%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC270+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 : n001.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 05:18:57 PM UTC 2026
% Result : Theorem 230.17s 159.56s
% Output : CNFRefutation 231.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 7 unt; 0 def)
% Number of atoms : 179 ( 18 equ)
% Maximal formula atoms : 30 ( 6 avg)
% Number of connectives : 238 ( 87 ~; 101 |; 25 &)
% ( 3 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 36 !; 0 ?)
% 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
| ~ segmentP(X4,X3)
| ~ strictorderedP(X3)
| totalorderedP(X1) ) ) ) ),
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,
! [X285,X286,X287,X288,X289,X290] :
( ( ~ strictorderedP(X285)
| ~ ssItem(X286)
| ~ ssItem(X287)
| ~ ssList(X288)
| ~ ssList(X289)
| ~ ssList(X290)
| app(app(X288,cons(X286,X289)),cons(X287,X290)) != X285
| lt(X286,X287)
| ~ ssList(X285) )
& ( ssItem(esk30_1(X285))
| strictorderedP(X285)
| ~ ssList(X285) )
& ( ssItem(esk31_1(X285))
| strictorderedP(X285)
| ~ ssList(X285) )
& ( ssList(esk32_1(X285))
| strictorderedP(X285)
| ~ ssList(X285) )
& ( ssList(esk33_1(X285))
| strictorderedP(X285)
| ~ ssList(X285) )
& ( ssList(esk34_1(X285))
| strictorderedP(X285)
| ~ ssList(X285) )
& ( app(app(esk32_1(X285),cons(esk30_1(X285),esk33_1(X285))),cons(esk31_1(X285),esk34_1(X285))) = X285
| strictorderedP(X285)
| ~ ssList(X285) )
& ( ~ lt(esk30_1(X285),esk31_1(X285))
| strictorderedP(X285)
| ~ ssList(X285) ) ),
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,
! [X274,X275,X276,X277,X278,X279] :
( ( ~ totalorderedP(X274)
| ~ ssItem(X275)
| ~ ssItem(X276)
| ~ ssList(X277)
| ~ ssList(X278)
| ~ ssList(X279)
| app(app(X277,cons(X275,X278)),cons(X276,X279)) != X274
| leq(X275,X276)
| ~ ssList(X274) )
& ( ssItem(esk25_1(X274))
| totalorderedP(X274)
| ~ ssList(X274) )
& ( ssItem(esk26_1(X274))
| totalorderedP(X274)
| ~ ssList(X274) )
& ( ssList(esk27_1(X274))
| totalorderedP(X274)
| ~ ssList(X274) )
& ( ssList(esk28_1(X274))
| totalorderedP(X274)
| ~ ssList(X274) )
& ( ssList(esk29_1(X274))
| totalorderedP(X274)
| ~ ssList(X274) )
& ( app(app(esk27_1(X274),cons(esk25_1(X274),esk28_1(X274))),cons(esk26_1(X274),esk29_1(X274))) = X274
| totalorderedP(X274)
| ~ ssList(X274) )
& ( ~ leq(esk25_1(X274),esk26_1(X274))
| totalorderedP(X274)
| ~ ssList(X274) ) ),
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
| ~ segmentP(X4,X3)
| ~ strictorderedP(X3)
| totalorderedP(X1) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_8,plain,
! [X451,X452] :
( ( X451 != X452
| ~ lt(X451,X452)
| ~ ssItem(X452)
| ~ ssItem(X451) )
& ( leq(X451,X452)
| ~ lt(X451,X452)
| ~ ssItem(X452)
| ~ ssItem(X451) )
& ( X451 = X452
| ~ leq(X451,X452)
| lt(X451,X452)
| ~ ssItem(X452)
| ~ ssItem(X451) ) ),
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,
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& segmentP(esk51_0,esk50_0)
& strictorderedP(esk50_0)
& ~ totalorderedP(esk48_0) ),
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 : SWC270+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 : n001.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 04:41:33 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 230.17/159.56 % Version : CSE_E---1.7
% 230.17/159.56 % Problem : theBenchmark.p
% 230.17/159.56 % SZS status Theorem for theBenchmark.p
% 230.17/159.56 % SZS output start CNFRefutation
% See solution above
% 231.27/160.62 % Total time : 117.476s
%------------------------------------------------------------------------------