%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP642+3 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 07:30:37 AM UTC 2026
% Result : Theorem 56.79s 9.17s
% Output : CNFRefutation 56.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 14 unt; 0 def)
% Number of atoms : 80 ( 6 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 86 ( 33 ~; 22 |; 25 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 3 sgn 9 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t2_xboole_1,axiom,
! [A] : r1_tarski(k1_xboole_0,A),
file('theBenchmark.p',t2_xboole_1) ).
fof(t19_latsubgr,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m1_group_2(B,A)
& v1_group_1(B) )
=> r2_hidden(k2_group_1(A),k1_funct_1(k1_latsubgr(A),B)) ) ),
file('theBenchmark.p',t19_latsubgr) ).
fof(t7_ordinal1,axiom,
! [A,B] :
~ ( r1_tarski(B,A)
& r2_hidden(A,B) ),
file('theBenchmark.p',t7_ordinal1) ).
fof(t20_latsubgr,conjecture,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m1_group_2(B,A)
& v1_group_1(B) )
=> k1_funct_1(k1_latsubgr(A),B) != k1_xboole_0 ) ),
file('theBenchmark.p',t20_latsubgr) ).
fof(t20_latsubgr_neg,negated_conjecture,
~ ! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( m1_group_2(B,A)
& v1_group_1(B) )
=> k1_funct_1(k1_latsubgr(A),B) != k1_xboole_0 ) ),
inference(assume_negation,[status(cth)],[t20_latsubgr]) ).
cnf(c_1111,plain,
( ~ r1_tarski(B,A)
| ~ r2_hidden(A,B) ),
inference(clausify,[status(thm)],[t7_ordinal1]) ).
cnf(c_1927,plain,
r1_tarski(k1_xboole_0,A),
inference(clausify,[status(thm)],[t2_xboole_1]) ).
cnf(c_2232,plain,
( r2_hidden(k2_group_1(A),k1_funct_1(k1_latsubgr(A),B))
| ~ m1_group_2(B,A)
| ~ v1_group_1(B)
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t19_latsubgr]) ).
fof(nnf_721,plain,
? [A] :
( ? [B] :
( k1_funct_1(k1_latsubgr(A),B) = k1_xboole_0
& m1_group_2(B,A)
& v1_group_1(B) )
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t20_latsubgr_neg]) ).
fof(sk_t20_latsubgr_neg,plain,
( k1_funct_1(k1_latsubgr(sK0),sK1) = k1_xboole_0
& m1_group_2(sK1,sK0)
& v1_group_1(sK1)
& l1_group_1(sK0)
& v4_group_1(sK0)
& v3_group_1(sK0)
& ~ v3_struct_0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_721]) ).
cnf(c_2233,negated_conjecture,
~ v3_struct_0(sK0),
inference(split_conjunct,[status(thm)],[sk_t20_latsubgr_neg]) ).
cnf(c_2234,negated_conjecture,
v3_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t20_latsubgr_neg]) ).
cnf(c_2235,negated_conjecture,
v4_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t20_latsubgr_neg]) ).
cnf(c_2236,negated_conjecture,
l1_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t20_latsubgr_neg]) ).
cnf(c_2237,negated_conjecture,
v1_group_1(sK1),
inference(split_conjunct,[status(thm)],[sk_t20_latsubgr_neg]) ).
cnf(c_2238,negated_conjecture,
m1_group_2(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t20_latsubgr_neg]) ).
cnf(c_2239,negated_conjecture,
k1_funct_1(k1_latsubgr(sK0),sK1) = k1_xboole_0,
inference(split_conjunct,[status(thm)],[sk_t20_latsubgr_neg]) ).
cnf(c_2240,negated_conjecture,
k1_xboole_0 = k1_funct_1(k1_latsubgr(sK0),sK1),
inference(copy,[status(thm)],[c_2239]) ).
cnf(c_3105,plain,
~ r2_hidden(A,k1_xboole_0),
inference(resolve,[status(thm)],[c_1927,c_1111]) ).
cnf(c_18350,negated_conjecture,
( r2_hidden(k2_group_1(sK0),k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ v1_group_1(sK1)
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_2232,c_2238]) ).
cnf(c_18351,negated_conjecture,
( r2_hidden(k2_group_1(sK0),k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ v1_group_1(sK1)
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_2233,c_18350]) ).
cnf(c_18352,negated_conjecture,
( r2_hidden(k2_group_1(sK0),k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ v1_group_1(sK1)
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0) ),
inference(resolve,[status(thm)],[c_2234,c_18351]) ).
cnf(c_18353,negated_conjecture,
( r2_hidden(k2_group_1(sK0),k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ v1_group_1(sK1)
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_2235,c_18352]) ).
cnf(c_18354,negated_conjecture,
( r2_hidden(k2_group_1(sK0),k1_funct_1(k1_latsubgr(sK0),sK1))
| ~ v1_group_1(sK1) ),
inference(resolve,[status(thm)],[c_2236,c_18353]) ).
cnf(c_18326,negated_conjecture,
r2_hidden(k2_group_1(sK0),k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(resolve,[status(thm)],[c_2237,c_18354]) ).
cnf(c_18348,plain,
~ r2_hidden(A,k1_funct_1(k1_latsubgr(sK0),sK1)),
inference(paramod,[status(thm)],[c_2240,c_3105]) ).
cnf(c_18349,plain,
$false,
inference(resolve,[status(thm)],[c_18348,c_18326]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP642+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.57 % Computer : n017.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.58 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Fri Sep 25 15:15:10 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.58 % Process 2623795 was started by sandbox on n017,
% 0.11/0.58 % Fri Sep 25 15:15:10 2026
% 0.11/0.58 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 56.79/9.17
% 56.79/9.17 % SInE (scan): 517 to sos (tol 1.5x), 212 to usable (tol 2.0x), 13254 zapped, of 13983 axioms (depth 3).
% 56.79/9.17
% 56.79/9.17 % From the command line: assign(max_seconds, 300).
% 56.79/9.17
% 56.79/9.17 % given #500 (F,wt=20): 10907 k1_tarski(A) != k1_relat_1(c3) | k2_relat_1(c14) != k1_tarski(B). [para(9433(a,1),10734(b,1,1))].
% 56.79/9.17
% 56.79/9.17 % given #1000 (W,wt=14): 7931 m1_subset_1(c14,k2_relat_1(c1)). [resolve(7845,a,6490,a)].
% 56.79/9.17
% 56.79/9.17 % SZS status Theorem for theBenchmark
% 56.79/9.17
% 56.79/9.17 % Proof 1 at 6.60 (+ 0.83) seconds.
% 56.79/9.17 % Length of proof is 19.
% 56.79/9.17 % Level of proof is 4.
% 56.79/9.17 % Maximum clause weight is 35.000.
% 56.79/9.17 % Given clauses 1264.
% 56.79/9.17
% 56.79/9.17 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------