%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC101-1 : 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 : n008.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 08:56:50 AM UTC 2026
% Result : Unsatisfiable 47.93s 7.93s
% Output : CNFRefutation 47.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 55 ( 20 unt; 0 def)
% Number of atoms : 112 ( 44 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 123 ( 66 ~; 57 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_13,axiom,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
file('theBenchmark.p',co1_13) ).
cnf(c_53,plain,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(clausify,[status(thm)],[co1_13]) ).
fof(co1_12,axiom,
( nil != sk1
| nil != sk2 ),
file('theBenchmark.p',co1_12) ).
cnf(c_54,plain,
( nil != sk1
| nil != sk2 ),
inference(clausify,[status(thm)],[co1_12]) ).
cnf(c_19127,plain,
( nil != sk1
| sk2 != nil ),
inference(copy,[status(thm)],[c_54]) ).
cnf(c_55,plain,
( sk1 != nil
| sk2 != nil ),
inference(copy,[status(thm)],[c_19127]) ).
fof(co1_11,axiom,
( nil != sk3
| nil = sk4 ),
file('theBenchmark.p',co1_11) ).
cnf(c_56,plain,
( nil != sk3
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_11]) ).
cnf(c_19128,plain,
( nil != sk3
| sk4 = nil ),
inference(copy,[status(thm)],[c_56]) ).
cnf(c_57,plain,
( sk3 != nil
| sk4 = nil ),
inference(copy,[status(thm)],[c_19128]) ).
fof(co1_8,axiom,
app(sk3,sk5) = sk4,
file('theBenchmark.p',co1_8) ).
cnf(c_59,plain,
app(sk3,sk5) = sk4,
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
ssList(sk5),
file('theBenchmark.p',co1_7) ).
cnf(c_60,plain,
ssList(sk5),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_61,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_62,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_63,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_64,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(clause144,axiom,
! [VAR_0,VAR_1,VAR_2] :
( frontsegP(VAR_2,VAR_0)
| ~ ssList(VAR_2)
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| app(VAR_0,VAR_1) != VAR_2 ),
file('theBenchmark.p',clause144) ).
cnf(c_100,plain,
( frontsegP(C,A)
| ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| app(A,B) != C ),
inference(clausify,[status(thm)],[clause144]) ).
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(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_219,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_19129,plain,
( sk1 != nil
| sk4 != nil ),
inference(paramod,[status(thm)],[c_62,c_55]) ).
cnf(c_327,plain,
( sk3 != nil
| sk4 != nil ),
inference(paramod,[status(thm)],[c_61,c_19129]) ).
cnf(c_19130,plain,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk3,nil) ),
inference(paramod,[status(thm)],[c_61,c_53]) ).
cnf(c_19131,plain,
( ~ frontsegP(sk4,sk1)
| ~ neq(sk3,nil) ),
inference(paramod,[status(thm)],[c_62,c_19130]) ).
cnf(c_328,plain,
( ~ frontsegP(sk4,sk3)
| ~ neq(sk3,nil) ),
inference(paramod,[status(thm)],[c_61,c_19131]) ).
cnf(c_19132,plain,
( frontsegP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ ssList(sk5) ),
inference(resolve,[status(thm)],[c_100,c_59]) ).
cnf(c_19133,plain,
( frontsegP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_60,c_19132]) ).
cnf(c_19134,plain,
( frontsegP(sk4,sk3)
| ~ ssList(sk4) ),
inference(resolve,[status(thm)],[c_64,c_19133]) ).
cnf(c_1136,plain,
frontsegP(sk4,sk3),
inference(resolve,[status(thm)],[c_63,c_19134]) ).
cnf(c_1148,plain,
~ neq(sk3,nil),
inference(resolve,[status(thm)],[c_1136,c_328]) ).
cnf(c_19135,plain,
( ~ ssList(A)
| ~ neq(A,sk3)
| A != sk3 ),
inference(resolve,[status(thm)],[c_127,c_64]) ).
