%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP642+4 : 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 : 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 07:30:37 AM UTC 2026
% Result : Theorem 146.73s 21.84s
% Output : CNFRefutation 146.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 41 unt; 0 def)
% Number of atoms : 133 ( 31 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 115 ( 46 ~; 33 |; 27 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 60 ( 16 sgn 19 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rc1_xboole_0,axiom,
? [A] : v1_xboole_0(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(d5_xboole_0,axiom,
! [A] :
( v1_xboole_0(A)
<=> A = k1_xboole_0 ),
file('theBenchmark.p',d5_xboole_0) ).
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(t4_xboole_0,axiom,
! [A,B] :
( ~ ( r1_xboole_0(A,B)
& ? [C] : r2_hidden(C,k3_xboole_0(A,B)) )
& ~ ( ! [C] : ~ r2_hidden(C,k3_xboole_0(A,B))
& ~ r1_xboole_0(A,B) ) ),
file('theBenchmark.p',t4_xboole_0) ).
fof(t12_xboole_1,axiom,
! [A,B] :
( r1_tarski(A,B)
=> k2_xboole_0(A,B) = B ),
file('theBenchmark.p',t12_xboole_1) ).
fof(t28_xboole_1,axiom,
! [A,B] :
( r1_tarski(A,B)
=> k3_xboole_0(A,B) = A ),
file('theBenchmark.p',t28_xboole_1) ).
fof(t51_xboole_1,axiom,
! [A,B] : k2_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B)) = A,
file('theBenchmark.p',t51_xboole_1) ).
fof(t90_xboole_1,axiom,
! [A,B] : r1_xboole_0(k4_xboole_0(A,k3_xboole_0(A,B)),B),
file('theBenchmark.p',t90_xboole_1) ).
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_900,plain,
( ~ r1_xboole_0(B,C)
| ~ r2_hidden(A,k3_xboole_0(B,C)) ),
inference(clausify,[status(thm)],[t4_xboole_0]) ).
cnf(c_917,plain,
( k2_xboole_0(A,B) = B
| ~ r1_tarski(A,B) ),
inference(clausify,[status(thm)],[t12_xboole_1]) ).
cnf(c_937,plain,
( k3_xboole_0(A,B) = A
| ~ r1_tarski(A,B) ),
inference(clausify,[status(thm)],[t28_xboole_1]) ).
cnf(c_953,plain,
k2_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B)) = A,
inference(clausify,[status(thm)],[t51_xboole_1]) ).
cnf(c_972,plain,
r1_xboole_0(k4_xboole_0(A,k3_xboole_0(A,B)),B),
inference(clausify,[status(thm)],[t90_xboole_1]) ).
fof(nnf_7,plain,
? [A] : v1_xboole_0(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(sk_rc1_xboole_0,plain,
v1_xboole_0(sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_7]) ).
cnf(c_3222,plain,
v1_xboole_0(sK0),
inference(split_conjunct,[status(thm)],[sk_rc1_xboole_0]) ).
cnf(c_3226,plain,
( k1_xboole_0 = A
| ~ v1_xboole_0(A) ),
inference(clausify,[status(thm)],[d5_xboole_0]) ).
cnf(c_3227,plain,
( k1_xboole_0 != A
| v1_xboole_0(A) ),
inference(clausify,[status(thm)],[d5_xboole_0]) ).
cnf(c_3234,plain,
r1_tarski(k1_xboole_0,A),
inference(clausify,[status(thm)],[t2_xboole_1]) ).
fof(t51_card_1,axiom,
np__0 = k1_xboole_0,
file('theBenchmark.p',t51_card_1) ).
cnf(c_3513,plain,
np__0 = k1_xboole_0,
inference(clausify,[status(thm)],[t51_card_1]) ).
cnf(c_3514,plain,
k1_xboole_0 = np__0,
inference(copy,[status(thm)],[c_3513]) ).
cnf(c_3995,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_882,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(sK1),sK2) = k1_xboole_0
& m1_group_2(sK2,sK1)
& v1_group_1(sK2)
& l1_group_1(sK1)
& v4_group_1(sK1)
& v3_group_1(sK1)
& ~ v3_struct_0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2)],[nnf_882]) ).
cnf(c_3996,negated_conjecture,
~ v3_struct_0(sK1),
inference(split_conjunct,[status(thm)],[sk_t20_latsubgr_neg]) ).
