%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC106-1 : 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 : n018.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 08:56:51 AM UTC 2026
% Result : Unsatisfiable 122.93s 21.01s
% Output : CNFRefutation 122.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 62 ( 27 unt; 0 def)
% Number of atoms : 120 ( 34 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 121 ( 63 ~; 58 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_18,axiom,
( ~ neq(sk4,nil)
| ~ rearsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
file('theBenchmark.p',co1_18) ).
cnf(c_51,plain,
( ~ neq(sk4,nil)
| ~ rearsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(clausify,[status(thm)],[co1_18]) ).
fof(co1_17,axiom,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
file('theBenchmark.p',co1_17) ).
cnf(c_52,plain,
( ~ neq(sk4,nil)
| app(sk6,cons(sk5,nil)) = sk4 ),
inference(clausify,[status(thm)],[co1_17]) ).
fof(co1_16,axiom,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk3 ),
file('theBenchmark.p',co1_16) ).
cnf(c_53,plain,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_16]) ).
fof(co1_15,axiom,
( ~ neq(sk4,nil)
| ssList(sk6) ),
file('theBenchmark.p',co1_15) ).
cnf(c_54,plain,
( ~ neq(sk4,nil)
| ssList(sk6) ),
inference(clausify,[status(thm)],[co1_15]) ).
fof(co1_14,axiom,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('theBenchmark.p',co1_14) ).
cnf(c_55,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_14]) ).
fof(co1_7,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('theBenchmark.p',co1_7) ).
cnf(c_62,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_63,plain,
neq(sk2,nil),
inference(copy,[status(thm)],[c_62]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_64,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
cnf(c_65,plain,
sk3 = sk1,
inference(copy,[status(thm)],[c_64]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_66,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_67,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_66]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_68,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
cnf(c_69,plain,
ssList(sk2),
inference(paramod,[status(thm)],[c_67,c_68]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_70,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
cnf(c_71,plain,
ssList(sk1),
inference(paramod,[status(thm)],[c_65,c_70]) ).
fof(clause143,axiom,
! [VAR_0,VAR_1,VAR_2] :
( rearsegP(VAR_2,VAR_1)
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0)
| app(VAR_0,VAR_1) != VAR_2 ),
file('theBenchmark.p',clause143) ).
cnf(c_106,plain,
( rearsegP(C,B)
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A)
| app(A,B) != C ),
inference(clausify,[status(thm)],[clause143]) ).
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_131,plain,
( singletonP(B)
| ~ ssList(B)
| ~ ssItem(A)
| cons(A,nil) != B ),
inference(clausify,[status(thm)],[clause116]) ).
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_147,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause11,axiom,
~ singletonP(nil),
file('theBenchmark.p',clause11) ).
cnf(c_221,plain,
~ singletonP(nil),
inference(clausify,[status(thm)],[clause11]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_224,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_17491,plain,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk1 ),
inference(paramod,[status(thm)],[c_65,c_53]) ).
cnf(c_17492,plain,
( ~ neq(sk2,nil)
| cons(sk5,nil) = sk1 ),
inference(paramod,[status(thm)],[c_67,c_17491]) ).
cnf(c_328,plain,
cons(sk5,nil) = sk1,
inference(resolve,[status(thm)],[c_63,c_17492]) ).
cnf(c_17493,plain,
( ~ neq(sk2,nil)
| ssItem(sk5) ),
inference(paramod,[status(thm)],[c_67,c_55]) ).
cnf(c_329,plain,
ssItem(sk5),
inference(resolve,[status(thm)],[c_63,c_17493]) ).
cnf(c_17494,plain,
( ~ neq(sk2,nil)
| ssList(sk6) ),
inference(paramod,[status(thm)],[c_67,c_54]) ).
cnf(c_330,plain,
ssList(sk6),
inference(resolve,[status(thm)],[c_63,c_17494]) ).
cnf(c_17495,plain,
( ~ neq(sk4,nil)
| app(sk6,sk1) = sk4 ),
inference(paramod,[status(thm)],[c_328,c_52]) ).
