%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC333-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:57:30 AM UTC 2026
% Result : Unsatisfiable 22.81s 6.64s
% Output : CNFRefutation 22.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 19
% Syntax : Number of formulae : 85 ( 39 unt; 0 def)
% Number of atoms : 186 ( 38 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 216 ( 115 ~; 101 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_14,axiom,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| totalorderedP(sk5) ),
file('theBenchmark.p',co1_14) ).
cnf(c_51,plain,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| totalorderedP(sk5) ),
inference(clausify,[status(thm)],[co1_14]) ).
fof(co1_13,axiom,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| segmentP(sk5,sk1) ),
file('theBenchmark.p',co1_13) ).
cnf(c_52,plain,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| segmentP(sk5,sk1) ),
inference(clausify,[status(thm)],[co1_13]) ).
fof(co1_12,axiom,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| segmentP(sk2,sk5) ),
file('theBenchmark.p',co1_12) ).
cnf(c_53,plain,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| segmentP(sk2,sk5) ),
inference(clausify,[status(thm)],[co1_12]) ).
fof(co1_11,axiom,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| neq(sk1,sk5) ),
file('theBenchmark.p',co1_11) ).
cnf(c_54,plain,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| neq(sk1,sk5) ),
inference(clausify,[status(thm)],[co1_11]) ).
fof(co1_10,axiom,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| ssList(sk5) ),
file('theBenchmark.p',co1_10) ).
cnf(c_55,plain,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| ssList(sk5) ),
inference(clausify,[status(thm)],[co1_10]) ).
fof(co1_9,axiom,
! [VAR_0] :
( ~ totalorderedP(VAR_0)
| ~ segmentP(VAR_0,sk3)
| ~ segmentP(sk4,VAR_0)
| ~ neq(sk3,VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',co1_9) ).
cnf(c_56,plain,
( ~ totalorderedP(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ neq(sk3,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[co1_9]) ).
fof(co1_8,axiom,
totalorderedP(sk3),
file('theBenchmark.p',co1_8) ).
cnf(c_57,plain,
totalorderedP(sk3),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
segmentP(sk4,sk3),
file('theBenchmark.p',co1_7) ).
cnf(c_58,plain,
segmentP(sk4,sk3),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_59,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
cnf(c_60,plain,
sk3 = sk1,
inference(copy,[status(thm)],[c_59]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_61,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_62,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_61]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_64,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(co1_1,axiom,
ssList(sk1),
file('theBenchmark.p',co1_1) ).
cnf(c_66,plain,
ssList(sk1),
inference(clausify,[status(thm)],[co1_1]) ).
fof(clause152,axiom,
! [VAR_0,VAR_1,VAR_2] :
( segmentP(VAR_0,VAR_2)
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| ~ ssList(VAR_2)
| ~ segmentP(VAR_1,VAR_2)
| ~ segmentP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause152) ).
cnf(c_92,plain,
( segmentP(A,C)
| ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ~ segmentP(B,C)
| ~ segmentP(A,B) ),
inference(clausify,[status(thm)],[clause152]) ).
fof(clause150,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_1 = VAR_2
| ~ ssList(VAR_2)
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| app(VAR_0,VAR_1) != app(VAR_0,VAR_2) ),
file('theBenchmark.p',clause150) ).
cnf(c_94,plain,
( B = C
| ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| app(A,B) != app(A,C) ),
inference(clausify,[status(thm)],[clause150]) ).
fof(clause115,axiom,
! [VAR_0,VAR_1] :
( ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| ~ neq(VAR_0,VAR_1)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',clause115) ).
cnf(c_127,plain,
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(A,B)
| A != B ),
inference(clausify,[status(thm)],[clause115]) ).
fof(clause100,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| neq(VAR_1,VAR_0)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause100) ).
cnf(c_142,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause74,axiom,
! [VAR_0] :
( app(nil,VAR_0) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause74) ).
cnf(c_159,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause74]) ).
fof(clause57,axiom,
! [VAR_0] :
( segmentP(VAR_0,VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause57) ).
cnf(c_170,plain,
( segmentP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause57]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_219,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_830,plain,
totalorderedP(sk1),
inference(paramod,[status(thm)],[c_60,c_57]) ).
cnf(c_831,plain,
segmentP(sk4,sk1),
inference(paramod,[status(thm)],[c_60,c_58]) ).