cnf(c_3997,negated_conjecture,
v3_group_1(sK1),
inference(split_conjunct,[status(thm)],[sk_t20_latsubgr_neg]) ).
cnf(c_3998,negated_conjecture,
v4_group_1(sK1),
inference(split_conjunct,[status(thm)],[sk_t20_latsubgr_neg]) ).
cnf(c_3999,negated_conjecture,
l1_group_1(sK1),
inference(split_conjunct,[status(thm)],[sk_t20_latsubgr_neg]) ).
cnf(c_4000,negated_conjecture,
v1_group_1(sK2),
inference(split_conjunct,[status(thm)],[sk_t20_latsubgr_neg]) ).
cnf(c_4001,negated_conjecture,
m1_group_2(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_t20_latsubgr_neg]) ).
cnf(c_4002,negated_conjecture,
k1_funct_1(k1_latsubgr(sK1),sK2) = k1_xboole_0,
inference(split_conjunct,[status(thm)],[sk_t20_latsubgr_neg]) ).
cnf(c_4003,negated_conjecture,
k1_funct_1(k1_latsubgr(sK1),sK2) = np__0,
inference(paramod,[status(thm)],[c_3514,c_4002]) ).
cnf(c_4139,plain,
r1_tarski(np__0,A),
inference(paramod,[status(thm)],[c_3514,c_3234]) ).
cnf(c_4140,plain,
( np__0 != A
| v1_xboole_0(A) ),
inference(paramod,[status(thm)],[c_3514,c_3227]) ).
cnf(c_4141,plain,
( np__0 = A
| ~ v1_xboole_0(A) ),
inference(paramod,[status(thm)],[c_3514,c_3226]) ).
cnf(c_6664,plain,
k3_xboole_0(np__0,A) = np__0,
inference(resolve,[status(thm)],[c_4139,c_937]) ).
cnf(c_6674,plain,
k2_xboole_0(np__0,A) = A,
inference(resolve,[status(thm)],[c_4139,c_917]) ).
cnf(c_39400,plain,
A = k2_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B)),
inference(copy,[status(thm)],[c_953]) ).
cnf(c_39401,plain,
v1_xboole_0(k2_xboole_0(k3_xboole_0(np__0,A),k4_xboole_0(np__0,A))),
inference(resolve,[status(thm)],[c_4140,c_39400]) ).
cnf(c_39402,plain,
v1_xboole_0(k2_xboole_0(np__0,k4_xboole_0(np__0,A))),
inference(paramod,[status(thm)],[c_6664,c_39401]) ).
cnf(c_9192,plain,
v1_xboole_0(k4_xboole_0(np__0,A)),
inference(paramod,[status(thm)],[c_6674,c_39402]) ).
cnf(c_39403,plain,
np__0 = k4_xboole_0(np__0,A),
inference(resolve,[status(thm)],[c_4141,c_9192]) ).
cnf(c_9352,plain,
k4_xboole_0(np__0,A) = np__0,
inference(copy,[status(thm)],[c_39403]) ).
cnf(c_9353,plain,
np__0 = sK0,
inference(resolve,[status(thm)],[c_4141,c_3222]) ).
cnf(c_39404,plain,
k4_xboole_0(sK0,A) = np__0,
inference(paramod,[status(thm)],[c_9353,c_9352]) ).
cnf(c_9483,plain,
k4_xboole_0(sK0,A) = sK0,
inference(paramod,[status(thm)],[c_9353,c_39404]) ).
cnf(c_39405,plain,
k3_xboole_0(sK0,A) = np__0,
inference(paramod,[status(thm)],[c_9353,c_6664]) ).
cnf(c_9737,plain,
k3_xboole_0(sK0,A) = sK0,
inference(paramod,[status(thm)],[c_9353,c_39405]) ).
cnf(c_10041,negated_conjecture,
k1_funct_1(k1_latsubgr(sK1),sK2) = sK0,
inference(paramod,[status(thm)],[c_9353,c_4003]) ).
cnf(c_11507,plain,
r1_xboole_0(sK0,A),
inference(paramod,[status(thm)],[c_9483,c_972]) ).
cnf(c_39406,plain,
~ r2_hidden(A,k3_xboole_0(sK0,B)),
inference(resolve,[status(thm)],[c_11507,c_900]) ).
