% 73.82/11.26 % Starting new_bool_1 with 300s (1) cores
% 73.82/11.26 % Starting sh5l with 300s (1) cores
% 73.82/11.26 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3074720 completed with status 0
% 73.82/11.26 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 73.82/11.26 % Preprocessing class: FSMSSMSSSSSNFFN.
% 73.82/11.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 73.82/11.26 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 73.82/11.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 73.82/11.26 % No SInE strategy applied
% 73.82/11.26 % Search class: FGUSM-FFMF21-MFFFFFNN
% 73.82/11.26 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 73.82/11.26 % Starting SubtermCWHack with 136s (1) cores
% 73.82/11.26 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 73.82/11.26 % Starting G-E--_200_B02_F1_AE_CS_SP_PI_S0S with 136s (1) cores
% 73.82/11.26 % Starting new_bool_3 with 136s (1) cores
% 73.82/11.26 % Starting new_bool_1 with 136s (1) cores
% 73.82/11.26 % new_bool_3 with pid 3074726 completed with status 0
% 73.82/11.26 % Result found by new_bool_3
% 73.82/11.26 % Preprocessing class: FSMSSMSSSSSNFFN.
% 73.82/11.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 73.82/11.26 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 73.82/11.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 73.82/11.26 % No SInE strategy applied
% 73.82/11.26 % Search class: FGUSM-FFMF21-MFFFFFNN
% 73.82/11.26 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 73.82/11.26 % Starting SubtermCWHack with 136s (1) cores
% 73.82/11.26 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 73.82/11.26 % Starting G-E--_200_B02_F1_AE_CS_SP_PI_S0S with 136s (1) cores
% 73.82/11.26 % Starting new_bool_3 with 136s (1) cores
% 73.82/11.26 % Preprocessing time : 0.002 s
% 73.82/11.26 % Presaturation interreduction done
% 73.82/11.26
% 73.82/11.26 % Proof found!
% 73.82/11.26 % SZS status Theorem
% 73.82/11.26 % SZS output start CNFRefutation
% See solution above
% 73.82/11.27 % Parsed axioms : 50
% 73.82/11.27 % Removed by relevancy pruning/SinE : 0
% 73.82/11.27 % Initial clauses : 57
% 73.82/11.27 % Removed in clause preprocessing : 0
% 73.82/11.27 % Initial clauses in saturation : 57
% 73.82/11.27 % Processed clauses : 19862
% 73.82/11.27 % ...of these trivial : 2293
% 73.82/11.27 % ...subsumed : 13542
% 73.82/11.27 % ...remaining for further processing : 4027
% 73.82/11.27 % Other redundant clauses eliminated : 34485
% 73.82/11.27 % Clauses deleted for lack of memory : 0
% 73.82/11.27 % Backward-subsumed : 795
% 73.82/11.27 % Backward-rewritten : 450
% 73.82/11.27 % Generated clauses : 929506
% 73.82/11.27 % ...of the previous two non-redundant : 755703
% 73.82/11.27 % ...aggressively subsumed : 0
% 73.82/11.27 % Contextual simplify-reflections : 68
% 73.82/11.27 % Paramodulations : 894731
% 73.82/11.27 % Factorizations : 10
% 73.82/11.27 % NegExts : 0
% 73.82/11.27 % Equation resolutions : 34493
% 73.82/11.27 % Disequality decompositions : 0
% 73.82/11.27 % Total rewrite steps : 318571
% 73.82/11.27 % ...of those cached : 295949
% 73.82/11.27 % Propositional unsat checks : 0
% 73.82/11.27 % Propositional check models : 0
% 73.82/11.27 % Propositional check unsatisfiable : 0
% 73.82/11.27 % Propositional clauses : 0
% 73.82/11.27 % Propositional clauses after purity: 0
% 73.82/11.27 % Propositional unsat core size : 0
% 73.82/11.27 % Propositional preprocessing time : 0.000
% 73.82/11.27 % Propositional encoding time : 0.000
% 73.82/11.27 % Propositional solver time : 0.000
% 73.82/11.27 % Success case prop preproc time : 0.000
% 73.82/11.27 % Success case prop encoding time : 0.000
% 73.82/11.27 % Success case prop solver time : 0.000
% 73.82/11.27 % Current number of processed clauses : 2453
% 73.82/11.27 % Positive orientable unit clauses : 1666
% 73.82/11.27 % Positive unorientable unit clauses: 1
% 73.82/11.27 % Negative unit clauses : 25
% 73.82/11.27 % Non-unit-clauses : 761
% 73.82/11.27 % Current number of unprocessed clauses: 727233
% 73.82/11.27 % ...number of literals in the above : 2375000
% 73.82/11.27 % Current number of archived formulas : 0
% 73.82/11.27 % Current number of archived clauses : 1573
% 73.82/11.27 % Clause-clause subsumption calls (NU) : 144471
% 73.82/11.27 % Rec. Clause-clause subsumption calls : 72889
% 73.82/11.27 % Non-unit clause-clause subsumptions : 2439
% 73.82/11.27 % Unit Clause-clause subsumption calls : 31546
% 73.82/11.27 % Rewrite failures with RHS unbound : 5800
% 73.82/11.27 % BW rewrite match attempts : 88118
% 73.82/11.27 % BW rewrite match successes : 5810
% 73.82/11.27 % Condensation attempts : 0
% 73.82/11.27 % Condensation successes : 0
% 73.82/11.27 % Termbank termtop insertions : 17696797
% 73.82/11.27 % Search garbage collected termcells : 433
% 73.82/11.27
% 73.82/11.27 % -------------------------------------------------
% 73.82/11.27 % User time : 9.932 s
% 73.82/11.27 % System time : 0.378 s
% 73.82/11.27 % Total time : 10.310 s
% 73.82/11.27 % Maximum resident set size: 3680 pages
% 73.82/11.27
% 73.82/11.27 % -------------------------------------------------
% 73.82/11.27 % User time : 50.228 s
% 73.82/11.27 % System time : 2.226 s
% 73.82/11.27 % Total time : 52.455 s
% 73.82/11.27 % Maximum resident set size: 4608 pages
% 73.82/11.27 % E exiting
%------------------------------------------------------------------------------