%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP623+1 : 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 : n004.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 07:30:32 AM UTC 2026
% Result : Theorem 22.84s 3.36s
% Output : CNFRefutation 22.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 67 ( 18 unt; 0 def)
% Number of atoms : 208 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 232 ( 91 ~; 87 |; 39 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 72 ( 2 sgn 35 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [A,B] :
( r1_tarski(A,B)
<=> ! [C] :
( r2_hidden(C,A)
=> r2_hidden(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(dt_k1_autgroup,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> m1_fraenkel(k1_autgroup(A),u1_struct_0(A),u1_struct_0(A)) ),
file('theBenchmark.p',dt_k1_autgroup) ).
fof(dt_k4_autgroup,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> m1_fraenkel(k4_autgroup(A),u1_struct_0(A),u1_struct_0(A)) ),
file('theBenchmark.p',dt_k4_autgroup) ).
fof(dt_l1_group_1,axiom,
! [A] :
( l1_group_1(A)
=> l1_struct_0(A) ),
file('theBenchmark.p',dt_l1_group_1) ).
fof(dt_m1_fraenkel,axiom,
! [A,B,C] :
( m1_fraenkel(C,A,B)
=> ( v1_fraenkel(C)
& ~ v1_xboole_0(C) ) ),
file('theBenchmark.p',dt_m1_fraenkel) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( l1_struct_0(A)
& ~ v3_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ),
file('theBenchmark.p',fc1_struct_0) ).
fof(redefinition_m2_fraenkel,axiom,
! [A,B,C] :
( ( m1_fraenkel(C,A,B)
& ~ v1_xboole_0(B) )
=> ! [D] :
( m2_fraenkel(D,A,B,C)
<=> m1_subset_1(D,C) ) ),
file('theBenchmark.p',redefinition_m2_fraenkel) ).
fof(t13_autgroup,axiom,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
=> m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) ) ),
file('theBenchmark.p',t13_autgroup) ).
fof(t1_subset,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t2_subset,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( r2_hidden(A,B)
| v1_xboole_0(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t14_autgroup,conjecture,
! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> r1_tarski(k4_autgroup(A),k1_autgroup(A)) ),
file('theBenchmark.p',t14_autgroup) ).
fof(t14_autgroup_neg,negated_conjecture,
~ ! [A] :
( ( l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) )
=> r1_tarski(k4_autgroup(A),k1_autgroup(A)) ),
inference(assume_negation,[status(cth)],[t14_autgroup]) ).
cnf(c_66,plain,
( m1_fraenkel(k1_autgroup(A),u1_struct_0(A),u1_struct_0(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_k1_autgroup]) ).
cnf(c_67,plain,
( m1_fraenkel(k4_autgroup(A),u1_struct_0(A),u1_struct_0(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[dt_k4_autgroup]) ).
cnf(c_72,plain,
( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
| ~ m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
| ~ l1_group_1(A)
| ~ v4_group_1(A)
| ~ v3_group_1(A)
| ~ v1_group_1(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[t13_autgroup]) ).
fof(nnf_63,plain,
? [A] :
( ~ r1_tarski(k4_autgroup(A),k1_autgroup(A))
& l1_group_1(A)
& v4_group_1(A)
& v3_group_1(A)
& v1_group_1(A)
& ~ v3_struct_0(A) ),
inference(fof_nnf,[status(thm)],[t14_autgroup_neg]) ).
fof(sk_t14_autgroup_neg,plain,
( ~ r1_tarski(k4_autgroup(sK0),k1_autgroup(sK0))
& l1_group_1(sK0)
& v4_group_1(sK0)
& v3_group_1(sK0)
& v1_group_1(sK0)
& ~ v3_struct_0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_63]) ).
cnf(c_73,negated_conjecture,
v1_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t14_autgroup_neg]) ).
cnf(c_115,plain,
( ~ v1_xboole_0(u1_struct_0(A))
| ~ l1_struct_0(A)
| v3_struct_0(A) ),
inference(clausify,[status(thm)],[fc1_struct_0]) ).
cnf(c_117,plain,
( l1_struct_0(A)
| ~ l1_group_1(A) ),
inference(clausify,[status(thm)],[dt_l1_group_1]) ).
cnf(c_236,negated_conjecture,
( m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_73,c_66]) ).
cnf(c_237,negated_conjecture,
( m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_73,c_67]) ).
