%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC083+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 02:42:55 PM UTC 2026
% Result : Theorem 0.88s 0.82s
% Output : CNFRefutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 112 ( 30 unt; 0 def)
% Number of atoms : 385 ( 116 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 471 ( 198 ~; 190 |; 31 &)
% ( 4 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 150 ( 0 sgn 80 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( app(X6,X8) != X4
| app(app(X6,X7),X8) != X3
| ~ ssList(X8) ) ) )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax82,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax79,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax79) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X1
& nil = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ? [X4] :
( app(app(X3,X2),X4) = X1
& ssList(X4) )
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax56,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( segmentP(X1,X2)
=> segmentP(app(app(X3,X1),X4),X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax56) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax80,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax80) ).
fof(ax53,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X2,X3)
& segmentP(X1,X2) )
=> segmentP(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax53) ).
fof(c_0_14,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( app(X6,X8) != X4
| app(app(X6,X7),X8) != X3
| ~ ssList(X8) ) ) )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( app(X6,X8) != X4
| app(app(X6,X7),X8) != X3
| ~ ssList(X8) ) ) )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_16,negated_conjecture,
! [X13] :
( app(esk5_0,esk7_0) = esk4_0
& app(app(esk5_0,esk6_0),esk7_0) = esk3_0
& ssList(esk7_0)
& ssList(esk6_0)
& ssList(esk5_0)
& ( ~ segmentP(esk1_0,X13)
| ~ segmentP(esk2_0,X13)
| ~ neq(X13,nil)
| ~ ssList(X13) )
& neq(esk2_0,nil)
& esk1_0 = esk3_0
& esk2_0 = esk4_0
& ssList(esk4_0)
& ssList(esk3_0)
& ssList(esk2_0)
& ssList(esk1_0) ),
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_15])])])])]) ).
fof(c_0_17,plain,
! [X36] :
( app(X36,nil) = X36
| ~ ssList(X36) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
fof(c_0_18,plain,
! [X31,X32,X33] :
( app(app(X31,X32),X33) = app(X31,app(X32,X33))
| ~ ssList(X33)
| ~ ssList(X32)
| ~ ssList(X31) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
fof(c_0_19,plain,
! [X17,X18] :
( ssList(app(X17,X18))
| ~ ssList(X18)
| ~ ssList(X17) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_20,plain,
! [X22] :
( app(nil,X22) = X22
| ~ ssList(X22) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_21,negated_conjecture,
app(esk5_0,esk7_0) = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_23,plain,
! [X23,X24,X25] :
( X25 = X23
| app(X25,X24) != app(X23,X24)
| ~ ssList(X25)
| ~ ssList(X24)
| ~ ssList(X23) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])])]) ).
cnf(c_0_24,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_27,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,negated_conjecture,
app(esk5_0,esk7_0) = esk2_0,
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,negated_conjecture,
ssList(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_31,negated_conjecture,
ssList(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_32,plain,
( app(X3,X2) != app(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,app(X2,nil)) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),c_0_27]) ).
cnf(c_0_34,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(nil,app(X1,X2)) = app(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_28]),c_0_26])]) ).
cnf(c_0_35,negated_conjecture,
( ~ ssList(X1)
| app(esk5_0,app(esk7_0,X1)) = app(esk2_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_29]),c_0_30]),c_0_31])]) ).
cnf(c_0_36,negated_conjecture,
( ~ ssList(X1)
| app(X1,esk7_0) != esk2_0
| X1 = esk5_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_29]),c_0_31]),c_0_30])]) ).
cnf(c_0_37,plain,
( ~ ssList(X1)
| app(X1,nil) = app(nil,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_26])]) ).
cnf(c_0_38,negated_conjecture,
app(esk2_0,nil) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_24]),c_0_29]),c_0_26]),c_0_30])]) ).
fof(c_0_39,plain,
! [X34,X35] :
( ( ~ ssList(X34)
| ~ ssList(X35)
| nil = app(X34,X35)
| nil != X34
| nil != X35 )
& ( ~ ssList(X34)
| ~ ssList(X35)
| nil != app(X34,X35)
| nil = X34 )
& ( ~ ssList(X34)
| ~ ssList(X35)
| nil != app(X34,X35)
| nil = X35 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])])]) ).
