%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC161+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 : n018.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 05:18:32 PM UTC 2026
% Result : Theorem 1.33s 1.93s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 22 unt; 0 def)
% Number of atoms : 277 ( 57 equ)
% Maximal formula atoms : 40 ( 5 avg)
% Number of connectives : 339 ( 116 ~; 122 |; 59 &)
% ( 1 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 13 con; 0-2 aty)
% Number of variables : 112 ( 0 sgn 72 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(app(X5,X3),X6) != X4
| ~ strictorderedP(X3)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X5
& ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X3
& lt(X7,X9) ) ) ) )
| ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(cons(X11,nil),X12) = X6
& ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssList(X14)
& app(X14,cons(X13,nil)) = X3
& lt(X13,X11) ) ) ) ) ) )
| ! [X15] :
( ssItem(X15)
=> ! [X16] :
( ssItem(X16)
=> ! [X17] :
( ssList(X17)
=> ! [X18] :
( ssList(X18)
=> ! [X19] :
( ~ ssList(X19)
| app(app(app(app(X17,cons(X15,nil)),X18),cons(X16,nil)),X19) != X1
| ~ leq(X16,X15)
| ( ! [X20] :
( ~ ssItem(X20)
| ~ memberP(X18,X20)
| ( leq(X15,X20)
& leq(X20,X16) ) )
& leq(X15,X16) ) ) ) ) ) )
| ( nil != X4
& nil = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
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(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(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
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(ax92,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( leq(X1,X2)
=> ( X1 = X2
| lt(X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax92) ).
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(c_0_9,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(app(X5,X3),X6) != X4
| ~ strictorderedP(X3)
| ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X5
& ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X3
& lt(X7,X9) ) ) ) )
| ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(cons(X11,nil),X12) = X6
& ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssList(X14)
& app(X14,cons(X13,nil)) = X3
& lt(X13,X11) ) ) ) ) ) )
| ! [X15] :
( ssItem(X15)
=> ! [X16] :
( ssItem(X16)
=> ! [X17] :
( ssList(X17)
=> ! [X18] :
( ssList(X18)
=> ! [X19] :
( ~ ssList(X19)
| app(app(app(app(X17,cons(X15,nil)),X18),cons(X16,nil)),X19) != X1
| ~ leq(X16,X15)
| ( ! [X20] :
( ~ ssItem(X20)
| ~ memberP(X18,X20)
| ( leq(X15,X20)
& leq(X20,X16) ) )
& leq(X15,X16) ) ) ) ) ) )
| ( nil != X4
& nil = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_10,negated_conjecture,
! [X494,X495,X496,X497,X498,X499,X500,X501] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ssList(esk52_0)
& ssList(esk53_0)
& app(app(esk52_0,esk50_0),esk53_0) = esk51_0
& strictorderedP(esk50_0)
& ( ~ ssItem(X494)
| ~ ssList(X495)
| app(X495,cons(X494,nil)) != esk52_0
| ~ ssItem(X496)
| ~ ssList(X497)
| app(cons(X496,nil),X497) != esk50_0
| ~ lt(X494,X496) )
& ( ~ ssItem(X498)
| ~ ssList(X499)
| app(cons(X498,nil),X499) != esk53_0
| ~ ssItem(X500)
| ~ ssList(X501)
| app(X501,cons(X500,nil)) != esk50_0
| ~ lt(X500,X498) )
& ssItem(esk54_0)
& ssItem(esk55_0)
& ssList(esk56_0)
& ssList(esk57_0)
& ssList(esk58_0)
& app(app(app(app(esk56_0,cons(esk54_0,nil)),esk57_0),cons(esk55_0,nil)),esk58_0) = esk48_0
& leq(esk55_0,esk54_0)
& ( ssItem(esk59_0)
| ~ leq(esk54_0,esk55_0) )
& ( memberP(esk57_0,esk59_0)
| ~ leq(esk54_0,esk55_0) )
& ( ~ leq(esk54_0,esk59_0)
| ~ leq(esk59_0,esk55_0)
| ~ leq(esk54_0,esk55_0) )
& ( nil = esk51_0
| nil != esk50_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])]) ).
cnf(c_0_11,negated_conjecture,
app(app(app(app(esk56_0,cons(esk54_0,nil)),esk57_0),cons(esk55_0,nil)),esk58_0) = esk48_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_12,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,plain,
! [X459,X460,X461] :
( ~ ssList(X459)
| ~ ssList(X460)
| ~ ssList(X461)
| app(app(X459,X460),X461) = app(X459,app(X460,X461)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_14,negated_conjecture,
app(app(app(app(esk56_0,cons(esk54_0,nil)),esk57_0),cons(esk55_0,nil)),esk58_0) = esk50_0,
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,negated_conjecture,
ssList(esk57_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
ssList(esk56_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_18,plain,
! [X348,X349] :
( ~ ssList(X348)
| ~ ssItem(X349)
| ssList(cons(X349,X348)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_19,negated_conjecture,
( app(app(app(esk56_0,app(cons(esk54_0,nil),esk57_0)),cons(esk55_0,nil)),esk58_0) = esk50_0
| ~ ssList(cons(esk54_0,nil)) ),
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])]) ).
cnf(c_0_20,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_22,negated_conjecture,
ssItem(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_23,plain,
! [X457,X458] :
( ~ ssList(X457)
| ~ ssItem(X458)
| cons(X458,X457) = app(cons(X458,nil),X457) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_24,negated_conjecture,
app(app(app(esk56_0,app(cons(esk54_0,nil),esk57_0)),cons(esk55_0,nil)),esk58_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]) ).
