%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT362+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 07:50:24 AM UTC 2026
% Result : Theorem 23.83s 13.48s
% Output : CNFRefutation 23.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 14 unt; 0 def)
% Number of atoms : 200 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 221 ( 73 ~; 81 |; 55 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 27 ( 26 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 30 ( 0 sgn 11 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc2_setfam_1,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ~ v1_xboole_0(A) ),
file('theBenchmark.p',cc2_setfam_1) ).
fof(d41_functor0,axiom,
! [A] :
( ( l2_altcat_1(A)
& v12_altcat_1(A)
& v2_altcat_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l2_altcat_1(B)
& v12_altcat_1(B)
& v2_altcat_1(B)
& ~ v3_struct_0(B) )
=> ( r2_functor0(A,B)
<=> ? [C] :
( v16_functor0(C,A,B)
& v21_functor0(C,A,B)
& m2_functor0(C,A,B) ) ) ) ),
file('theBenchmark.p',d41_functor0) ).
fof(dt_k4_waybel34,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( l2_altcat_1(k4_waybel34(A))
& v2_yellow21(k4_waybel34(A))
& v12_altcat_1(k4_waybel34(A))
& v11_altcat_1(k4_waybel34(A))
& v6_altcat_1(k4_waybel34(A))
& v2_altcat_1(k4_waybel34(A))
& ~ v3_struct_0(k4_waybel34(A)) ) ),
file('theBenchmark.p',dt_k4_waybel34) ).
fof(dt_k5_waybel34,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( l2_altcat_1(k5_waybel34(A))
& v2_yellow21(k5_waybel34(A))
& v12_altcat_1(k5_waybel34(A))
& v11_altcat_1(k5_waybel34(A))
& v6_altcat_1(k5_waybel34(A))
& v2_altcat_1(k5_waybel34(A))
& ~ v3_struct_0(k5_waybel34(A)) ) ),
file('theBenchmark.p',dt_k5_waybel34) ).
fof(dt_k6_waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ( m2_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
& v16_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
& v9_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A)) ) ),
file('theBenchmark.p',dt_k6_waybel34) ).
fof(fc5_waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ( v3_yellow21(k4_waybel34(A))
& v2_yellow21(k4_waybel34(A))
& v1_yellow21(k4_waybel34(A))
& v4_yellow18(k4_waybel34(A))
& v3_yellow18(k4_waybel34(A))
& v2_yellow18(k4_waybel34(A))
& v1_altcat_2(k4_waybel34(A))
& v12_altcat_1(k4_waybel34(A))
& v11_altcat_1(k4_waybel34(A))
& v9_altcat_1(k4_waybel34(A))
& v6_altcat_1(k4_waybel34(A))
& v2_altcat_1(k4_waybel34(A))
& ~ v3_struct_0(k4_waybel34(A)) ) ),
file('theBenchmark.p',fc5_waybel34) ).
fof(fc6_waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ( v3_yellow21(k5_waybel34(A))
& v2_yellow21(k5_waybel34(A))
& v1_yellow21(k5_waybel34(A))
& v4_yellow18(k5_waybel34(A))
& v3_yellow18(k5_waybel34(A))
& v2_yellow18(k5_waybel34(A))
& v1_altcat_2(k5_waybel34(A))
& v12_altcat_1(k5_waybel34(A))
& v11_altcat_1(k5_waybel34(A))
& v9_altcat_1(k5_waybel34(A))
& v6_altcat_1(k5_waybel34(A))
& v2_altcat_1(k5_waybel34(A))
& ~ v3_struct_0(k5_waybel34(A)) ) ),
file('theBenchmark.p',fc6_waybel34) ).
fof(fc7_waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ( v21_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
& v16_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
& v14_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
& v12_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
& v11_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
& v9_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
& v8_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
& v6_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A)) ) ),
file('theBenchmark.p',fc7_waybel34) ).
fof(t20_waybel34,conjecture,
! [A] :
( ~ v2_setfam_1(A)
=> r2_functor0(k4_waybel34(A),k5_waybel34(A)) ),
file('theBenchmark.p',t20_waybel34) ).
fof(t20_waybel34_neg,negated_conjecture,
~ ! [A] :
( ~ v2_setfam_1(A)
=> r2_functor0(k4_waybel34(A),k5_waybel34(A)) ),
inference(assume_negation,[status(cth)],[t20_waybel34]) ).
cnf(c_176,plain,
( m2_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
| v2_setfam_1(A) ),
inference(clausify,[status(thm)],[dt_k6_waybel34]) ).
