%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC175+1 : TPTP v9.2.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:18:36 PM UTC 2026
% Result : Theorem 1.59s 1.81s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 19 unt; 0 def)
% Number of atoms : 225 ( 48 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 272 ( 95 ~; 95 |; 38 &)
% ( 2 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 94 ( 0 sgn 62 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ( app(X3,X5) != X4
| ~ strictorderedP(X3)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X5
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(X9,cons(X8,nil)) = X3
& lt(X8,X6) ) ) ) ) ) )
| ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssItem(X11)
=> ( ! [X12] :
( ssList(X12)
=> ! [X13] :
( ssList(X13)
=> app(app(app(X12,cons(X10,nil)),cons(X11,nil)),X13) != X1 ) )
| neq(X10,X11) ) ) )
| ( nil != X4
& nil = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax1,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax1) ).
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(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax12,axiom,
! [X1] :
( ssList(X1)
=> ( strictorderedP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> lt(X2,X3) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax12) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax33,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
=> ~ lt(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax33) ).
fof(c_0_9,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ( app(X3,X5) != X4
| ~ strictorderedP(X3)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X5
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(X9,cons(X8,nil)) = X3
& lt(X8,X6) ) ) ) ) ) )
| ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssItem(X11)
=> ( ! [X12] :
( ssList(X12)
=> ! [X13] :
( ssList(X13)
=> app(app(app(X12,cons(X10,nil)),cons(X11,nil)),X13) != X1 ) )
| neq(X10,X11) ) ) )
| ( nil != X4
& nil = X3 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_10,negated_conjecture,
! [X479,X480,X481,X482] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ssList(esk52_0)
& app(esk50_0,esk52_0) = esk51_0
& strictorderedP(esk50_0)
& ( ~ ssItem(X479)
| ~ ssList(X480)
| app(cons(X479,nil),X480) != esk52_0
| ~ ssItem(X481)
| ~ ssList(X482)
| app(X482,cons(X481,nil)) != esk50_0
| ~ lt(X481,X479) )
& ssItem(esk53_0)
& ssItem(esk54_0)
& ssList(esk55_0)
& ssList(esk56_0)
& app(app(app(esk55_0,cons(esk53_0,nil)),cons(esk54_0,nil)),esk56_0) = esk48_0
& ~ neq(esk53_0,esk54_0)
& ( nil = esk51_0
| nil != esk50_0 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_11,plain,
! [X230,X231] :
( ( ~ neq(X230,X231)
| X230 != X231
| ~ ssItem(X231)
| ~ ssItem(X230) )
& ( X230 = X231
| neq(X230,X231)
| ~ ssItem(X231)
| ~ ssItem(X230) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax1])])])]) ).
cnf(c_0_12,negated_conjecture,
app(app(app(esk55_0,cons(esk53_0,nil)),cons(esk54_0,nil)),esk56_0) = esk48_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
~ neq(esk53_0,esk54_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
ssItem(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
ssItem(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
app(app(app(esk55_0,cons(esk53_0,nil)),cons(esk54_0,nil)),esk56_0) = esk50_0,
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,negated_conjecture,
esk54_0 = esk53_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]) ).
fof(c_0_20,plain,
! [X445,X446,X447] :
( ~ ssList(X445)
| ~ ssList(X446)
| ~ ssList(X447)
| app(app(X445,X446),X447) = app(X445,app(X446,X447)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_21,negated_conjecture,
app(app(app(esk55_0,cons(esk53_0,nil)),cons(esk53_0,nil)),esk56_0) = esk50_0,
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,negated_conjecture,
ssList(esk56_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_24,plain,
! [X334,X335] :
( ~ ssList(X334)
| ~ ssItem(X335)
| ssList(cons(X335,X334)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_25,negated_conjecture,
( app(app(esk55_0,cons(esk53_0,nil)),app(cons(esk53_0,nil),esk56_0)) = esk50_0
| ~ ssList(app(esk55_0,cons(esk53_0,nil)))
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_26,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_27,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_28,plain,
! [X353,X354] :
( ~ ssList(X353)
| ~ ssList(X354)
| ssList(app(X353,X354)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_29,negated_conjecture,
( app(app(esk55_0,cons(esk53_0,nil)),app(cons(esk53_0,nil),esk56_0)) = esk50_0
| ~ ssList(app(esk55_0,cons(esk53_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_17])]) ).