cnf(c_11525,plain,
~ r2_hidden(A,sK0),
inference(paramod,[status(thm)],[c_9737,c_39406]) ).
cnf(c_39407,negated_conjecture,
( r2_hidden(k2_group_1(sK1),k1_funct_1(k1_latsubgr(sK1),sK2))
| ~ v1_group_1(sK2)
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| v3_struct_0(sK1) ),
inference(resolve,[status(thm)],[c_3995,c_4001]) ).
cnf(c_39408,negated_conjecture,
( r2_hidden(k2_group_1(sK1),sK0)
| ~ v1_group_1(sK2)
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1)
| v3_struct_0(sK1) ),
inference(paramod,[status(thm)],[c_10041,c_39407]) ).
cnf(c_39409,negated_conjecture,
( r2_hidden(k2_group_1(sK1),sK0)
| ~ v1_group_1(sK2)
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1)
| ~ v3_group_1(sK1) ),
inference(resolve,[status(thm)],[c_3996,c_39408]) ).
cnf(c_39410,negated_conjecture,
( r2_hidden(k2_group_1(sK1),sK0)
| ~ v1_group_1(sK2)
| ~ l1_group_1(sK1)
| ~ v4_group_1(sK1) ),
inference(resolve,[status(thm)],[c_3997,c_39409]) ).
cnf(c_39411,negated_conjecture,
( r2_hidden(k2_group_1(sK1),sK0)
| ~ v1_group_1(sK2)
| ~ l1_group_1(sK1) ),
inference(resolve,[status(thm)],[c_3998,c_39410]) ).
cnf(c_39412,negated_conjecture,
( r2_hidden(k2_group_1(sK1),sK0)
| ~ v1_group_1(sK2) ),
inference(resolve,[status(thm)],[c_3999,c_39411]) ).
cnf(c_39413,negated_conjecture,
r2_hidden(k2_group_1(sK1),sK0),
inference(resolve,[status(thm)],[c_4000,c_39412]) ).
cnf(c_39399,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_11525,c_39413]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP642+4 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Fri Sep 25 15:20:09 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.30 % Process 2422062 was started by sandbox on n012,
% 0.04/0.30 % Fri Sep 25 15:20:09 2026
% 0.04/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 146.73/21.84
% 146.73/21.84 % SInE (scan): 663 to sos (tol 1.5x), 233 to usable (tol 2.0x), 35613 zapped, of 36509 axioms (depth 3).
% 146.73/21.84
% 146.73/21.84 % From the command line: assign(max_seconds, 300).
% 146.73/21.84
% 146.73/21.84 % given #500 (F,wt=8): 14842 -r2_hidden(k2_xboole_0(k2_xboole_0(k1_tarski(A),B),C),A). [para(903(a,1),14837(a,1))].
% 146.73/21.84
% 146.73/21.84 % given #1000 (W,wt=4): 22564 -r2_hidden(k2_numbers,f11(k1_numbers)). [resolve(22512,a,3208,b)].
% 146.73/21.84
% 146.73/21.84 % given #1500 (F,wt=6): 27032 -r2_hidden(k1_numbers,f319(f11(u1_struct_0(c26)))). [resolve(22760,a,3208,b)].
% 146.73/21.84
% 146.73/21.84 % given #2000 (T,wt=5): 30747 r2_hidden(f37(f11(k1_numbers)),k1_numbers). [resolve(30727,a,3478,a)].
% 146.73/21.84
% 146.73/21.84 % given #2500 (F,wt=8): 31907 -r2_hidden(k2_xboole_0(A,k1_tarski(k2_numbers)),f1(k2_numbers,k5_numbers)). [resolve(23367,a,7667,a)].
% 146.73/21.84
% 146.73/21.84 % given #3000 (T,wt=5): 33693 v1_finset_1(k1_zfmisc_1(f46(k1_zfmisc_1(c6)))). [resolve(33368,a,3468,a)].
% 146.73/21.84
% 146.73/21.84 % SZS status Theorem for theBenchmark
% 146.73/21.84
% 146.73/21.84 % Proof 1 at 18.98 (+ 1.63) seconds.
% 146.73/21.84 % Length of proof is 44.
% 146.73/21.84 % Level of proof is 9.
% 146.73/21.84 % Maximum clause weight is 102.000.
% 146.73/21.84 % Given clauses 3257.
% 146.73/21.84
% 146.73/21.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------