%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC027-1 : 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 : n012.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 08:56:35 AM UTC 2026
% Result : Unsatisfiable 26.86s 14.22s
% Output : CNFRefutation 26.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 56 ( 14 unt; 0 def)
% Number of atoms : 106 ( 61 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 82 ( 32 ~; 50 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 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 : 6 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause11,axiom,
~ singletonP(nil),
file('theBenchmark.p',clause11) ).
cnf(c_52,plain,
~ singletonP(nil),
inference(clausify,[status(thm)],[clause11]) ).
fof(clause71,axiom,
! [VAR_0] :
( ~ ssItem(VAR_0)
| ~ memberP(nil,VAR_0) ),
file('theBenchmark.p',clause71) ).
cnf(c_107,plain,
( ~ ssItem(A)
| ~ memberP(nil,A) ),
inference(clausify,[status(thm)],[clause71]) ).
fof(clause116,axiom,
! [VAR_0,VAR_1] :
( singletonP(VAR_1)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0)
| cons(VAR_0,nil) != VAR_1 ),
file('theBenchmark.p',clause116) ).
cnf(c_139,plain,
( singletonP(B)
| ~ ssList(B)
| ~ ssItem(A)
| cons(A,nil) != B ),
inference(clausify,[status(thm)],[clause116]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_200,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_202,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_203,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_7,axiom,
( nil = sk4
| ssItem(sk5) ),
file('theBenchmark.p',co1_7) ).
cnf(c_204,plain,
( nil = sk4
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_205,plain,
( sk4 = nil
| ssItem(sk5) ),
inference(copy,[status(thm)],[c_204]) ).
fof(co1_8,axiom,
( nil = sk3
| ssItem(sk5) ),
file('theBenchmark.p',co1_8) ).
cnf(c_206,plain,
( nil = sk3
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_207,plain,
( sk3 = nil
| ssItem(sk5) ),
inference(copy,[status(thm)],[c_206]) ).
fof(co1_9,axiom,
( nil = sk4
| cons(sk5,nil) = sk3 ),
file('theBenchmark.p',co1_9) ).
cnf(c_208,plain,
( nil = sk4
| cons(sk5,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_209,plain,
( sk4 = nil
| cons(sk5,nil) = sk3 ),
inference(copy,[status(thm)],[c_208]) ).
fof(co1_10,axiom,
( nil = sk4
| memberP(sk4,sk5) ),
file('theBenchmark.p',co1_10) ).
cnf(c_210,plain,
( nil = sk4
| memberP(sk4,sk5) ),
inference(clausify,[status(thm)],[co1_10]) ).
cnf(c_211,plain,
( sk4 = nil
| memberP(sk4,sk5) ),
inference(copy,[status(thm)],[c_210]) ).
fof(co1_13,axiom,
( nil = sk3
| memberP(sk4,sk5) ),
file('theBenchmark.p',co1_13) ).
cnf(c_216,plain,
( nil = sk3
| memberP(sk4,sk5) ),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_217,plain,
( sk3 = nil
| memberP(sk4,sk5) ),
inference(copy,[status(thm)],[c_216]) ).
fof(co1_15,axiom,
( nil = sk1
| nil = sk2 ),
file('theBenchmark.p',co1_15) ).
cnf(c_220,plain,
( nil = sk1
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_15]) ).
cnf(c_10955,plain,
( nil = sk1
| nil = sk4 ),
inference(paramod,[status(thm)],[c_202,c_220]) ).
cnf(c_10956,plain,
( nil = sk3
| nil = sk4 ),
inference(paramod,[status(thm)],[c_203,c_10955]) ).
cnf(c_10957,plain,
( nil = sk3
| sk4 = nil ),
inference(copy,[status(thm)],[c_10956]) ).
cnf(c_221,plain,
( sk3 = nil
| sk4 = nil ),
inference(copy,[status(thm)],[c_10957]) ).
fof(co1_18,axiom,
( nil != sk2
| nil != sk1 ),
file('theBenchmark.p',co1_18) ).
cnf(c_224,plain,
( nil != sk2
| nil != sk1 ),
inference(clausify,[status(thm)],[co1_18]) ).
cnf(c_10958,plain,
( nil != sk2
| nil != sk3 ),
inference(paramod,[status(thm)],[c_203,c_224]) ).
cnf(c_10959,plain,
( nil != sk4
| nil != sk3 ),
inference(paramod,[status(thm)],[c_202,c_10958]) ).
cnf(c_10960,plain,
( nil != sk4
| sk3 != nil ),
inference(copy,[status(thm)],[c_10959]) ).
