%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC112-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 08:56:52 AM UTC 2026
% Result : Unsatisfiable 220.54s 44.64s
% Output : CNFRefutation 220.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 70 ( 29 unt; 0 def)
% Number of atoms : 149 ( 54 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 157 ( 78 ~; 79 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_16,axiom,
( neq(sk2,nil)
| nil != sk1 ),
file('theBenchmark.p',co1_16) ).
cnf(c_53,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(clausify,[status(thm)],[co1_16]) ).
cnf(c_54,plain,
( neq(sk2,nil)
| sk1 != nil ),
inference(copy,[status(thm)],[c_53]) ).
fof(co1_15,axiom,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ),
file('theBenchmark.p',co1_15) ).
cnf(c_55,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_15]) ).
cnf(c_56,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil)
| sk2 = nil ),
inference(copy,[status(thm)],[c_55]) ).
fof(co1_13,axiom,
( nil != sk3
| nil = sk4 ),
file('theBenchmark.p',co1_13) ).
cnf(c_59,plain,
( nil != sk3
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_6805,plain,
( nil != sk3
| sk4 = nil ),
inference(copy,[status(thm)],[c_59]) ).
cnf(c_60,plain,
( sk3 != nil
| sk4 = nil ),
inference(copy,[status(thm)],[c_6805]) ).
fof(co1_9,axiom,
app(app(sk5,sk3),sk6) = sk4,
file('theBenchmark.p',co1_9) ).
cnf(c_64,plain,
app(app(sk5,sk3),sk6) = sk4,
inference(clausify,[status(thm)],[co1_9]) ).
fof(co1_8,axiom,
ssList(sk6),
file('theBenchmark.p',co1_8) ).
cnf(c_65,plain,
ssList(sk6),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
ssList(sk5),
file('theBenchmark.p',co1_7) ).
cnf(c_66,plain,
ssList(sk5),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_67,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
cnf(c_68,plain,
sk3 = sk1,
inference(copy,[status(thm)],[c_67]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_69,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_70,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_69]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_71,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
cnf(c_72,plain,
ssList(sk2),
inference(paramod,[status(thm)],[c_70,c_71]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_73,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
cnf(c_74,plain,
ssList(sk1),
inference(paramod,[status(thm)],[c_68,c_73]) ).
fof(clause173,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( segmentP(VAR_3,VAR_1)
| ~ ssList(VAR_3)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0)
| ~ ssList(VAR_2)
| app(app(VAR_0,VAR_1),VAR_2) != VAR_3 ),
file('theBenchmark.p',clause173) ).
cnf(c_82,plain,
( segmentP(D,B)
| ~ ssList(D)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != D ),
inference(clausify,[status(thm)],[clause173]) ).
fof(clause127,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| ~ ssList(VAR_1)
| ~ ssList(VAR_0)
| ~ segmentP(VAR_1,VAR_0)
| ~ segmentP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause127) ).
cnf(c_124,plain,
( B = A
| ~ ssList(B)
| ~ ssList(A)
| ~ segmentP(B,A)
| ~ segmentP(A,B) ),
inference(clausify,[status(thm)],[clause127]) ).
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_135,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_150,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause56,axiom,
! [VAR_0] :
( segmentP(VAR_0,nil)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause56) ).
cnf(c_179,plain,
( segmentP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause56]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_227,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_6806,plain,
app(app(sk5,sk1),sk6) = sk4,
inference(paramod,[status(thm)],[c_68,c_64]) ).
cnf(c_333,plain,
app(app(sk5,sk1),sk6) = sk2,
inference(paramod,[status(thm)],[c_70,c_6806]) ).
cnf(c_6807,plain,
( sk3 != nil
| sk2 = nil ),
inference(paramod,[status(thm)],[c_70,c_60]) ).
cnf(c_337,plain,
( sk1 != nil
| sk2 = nil ),
inference(paramod,[status(thm)],[c_68,c_6807]) ).
cnf(c_6808,plain,
( ~ ssList(A)
| ~ neq(A,A)
| A != A ),
inference(factor,[status(thm)],[c_135]) ).
cnf(c_402,plain,
( ~ ssList(A)
| ~ neq(A,A) ),
inference(copy,[status(thm)],[c_6808]) ).
cnf(c_1245,plain,
( sk1 = A
| neq(sk1,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_150,c_74]) ).
cnf(c_1347,plain,
segmentP(sk1,nil),
inference(resolve,[status(thm)],[c_179,c_74]) ).
cnf(c_6809,plain,
( segmentP(sk2,sk1)
| ~ ssList(sk2)
| ~ ssList(sk1)
| ~ ssList(sk5)
| ~ ssList(sk6) ),
inference(resolve,[status(thm)],[c_333,c_82]) ).
cnf(c_6810,plain,
( segmentP(sk2,sk1)
| ~ ssList(sk2)
| ~ ssList(sk1)
| ~ ssList(sk5) ),
inference(resolve,[status(thm)],[c_65,c_6809]) ).
