%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC346-1 : 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 : 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 08:57:32 AM UTC 2026
% Result : Unsatisfiable 37.59s 5.13s
% Output : CNFRefutation 37.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 16
% Syntax : Number of formulae : 77 ( 24 unt; 0 def)
% Number of atoms : 163 ( 40 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 153 ( 67 ~; 86 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause3,axiom,
strictorderedP(nil),
file('theBenchmark.p',clause3) ).
cnf(c_47,plain,
strictorderedP(nil),
inference(clausify,[status(thm)],[clause3]) ).
fof(clause11,axiom,
~ singletonP(nil),
file('theBenchmark.p',clause11) ).
cnf(c_52,plain,
~ singletonP(nil),
inference(clausify,[status(thm)],[clause11]) ).
fof(clause56,axiom,
! [VAR_0] :
( segmentP(VAR_0,nil)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause56) ).
cnf(c_97,plain,
( segmentP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause56]) ).
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(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_139,plain,
( singletonP(B)
| ~ ssList(B)
| ~ ssItem(A)
| cons(A,nil) != B ),
inference(clausify,[status(thm)],[clause116]) ).
fof(clause173,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( segmentP(VAR_3,VAR_1)
| ~ ssList(VAR_3)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0)
| ~ ssList(VAR_2)
| app(app(VAR_0,VAR_1),VAR_2) != VAR_3 ),
file('theBenchmark.p',clause173) ).
cnf(c_190,plain,
( segmentP(D,B)
| ~ ssList(D)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != D ),
inference(clausify,[status(thm)],[clause173]) ).
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_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_201,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
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_8,axiom,
( nil = sk3
| ssItem(sk5) ),
file('theBenchmark.p',co1_8) ).
cnf(c_206,plain,
( nil = sk3
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_207,plain,
( sk3 = nil
| ssItem(sk5) ),
inference(copy,[status(thm)],[c_206]) ).
fof(co1_15,axiom,
( nil = sk3
| ssList(sk6) ),
file('theBenchmark.p',co1_15) ).
cnf(c_220,plain,
( nil = sk3
| ssList(sk6) ),
inference(clausify,[status(thm)],[co1_15]) ).
cnf(c_221,plain,
( sk3 = nil
| ssList(sk6) ),
inference(copy,[status(thm)],[c_220]) ).
fof(co1_16,axiom,
( nil = sk3
| ssList(sk7) ),
file('theBenchmark.p',co1_16) ).
cnf(c_222,plain,
( nil = sk3
| ssList(sk7) ),
inference(clausify,[status(thm)],[co1_16]) ).
cnf(c_223,plain,
( sk3 = nil
| ssList(sk7) ),
inference(copy,[status(thm)],[c_222]) ).
fof(co1_17,axiom,
( nil = sk3
| cons(sk5,nil) = sk3 ),
file('theBenchmark.p',co1_17) ).
cnf(c_224,plain,
( nil = sk3
| cons(sk5,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_17]) ).
cnf(c_225,plain,
( sk3 = nil
| cons(sk5,nil) = sk3 ),
inference(copy,[status(thm)],[c_224]) ).
fof(co1_18,axiom,
( nil = sk3
| app(app(sk6,sk3),sk7) = sk4 ),
file('theBenchmark.p',co1_18) ).
cnf(c_226,plain,
( nil = sk3
| app(app(sk6,sk3),sk7) = sk4 ),
inference(clausify,[status(thm)],[co1_18]) ).
cnf(c_227,plain,
( sk3 = nil
| app(app(sk6,sk3),sk7) = sk4 ),
inference(copy,[status(thm)],[c_226]) ).
fof(co1_21,axiom,
( ~ strictorderedP(sk1)
| ~ segmentP(sk2,sk1) ),
file('theBenchmark.p',co1_21) ).
cnf(c_232,plain,
( ~ strictorderedP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(clausify,[status(thm)],[co1_21]) ).
cnf(c_11504,plain,
( ~ strictorderedP(sk1)
| ~ segmentP(sk4,sk1) ),
inference(paramod,[status(thm)],[c_202,c_232]) ).
cnf(c_11505,plain,
( ~ strictorderedP(sk1)
| ~ segmentP(sk4,sk3) ),
inference(paramod,[status(thm)],[c_203,c_11504]) ).
cnf(c_233,plain,
( ~ strictorderedP(sk3)
| ~ segmentP(sk4,sk3) ),
inference(paramod,[status(thm)],[c_203,c_11505]) ).
cnf(c_7268,plain,
segmentP(sk4,nil),
inference(resolve,[status(thm)],[c_201,c_97]) ).
cnf(c_11506,plain,
( singletonP(sk3)
| ~ ssList(sk3)
| ~ ssItem(sk5)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_225,c_139]) ).
cnf(c_8346,plain,
( singletonP(sk3)
| ~ ssItem(sk5)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_200,c_11506]) ).
cnf(c_11507,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(sk7)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_227,c_190]) ).
cnf(c_11508,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk6)
| ~ ssList(sk7)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_200,c_11507]) ).
cnf(c_8371,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk6)
| ~ ssList(sk7)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_201,c_11508]) ).
cnf(c_11509,plain,
( ~ strictorderedP(sk3)
| ~ segmentP(sk4,nil)
| ssItem(sk5) ),
inference(paramod,[status(thm)],[c_207,c_233]) ).
cnf(c_8433,plain,
( ~ strictorderedP(sk3)
| ssItem(sk5) ),
inference(resolve,[status(thm)],[c_7268,c_11509]) ).