cnf(c_0_25,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_26,negated_conjecture,
app(app(app(esk56_0,cons(esk54_0,esk57_0)),cons(esk55_0,nil)),esk58_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_16]),c_0_22])]) ).
cnf(c_0_27,negated_conjecture,
ssList(esk58_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_28,negated_conjecture,
( app(app(esk56_0,cons(esk54_0,esk57_0)),app(cons(esk55_0,nil),esk58_0)) = esk50_0
| ~ ssList(app(esk56_0,cons(esk54_0,esk57_0)))
| ~ ssList(cons(esk55_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_26]),c_0_27])]) ).
cnf(c_0_29,negated_conjecture,
ssItem(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_30,plain,
! [X367,X368] :
( ~ ssList(X367)
| ~ ssList(X368)
| ssList(app(X367,X368)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_31,negated_conjecture,
( app(app(esk56_0,cons(esk54_0,esk57_0)),app(cons(esk55_0,nil),esk58_0)) = esk50_0
| ~ ssList(app(esk56_0,cons(esk54_0,esk57_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_20]),c_0_21]),c_0_29])]) ).
cnf(c_0_32,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_33,plain,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
=> ~ lt(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[ax33]) ).
fof(c_0_34,plain,
! [X479,X480] :
( ~ ssItem(X479)
| ~ ssItem(X480)
| ~ leq(X479,X480)
| X479 = X480
| lt(X479,X480) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax92])])]) ).
fof(c_0_35,plain,
! [X315,X316,X317,X318,X319,X320] :
( ( ~ strictorderedP(X315)
| ~ ssItem(X316)
| ~ ssItem(X317)
| ~ ssList(X318)
| ~ ssList(X319)
| ~ ssList(X320)
| app(app(X318,cons(X316,X319)),cons(X317,X320)) != X315
| lt(X316,X317)
| ~ ssList(X315) )
& ( ssItem(esk30_1(X315))
| strictorderedP(X315)
| ~ ssList(X315) )
& ( ssItem(esk31_1(X315))
| strictorderedP(X315)
| ~ ssList(X315) )
& ( ssList(esk32_1(X315))
| strictorderedP(X315)
| ~ ssList(X315) )
& ( ssList(esk33_1(X315))
| strictorderedP(X315)
| ~ ssList(X315) )
& ( ssList(esk34_1(X315))
| strictorderedP(X315)
| ~ ssList(X315) )
& ( app(app(esk32_1(X315),cons(esk30_1(X315),esk33_1(X315))),cons(esk31_1(X315),esk34_1(X315))) = X315
| strictorderedP(X315)
| ~ ssList(X315) )
& ( ~ lt(esk30_1(X315),esk31_1(X315))
| strictorderedP(X315)
| ~ ssList(X315) ) ),
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_36,negated_conjecture,
( app(app(esk56_0,cons(esk54_0,esk57_0)),app(cons(esk55_0,nil),esk58_0)) = esk50_0
| ~ ssList(cons(esk54_0,esk57_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_17])]) ).
fof(c_0_37,plain,
! [X381,X382] :
( ~ ssItem(X381)
| ~ ssItem(X382)
| ~ lt(X381,X382)
| ~ lt(X382,X381) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])]) ).
cnf(c_0_38,plain,
( X1 = X2
| lt(X1,X2)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,negated_conjecture,
leq(esk55_0,esk54_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_40,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_35]) ).
cnf(c_0_41,negated_conjecture,
app(app(esk56_0,cons(esk54_0,esk57_0)),app(cons(esk55_0,nil),esk58_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_20]),c_0_16]),c_0_22])]) ).
cnf(c_0_42,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_43,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ lt(X1,X2)
| ~ lt(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_44,negated_conjecture,
( esk55_0 = esk54_0
| lt(esk55_0,esk54_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_22]),c_0_29])]) ).
cnf(c_0_45,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_40]) ).
cnf(c_0_46,negated_conjecture,
app(app(esk56_0,cons(esk54_0,esk57_0)),cons(esk55_0,esk58_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_25]),c_0_27]),c_0_29])]) ).
cnf(c_0_47,negated_conjecture,
strictorderedP(esk50_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_48,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_42,c_0_12]) ).
cnf(c_0_49,negated_conjecture,
( esk55_0 = esk54_0
| ~ lt(esk54_0,esk55_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_29]),c_0_22])]) ).
cnf(c_0_50,negated_conjecture,
lt(esk54_0,esk55_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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_48]),c_0_27]),c_0_16]),c_0_17]),c_0_29]),c_0_22])]) ).
cnf(c_0_51,negated_conjecture,
esk55_0 = esk54_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).
cnf(c_0_52,negated_conjecture,
lt(esk54_0,esk54_0),
inference(rw,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_52]),c_0_52]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.22 % Problem : SWC161+1 : TPTP v9.2.1. Released v2.4.0.
% 0.03/0.22 % 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
% 0.12/0.46 % Computer : n018.cluster.edu
% 0.12/0.46 % Model : x86_64 x86_64
% 0.12/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.46 % Memory : 8042.1875MB
% 0.12/0.46 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.46 % CPULimit : 300
% 0.12/0.46 % WCLimit : 300
% 0.12/0.46 % DateTime : Tue May 5 04:30:47 EDT 2026
% 0.12/0.46 % CPUTime :
% 0.12/0.47 % start to proof: theBenchmark
% 1.33/1.93 % Version : CSE_E---1.7
% 1.33/1.93 % Problem : theBenchmark.p
% 1.33/1.93 % SZS status Theorem for theBenchmark.p
% 1.33/1.93 % SZS output start CNFRefutation
% See solution above
% 1.33/1.93 % Total time : 1.383s
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