cnf(c_1303,plain,
( ~ ssList(A)
| ~ neq(A,sk3)
| sk3 != A ),
inference(copy,[status(thm)],[c_19135]) ).
cnf(c_19136,plain,
( A = sk3
| neq(A,sk3)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_142,c_64]) ).
cnf(c_1324,plain,
( sk3 = A
| neq(A,sk3)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_19136]) ).
cnf(c_1327,plain,
( sk3 = A
| neq(sk3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_142,c_64]) ).
cnf(c_12715,plain,
( ~ neq(nil,sk3)
| sk3 != nil ),
inference(resolve,[status(thm)],[c_1303,c_219]) ).
cnf(c_14984,plain,
( sk3 = nil
| neq(nil,sk3) ),
inference(resolve,[status(thm)],[c_1324,c_219]) ).
cnf(c_15017,plain,
( sk4 != nil
| neq(nil,sk3) ),
inference(resolve,[status(thm)],[c_14984,c_327]) ).
cnf(c_15020,plain,
( sk4 = nil
| neq(nil,sk3) ),
inference(resolve,[status(thm)],[c_14984,c_57]) ).
cnf(c_19137,plain,
( neq(nil,sk3)
| neq(nil,sk3) ),
inference(resolve,[status(thm)],[c_15020,c_15017]) ).
cnf(c_15459,plain,
neq(nil,sk3),
inference(copy,[status(thm)],[c_19137]) ).
cnf(c_15462,plain,
sk3 != nil,
inference(resolve,[status(thm)],[c_15459,c_12715]) ).
cnf(c_19138,plain,
( sk3 = nil
| neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_1327,c_219]) ).
cnf(c_19139,plain,
sk3 = nil,
inference(resolve,[status(thm)],[c_1148,c_19138]) ).
cnf(c_19126,plain,
$false,
inference(resolve,[status(thm)],[c_15462,c_19139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC101-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.97 % Computer : n008.cluster.edu
% 0.11/0.97 % Model : x86_64 x86_64
% 0.11/0.97 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.97 % Memory : 8046.5625MB
% 0.11/0.97 % OS : Linux 6.8.0-71-generic
% 0.11/0.97 % CPULimit : 300
% 0.11/0.97 % WCLimit : 300
% 0.11/0.97 % DateTime : Sat Sep 26 12:15:56 UTC 2026
% 0.11/0.97 % CPUTime :
% 0.11/0.97 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.97 % Process 3631451 was started by sandbox2 on n008,
% 0.11/0.97 % Sat Sep 26 12:15:56 2026
% 0.11/0.97 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.98
% 0.11/0.98 % From the command line: assign(max_seconds, 300).
% 47.93/7.93
% 47.93/7.93 % given #500 (I,wt=37): 563 app(app(A,cons(B,C)),cons(B,D)) != D | -ssList(D) | -ssList(C) | -ssList(A) | -ssItem(B) | lt(B,B) | -lt(skaf59(D),skaf60(D)). [factor(296,e,f),merge(g)].
% 47.93/7.93
% 47.93/7.93 % given #1000 (A,wt=20): 880 app(sk5,cons(A,B)) != B | -ssList(B) | -ssItem(A) | memberP(B,A). [factor(870,b,d)].
% 47.93/7.93
% 47.93/7.93 % given #1500 (T,wt=8): 16255 rearsegP(sk4,sk3) | sk4 != sk3. [resolve(15119,a,12743,b)].
% 47.93/7.93
% 47.93/7.93 % SZS status Unsatisfiable for theBenchmark
% 47.93/7.93
% 47.93/7.93 % Proof 1 at 5.05 (+ 1.75) seconds.
% 47.93/7.93 % Length of proof is 29.
% 47.93/7.93 % Level of proof is 6.
% 47.93/7.93 % Maximum clause weight is 18.000.
% 47.93/7.93 % Given clauses 1820.
% 47.93/7.93
% 47.93/7.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------