cnf(c_0_40,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,app(X2,esk7_0)) != esk2_0
| app(X1,X2) = esk5_0 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_25]),c_0_30])]),c_0_27]) ).
cnf(c_0_41,negated_conjecture,
app(esk5_0,app(nil,esk7_0)) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_37]),c_0_38]),c_0_26]),c_0_30])]) ).
cnf(c_0_42,negated_conjecture,
app(app(esk5_0,esk6_0),esk7_0) = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_43,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_44,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != app(X2,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_45,plain,
! [X37,X38,X41,X42] :
( ( ~ ssList(X37)
| ~ ssList(X38)
| segmentP(X37,X38)
| app(app(X41,X38),X42) != X37
| ~ ssList(X42)
| ~ ssList(X41) )
& ( ~ ssList(X37)
| ~ ssList(X38)
| ~ segmentP(X37,X38)
| app(app(esk8_2(X37,X38),X38),esk9_2(X37,X38)) = X37 )
& ( ~ ssList(X37)
| ~ ssList(X38)
| ~ segmentP(X37,X38)
| ssList(esk9_2(X37,X38)) )
& ( ~ ssList(X37)
| ~ ssList(X38)
| ~ segmentP(X37,X38)
| ssList(esk8_2(X37,X38)) ) ),
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)],[ax7])])])])])]) ).
cnf(c_0_46,negated_conjecture,
app(esk5_0,nil) = esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_26]),c_0_31])]) ).
fof(c_0_47,plain,
! [X49,X50,X51,X52] :
( segmentP(app(app(X51,X49),X52),X50)
| ~ segmentP(X49,X50)
| ~ ssList(X52)
| ~ ssList(X51)
| ~ ssList(X50)
| ~ ssList(X49) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])])]) ).
cnf(c_0_48,negated_conjecture,
app(app(esk5_0,esk6_0),esk7_0) = esk1_0,
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
( esk2_0 != nil
| esk7_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_29]),c_0_31]),c_0_30])]) ).
fof(c_0_50,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_51,plain,
( ~ ssList(X4)
| ~ ssList(X3)
| app(app(X1,X3),X2) != X4
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ssList(app(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_25]),c_0_27]) ).
cnf(c_0_53,negated_conjecture,
( ~ ssList(X1)
| app(esk5_0,app(nil,X1)) = app(esk5_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_46]),c_0_26]),c_0_31])]) ).
cnf(c_0_54,plain,
( ~ segmentP(X1,X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(app(app(X3,X1),X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_55,negated_conjecture,
( esk2_0 != nil
| app(app(esk5_0,esk6_0),nil) = esk1_0 ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
fof(c_0_56,plain,
! [X57,X58] :
( ( ~ ssList(X57)
| ~ ssList(X58)
| neq(X57,X58)
| X57 = X58 )
& ( ~ ssList(X57)
| ~ ssList(X58)
| X57 != X58
| ~ neq(X57,X58) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])])])]) ).
cnf(c_0_57,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(app(app(X1,X2),X3))
| segmentP(app(app(X1,X2),X3),X2) ),
inference(er,[status(thm)],[c_0_51]) ).
cnf(c_0_58,negated_conjecture,
app(nil,esk5_0) = esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_46]),c_0_26]),c_0_31])]) ).
cnf(c_0_59,negated_conjecture,
( ~ ssList(X1)
| ssList(app(esk5_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_26]),c_0_31])]) ).
cnf(c_0_60,negated_conjecture,
ssList(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_61,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X1,X3)
| segmentP(app(X1,X2),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_28]),c_0_26])]) ).
fof(c_0_62,plain,
! [X48] :
( segmentP(X48,X48)
| ~ ssList(X48) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])])]) ).
fof(c_0_63,plain,
! [X26,X27,X28] :
( X28 = X26
| app(X27,X28) != app(X27,X26)
| ~ ssList(X28)
| ~ ssList(X27)
| ~ ssList(X26) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])])]) ).