cnf(c_177,plain,
( v16_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
| v2_setfam_1(A) ),
inference(clausify,[status(thm)],[dt_k6_waybel34]) ).
cnf(c_179,plain,
( l2_altcat_1(k5_waybel34(A))
| v1_xboole_0(A) ),
inference(clausify,[status(thm)],[dt_k5_waybel34]) ).
cnf(c_185,plain,
( l2_altcat_1(k4_waybel34(A))
| v1_xboole_0(A) ),
inference(clausify,[status(thm)],[dt_k4_waybel34]) ).
cnf(c_195,plain,
( ~ v16_functor0(C,A,B)
| ~ v21_functor0(C,A,B)
| ~ m2_functor0(C,A,B)
| r2_functor0(A,B)
| ~ l2_altcat_1(B)
| ~ v12_altcat_1(B)
| ~ v2_altcat_1(B)
| v3_struct_0(B)
| ~ l2_altcat_1(A)
| ~ v12_altcat_1(A)
| ~ v2_altcat_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[d41_functor0]) ).
cnf(c_217,plain,
( ~ v1_xboole_0(A)
| v2_setfam_1(A) ),
inference(clausify,[status(thm)],[cc2_setfam_1]) ).
cnf(c_315,plain,
( ~ v3_struct_0(k4_waybel34(A))
| v2_setfam_1(A) ),
inference(clausify,[status(thm)],[fc5_waybel34]) ).
cnf(c_316,plain,
( v2_altcat_1(k4_waybel34(A))
| v2_setfam_1(A) ),
inference(clausify,[status(thm)],[fc5_waybel34]) ).
cnf(c_319,plain,
( v12_altcat_1(k4_waybel34(A))
| v2_setfam_1(A) ),
inference(clausify,[status(thm)],[fc5_waybel34]) ).
cnf(c_333,plain,
( ~ v3_struct_0(k5_waybel34(A))
| v2_setfam_1(A) ),
inference(clausify,[status(thm)],[fc6_waybel34]) ).
cnf(c_334,plain,
( v2_altcat_1(k5_waybel34(A))
| v2_setfam_1(A) ),
inference(clausify,[status(thm)],[fc6_waybel34]) ).
cnf(c_337,plain,
( v12_altcat_1(k5_waybel34(A))
| v2_setfam_1(A) ),
inference(clausify,[status(thm)],[fc6_waybel34]) ).
cnf(c_350,plain,
( v21_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
| v2_setfam_1(A) ),
inference(clausify,[status(thm)],[fc7_waybel34]) ).
fof(nnf_113,plain,
? [A] :
( ~ r2_functor0(k4_waybel34(A),k5_waybel34(A))
& ~ v2_setfam_1(A) ),
inference(fof_nnf,[status(thm)],[t20_waybel34_neg]) ).
fof(sk_t20_waybel34_neg,plain,
( ~ r2_functor0(k4_waybel34(sK0),k5_waybel34(sK0))
& ~ v2_setfam_1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_113]) ).
cnf(c_424,negated_conjecture,
~ v2_setfam_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t20_waybel34_neg]) ).
cnf(c_425,negated_conjecture,
~ r2_functor0(k4_waybel34(sK0),k5_waybel34(sK0)),
inference(split_conjunct,[status(thm)],[sk_t20_waybel34_neg]) ).
cnf(c_644,plain,
( l2_altcat_1(k4_waybel34(A))
| v2_setfam_1(A) ),
inference(resolve,[status(thm)],[c_217,c_185]) ).
cnf(c_645,plain,
( l2_altcat_1(k5_waybel34(A))
| v2_setfam_1(A) ),
inference(resolve,[status(thm)],[c_217,c_179]) ).
cnf(c_1148,plain,
v21_functor0(k6_waybel34(sK0),k4_waybel34(sK0),k5_waybel34(sK0)),
inference(resolve,[status(thm)],[c_424,c_350]) ).
cnf(c_1161,plain,
v12_altcat_1(k5_waybel34(sK0)),
inference(resolve,[status(thm)],[c_424,c_337]) ).
cnf(c_1164,plain,
v2_altcat_1(k5_waybel34(sK0)),
inference(resolve,[status(thm)],[c_424,c_334]) ).
cnf(c_1172,plain,
v12_altcat_1(k4_waybel34(sK0)),
inference(resolve,[status(thm)],[c_424,c_319]) ).
