%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC293-1 : 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 : 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 08:57:24 AM UTC 2026
% Result : Unsatisfiable 48.50s 7.32s
% Output : CNFRefutation 48.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 11 unt; 0 def)
% Number of atoms : 56 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 11 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 4 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause3,axiom,
strictorderedP(nil),
file('theBenchmark.p',clause3) ).
cnf(c_47,plain,
strictorderedP(nil),
inference(clausify,[status(thm)],[clause3]) ).
fof(clause66,axiom,
! [VAR_0] :
( strictorderedP(cons(VAR_0,nil))
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',clause66) ).
cnf(c_105,plain,
( strictorderedP(cons(A,nil))
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[clause66]) ).
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(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,
~ strictorderedP(sk1),
file('theBenchmark.p',co1_7) ).
cnf(c_204,plain,
~ strictorderedP(sk1),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_8,axiom,
( nil = sk4
| ssItem(sk5) ),
file('theBenchmark.p',co1_8) ).
cnf(c_205,plain,
( nil = sk4
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_206,plain,
( sk4 = nil
| ssItem(sk5) ),
inference(copy,[status(thm)],[c_205]) ).
fof(co1_9,axiom,
( nil = sk3
| ssItem(sk5) ),
file('theBenchmark.p',co1_9) ).
cnf(c_207,plain,
( nil = sk3
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_208,plain,
( sk3 = nil
| ssItem(sk5) ),
inference(copy,[status(thm)],[c_207]) ).
fof(co1_10,axiom,
( nil = sk4
| cons(sk5,nil) = sk3 ),
file('theBenchmark.p',co1_10) ).
cnf(c_209,plain,
( nil = sk4
| cons(sk5,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_10]) ).
cnf(c_210,plain,
( sk4 = nil
| cons(sk5,nil) = sk3 ),
inference(copy,[status(thm)],[c_209]) ).
fof(co1_13,axiom,
( nil = sk3
| memberP(sk4,sk5) ),
file('theBenchmark.p',co1_13) ).
cnf(c_215,plain,
( nil = sk3
| memberP(sk4,sk5) ),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_216,plain,
( sk3 = nil
| memberP(sk4,sk5) ),
inference(copy,[status(thm)],[c_215]) ).
cnf(c_6733,plain,
~ strictorderedP(sk3),
inference(paramod,[status(thm)],[c_203,c_204]) ).
cnf(c_6752,plain,
( strictorderedP(cons(sk5,nil))
| sk4 = nil ),
inference(resolve,[status(thm)],[c_206,c_105]) ).
cnf(c_22024,plain,
( strictorderedP(sk3)
| sk4 = nil
| sk4 = nil ),
inference(paramod,[status(thm)],[c_210,c_6752]) ).
cnf(c_22025,plain,
( strictorderedP(sk3)
| sk4 = nil ),
inference(copy,[status(thm)],[c_22024]) ).
cnf(c_21739,plain,
sk4 = nil,
inference(resolve,[status(thm)],[c_6733,c_22025]) ).
cnf(c_21765,plain,
( sk3 = nil
| memberP(nil,sk5) ),
inference(paramod,[status(thm)],[c_21739,c_216]) ).
cnf(c_21996,plain,
( ~ ssItem(sk5)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_21765,c_107]) ).
cnf(c_22026,plain,
( sk3 = nil
| sk3 = nil ),
inference(resolve,[status(thm)],[c_21996,c_208]) ).
cnf(c_21997,plain,
sk3 = nil,
inference(copy,[status(thm)],[c_22026]) ).
cnf(c_22027,plain,
~ strictorderedP(nil),
inference(paramod,[status(thm)],[c_21997,c_6733]) ).
cnf(c_22023,plain,
$false,
inference(resolve,[status(thm)],[c_47,c_22027]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC293-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.29 % Computer : n012.cluster.edu
% 0.04/0.29 % Model : x86_64 x86_64
% 0.04/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.29 % Memory : 8046.5625MB
% 0.04/0.29 % OS : Linux 6.8.0-71-generic
% 0.04/0.29 % CPULimit : 300
% 0.04/0.29 % WCLimit : 300
% 0.04/0.29 % DateTime : Sat Sep 26 12:42:37 UTC 2026
% 0.04/0.29 % CPUTime :
% 0.04/0.29 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.29 % Process 621328 was started by sandbox on n012,
% 0.04/0.29 % Sat Sep 26 12:42:37 2026
% 0.04/0.29 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.04/0.30
% 0.04/0.30 % From the command line: assign(max_seconds, 300).
% 48.50/7.32
% 48.50/7.32 % given #500 (I,wt=70): 570 app(app(A,cons(B,C)),cons(D,A)) != A | -ssList(A) | -ssList(C) | -ssItem(D) | -ssItem(B) | lt(B,D) | lt(D,B) | app(app(skaf61(A),cons(skaf59(A),skaf62(A))),cons(skaf60(A),skaf63(A))) = A. [factor(380,b,f)].
% 48.50/7.32
% 48.50/7.32 % given #1000 (T,wt=13): 13482 -rearsegP(sk4,A) | -ssList(A) | rearsegP(sk2,A). [resolve(12845,a,173,a),unit_del(c,201),unit_del(d,199)].
% 48.50/7.32
% 48.50/7.32 % given #1500 (A,wt=62): 1021 -ssList(A) | app(app(skaf75(A),cons(skaf74(A),skaf76(A))),cons(skaf74(A),skaf77(A))) = A | app(app(B,cons(skac2,C)),cons(skac2,A)) != A | -ssList(C) | -ssList(B). [factor(1012,a,d)].
% 48.50/7.32
% 48.50/7.32 % given #2000 (F,wt=22): 21705 cons(skaf60(A),skaf68(B)) != nil. [resolve(4668,b,68,a)].
% 48.50/7.32
% 48.50/7.32 % SZS status Unsatisfiable for theBenchmark
% 48.50/7.32
% 48.50/7.32 % Proof 1 at 6.32 (+ 0.63) seconds.
% 48.50/7.32 % Length of proof is 20.
% 48.50/7.32 % Level of proof is 7.
% 48.50/7.32 % Maximum clause weight is 18.000.
% 48.50/7.32 % Given clauses 2004.
% 48.50/7.32
% 48.50/7.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------