cnf(c_0_64,negated_conjecture,
( ~ ssList(app(esk5_0,esk6_0))
| esk2_0 != nil
| app(esk5_0,esk6_0) = esk1_0 ),
inference(spm,[status(thm)],[c_0_24,c_0_55]) ).
cnf(c_0_65,negated_conjecture,
( esk2_0 != nil
| app(esk5_0,nil) = esk2_0 ),
inference(spm,[status(thm)],[c_0_29,c_0_49]) ).
cnf(c_0_66,negated_conjecture,
( ~ segmentP(esk1_0,X1)
| ~ segmentP(esk2_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_67,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_68,negated_conjecture,
( ~ ssList(X1)
| segmentP(app(esk5_0,X1),esk5_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_31]),c_0_26])]),c_0_59]) ).
cnf(c_0_69,negated_conjecture,
app(esk5_0,app(esk6_0,esk7_0)) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_25]),c_0_30]),c_0_60]),c_0_31])]) ).
cnf(c_0_70,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk5_0,X1)
| segmentP(esk2_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_29]),c_0_30]),c_0_31])]) ).
cnf(c_0_71,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_72,plain,
( app(X2,X3) != app(X2,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_73,negated_conjecture,
( esk2_0 != nil
| app(esk5_0,esk6_0) = esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_27]),c_0_60]),c_0_31])]) ).
cnf(c_0_74,negated_conjecture,
( esk2_0 != nil
| esk5_0 = esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_65]),c_0_31])]) ).
cnf(c_0_75,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_76,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk2_0,X1)
| ~ segmentP(esk1_0,X1)
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_26])]) ).
cnf(c_0_77,negated_conjecture,
( ~ ssList(app(esk6_0,esk7_0))
| segmentP(esk1_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_78,negated_conjecture,
segmentP(esk2_0,esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_31])]) ).
cnf(c_0_79,negated_conjecture,
( ~ ssList(X1)
| app(esk5_0,X1) != esk2_0
| X1 = esk7_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_29]),c_0_30]),c_0_31])]) ).
cnf(c_0_80,negated_conjecture,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(esk7_0,X2)
| segmentP(app(esk2_0,X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_29]),c_0_31]),c_0_30])]) ).
cnf(c_0_81,negated_conjecture,
ssList(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_82,negated_conjecture,
( esk2_0 != nil
| app(esk2_0,esk6_0) = esk1_0 ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_83,negated_conjecture,
( esk2_0 != nil
| esk5_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_29]),c_0_30]),c_0_31])]) ).
cnf(c_0_84,negated_conjecture,
( ~ ssList(app(esk6_0,esk7_0))
| esk5_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_31])]) ).
cnf(c_0_85,negated_conjecture,
( ~ ssList(app(nil,esk7_0))
| app(nil,esk7_0) = esk7_0 ),
inference(spm,[status(thm)],[c_0_79,c_0_41]) ).
fof(c_0_86,plain,
! [X43,X44,X45] :
( segmentP(X43,X45)
| ~ segmentP(X44,X45)
| ~ segmentP(X43,X44)
| ~ ssList(X45)
| ~ ssList(X44)
| ~ ssList(X43) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax53])])])]) ).
cnf(c_0_87,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk7_0,X1)
| segmentP(esk2_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_24]),c_0_26]),c_0_81])]) ).
cnf(c_0_88,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk7_0,X1)
| esk2_0 != nil
| segmentP(esk1_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_82]),c_0_60])]) ).
cnf(c_0_89,negated_conjecture,
( esk2_0 != nil
| app(nil,esk7_0) = esk2_0 ),
inference(spm,[status(thm)],[c_0_29,c_0_83]) ).
cnf(c_0_90,negated_conjecture,
esk5_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_27]),c_0_30]),c_0_60])]) ).
cnf(c_0_91,negated_conjecture,
app(nil,esk7_0) = esk7_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_27]),c_0_30]),c_0_26])]) ).
cnf(c_0_92,plain,
( ~ segmentP(X2,X3)
| ~ segmentP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_93,negated_conjecture,
segmentP(esk2_0,esk7_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_71]),c_0_30])]) ).
