%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC272+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 : n003.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 05:18:58 PM UTC 2026
% Result : Theorem 244.33s 176.46s
% Output : CNFRefutation 245.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 7 unt; 0 def)
% Number of atoms : 209 ( 33 equ)
% Maximal formula atoms : 30 ( 7 avg)
% Number of connectives : 280 ( 99 ~; 114 |; 42 &)
% ( 3 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 42 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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(ax11,axiom,
! [X1] :
( ssList(X1)
=> ( totalorderedP(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
=> leq(X2,X3) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax11) ).
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) ) ) ) ) )
| totalorderedP(X1)
| ( nil != X4
& nil = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax93,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
<=> ( X1 != X2
& leq(X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax93) ).
fof(c_0_4,plain,
! [X293,X294,X295,X296,X297,X298] :
( ( ~ strictorderedP(X293)
| ~ ssItem(X294)
| ~ ssItem(X295)
| ~ ssList(X296)
| ~ ssList(X297)
| ~ ssList(X298)
| app(app(X296,cons(X294,X297)),cons(X295,X298)) != X293
| lt(X294,X295)
| ~ ssList(X293) )
& ( ssItem(esk30_1(X293))
| strictorderedP(X293)
| ~ ssList(X293) )
& ( ssItem(esk31_1(X293))
| strictorderedP(X293)
| ~ ssList(X293) )
& ( ssList(esk32_1(X293))
| strictorderedP(X293)
| ~ ssList(X293) )
& ( ssList(esk33_1(X293))
| strictorderedP(X293)
| ~ ssList(X293) )
& ( ssList(esk34_1(X293))
| strictorderedP(X293)
| ~ ssList(X293) )
& ( app(app(esk32_1(X293),cons(esk30_1(X293),esk33_1(X293))),cons(esk31_1(X293),esk34_1(X293))) = X293
| strictorderedP(X293)
| ~ ssList(X293) )
& ( ~ lt(esk30_1(X293),esk31_1(X293))
| strictorderedP(X293)
| ~ ssList(X293) ) ),
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_5,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_4]) ).
fof(c_0_6,plain,
! [X282,X283,X284,X285,X286,X287] :
( ( ~ totalorderedP(X282)
| ~ ssItem(X283)
| ~ ssItem(X284)
| ~ ssList(X285)
| ~ ssList(X286)
| ~ ssList(X287)
| app(app(X285,cons(X283,X286)),cons(X284,X287)) != X282
| leq(X283,X284)
| ~ ssList(X282) )
& ( ssItem(esk25_1(X282))
| totalorderedP(X282)
| ~ ssList(X282) )
& ( ssItem(esk26_1(X282))
| totalorderedP(X282)
| ~ ssList(X282) )
& ( ssList(esk27_1(X282))
| totalorderedP(X282)
| ~ ssList(X282) )
& ( ssList(esk28_1(X282))
| totalorderedP(X282)
| ~ ssList(X282) )
& ( ssList(esk29_1(X282))
| totalorderedP(X282)
| ~ ssList(X282) )
& ( app(app(esk27_1(X282),cons(esk25_1(X282),esk28_1(X282))),cons(esk26_1(X282),esk29_1(X282))) = X282
| totalorderedP(X282)
| ~ ssList(X282) )
& ( ~ leq(esk25_1(X282),esk26_1(X282))
| totalorderedP(X282)
| ~ ssList(X282) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax11])])])])]) ).
fof(c_0_7,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) ) ) ) ) )
| totalorderedP(X1)
| ( nil != X4
& nil = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_8,plain,
! [X459,X460] :
( ( X459 != X460
| ~ lt(X459,X460)
| ~ ssItem(X460)
| ~ ssItem(X459) )
& ( leq(X459,X460)
| ~ lt(X459,X460)
| ~ ssItem(X460)
| ~ ssItem(X459) )
& ( X459 = X460
| ~ leq(X459,X460)
| lt(X459,X460)
| ~ ssItem(X460)
| ~ ssItem(X459) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax93])])])]) ).
cnf(c_0_9,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_5]) ).
cnf(c_0_10,plain,
( app(app(esk27_1(X1),cons(esk25_1(X1),esk28_1(X1))),cons(esk26_1(X1),esk29_1(X1))) = X1
| totalorderedP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( ssItem(esk25_1(X1))
| totalorderedP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( ssItem(esk26_1(X1))
| totalorderedP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,plain,
( ssList(esk27_1(X1))
| totalorderedP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
( ssList(esk28_1(X1))
| totalorderedP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,plain,
( ssList(esk29_1(X1))
| totalorderedP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_16,negated_conjecture,
! [X471,X472,X473,X474] :
( 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(X471)
| ~ ssList(X472)
| app(cons(X471,nil),X472) != esk52_0
| ~ ssItem(X473)
| ~ ssList(X474)
| app(X474,cons(X473,nil)) != esk50_0
| ~ lt(X473,X471) )
& ~ totalorderedP(esk48_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_7])])])]) ).
cnf(c_0_17,plain,
( leq(X1,X2)
| ~ lt(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,plain,
( totalorderedP(X1)
| lt(esk25_1(X1),esk26_1(X1))
| ~ strictorderedP(X1)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12]),c_0_13]),c_0_14]),c_0_15]) ).
cnf(c_0_19,plain,
( totalorderedP(X1)
| ~ leq(esk25_1(X1),esk26_1(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
~ totalorderedP(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( totalorderedP(X1)
| ~ strictorderedP(X1)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_11]),c_0_12]),c_0_19]) ).
cnf(c_0_24,negated_conjecture,
strictorderedP(esk50_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
~ totalorderedP(esk50_0),
inference(rw,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC272+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
% 0.15/0.33 % Computer : n003.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 04:41:11 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 244.33/176.46 % Version : CSE_E---1.7
% 244.33/176.46 % Problem : theBenchmark.p
% 244.33/176.46 % SZS status Theorem for theBenchmark.p
% 244.33/176.46 % SZS output start CNFRefutation
% See solution above
% 245.63/177.70 % Total time : 131.415s
%------------------------------------------------------------------------------