cnf(c_1175,plain,
v2_altcat_1(k4_waybel34(sK0)),
inference(resolve,[status(thm)],[c_424,c_316]) ).
cnf(c_1177,plain,
v16_functor0(k6_waybel34(sK0),k4_waybel34(sK0),k5_waybel34(sK0)),
inference(resolve,[status(thm)],[c_424,c_177]) ).
cnf(c_1178,plain,
m2_functor0(k6_waybel34(sK0),k4_waybel34(sK0),k5_waybel34(sK0)),
inference(resolve,[status(thm)],[c_424,c_176]) ).
cnf(c_2224,plain,
l2_altcat_1(k4_waybel34(sK0)),
inference(resolve,[status(thm)],[c_644,c_424]) ).
cnf(c_2267,plain,
l2_altcat_1(k5_waybel34(sK0)),
inference(resolve,[status(thm)],[c_645,c_424]) ).
cnf(c_12322,plain,
( ~ v16_functor0(k6_waybel34(sK0),k4_waybel34(sK0),k5_waybel34(sK0))
| ~ m2_functor0(k6_waybel34(sK0),k4_waybel34(sK0),k5_waybel34(sK0))
| r2_functor0(k4_waybel34(sK0),k5_waybel34(sK0))
| ~ l2_altcat_1(k5_waybel34(sK0))
| ~ v12_altcat_1(k5_waybel34(sK0))
| ~ v2_altcat_1(k5_waybel34(sK0))
| v3_struct_0(k5_waybel34(sK0))
| ~ l2_altcat_1(k4_waybel34(sK0))
| ~ v12_altcat_1(k4_waybel34(sK0))
| ~ v2_altcat_1(k4_waybel34(sK0))
| v3_struct_0(k4_waybel34(sK0)) ),
inference(resolve,[status(thm)],[c_1148,c_195]) ).
cnf(c_12323,plain,
( ~ v16_functor0(k6_waybel34(sK0),k4_waybel34(sK0),k5_waybel34(sK0))
| ~ m2_functor0(k6_waybel34(sK0),k4_waybel34(sK0),k5_waybel34(sK0))
| r2_functor0(k4_waybel34(sK0),k5_waybel34(sK0))
| ~ l2_altcat_1(k5_waybel34(sK0))
| ~ v12_altcat_1(k5_waybel34(sK0))
| ~ v2_altcat_1(k5_waybel34(sK0))
| v3_struct_0(k5_waybel34(sK0))
| ~ l2_altcat_1(k4_waybel34(sK0))
| ~ v12_altcat_1(k4_waybel34(sK0))
| v3_struct_0(k4_waybel34(sK0)) ),
inference(resolve,[status(thm)],[c_1175,c_12322]) ).
cnf(c_12324,plain,
( ~ v16_functor0(k6_waybel34(sK0),k4_waybel34(sK0),k5_waybel34(sK0))
| ~ m2_functor0(k6_waybel34(sK0),k4_waybel34(sK0),k5_waybel34(sK0))
| r2_functor0(k4_waybel34(sK0),k5_waybel34(sK0))
| ~ l2_altcat_1(k5_waybel34(sK0))
| ~ v12_altcat_1(k5_waybel34(sK0))
| ~ v2_altcat_1(k5_waybel34(sK0))
| v3_struct_0(k5_waybel34(sK0))
| ~ l2_altcat_1(k4_waybel34(sK0))
| v3_struct_0(k4_waybel34(sK0)) ),
inference(resolve,[status(thm)],[c_1172,c_12323]) ).
cnf(c_12325,plain,
( ~ v16_functor0(k6_waybel34(sK0),k4_waybel34(sK0),k5_waybel34(sK0))
| ~ m2_functor0(k6_waybel34(sK0),k4_waybel34(sK0),k5_waybel34(sK0))
| r2_functor0(k4_waybel34(sK0),k5_waybel34(sK0))
| ~ l2_altcat_1(k5_waybel34(sK0))
| ~ v12_altcat_1(k5_waybel34(sK0))
| ~ v2_altcat_1(k5_waybel34(sK0))
| v3_struct_0(k5_waybel34(sK0))
| v3_struct_0(k4_waybel34(sK0)) ),
inference(resolve,[status(thm)],[c_2224,c_12324]) ).