cnf(c_11510,plain,
( ~ strictorderedP(sk3)
| ~ segmentP(sk4,nil)
| ssList(sk6) ),
inference(paramod,[status(thm)],[c_221,c_233]) ).
cnf(c_8439,plain,
( ~ strictorderedP(sk3)
| ssList(sk6) ),
inference(resolve,[status(thm)],[c_7268,c_11510]) ).
cnf(c_11511,plain,
( ~ strictorderedP(sk3)
| ~ segmentP(sk4,nil)
| ssList(sk7) ),
inference(paramod,[status(thm)],[c_223,c_233]) ).
cnf(c_8441,plain,
( ~ strictorderedP(sk3)
| ssList(sk7) ),
inference(resolve,[status(thm)],[c_7268,c_11511]) ).
cnf(c_11512,plain,
( ~ strictorderedP(nil)
| ssItem(sk5)
| ssItem(sk5) ),
inference(paramod,[status(thm)],[c_207,c_8433]) ).
cnf(c_11513,plain,
( ~ strictorderedP(nil)
| ssItem(sk5) ),
inference(copy,[status(thm)],[c_11512]) ).
cnf(c_10648,plain,
ssItem(sk5),
inference(resolve,[status(thm)],[c_47,c_11513]) ).
cnf(c_10695,plain,
( singletonP(sk3)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_10648,c_8346]) ).
cnf(c_10811,plain,
strictorderedP(cons(sk5,nil)),
inference(resolve,[status(thm)],[c_10648,c_105]) ).
cnf(c_11514,plain,
( ~ strictorderedP(nil)
| ssList(sk6)
| ssList(sk6) ),
inference(paramod,[status(thm)],[c_221,c_8439]) ).
cnf(c_11515,plain,
( ~ strictorderedP(nil)
| ssList(sk6) ),
inference(copy,[status(thm)],[c_11514]) ).
cnf(c_10817,plain,
ssList(sk6),
inference(resolve,[status(thm)],[c_47,c_11515]) ).
cnf(c_10821,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk7)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_10817,c_8371]) ).
cnf(c_11516,plain,
( ~ strictorderedP(nil)
| ssList(sk7)
| ssList(sk7) ),
inference(paramod,[status(thm)],[c_223,c_8441]) ).
cnf(c_11517,plain,
( ~ strictorderedP(nil)
| ssList(sk7) ),
inference(copy,[status(thm)],[c_11516]) ).
cnf(c_11106,plain,
ssList(sk7),
inference(resolve,[status(thm)],[c_47,c_11517]) ).
cnf(c_11111,plain,
( segmentP(sk4,sk3)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_11106,c_10821]) ).
cnf(c_11518,plain,
( ~ strictorderedP(sk3)
| ~ segmentP(sk4,nil)
| singletonP(sk3) ),
inference(paramod,[status(thm)],[c_10695,c_233]) ).
cnf(c_11472,plain,
( ~ strictorderedP(sk3)
| singletonP(sk3) ),
inference(resolve,[status(thm)],[c_7268,c_11518]) ).
cnf(c_11519,plain,
( ~ strictorderedP(nil)
| singletonP(sk3)
| singletonP(sk3) ),
inference(paramod,[status(thm)],[c_10695,c_11472]) ).
cnf(c_11520,plain,
( ~ strictorderedP(nil)
| singletonP(sk3) ),
inference(copy,[status(thm)],[c_11519]) ).
cnf(c_11476,plain,
singletonP(sk3),
inference(resolve,[status(thm)],[c_47,c_11520]) ).
cnf(c_11521,plain,
( singletonP(nil)
| cons(sk5,nil) = sk3 ),
inference(paramod,[status(thm)],[c_225,c_11476]) ).
cnf(c_11478,plain,
cons(sk5,nil) = sk3,
inference(resolve,[status(thm)],[c_52,c_11521]) ).
cnf(c_11480,plain,
strictorderedP(sk3),
inference(paramod,[status(thm)],[c_11478,c_10811]) ).
cnf(c_11500,plain,
~ segmentP(sk4,sk3),
inference(resolve,[status(thm)],[c_11480,c_233]) ).
cnf(c_11502,plain,
sk3 = nil,
inference(resolve,[status(thm)],[c_11500,c_11111]) ).
cnf(c_11522,plain,
~ segmentP(sk4,nil),
inference(paramod,[status(thm)],[c_11502,c_11500]) ).
cnf(c_11503,plain,
$false,
inference(resolve,[status(thm)],[c_7268,c_11522]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC346-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sat Sep 26 12:51:04 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.29 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.29 % Process 637640 was started by sandbox2 on n012,
% 0.02/0.29 % Sat Sep 26 12:51:04 2026
% 0.02/0.29 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.02/0.30
% 0.02/0.30 % From the command line: assign(max_seconds, 300).
% 37.59/5.13
% 37.59/5.13 % given #500 (I,wt=34): 569 app(app(A,cons(B,A)),cons(C,D)) != D | -ssList(D) | -ssList(A) | -ssItem(C) | -ssItem(B) | -totalorderedP(D) | leq(B,C). [factor(379,c,d)].
% 37.59/5.13
% 37.59/5.13 % SZS status Unsatisfiable for theBenchmark
% 37.59/5.13
% 37.59/5.13 % Proof 1 at 3.68 (+ 1.06) seconds.
% 37.59/5.13 % Length of proof is 42.
% 37.59/5.13 % Level of proof is 11.
% 37.59/5.13 % Maximum clause weight is 26.000.
% 37.59/5.13 % Given clauses 905.
% 37.59/5.13
% 37.59/5.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------