cnf(c_832,plain,
( ~ segmentP(sk2,sk1)
| ssList(sk5) ),
inference(resolve,[status(thm)],[c_830,c_55]) ).
cnf(c_833,plain,
( ~ segmentP(sk2,sk1)
| neq(sk1,sk5) ),
inference(resolve,[status(thm)],[c_830,c_54]) ).
cnf(c_834,plain,
( ~ segmentP(sk2,sk1)
| segmentP(sk2,sk5) ),
inference(resolve,[status(thm)],[c_830,c_53]) ).
cnf(c_835,plain,
( ~ segmentP(sk2,sk1)
| segmentP(sk5,sk1) ),
inference(resolve,[status(thm)],[c_830,c_52]) ).
cnf(c_836,plain,
( ~ segmentP(sk2,sk1)
| totalorderedP(sk5) ),
inference(resolve,[status(thm)],[c_830,c_51]) ).
cnf(c_929,plain,
( sk1 = B
| ~ ssList(B)
| ~ ssList(A)
| app(A,sk1) != app(A,B) ),
inference(resolve,[status(thm)],[c_94,c_66]) ).
cnf(c_1060,plain,
( sk3 = A
| neq(sk3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_142,c_64]) ).
cnf(c_1092,plain,
app(nil,sk3) = sk3,
inference(resolve,[status(thm)],[c_159,c_64]) ).
cnf(c_1116,plain,
segmentP(sk3,sk3),
inference(resolve,[status(thm)],[c_170,c_64]) ).
cnf(c_4837,plain,
segmentP(sk2,sk1),
inference(paramod,[status(thm)],[c_62,c_831]) ).
cnf(c_4838,plain,
totalorderedP(sk5),
inference(resolve,[status(thm)],[c_4837,c_836]) ).
cnf(c_4839,plain,
segmentP(sk5,sk1),
inference(resolve,[status(thm)],[c_4837,c_835]) ).
cnf(c_4840,plain,
segmentP(sk2,sk5),
inference(resolve,[status(thm)],[c_4837,c_834]) ).
cnf(c_4841,plain,
neq(sk1,sk5),
inference(resolve,[status(thm)],[c_4837,c_833]) ).
cnf(c_4842,plain,
ssList(sk5),
inference(resolve,[status(thm)],[c_4837,c_832]) ).
cnf(c_4944,plain,
app(nil,sk5) = sk5,
inference(resolve,[status(thm)],[c_4842,c_159]) ).
cnf(c_5557,plain,
segmentP(sk1,sk3),
inference(paramod,[status(thm)],[c_60,c_1116]) ).
cnf(c_21702,plain,
( segmentP(sk5,A)
| ~ ssList(sk5)
| ~ ssList(sk1)
| ~ ssList(A)
| ~ segmentP(sk1,A) ),
inference(resolve,[status(thm)],[c_4839,c_92]) ).
cnf(c_21703,plain,
( segmentP(sk5,A)
| ~ ssList(sk5)
| ~ ssList(A)
| ~ segmentP(sk1,A) ),
inference(resolve,[status(thm)],[c_66,c_21702]) ).
cnf(c_6385,plain,
( segmentP(sk5,A)
| ~ ssList(A)
| ~ segmentP(sk1,A) ),
inference(resolve,[status(thm)],[c_4842,c_21703]) ).
cnf(c_21704,plain,
( ~ ssList(sk1)
| ~ ssList(sk5)
| sk1 != sk5 ),
inference(resolve,[status(thm)],[c_4841,c_127]) ).
cnf(c_21705,plain,
( ~ ssList(sk1)
| ~ ssList(sk5)
| sk5 != sk1 ),
inference(copy,[status(thm)],[c_21704]) ).
cnf(c_21706,plain,
( ~ ssList(sk1)
| sk5 != sk1 ),
inference(resolve,[status(thm)],[c_4842,c_21705]) ).
cnf(c_6744,plain,
sk5 != sk1,
inference(resolve,[status(thm)],[c_66,c_21706]) ).
cnf(c_10533,plain,
app(nil,sk1) = sk3,
inference(paramod,[status(thm)],[c_60,c_1092]) ).
cnf(c_21707,plain,
( sk1 = sk5
| ~ ssList(A)
| app(A,sk1) != app(A,sk5) ),
inference(resolve,[status(thm)],[c_929,c_4842]) ).
cnf(c_21708,plain,
( sk1 = sk5
| ~ ssList(A)
| app(A,sk5) != app(A,sk1) ),
inference(copy,[status(thm)],[c_21707]) ).