cnf(c_238,negated_conjecture,
( m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0)
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_73,c_72]) ).
cnf(c_251,negated_conjecture,
~ r1_tarski(k4_autgroup(sK0),k1_autgroup(sK0)),
inference(split_conjunct,[status(thm)],[sk_t14_autgroup_neg]) ).
cnf(c_252,negated_conjecture,
l1_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t14_autgroup_neg]) ).
cnf(c_253,negated_conjecture,
v4_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t14_autgroup_neg]) ).
cnf(c_254,negated_conjecture,
v3_group_1(sK0),
inference(split_conjunct,[status(thm)],[sk_t14_autgroup_neg]) ).
cnf(c_255,negated_conjecture,
~ v3_struct_0(sK0),
inference(split_conjunct,[status(thm)],[sk_t14_autgroup_neg]) ).
cnf(c_263,plain,
( r2_hidden(A,B)
| v1_xboole_0(B)
| ~ m1_subset_1(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
cnf(c_264,plain,
( m1_subset_1(A,B)
| ~ r2_hidden(A,B) ),
inference(clausify,[status(thm)],[t1_subset]) ).
cnf(c_266,plain,
( ~ m1_subset_1(D,B)
| m2_fraenkel(D,C,A,B)
| ~ m1_fraenkel(B,C,A)
| v1_xboole_0(A) ),
inference(clausify,[status(thm)],[redefinition_m2_fraenkel]) ).
cnf(c_267,plain,
( m1_subset_1(D,B)
| ~ m2_fraenkel(D,C,A,B)
| ~ m1_fraenkel(B,C,A)
| v1_xboole_0(A) ),
inference(clausify,[status(thm)],[redefinition_m2_fraenkel]) ).
cnf(c_292,plain,
( ~ v1_xboole_0(A)
| ~ m1_fraenkel(A,B,C) ),
inference(clausify,[status(thm)],[dt_m1_fraenkel]) ).
fof(nnf_11,plain,
! [A,B] :
( ( ? [C] :
( ~ r2_hidden(C,B)
& r2_hidden(C,A) )
| r1_tarski(A,B) )
& ( ! [X0] :
( r2_hidden(X0,B)
| ~ r2_hidden(X0,A) )
| ~ r1_tarski(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(sk_d3_tarski_sk,plain,
! [A,B] :
( ( ( ~ r2_hidden(sK1(A,B),B)
& r2_hidden(sK1(A,B),A) )
| r1_tarski(A,B) )
& ( ! [X0] :
( r2_hidden(X0,B)
| ~ r2_hidden(X0,A) )
| ~ r1_tarski(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(C,sK1(A,B))],[nnf_11]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ r2_hidden(sK1(VAR_0,VAR_1),VAR_1)
| r1_tarski(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( r2_hidden(sK1(VAR_0,VAR_1),VAR_0)
| r1_tarski(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( r2_hidden(VAR_2,VAR_1)
| ~ r2_hidden(VAR_2,VAR_0)
| ~ r1_tarski(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_tarski_sk]) ).
cnf(c_293,plain,
( ~ r2_hidden(sK1(A,B),B)
| r1_tarski(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_294,plain,
( r2_hidden(sK1(A,B),A)
| r1_tarski(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_306,plain,
( ~ v1_xboole_0(u1_struct_0(A))
| v3_struct_0(A)
| ~ l1_group_1(A) ),
inference(resolve,[status(thm)],[c_117,c_115]) ).
cnf(c_12508,negated_conjecture,
( m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_255,c_238]) ).
cnf(c_12509,negated_conjecture,
( m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0) ),
inference(resolve,[status(thm)],[c_254,c_12508]) ).
cnf(c_12510,negated_conjecture,
( m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_253,c_12509]) ).
cnf(c_312,negated_conjecture,
( m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(resolve,[status(thm)],[c_252,c_12510]) ).
cnf(c_12511,negated_conjecture,
( m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_255,c_237]) ).
cnf(c_12512,negated_conjecture,
( m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0) ),
inference(resolve,[status(thm)],[c_254,c_12511]) ).
cnf(c_12513,negated_conjecture,
( m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_253,c_12512]) ).
cnf(c_313,negated_conjecture,
m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)),
inference(resolve,[status(thm)],[c_252,c_12513]) ).
cnf(c_12514,negated_conjecture,
( m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v3_group_1(sK0) ),
inference(resolve,[status(thm)],[c_255,c_236]) ).