cnf(c_0_94,negated_conjecture,
neq(esk2_0,nil),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_95,negated_conjecture,
( esk2_0 != nil
| segmentP(esk1_0,esk7_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_71]),c_0_30])]) ).
cnf(c_0_96,negated_conjecture,
( esk2_0 != nil
| esk7_0 = esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_89]),c_0_30])]) ).
cnf(c_0_97,negated_conjecture,
esk7_0 = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_90]),c_0_91]) ).
cnf(c_0_98,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(X1,esk2_0)
| segmentP(X1,esk7_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_30]),c_0_81])]) ).
cnf(c_0_99,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_100,negated_conjecture,
( ~ segmentP(esk2_0,esk2_0)
| ~ segmentP(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_94]),c_0_81])]) ).
cnf(c_0_101,negated_conjecture,
( esk2_0 != nil
| segmentP(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_102,negated_conjecture,
( esk2_0 != nil
| segmentP(esk2_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_93,c_0_96]) ).
cnf(c_0_103,negated_conjecture,
app(nil,app(esk6_0,esk2_0)) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_90]),c_0_97]) ).
cnf(c_0_104,negated_conjecture,
( ~ segmentP(esk1_0,esk2_0)
| esk7_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_98]),c_0_93]),c_0_30]),c_0_99])]) ).
cnf(c_0_105,negated_conjecture,
esk2_0 != nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102]) ).
cnf(c_0_106,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ segmentP(X2,X3)
| segmentP(app(X1,X2),X3) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_24]),c_0_26])]),c_0_27]) ).
cnf(c_0_107,negated_conjecture,
app(esk6_0,esk2_0) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_103]),c_0_81]),c_0_60])]) ).
cnf(c_0_108,negated_conjecture,
~ segmentP(esk1_0,esk2_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_97]),c_0_105]) ).
cnf(c_0_109,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk2_0,X1)
| segmentP(esk1_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_60]),c_0_81])]) ).
cnf(c_0_110,negated_conjecture,
segmentP(esk2_0,esk2_0),
inference(rw,[status(thm)],[c_0_93,c_0_97]) ).
cnf(c_0_111,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_110]),c_0_81])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC083+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.46 % Computer : n016.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 07:59:08 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.55 Running first-order theorem proving
% 0.24/0.55 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
% 0.88/0.82 % Version: 3.5.1
% 0.88/0.82 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.88/0.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.88/0.82 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.88/0.82 % Starting new_bool_3 with 300s (1) cores
% 0.88/0.82 % Starting new_bool_1 with 300s (1) cores
% 0.88/0.82 % Starting sh5l with 300s (1) cores
% 0.88/0.82 % new_bool_1 with pid 1956906 completed with status 0
% 0.88/0.82 % Result found by new_bool_1
% 0.88/0.82 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.88/0.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.88/0.82 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.88/0.82 % Starting new_bool_3 with 300s (1) cores
% 0.88/0.82 % Starting new_bool_1 with 300s (1) cores
% 0.88/0.82 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.88/0.82 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.88/0.82 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.88/0.82 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.88/0.82 % Starting SubtermCWHack with 31s (1) cores
% 0.88/0.82 % SubtermCWHack with pid 1956908 completed with status 0
% 0.88/0.82 % Result found by SubtermCWHack
% 0.88/0.82 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.88/0.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.88/0.82 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.88/0.82 % Starting new_bool_3 with 300s (1) cores
% 0.88/0.82 % Starting new_bool_1 with 300s (1) cores
% 0.88/0.82 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.88/0.82 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.88/0.82 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.88/0.82 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.88/0.82 % Starting SubtermCWHack with 31s (1) cores
% 0.88/0.82 % Preprocessing time : 0.003 s
% 0.88/0.82
% 0.88/0.82 % Proof found!