cnf(c_21709,plain,
( sk5 = sk1
| ~ ssList(A)
| app(A,sk5) != app(A,sk1) ),
inference(copy,[status(thm)],[c_21708]) ).
cnf(c_11860,plain,
( ~ ssList(A)
| app(A,sk5) != app(A,sk1) ),
inference(resolve,[status(thm)],[c_6744,c_21709]) ).
cnf(c_12114,plain,
app(nil,sk5) != app(nil,sk1),
inference(resolve,[status(thm)],[c_11860,c_219]) ).
cnf(c_21710,plain,
sk5 != app(nil,sk1),
inference(paramod,[status(thm)],[c_4944,c_12114]) ).
cnf(c_12148,plain,
app(nil,sk1) != sk5,
inference(copy,[status(thm)],[c_21710]) ).
cnf(c_13038,plain,
sk3 != sk5,
inference(paramod,[status(thm)],[c_10533,c_12148]) ).
cnf(c_21711,plain,
( sk3 = sk5
| neq(sk3,sk5) ),
inference(resolve,[status(thm)],[c_1060,c_4842]) ).
cnf(c_13732,plain,
neq(sk3,sk5),
inference(resolve,[status(thm)],[c_13038,c_21711]) ).
cnf(c_21712,plain,
( ~ totalorderedP(sk5)
| ~ segmentP(sk5,sk3)
| ~ segmentP(sk4,sk5)
| ~ ssList(sk5) ),
inference(resolve,[status(thm)],[c_13732,c_56]) ).
cnf(c_21713,plain,
( ~ totalorderedP(sk5)
| ~ segmentP(sk5,sk3)
| ~ segmentP(sk4,sk5) ),
inference(resolve,[status(thm)],[c_4842,c_21712]) ).
cnf(c_13766,plain,
( ~ segmentP(sk5,sk3)
| ~ segmentP(sk4,sk5) ),
inference(resolve,[status(thm)],[c_4838,c_21713]) ).
cnf(c_21714,plain,
( segmentP(sk5,sk3)
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_6385,c_5557]) ).
cnf(c_21673,plain,
segmentP(sk5,sk3),
inference(resolve,[status(thm)],[c_64,c_21714]) ).
cnf(c_21674,plain,
~ segmentP(sk4,sk5),
inference(resolve,[status(thm)],[c_21673,c_13766]) ).
cnf(c_21715,plain,
~ segmentP(sk2,sk5),
inference(paramod,[status(thm)],[c_62,c_21674]) ).
cnf(c_21701,plain,
$false,
inference(resolve,[status(thm)],[c_4840,c_21715]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC333-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.57 % Computer : n009.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.58 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Sat Sep 26 12:49:14 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.58 % Process 162009 was started by sandbox on n009,
% 0.11/0.58 % Sat Sep 26 12:49:14 2026
% 0.11/0.58 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.59
% 0.11/0.59 % From the command line: assign(max_seconds, 300).
% 22.81/6.64
% 22.81/6.64 % given #500 (I,wt=38): 557 app(app(A,cons(B,A)),cons(C,D)) != A | -ssList(D) | -ssList(A) | -ssItem(C) | -ssItem(B) | lt(B,C) | lt(C,B) | -lt(skaf59(A),skaf60(A)). [factor(297,c,f)].
% 22.81/6.64
% 22.81/6.64 % given #1000 (A,wt=20): 874 app(app(A,sk1),A) != B | -ssList(A) | -ssList(B) | segmentP(B,sk1). [factor(850,b,c)].
% 22.81/6.64
% 22.81/6.64 % given #1500 (T,wt=9): 10536 app(nil,sk4) = sk2. [para(62(a,1),1093(a,2))].
% 22.81/6.64
% 22.81/6.64 % given #2000 (F,wt=13): 19424 cons(skac2,cons(skac3,sk2)) != nil. [resolve(19242,a,3358,b)].
% 22.81/6.64
% 22.81/6.64 % SZS status Unsatisfiable for theBenchmark
% 22.81/6.64
% 22.81/6.64 % Proof 1 at 2.33 (+ 0.88) seconds.
% 22.81/6.64 % Length of proof is 52.
% 22.81/6.64 % Level of proof is 13.
% 22.81/6.64 % Maximum clause weight is 20.000.
% 22.81/6.64 % Given clauses 2174.
% 22.81/6.64
% 22.81/6.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------