%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC153+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 : n017.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 05:18:30 PM UTC 2026
% Result : Theorem 1.29s 1.91s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 34 ( 18 unt; 0 def)
% Number of atoms : 186 ( 26 equ)
% Maximal formula atoms : 48 ( 5 avg)
% Number of connectives : 245 ( 93 ~; 88 |; 41 &)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 30 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X4 != X2
| X3 != X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) = X3
& leq(X6,X5)
& ( ~ leq(X5,X6)
| ? [X10] :
( ssItem(X10)
& memberP(X8,X10)
& ( ~ leq(X5,X10)
| ~ leq(X10,X6) ) ) ) ) ) ) ) )
| ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssItem(X12)
=> ! [X13] :
( ssList(X13)
=> ! [X14] :
( ssList(X14)
=> ! [X15] :
( ssList(X15)
=> ( app(app(app(app(X13,cons(X11,nil)),X14),cons(X12,nil)),X15) != X1
| ~ leq(X12,X11)
| ( ! [X16] :
( ssItem(X16)
=> ( ~ memberP(X14,X16)
| ( leq(X16,X12)
& leq(X11,X16) ) ) )
& leq(X11,X12) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax29,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( leq(X1,X2)
& leq(X2,X1) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax29) ).
fof(c_0_2,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X4 != X2
| X3 != X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) = X3
& leq(X6,X5)
& ( ~ leq(X5,X6)
| ? [X10] :
( ssItem(X10)
& memberP(X8,X10)
& ( ~ leq(X5,X10)
| ~ leq(X10,X6) ) ) ) ) ) ) ) )
| ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssItem(X12)
=> ! [X13] :
( ssList(X13)
=> ! [X14] :
( ssList(X14)
=> ! [X15] :
( ssList(X15)
=> ( app(app(app(app(X13,cons(X11,nil)),X14),cons(X12,nil)),X15) != X1
| ~ leq(X12,X11)
| ( ! [X16] :
( ssItem(X16)
=> ( ~ memberP(X14,X16)
| ( leq(X16,X12)
& leq(X11,X16) ) ) )
& leq(X11,X12) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_3,negated_conjecture,
! [X484,X485,X486,X487,X488,X489] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk51_0 = esk49_0
& esk50_0 = esk48_0
& ( leq(X484,X485)
| ~ ssList(X488)
| app(app(app(app(X486,cons(X484,nil)),X487),cons(X485,nil)),X488) != esk50_0
| ~ leq(X485,X484)
| ~ ssList(X487)
| ~ ssList(X486)
| ~ ssItem(X485)
| ~ ssItem(X484) )
& ( leq(X484,X489)
| ~ ssItem(X489)
| ~ memberP(X487,X489)
| ~ ssList(X488)
| app(app(app(app(X486,cons(X484,nil)),X487),cons(X485,nil)),X488) != esk50_0
| ~ leq(X485,X484)
| ~ ssList(X487)
| ~ ssList(X486)
| ~ ssItem(X485)
| ~ ssItem(X484) )
& ( leq(X489,X485)
| ~ ssItem(X489)
| ~ memberP(X487,X489)
| ~ ssList(X488)
| app(app(app(app(X486,cons(X484,nil)),X487),cons(X485,nil)),X488) != esk50_0
| ~ leq(X485,X484)
| ~ ssList(X487)
| ~ ssList(X486)
| ~ ssItem(X485)
| ~ ssItem(X484) )
& ssItem(esk52_0)
& ssItem(esk53_0)
& ssList(esk54_0)
& ssList(esk55_0)
& ssList(esk56_0)
& app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk48_0
& leq(esk53_0,esk52_0)
& ( ssItem(esk57_0)
| ~ leq(esk52_0,esk53_0) )
& ( memberP(esk55_0,esk57_0)
| ~ leq(esk52_0,esk53_0) )
& ( ~ leq(esk57_0,esk53_0)
| ~ leq(esk52_0,esk57_0)
| ~ leq(esk52_0,esk53_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_2])])])])]) ).
fof(c_0_4,plain,
! [X365,X366] :
( ~ ssItem(X365)
| ~ ssItem(X366)
| ~ leq(X365,X366)
| ~ leq(X366,X365)
| X365 = X366 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax29])])]) ).