% 0.88/0.82 % SZS status Theorem
% 0.88/0.82 % SZS output start CNFRefutation
% See solution above
% 0.88/0.82 % Parsed axioms : 96
% 0.88/0.82 % Removed by relevancy pruning/SinE : 70
% 0.88/0.82 % Initial clauses : 51
% 0.88/0.82 % Removed in clause preprocessing : 0
% 0.88/0.82 % Initial clauses in saturation : 51
% 0.88/0.82 % Processed clauses : 2032
% 0.88/0.82 % ...of these trivial : 109
% 0.88/0.82 % ...subsumed : 1321
% 0.88/0.82 % ...remaining for further processing : 602
% 0.88/0.82 % Other redundant clauses eliminated : 27
% 0.88/0.82 % Clauses deleted for lack of memory : 0
% 0.88/0.82 % Backward-subsumed : 274
% 0.88/0.82 % Backward-rewritten : 136
% 0.88/0.82 % Generated clauses : 9508
% 0.88/0.82 % ...of the previous two non-redundant : 8202
% 0.88/0.82 % ...aggressively subsumed : 0
% 0.88/0.82 % Contextual simplify-reflections : 55
% 0.88/0.82 % Paramodulations : 9478
% 0.88/0.82 % Factorizations : 0
% 0.88/0.82 % NegExts : 0
% 0.88/0.82 % Equation resolutions : 31
% 0.88/0.82 % Disequality decompositions : 0
% 0.88/0.82 % Total rewrite steps : 10584
% 0.88/0.82 % ...of those cached : 10553
% 0.88/0.82 % Propositional unsat checks : 0
% 0.88/0.82 % Propositional check models : 0
% 0.88/0.82 % Propositional check unsatisfiable : 0
% 0.88/0.82 % Propositional clauses : 0
% 0.88/0.82 % Propositional clauses after purity: 0
% 0.88/0.82 % Propositional unsat core size : 0
% 0.88/0.82 % Propositional preprocessing time : 0.000
% 0.88/0.82 % Propositional encoding time : 0.000
% 0.88/0.82 % Propositional solver time : 0.000
% 0.88/0.82 % Success case prop preproc time : 0.000
% 0.88/0.82 % Success case prop encoding time : 0.000
% 0.88/0.82 % Success case prop solver time : 0.000
% 0.88/0.82 % Current number of processed clauses : 187
% 0.88/0.82 % Positive orientable unit clauses : 23
% 0.88/0.82 % Positive unorientable unit clauses: 0
% 0.88/0.82 % Negative unit clauses : 11
% 0.88/0.82 % Non-unit-clauses : 153
% 0.88/0.82 % Current number of unprocessed clauses: 5176
% 0.88/0.82 % ...number of literals in the above : 26767
% 0.88/0.82 % Current number of archived formulas : 0
% 0.88/0.82 % Current number of archived clauses : 410
% 0.88/0.82 % Clause-clause subsumption calls (NU) : 42043
% 0.88/0.82 % Rec. Clause-clause subsumption calls : 27243
% 0.88/0.82 % Non-unit clause-clause subsumptions : 1234
% 0.88/0.82 % Unit Clause-clause subsumption calls : 1278
% 0.88/0.82 % Rewrite failures with RHS unbound : 0
% 0.88/0.82 % BW rewrite match attempts : 12
% 0.88/0.82 % BW rewrite match successes : 12
% 0.88/0.82 % Condensation attempts : 0
% 0.88/0.82 % Condensation successes : 0
% 0.88/0.82 % Termbank termtop insertions : 142512
% 0.88/0.82 % Search garbage collected termcells : 1543
% 0.88/0.82
% 0.88/0.82 % -------------------------------------------------
% 0.88/0.82 % User time : 0.155 s
% 0.88/0.82 % System time : 0.005 s
% 0.88/0.82 % Total time : 0.160 s
% 0.88/0.82 % Maximum resident set size: 3760 pages
% 0.88/0.82
% 0.88/0.82 % -------------------------------------------------
% 0.88/0.82 % User time : 0.161 s
% 0.88/0.82 % System time : 0.011 s
% 0.88/0.82 % Total time : 0.172 s
% 0.88/0.82 % Maximum resident set size: 4864 pages
% 0.88/0.82 % E exiting
%------------------------------------------------------------------------------