%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC352-1 : 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 : n020.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 08:57:34 AM UTC 2026
% Result : Unsatisfiable 21.75s 3.50s
% Output : CNFRefutation 21.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 50 ( 23 unt; 0 def)
% Number of atoms : 95 ( 36 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 89 ( 44 ~; 45 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 13 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_10,axiom,
( frontsegP(sk4,sk3)
| ~ neq(sk4,nil) ),
file('theBenchmark.p',co1_10) ).
cnf(c_51,plain,
( frontsegP(sk4,sk3)
| ~ neq(sk4,nil) ),
inference(clausify,[status(thm)],[co1_10]) ).
fof(co1_8,axiom,
( nil != sk4
| nil = sk3 ),
file('theBenchmark.p',co1_8) ).
cnf(c_53,plain,
( nil != sk4
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_16127,plain,
( nil != sk4
| sk3 = nil ),
inference(copy,[status(thm)],[c_53]) ).
cnf(c_54,plain,
( sk4 != nil
| sk3 = nil ),
inference(copy,[status(thm)],[c_16127]) ).
fof(co1_7,axiom,
~ frontsegP(sk2,sk1),
file('theBenchmark.p',co1_7) ).
cnf(c_55,plain,
~ frontsegP(sk2,sk1),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_56,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_57,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_58,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_2,axiom,
ssList(sk2),
file('theBenchmark.p',co1_2) ).
cnf(c_60,plain,
ssList(sk2),
inference(clausify,[status(thm)],[co1_2]) ).
fof(co1_1,axiom,
ssList(sk1),
file('theBenchmark.p',co1_1) ).
cnf(c_61,plain,
ssList(sk1),
inference(clausify,[status(thm)],[co1_1]) ).
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_122,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_137,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause83,axiom,
! [VAR_0] :
( frontsegP(nil,VAR_0)
| ~ ssList(VAR_0)
| nil != VAR_0 ),
file('theBenchmark.p',clause83) ).
cnf(c_147,plain,
( frontsegP(nil,A)
| ~ ssList(A)
| nil != A ),
inference(clausify,[status(thm)],[clause83]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_214,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_825,plain,
~ frontsegP(sk2,sk3),
inference(paramod,[status(thm)],[c_56,c_55]) ).
cnf(c_16128,plain,
( A = sk4
| neq(A,sk4)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_137,c_58]) ).
cnf(c_1042,plain,
( sk4 = A
| neq(A,sk4)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_16128]) ).
cnf(c_1044,plain,
( sk2 = A
| neq(sk2,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_137,c_60]) ).
cnf(c_16129,plain,
( frontsegP(nil,sk1)
| nil != sk1 ),
inference(resolve,[status(thm)],[c_147,c_61]) ).
cnf(c_1055,plain,
( frontsegP(nil,sk1)
| sk1 != nil ),
inference(copy,[status(thm)],[c_16129]) ).
cnf(c_11486,plain,
~ frontsegP(sk4,sk3),
inference(paramod,[status(thm)],[c_57,c_825]) ).
cnf(c_11487,plain,
~ neq(sk4,nil),
inference(resolve,[status(thm)],[c_11486,c_51]) ).
cnf(c_13660,plain,
( frontsegP(nil,sk1)
| sk3 != nil ),
inference(paramod,[status(thm)],[c_56,c_1055]) ).
cnf(c_15530,plain,
( sk4 = nil
| neq(nil,sk4) ),
inference(resolve,[status(thm)],[c_1042,c_214]) ).
cnf(c_15563,plain,
( sk3 = nil
| neq(nil,sk4) ),
inference(resolve,[status(thm)],[c_15530,c_54]) ).
cnf(c_15649,plain,
( frontsegP(nil,sk1)
| neq(nil,sk4) ),
inference(resolve,[status(thm)],[c_15563,c_13660]) ).
cnf(c_16130,plain,
( ~ ssList(nil)
| ~ ssList(sk4)
| nil != sk4
| frontsegP(nil,sk1) ),
inference(resolve,[status(thm)],[c_15649,c_122]) ).
cnf(c_16131,plain,
( ~ ssList(nil)
| ~ ssList(sk4)
| sk4 != nil
| frontsegP(nil,sk1) ),
inference(copy,[status(thm)],[c_16130]) ).
cnf(c_16132,plain,
( ~ ssList(nil)
| sk4 != nil
| frontsegP(nil,sk1) ),
inference(resolve,[status(thm)],[c_58,c_16131]) ).
cnf(c_15736,plain,
( sk4 != nil
| frontsegP(nil,sk1) ),
inference(resolve,[status(thm)],[c_214,c_16132]) ).
cnf(c_16069,plain,
( sk2 = nil
| neq(sk2,nil) ),
inference(resolve,[status(thm)],[c_1044,c_214]) ).
cnf(c_16133,plain,
( sk2 = nil
| neq(sk4,nil) ),
inference(paramod,[status(thm)],[c_57,c_16069]) ).
cnf(c_16100,plain,
sk2 = nil,
inference(resolve,[status(thm)],[c_11487,c_16133]) ).
cnf(c_16107,plain,
~ frontsegP(nil,sk1),
inference(paramod,[status(thm)],[c_16100,c_55]) ).
cnf(c_16134,plain,
nil = sk4,
inference(paramod,[status(thm)],[c_16100,c_57]) ).
cnf(c_16108,plain,
sk4 = nil,
inference(copy,[status(thm)],[c_16134]) ).
cnf(c_16135,plain,
sk4 != nil,
inference(resolve,[status(thm)],[c_16107,c_15736]) ).
cnf(c_16126,plain,
$false,
inference(resolve,[status(thm)],[c_16108,c_16135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC352-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 12:53:04 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 1617286 was started by sandbox on n020,
% 0.10/0.36 % Sat Sep 26 12:53:04 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 21.75/3.50
% 21.75/3.50 % given #500 (I,wt=66): 561 app(app(A,cons(B,C)),cons(D,A)) != C | -ssList(A) | -ssList(C) | -ssItem(D) | -ssItem(B) | lt(B,D) | lt(D,B) | app(app(skaf61(C),cons(skaf59(C),skaf62(C))),cons(skaf60(C),skaf63(C))) = C. [factor(297,c,f)].
% 21.75/3.50
% 21.75/3.50 % given #1000 (T,wt=11): 15414 neq(nil,sk3) | sk3 = nil. [resolve(1041,a,214,a)].
% 21.75/3.50
% 21.75/3.50 % SZS status Unsatisfiable for theBenchmark
% 21.75/3.50
% 21.75/3.50 % Proof 1 at 2.77 (+ 0.32) seconds.
% 21.75/3.50 % Length of proof is 29.
% 21.75/3.50 % Level of proof is 6.
% 21.75/3.50 % Maximum clause weight is 15.000.
% 21.75/3.50 % Given clauses 1083.
% 21.75/3.50
% 21.75/3.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------