%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC220+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 : n007.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 05:18:47 PM UTC 2026
% Result : Theorem 1.35s 1.73s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 27 ( 12 unt; 0 def)
% Number of atoms : 156 ( 40 equ)
% Maximal formula atoms : 46 ( 5 avg)
% Number of connectives : 206 ( 77 ~; 79 |; 34 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 45 ( 0 sgn 20 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ leq(X5,X8)
| leq(X8,X5) ) ) ) ) )
| ( nil != X3
& ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ! [X11] :
( ssList(X11)
=> ( app(app(X10,cons(X9,nil)),X11) != X3
| ? [X12] :
( ssItem(X12)
& ~ leq(X12,X9)
& memberP(X10,X12)
& memberP(X11,X12)
& leq(X9,X12) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(c_0_1,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ leq(X5,X8)
| leq(X8,X5) ) ) ) ) )
| ( nil != X3
& ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ! [X11] :
( ssList(X11)
=> ( app(app(X10,cons(X9,nil)),X11) != X3
| ? [X12] :
( ssItem(X12)
& ~ leq(X12,X9)
& memberP(X10,X12)
& memberP(X11,X12)
& leq(X9,X12) ) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_2,negated_conjecture,
! [X476,X477,X478,X483] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& nil != esk48_0
& ( ssItem(esk52_3(X476,X477,X478))
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( memberP(X477,esk52_3(X476,X477,X478))
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( memberP(X478,esk52_3(X476,X477,X478))
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( leq(X476,esk52_3(X476,X477,X478))
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( ~ leq(esk52_3(X476,X477,X478),X476)
| ~ ssList(X478)
| app(app(X477,cons(X476,nil)),X478) != esk48_0
| ~ ssList(X477)
| ~ ssItem(X476) )
& ( ssItem(esk53_0)
| nil = esk50_0 )
& ( ssList(esk54_0)
| nil = esk50_0 )
& ( ssList(esk55_0)
| nil = esk50_0 )
& ( app(app(esk54_0,cons(esk53_0,nil)),esk55_0) = esk50_0
| nil = esk50_0 )
& ( ~ ssItem(X483)
| leq(X483,esk53_0)
| ~ memberP(esk54_0,X483)
| ~ memberP(esk55_0,X483)
| ~ leq(esk53_0,X483)
| 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_1])])])])]) ).
cnf(c_0_3,negated_conjecture,
( app(app(esk54_0,cons(esk53_0,nil)),esk55_0) = esk50_0
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5,negated_conjecture,
nil != esk48_0,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_6,negated_conjecture,
( ssList(esk54_0)
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_7,negated_conjecture,
( ssList(esk55_0)
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_8,negated_conjecture,
( ssItem(esk53_0)
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_9,negated_conjecture,
( leq(X1,esk53_0)
| nil = esk50_0
| ~ ssItem(X1)
| ~ memberP(esk54_0,X1)
| ~ memberP(esk55_0,X1)
| ~ leq(esk53_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_10,negated_conjecture,
( memberP(X1,esk52_3(X2,X3,X1))
| ~ ssList(X1)
| app(app(X3,cons(X2,nil)),X1) != esk48_0
| ~ ssList(X3)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_11,negated_conjecture,
app(app(esk54_0,cons(esk53_0,nil)),esk55_0) = esk48_0,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_3,c_0_4]),c_0_4]),c_0_5]) ).
cnf(c_0_12,negated_conjecture,
ssList(esk54_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_4]),c_0_5]) ).
cnf(c_0_13,negated_conjecture,
ssList(esk55_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_4]),c_0_5]) ).
cnf(c_0_14,negated_conjecture,
ssItem(esk53_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_4]),c_0_5]) ).
cnf(c_0_15,negated_conjecture,
( ssItem(esk52_3(X1,X2,X3))
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_16,negated_conjecture,
( ~ leq(esk52_3(X1,X2,X3),X1)
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_17,negated_conjecture,
( leq(X1,esk53_0)
| ~ leq(esk53_0,X1)
| ~ memberP(esk54_0,X1)
| ~ memberP(esk55_0,X1)
| ~ ssItem(X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_4]),c_0_5]) ).
cnf(c_0_18,negated_conjecture,
memberP(esk55_0,esk52_3(esk53_0,esk54_0,esk55_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13]),c_0_14])]) ).
cnf(c_0_19,negated_conjecture,
ssItem(esk52_3(esk53_0,esk54_0,esk55_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_11]),c_0_13]),c_0_12]),c_0_14])]) ).
cnf(c_0_20,negated_conjecture,
~ leq(esk52_3(esk53_0,esk54_0,esk55_0),esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_11]),c_0_13]),c_0_12]),c_0_14])]) ).
cnf(c_0_21,negated_conjecture,
( memberP(X1,esk52_3(X2,X1,X3))
| ~ ssList(X3)
| app(app(X1,cons(X2,nil)),X3) != esk48_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_22,negated_conjecture,
( ~ leq(esk53_0,esk52_3(esk53_0,esk54_0,esk55_0))
| ~ memberP(esk54_0,esk52_3(esk53_0,esk54_0,esk55_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_23,negated_conjecture,
memberP(esk54_0,esk52_3(esk53_0,esk54_0,esk55_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_11]),c_0_13]),c_0_12]),c_0_14])]) ).
cnf(c_0_24,negated_conjecture,
( leq(X1,esk52_3(X1,X2,X3))
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_25,negated_conjecture,
~ leq(esk53_0,esk52_3(esk53_0,esk54_0,esk55_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_11]),c_0_13]),c_0_12]),c_0_14])]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC220+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.11 % 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
% 0.13/0.32 % Computer : n007.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 04:35:08 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.35/1.73 % Version : CSE_E---1.7
% 1.35/1.73 % Problem : theBenchmark.p
% 1.35/1.73 % SZS status Theorem for theBenchmark.p
% 1.35/1.73 % SZS output start CNFRefutation
% See solution above
% 1.35/1.73 % Total time : 1.369s
%------------------------------------------------------------------------------