cnf(c_0_5,negated_conjecture,
app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk48_0,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,negated_conjecture,
esk50_0 = esk48_0,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_7,plain,
( X1 = X2
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ leq(X1,X2)
| ~ leq(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
leq(esk53_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_9,negated_conjecture,
ssItem(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_10,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_11,negated_conjecture,
( leq(X1,X2)
| ~ ssList(X3)
| app(app(app(app(X4,cons(X1,nil)),X5),cons(X2,nil)),X3) != esk50_0
| ~ leq(X2,X1)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_12,negated_conjecture,
app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk50_0,
inference(rw,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_13,negated_conjecture,
ssList(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_14,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_15,negated_conjecture,
ssList(esk56_0),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_16,negated_conjecture,
( esk53_0 = esk52_0
| ~ leq(esk52_0,esk53_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]),c_0_10])]) ).
cnf(c_0_17,negated_conjecture,
leq(esk52_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_11,c_0_12]),c_0_8]),c_0_13]),c_0_14]),c_0_15]),c_0_9]),c_0_10])]) ).
cnf(c_0_18,negated_conjecture,
esk53_0 = esk52_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).
cnf(c_0_19,negated_conjecture,
( leq(X1,X2)
| ~ ssItem(X1)
| ~ memberP(X3,X1)
| ~ ssList(X4)
| app(app(app(app(X5,cons(X6,nil)),X3),cons(X2,nil)),X4) != esk50_0
| ~ leq(X2,X6)
| ~ ssList(X3)
| ~ ssList(X5)
| ~ ssItem(X2)
| ~ ssItem(X6) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_20,negated_conjecture,
app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk52_0,nil)),esk56_0) = esk50_0,
inference(rw,[status(thm)],[c_0_12,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
leq(esk52_0,esk52_0),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( memberP(esk55_0,esk57_0)
| ~ leq(esk52_0,esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_23,negated_conjecture,
( ssItem(esk57_0)
| ~ leq(esk52_0,esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_24,negated_conjecture,
( ~ leq(esk57_0,esk53_0)
| ~ leq(esk52_0,esk57_0)
| ~ leq(esk52_0,esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_25,negated_conjecture,
( leq(X1,esk52_0)
| ~ memberP(esk55_0,X1)
| ~ ssItem(X1) ),
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(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_14]),c_0_15]),c_0_13]),c_0_10])]) ).
cnf(c_0_26,negated_conjecture,
memberP(esk55_0,esk57_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_17])]) ).
cnf(c_0_27,negated_conjecture,
ssItem(esk57_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_17])]) ).
cnf(c_0_28,negated_conjecture,
( leq(X1,X2)
| ~ ssItem(X2)
| ~ memberP(X3,X2)
| ~ ssList(X4)
| app(app(app(app(X5,cons(X1,nil)),X3),cons(X6,nil)),X4) != esk50_0
| ~ leq(X6,X1)
| ~ ssList(X3)
| ~ ssList(X5)
| ~ ssItem(X6)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_29,negated_conjecture,
( ~ leq(esk52_0,esk57_0)
| ~ leq(esk57_0,esk52_0) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_17])]),c_0_18]) ).
cnf(c_0_30,negated_conjecture,
leq(esk57_0,esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_31,negated_conjecture,
( leq(esk52_0,X1)
| ~ memberP(esk55_0,X1)
| ~ ssItem(X1) ),
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(spm,[status(thm)],[c_0_28,c_0_20]),c_0_21]),c_0_14]),c_0_15]),c_0_13]),c_0_10])]) ).
cnf(c_0_32,negated_conjecture,
~ leq(esk52_0,esk57_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_26]),c_0_27])]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.21 % Problem : SWC153+1 : TPTP v9.2.1. Released v2.4.0.
% 0.03/0.21 % 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
% 0.13/0.46 % Computer : n017.cluster.edu
% 0.13/0.46 % Model : x86_64 x86_64
% 0.13/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.46 % Memory : 8042.1875MB
% 0.13/0.46 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.46 % CPULimit : 300
% 0.13/0.46 % WCLimit : 300
% 0.13/0.46 % DateTime : Tue May 5 04:28:42 EDT 2026
% 0.13/0.46 % CPUTime :
% 0.13/0.47 % start to proof: theBenchmark
% 1.29/1.91 % Version : CSE_E---1.7
% 1.29/1.91 % Problem : theBenchmark.p
% 1.29/1.91 % SZS status Theorem for theBenchmark.p
% 1.29/1.91 % SZS output start CNFRefutation
% See solution above
% 1.29/1.91 % Total time : 1.389s
%------------------------------------------------------------------------------