cnf(c_6811,plain,
( segmentP(sk2,sk1)
| ~ ssList(sk2)
| ~ ssList(sk1) ),
inference(resolve,[status(thm)],[c_66,c_6810]) ).
cnf(c_6812,plain,
( segmentP(sk2,sk1)
| ~ ssList(sk2) ),
inference(resolve,[status(thm)],[c_74,c_6811]) ).
cnf(c_4722,plain,
segmentP(sk2,sk1),
inference(resolve,[status(thm)],[c_72,c_6812]) ).
cnf(c_4723,plain,
( ~ neq(sk1,nil)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_4722,c_56]) ).
cnf(c_5350,plain,
~ neq(nil,nil),
inference(resolve,[status(thm)],[c_402,c_227]) ).
cnf(c_6813,plain,
( sk2 = sk1
| ~ ssList(sk2)
| ~ ssList(sk1)
| ~ segmentP(sk1,sk2) ),
inference(resolve,[status(thm)],[c_4722,c_124]) ).
cnf(c_6814,plain,
( sk1 = sk2
| ~ ssList(sk2)
| ~ ssList(sk1)
| ~ segmentP(sk1,sk2) ),
inference(copy,[status(thm)],[c_6813]) ).
cnf(c_6815,plain,
( sk1 = sk2
| ~ ssList(sk2)
| ~ segmentP(sk1,sk2) ),
inference(resolve,[status(thm)],[c_74,c_6814]) ).
cnf(c_5867,plain,
( sk1 = sk2
| ~ segmentP(sk1,sk2) ),
inference(resolve,[status(thm)],[c_72,c_6815]) ).
cnf(c_6640,plain,
( sk1 = nil
| neq(sk1,nil) ),
inference(resolve,[status(thm)],[c_1245,c_227]) ).
cnf(c_6668,plain,
( sk2 = nil
| sk1 = nil ),
inference(resolve,[status(thm)],[c_6640,c_4723]) ).
cnf(c_6816,plain,
( sk2 = nil
| sk2 = nil ),
inference(resolve,[status(thm)],[c_6668,c_337]) ).
cnf(c_6682,plain,
sk2 = nil,
inference(copy,[status(thm)],[c_6816]) ).
cnf(c_6817,plain,
( sk1 = sk2
| ~ segmentP(sk1,nil) ),
inference(paramod,[status(thm)],[c_6682,c_5867]) ).
cnf(c_6818,plain,
( sk1 = nil
| ~ segmentP(sk1,nil) ),
inference(paramod,[status(thm)],[c_6682,c_6817]) ).
cnf(c_6791,plain,
sk1 = nil,
inference(resolve,[status(thm)],[c_1347,c_6818]) ).
cnf(c_6819,plain,
( neq(sk2,nil)
| nil != nil ),
inference(paramod,[status(thm)],[c_6791,c_54]) ).
cnf(c_6820,plain,
( neq(nil,nil)
| nil != nil ),
inference(paramod,[status(thm)],[c_6682,c_6819]) ).
cnf(c_6821,plain,
neq(nil,nil),
inference(copy,[status(thm)],[c_6820]) ).
cnf(c_6804,plain,
$false,
inference(resolve,[status(thm)],[c_5350,c_6821]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC112-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/15.55 % Computer : n019.cluster.edu
% 0.09/15.55 % Model : x86_64 x86_64
% 0.09/15.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/15.55 % Memory : 8046.5625MB
% 0.09/15.55 % OS : Linux 6.8.0-71-generic
% 0.09/15.55 % CPULimit : 300
% 0.09/15.55 % WCLimit : 300
% 0.09/15.55 % DateTime : Sat Sep 26 12:17:06 UTC 2026
% 0.09/15.55 % CPUTime :
% 0.09/15.55 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/15.55 % Process 1271947 was started by sandbox2 on n019,
% 0.09/15.55 % Sat Sep 26 12:17:06 2026
% 0.09/15.55 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/15.56
% 0.09/15.56 % From the command line: assign(max_seconds, 300).
% 220.54/44.64
% 220.54/44.64 % given #500 (I,wt=49): 562 app(app(A,cons(B,C)),cons(B,D)) != A | -ssList(D) | -ssList(C) | -ssList(A) | -ssItem(B) | lt(B,B) | -lt(skaf60(A),skaf59(A)). [factor(300,e,f),merge(g)].
% 220.54/44.64
% 220.54/44.64 % SZS status Unsatisfiable for theBenchmark
% 220.54/44.64
% 220.54/44.64 % Proof 1 at 3.42 (+ 1.34) seconds.
% 220.54/44.64 % Length of proof is 37.
% 220.54/44.64 % Level of proof is 8.
% 220.54/44.64 % Maximum clause weight is 35.000.
% 220.54/44.64 % Given clauses 934.
% 220.54/44.64
% 220.54/44.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------