%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC189-1 : 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 : n005.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 08:57:06 AM UTC 2026
% Result : Unsatisfiable 17.24s 7.93s
% Output : CNFRefutation 17.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 18 unt; 0 def)
% Number of atoms : 55 ( 20 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 61 ( 32 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_204,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
cnf(c_205,plain,
sk3 = sk1,
inference(copy,[status(thm)],[c_204]) ).
fof(co1_7,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( app(app(app(VAR_2,cons(VAR_0,nil)),cons(VAR_1,nil)),VAR_3) != sk3
| VAR_0 = VAR_1
| ~ ssList(VAR_3)
| ~ ssList(VAR_2)
| ~ ssItem(VAR_1)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_7) ).
cnf(c_206,plain,
( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk3
| A = B
| ~ ssList(D)
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_207,plain,
( app(app(app(C,cons(A,nil)),cons(B,nil)),D) != sk1
| A = B
| ~ ssList(D)
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_205,c_206]) ).
fof(co1_8,axiom,
ssItem(sk5),
file('theBenchmark.p',co1_8) ).
cnf(c_208,plain,
ssItem(sk5),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_9,axiom,
ssItem(sk6),
file('theBenchmark.p',co1_9) ).
cnf(c_209,plain,
ssItem(sk6),
inference(clausify,[status(thm)],[co1_9]) ).
fof(co1_10,axiom,
ssList(sk7),
file('theBenchmark.p',co1_10) ).
cnf(c_210,plain,
ssList(sk7),
inference(clausify,[status(thm)],[co1_10]) ).
fof(co1_11,axiom,
ssList(sk8),
file('theBenchmark.p',co1_11) ).
cnf(c_211,plain,
ssList(sk8),
inference(clausify,[status(thm)],[co1_11]) ).
fof(co1_12,axiom,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1,
file('theBenchmark.p',co1_12) ).
cnf(c_212,plain,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1,
inference(clausify,[status(thm)],[co1_12]) ).
fof(co1_13,axiom,
sk5 != sk6,
file('theBenchmark.p',co1_13) ).
cnf(c_213,plain,
sk5 != sk6,
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_214,plain,
sk6 != sk5,
inference(copy,[status(thm)],[c_213]) ).
cnf(c_7832,plain,
( sk5 = sk6
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6)
| ~ ssItem(sk5) ),
inference(resolve,[status(thm)],[c_212,c_207]) ).
cnf(c_7833,plain,
( sk6 = sk5
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6)
| ~ ssItem(sk5) ),
inference(copy,[status(thm)],[c_7832]) ).
cnf(c_7834,plain,
( sk6 = sk5
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolve,[status(thm)],[c_208,c_7833]) ).
cnf(c_7835,plain,
( sk6 = sk5
| ~ ssList(sk8)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_209,c_7834]) ).
cnf(c_7836,plain,
( sk6 = sk5
| ~ ssList(sk8) ),
inference(resolve,[status(thm)],[c_210,c_7835]) ).
cnf(c_7837,plain,
sk6 = sk5,
inference(resolve,[status(thm)],[c_211,c_7836]) ).
cnf(c_7831,plain,
$false,
inference(resolve,[status(thm)],[c_214,c_7837]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC189-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n005.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Sat Sep 26 12:27:52 UTC 2026
% 0.16/5.44 % CPUTime :
% 0.16/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.45 % Process 2131943 was started by sandbox2 on n005,
% 0.16/5.45 % Sat Sep 26 12:27:52 2026
% 0.16/5.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.46
% 0.16/5.46 % From the command line: assign(max_seconds, 300).
% 17.24/7.93
% 17.24/7.93 % SZS status Unsatisfiable for theBenchmark
% 17.24/7.93
% 17.24/7.93 % Proof 1 at 1.91 (+ 0.37) seconds.
% 17.24/7.93 % Length of proof is 12.
% 17.24/7.93 % Level of proof is 3.
% 17.24/7.93 % Maximum clause weight is 38.000.
% 17.24/7.93 % Given clauses 167.
% 17.24/7.93
% 17.24/7.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------