cnf(c_12515,negated_conjecture,
( m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0) ),
inference(resolve,[status(thm)],[c_254,c_12514]) ).
cnf(c_12516,negated_conjecture,
( m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0) ),
inference(resolve,[status(thm)],[c_253,c_12515]) ).
cnf(c_314,negated_conjecture,
m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)),
inference(resolve,[status(thm)],[c_252,c_12516]) ).
cnf(c_569,plain,
r2_hidden(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),k4_autgroup(sK0)),
inference(resolve,[status(thm)],[c_294,c_251]) ).
cnf(c_12517,negated_conjecture,
( ~ v1_xboole_0(u1_struct_0(sK0))
| v3_struct_0(sK0) ),
inference(resolve,[status(thm)],[c_306,c_252]) ).
cnf(c_599,negated_conjecture,
~ v1_xboole_0(u1_struct_0(sK0)),
inference(resolve,[status(thm)],[c_255,c_12517]) ).
cnf(c_12518,negated_conjecture,
( ~ m1_subset_1(A,k4_autgroup(sK0))
| m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_313,c_266]) ).
cnf(c_615,negated_conjecture,
( ~ m1_subset_1(A,k4_autgroup(sK0))
| m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(resolve,[status(thm)],[c_599,c_12518]) ).
cnf(c_635,plain,
~ v1_xboole_0(k1_autgroup(sK0)),
inference(resolve,[status(thm)],[c_314,c_292]) ).
cnf(c_12519,negated_conjecture,
( m1_subset_1(A,k1_autgroup(sK0))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| v1_xboole_0(u1_struct_0(sK0)) ),
inference(resolve,[status(thm)],[c_314,c_267]) ).
cnf(c_638,negated_conjecture,
( m1_subset_1(A,k1_autgroup(sK0))
| ~ m2_fraenkel(A,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) ),
inference(resolve,[status(thm)],[c_599,c_12519]) ).
cnf(c_1454,plain,
m1_subset_1(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),k4_autgroup(sK0)),
inference(resolve,[status(thm)],[c_569,c_264]) ).
cnf(c_1626,plain,
m2_fraenkel(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)),
inference(resolve,[status(thm)],[c_1454,c_615]) ).
cnf(c_6809,plain,
m2_fraenkel(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)),
inference(resolve,[status(thm)],[c_1626,c_312]) ).
cnf(c_12501,plain,
m1_subset_1(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0)),
inference(resolve,[status(thm)],[c_6809,c_638]) ).
cnf(c_12520,plain,
( r2_hidden(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0))
| v1_xboole_0(k1_autgroup(sK0)) ),
inference(resolve,[status(thm)],[c_12501,c_263]) ).
cnf(c_12503,plain,
r2_hidden(sK1(k4_autgroup(sK0),k1_autgroup(sK0)),k1_autgroup(sK0)),
inference(resolve,[status(thm)],[c_635,c_12520]) ).
cnf(c_12521,plain,
r1_tarski(k4_autgroup(sK0),k1_autgroup(sK0)),
inference(resolve,[status(thm)],[c_12503,c_293]) ).
cnf(c_12507,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_251,c_12521]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP623+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 15:04:05 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 3500213 was started by sandbox on n004,
% 0.13/0.36 % Fri Sep 25 15:04:05 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 22.84/3.36
% 22.84/3.36 % given #500 (T,wt=24): 2276 m1_subset_1(f1(A,k1_xboole_0),A) | m1_subset_1(B,k1_zfmisc_1(C)) | -r2_hidden(B,f1(B,A)). [resolve(1839,b,296,b)].
% 22.84/3.36
% 22.84/3.36 % given #1000 (T,wt=27): 5185 r2_hidden(f4(f9(c12)),A) | -r2_hidden(u1_struct_0(c12),f1(f9(c12),A)). [resolve(891,b,296,b)].
% 22.84/3.36
% 22.84/3.36 % SZS status Theorem for theBenchmark
% 22.84/3.36
% 22.84/3.36 % Proof 1 at 2.44 (+ 0.50) seconds.
% 22.84/3.36 % Length of proof is 47.
% 22.84/3.36 % Level of proof is 9.
% 22.84/3.36 % Maximum clause weight is 34.000.
% 22.84/3.36 % Given clauses 1129.
% 22.84/3.36
% 22.84/3.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
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