cnf(c_17496,plain,
( ~ neq(sk4,nil)
| app(sk6,sk1) = sk2 ),
inference(paramod,[status(thm)],[c_67,c_17495]) ).
cnf(c_17497,plain,
( ~ neq(sk2,nil)
| app(sk6,sk1) = sk2 ),
inference(paramod,[status(thm)],[c_67,c_17496]) ).
cnf(c_331,plain,
app(sk6,sk1) = sk2,
inference(resolve,[status(thm)],[c_63,c_17497]) ).
cnf(c_17498,plain,
( ~ neq(sk2,nil)
| ~ rearsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(paramod,[status(thm)],[c_67,c_51]) ).
cnf(c_332,plain,
( ~ rearsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(resolve,[status(thm)],[c_63,c_17498]) ).
cnf(c_918,plain,
( rearsegP(B,sk1)
| ~ ssList(B)
| ~ ssList(A)
| app(A,sk1) != B ),
inference(resolve,[status(thm)],[c_106,c_71]) ).
cnf(c_955,plain,
( sk1 = A
| neq(sk1,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_147,c_71]) ).
cnf(c_17499,plain,
( singletonP(A)
| ~ ssList(A)
| cons(sk5,nil) != A ),
inference(resolve,[status(thm)],[c_329,c_131]) ).
cnf(c_10012,plain,
( singletonP(A)
| ~ ssList(A)
| sk1 != A ),
inference(paramod,[status(thm)],[c_328,c_17499]) ).
cnf(c_17500,plain,
( singletonP(nil)
| sk1 != nil ),
inference(resolve,[status(thm)],[c_10012,c_224]) ).
cnf(c_13813,plain,
sk1 != nil,
inference(resolve,[status(thm)],[c_221,c_17500]) ).
cnf(c_17501,plain,
( sk1 = nil
| neq(sk1,nil) ),
inference(resolve,[status(thm)],[c_955,c_224]) ).
cnf(c_14282,plain,
neq(sk1,nil),
inference(resolve,[status(thm)],[c_13813,c_17501]) ).
cnf(c_14310,plain,
~ rearsegP(sk2,sk1),
inference(resolve,[status(thm)],[c_14282,c_332]) ).
cnf(c_17502,plain,
( rearsegP(sk2,sk1)
| ~ ssList(A)
| app(A,sk1) != sk2 ),
inference(resolve,[status(thm)],[c_918,c_69]) ).
cnf(c_17487,plain,
( ~ ssList(A)
| app(A,sk1) != sk2 ),
inference(resolve,[status(thm)],[c_14310,c_17502]) ).
cnf(c_17503,plain,
app(sk6,sk1) != sk2,
inference(resolve,[status(thm)],[c_17487,c_330]) ).
cnf(c_17504,plain,
sk2 != sk2,
inference(paramod,[status(thm)],[c_331,c_17503]) ).
cnf(c_17490,plain,
$false,
inference(copy,[status(thm)],[c_17504]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC106-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.39 % Computer : n018.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Sat Sep 26 12:18:13 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/5.39 % Process 419239 was started by sandbox2 on n018,
% 0.12/5.39 % Sat Sep 26 12:18:13 2026
% 0.12/5.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.41
% 0.17/5.41 % From the command line: assign(max_seconds, 300).
% 122.93/21.01
% 122.93/21.01 % given #500 (I,wt=66): 576 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(307,c,f)].
% 122.93/21.01
% 122.93/21.01 % given #1000 (F,wt=21): 12028 app(sk2,skaf73(A)) != nil. [resolve(944,b,210,a)].
% 122.93/21.01
% 122.93/21.01 % SZS status Unsatisfiable for theBenchmark
% 122.93/21.01
% 122.93/21.01 % Proof 1 at 6.59 (+ 0.66) seconds.
% 122.93/21.01 % Length of proof is 33.
% 122.93/21.01 % Level of proof is 8.
% 122.93/21.01 % Maximum clause weight is 25.000.
% 122.93/21.01 % Given clauses 1065.
% 122.93/21.01
% 122.93/21.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------