%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC094-1 : 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 : n016.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 08:56:48 AM UTC 2026
% Result : Unsatisfiable 34.57s 5.01s
% Output : CNFRefutation 34.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 15 unt; 0 def)
% Number of atoms : 60 ( 31 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 75 ( 43 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_49,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
fof(clause73,axiom,
! [VAR_0] :
( app(VAR_0,nil) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause73) ).
cnf(c_108,plain,
( app(A,nil) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause73]) ).
fof(clause74,axiom,
! [VAR_0] :
( app(nil,VAR_0) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause74) ).
cnf(c_109,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause74]) ).
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,
sk4 = sk3,
file('theBenchmark.p',co1_7) ).
cnf(c_204,plain,
sk4 = sk3,
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_8,axiom,
! [VAR_0,VAR_1,VAR_2] :
( app(VAR_0,VAR_2) != sk2
| app(app(VAR_0,VAR_1),VAR_2) != sk1
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',co1_8) ).
cnf(c_205,plain,
( app(A,C) != sk2
| app(app(A,B),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_11663,plain,
( app(A,C) != sk2
| app(app(A,B),C) != sk3
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_203,c_205]) ).
cnf(c_11664,plain,
( app(A,C) != sk4
| app(app(A,B),C) != sk3
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_202,c_11663]) ).
cnf(c_206,plain,
( app(A,C) != sk3
| app(app(A,B),C) != sk3
| ~ ssList(C)
| ~ ssList(B)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_204,c_11664]) ).
cnf(c_357,plain,
( app(A,B) != sk3
| app(app(A,A),B) != sk3
| ~ ssList(B)
| ~ ssList(A) ),
inference(factor,[status(thm)],[c_206]) ).
cnf(c_1111,plain,
app(nil,nil) = nil,
inference(resolve,[status(thm)],[c_108,c_49]) ).
cnf(c_7065,plain,
app(nil,sk3) = sk3,
inference(resolve,[status(thm)],[c_200,c_109]) ).
cnf(c_11665,plain,
( app(nil,A) != sk3
| app(app(nil,nil),A) != sk3
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_357,c_49]) ).
cnf(c_11666,plain,
( app(nil,A) != sk3
| app(nil,A) != sk3
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_1111,c_11665]) ).
cnf(c_9710,plain,
( app(nil,A) != sk3
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_11666]) ).
cnf(c_11667,plain,
app(nil,sk3) != sk3,
inference(resolve,[status(thm)],[c_9710,c_200]) ).
cnf(c_11668,plain,
sk3 != sk3,
inference(paramod,[status(thm)],[c_7065,c_11667]) ).
cnf(c_11662,plain,
$false,
inference(copy,[status(thm)],[c_11668]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC094-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.54 % Computer : n016.cluster.edu
% 0.09/0.54 % Model : x86_64 x86_64
% 0.09/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.54 % Memory : 8046.5625MB
% 0.09/0.54 % OS : Linux 6.8.0-71-generic
% 0.09/0.54 % CPULimit : 300
% 0.09/0.54 % WCLimit : 300
% 0.09/0.54 % DateTime : Sat Sep 26 12:18:48 UTC 2026
% 0.09/0.54 % CPUTime :
% 0.09/0.54 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.54 % Process 844204 was started by sandbox on n016,
% 0.09/0.54 % Sat Sep 26 12:18:48 2026
% 0.09/0.54 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.55
% 0.09/0.55 % From the command line: assign(max_seconds, 300).
% 34.57/5.01
% 34.57/5.01 % given #500 (I,wt=40): 557 app(A,cons(B,cons(C,cons(C,nil)))) != cons(C,nil) | -ssList(cons(C,nil)) | -ssList(A) | -ssItem(C) | -ssItem(B) | B = C. [factor(368,d,g)].
% 34.57/5.01
% 34.57/5.01 % given #1000 (F,wt=11): 9710 -ssList(A) | app(nil,A) != sk3. [resolve(357,a,49,a),rewrite([1111(4)]),merge(c)].
% 34.57/5.01
% 34.57/5.01 % SZS status Unsatisfiable for theBenchmark
% 34.57/5.01
% 34.57/5.01 % Proof 1 at 3.41 (+ 0.98) seconds.
% 34.57/5.01 % Length of proof is 14.
% 34.57/5.01 % Level of proof is 4.
% 34.57/5.01 % Maximum clause weight is 26.000.
% 34.57/5.01 % Given clauses 1000.
% 34.57/5.01
% 34.57/5.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------