cnf(c_12326,plain,
( ~ v16_functor0(k6_waybel34(sK0),k4_waybel34(sK0),k5_waybel34(sK0))
| ~ m2_functor0(k6_waybel34(sK0),k4_waybel34(sK0),k5_waybel34(sK0))
| r2_functor0(k4_waybel34(sK0),k5_waybel34(sK0))
| ~ l2_altcat_1(k5_waybel34(sK0))
| ~ v12_altcat_1(k5_waybel34(sK0))
| v3_struct_0(k5_waybel34(sK0))
| v3_struct_0(k4_waybel34(sK0)) ),
inference(resolve,[status(thm)],[c_1164,c_12325]) ).
cnf(c_12327,plain,
( ~ v16_functor0(k6_waybel34(sK0),k4_waybel34(sK0),k5_waybel34(sK0))
| ~ m2_functor0(k6_waybel34(sK0),k4_waybel34(sK0),k5_waybel34(sK0))
| r2_functor0(k4_waybel34(sK0),k5_waybel34(sK0))
| ~ l2_altcat_1(k5_waybel34(sK0))
| v3_struct_0(k5_waybel34(sK0))
| v3_struct_0(k4_waybel34(sK0)) ),
inference(resolve,[status(thm)],[c_1161,c_12326]) ).
cnf(c_12328,plain,
( ~ v16_functor0(k6_waybel34(sK0),k4_waybel34(sK0),k5_waybel34(sK0))
| ~ m2_functor0(k6_waybel34(sK0),k4_waybel34(sK0),k5_waybel34(sK0))
| r2_functor0(k4_waybel34(sK0),k5_waybel34(sK0))
| v3_struct_0(k5_waybel34(sK0))
| v3_struct_0(k4_waybel34(sK0)) ),
inference(resolve,[status(thm)],[c_2267,c_12327]) ).
cnf(c_12329,negated_conjecture,
( ~ v16_functor0(k6_waybel34(sK0),k4_waybel34(sK0),k5_waybel34(sK0))
| ~ m2_functor0(k6_waybel34(sK0),k4_waybel34(sK0),k5_waybel34(sK0))
| v3_struct_0(k5_waybel34(sK0))
| v3_struct_0(k4_waybel34(sK0)) ),
inference(resolve,[status(thm)],[c_425,c_12328]) ).
cnf(c_12330,negated_conjecture,
( ~ v16_functor0(k6_waybel34(sK0),k4_waybel34(sK0),k5_waybel34(sK0))
| v3_struct_0(k5_waybel34(sK0))
| v3_struct_0(k4_waybel34(sK0)) ),
inference(resolve,[status(thm)],[c_1178,c_12329]) ).
cnf(c_12318,negated_conjecture,
( v3_struct_0(k5_waybel34(sK0))
| v3_struct_0(k4_waybel34(sK0)) ),
inference(resolve,[status(thm)],[c_1177,c_12330]) ).
cnf(c_12331,plain,
( v2_setfam_1(sK0)
| v3_struct_0(k5_waybel34(sK0)) ),
inference(resolve,[status(thm)],[c_12318,c_315]) ).
cnf(c_12319,negated_conjecture,
v3_struct_0(k5_waybel34(sK0)),
inference(resolve,[status(thm)],[c_424,c_12331]) ).
cnf(c_12332,plain,
v2_setfam_1(sK0),
inference(resolve,[status(thm)],[c_12319,c_333]) ).
cnf(c_12321,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_424,c_12332]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT362+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/10.38 % Computer : n009.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Fri Sep 25 21:21:24 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.38 % Process 2574984 was started by sandbox2 on n009,
% 0.09/10.38 % Fri Sep 25 21:21:24 2026
% 0.09/10.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/10.42
% 0.14/10.42 % From the command line: assign(max_seconds, 300).
% 23.83/13.48
% 23.83/13.48 % given #500 (T,wt=13): 1171 v1_altcat_2(k4_waybel34(c13)). [resolve(424,a,320,a)].
% 23.83/13.48
% 23.83/13.48 % given #1000 (T,wt=15): 9712 -v5_membered(c13) | v2_membered(f11(c13)). [resolve(9697,a,225,b)].
% 23.83/13.48
% 23.83/13.48 % SZS status Theorem for theBenchmark
% 23.83/13.48
% 23.83/13.48 % Proof 1 at 2.86 (+ 0.17) seconds.
% 23.83/13.48 % Length of proof is 38.
% 23.83/13.48 % Level of proof is 6.
% 23.83/13.48 % Maximum clause weight is 36.000.
% 23.83/13.48 % Given clauses 1283.
% 23.83/13.48
% 23.83/13.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------