cnf(c_225,plain,
( sk4 != nil
| sk3 != nil ),
inference(copy,[status(thm)],[c_10960]) ).
cnf(c_10961,plain,
( singletonP(sk3)
| ~ ssList(sk3)
| ~ ssItem(sk5)
| sk4 = nil ),
inference(resolve,[status(thm)],[c_209,c_139]) ).
cnf(c_7526,plain,
( singletonP(sk3)
| ~ ssItem(sk5)
| sk4 = nil ),
inference(resolve,[status(thm)],[c_200,c_10961]) ).
cnf(c_10962,plain,
( sk3 = nil
| memberP(nil,sk5)
| sk3 = nil ),
inference(paramod,[status(thm)],[c_221,c_217]) ).
cnf(c_7697,plain,
( memberP(nil,sk5)
| sk3 = nil ),
inference(copy,[status(thm)],[c_10962]) ).
cnf(c_7704,plain,
( ssItem(sk5)
| sk4 != nil ),
inference(resolve,[status(thm)],[c_225,c_207]) ).
cnf(c_7705,plain,
( memberP(sk4,sk5)
| sk3 != nil ),
inference(resolve,[status(thm)],[c_225,c_211]) ).
cnf(c_10963,plain,
( ssItem(sk5)
| ssItem(sk5) ),
inference(resolve,[status(thm)],[c_7704,c_205]) ).
cnf(c_10741,plain,
ssItem(sk5),
inference(copy,[status(thm)],[c_10963]) ).
cnf(c_10839,plain,
( singletonP(sk3)
| sk4 = nil ),
inference(resolve,[status(thm)],[c_10741,c_7526]) ).
cnf(c_10940,plain,
~ memberP(nil,sk5),
inference(resolve,[status(thm)],[c_10741,c_107]) ).
cnf(c_10947,plain,
sk3 = nil,
inference(resolve,[status(thm)],[c_10940,c_7697]) ).
cnf(c_10964,plain,
( singletonP(nil)
| sk4 = nil ),
inference(paramod,[status(thm)],[c_10947,c_10839]) ).
cnf(c_10952,plain,
sk4 = nil,
inference(resolve,[status(thm)],[c_52,c_10964]) ).
cnf(c_10965,plain,
( memberP(sk4,sk5)
| nil != nil ),
inference(paramod,[status(thm)],[c_10947,c_7705]) ).
cnf(c_10966,plain,
( memberP(nil,sk5)
| nil != nil ),
inference(paramod,[status(thm)],[c_10952,c_10965]) ).
cnf(c_10967,plain,
memberP(nil,sk5),
inference(copy,[status(thm)],[c_10966]) ).
cnf(c_10954,plain,
$false,
inference(resolve,[status(thm)],[c_10940,c_10967]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC027-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/10.33 % Computer : n012.cluster.edu
% 0.04/10.33 % Model : x86_64 x86_64
% 0.04/10.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/10.33 % Memory : 8046.5625MB
% 0.04/10.33 % OS : Linux 6.8.0-71-generic
% 0.04/10.33 % CPULimit : 300
% 0.04/10.33 % WCLimit : 300
% 0.04/10.33 % DateTime : Sat Sep 26 12:05:35 UTC 2026
% 0.04/10.33 % CPUTime :
% 0.04/10.33 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/10.33 % Process 536202 was started by sandbox2 on n012,
% 0.04/10.33 % Sat Sep 26 12:05:35 2026
% 0.04/10.33 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.04/10.34
% 0.04/10.34 % From the command line: assign(max_seconds, 300).
% 26.86/14.22
% 26.86/14.22 % given #500 (I,wt=72): 566 app(A,cons(app(skaf80(A),cons(skaf78(A),cons(skaf79(A),skaf81(A)))),cons(A,B))) != A | -ssList(B) | -ssList(A) | -ssItem(A) | -ssItem(app(skaf80(A),cons(skaf78(A),cons(skaf79(A),skaf81(A))))) | app(skaf80(A),cons(skaf78(A),cons(skaf79(A),skaf81(A)))) = A. [factor(377,f,g)].
% 26.86/14.22
% 26.86/14.22 % SZS status Unsatisfiable for theBenchmark
% 26.86/14.22
% 26.86/14.22 % Proof 1 at 2.94 (+ 0.88) seconds.
% 26.86/14.22 % Length of proof is 30.
% 26.86/14.22 % Level of proof is 7.
% 26.86/14.22 % Maximum clause weight is 15.000.
% 26.86/14.22 % Given clauses 822.
% 26.86/14.22
% 26.86/14.22 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------