cnf(c_0_30,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_31,negated_conjecture,
ssList(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_32,plain,
! [X301,X302,X303,X304,X305,X306] :
( ( ~ strictorderedP(X301)
| ~ ssItem(X302)
| ~ ssItem(X303)
| ~ ssList(X304)
| ~ ssList(X305)
| ~ ssList(X306)
| app(app(X304,cons(X302,X305)),cons(X303,X306)) != X301
| lt(X302,X303)
| ~ ssList(X301) )
& ( ssItem(esk30_1(X301))
| strictorderedP(X301)
| ~ ssList(X301) )
& ( ssItem(esk31_1(X301))
| strictorderedP(X301)
| ~ ssList(X301) )
& ( ssList(esk32_1(X301))
| strictorderedP(X301)
| ~ ssList(X301) )
& ( ssList(esk33_1(X301))
| strictorderedP(X301)
| ~ ssList(X301) )
& ( ssList(esk34_1(X301))
| strictorderedP(X301)
| ~ ssList(X301) )
& ( app(app(esk32_1(X301),cons(esk30_1(X301),esk33_1(X301))),cons(esk31_1(X301),esk34_1(X301))) = X301
| strictorderedP(X301)
| ~ ssList(X301) )
& ( ~ lt(esk30_1(X301),esk31_1(X301))
| strictorderedP(X301)
| ~ ssList(X301) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax12])])])])]) ).
cnf(c_0_33,negated_conjecture,
( app(app(esk55_0,cons(esk53_0,nil)),app(cons(esk53_0,nil),esk56_0)) = esk50_0
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
fof(c_0_34,plain,
! [X443,X444] :
( ~ ssList(X443)
| ~ ssItem(X444)
| cons(X444,X443) = app(cons(X444,nil),X443) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
fof(c_0_35,plain,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
=> ~ lt(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[ax33]) ).
cnf(c_0_36,plain,
( lt(X2,X3)
| ~ strictorderedP(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,negated_conjecture,
app(app(esk55_0,cons(esk53_0,nil)),app(cons(esk53_0,nil),esk56_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_26]),c_0_27]),c_0_17])]) ).
cnf(c_0_38,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_40,plain,
! [X367,X368] :
( ~ ssItem(X367)
| ~ ssItem(X368)
| ~ lt(X367,X368)
| ~ lt(X368,X367) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).
cnf(c_0_41,plain,
( lt(X1,X2)
| ~ strictorderedP(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| ~ ssList(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_36]) ).
cnf(c_0_42,negated_conjecture,
app(app(esk55_0,cons(esk53_0,nil)),cons(esk53_0,esk56_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_23]),c_0_17])]) ).
cnf(c_0_43,negated_conjecture,
strictorderedP(esk50_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_44,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_39,c_0_13]) ).
cnf(c_0_45,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ lt(X1,X2)
| ~ lt(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,negated_conjecture,
lt(esk53_0,esk53_0),
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_41,c_0_42]),c_0_43]),c_0_44]),c_0_23]),c_0_27]),c_0_31]),c_0_17])]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_46]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC175+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n005.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:32:00 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.59/1.81 % Version : CSE_E---1.7
% 1.59/1.81 % Problem : theBenchmark.p
% 1.59/1.81 % SZS status Theorem for theBenchmark.p
% 1.59/1.81 % SZS output start CNFRefutation
% See solution above
% 1.59/1.81 % Total time : 1.373s
%------------------------------------------------------------------------------