%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP623+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n008.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 : Fri Sep 25 01:34:53 PM UTC 2026
% Result : Theorem 4.50s 1.27s
% Output : CNFRefutation 4.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 110 ( 19 unt; 0 def)
% Number of atoms : 410 ( 12 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 452 ( 187 ~; 201 |; 46 &)
% ( 5 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 4 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 160 ( 0 sgn 156 !; 4 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> r1_tarski(k4_autgroup(X0),k1_autgroup(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_autgroup) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> r1_tarski(k4_autgroup(X0),k1_autgroup(X0)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f13,axiom,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X0)
=> r2_hidden(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f15,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_autgroup) ).
fof(f19,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_autgroup) ).
fof(f20,axiom,
! [X0] :
( l1_group_1(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(f22,axiom,
! [X0,X1,X2] :
( m1_fraenkel(X2,X0,X1)
=> ( v1_fraenkel(X2)
& ~ v1_xboole_0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_fraenkel) ).
fof(f37,axiom,
! [X0] :
( ( l1_struct_0(X0)
& ~ v3_struct_0(X0) )
=> ~ v1_xboole_0(u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f54,axiom,
! [X0,X1,X2] :
( ( m1_fraenkel(X2,X0,X1)
& ~ v1_xboole_0(X1) )
=> ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_fraenkel) ).
fof(f57,axiom,
! [X0] :
( ( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
=> m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_autgroup) ).
fof(f58,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f59,axiom,
! [X0,X1] :
( m1_subset_1(X0,X1)
=> ( r2_hidden(X0,X1)
| v1_xboole_0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f72,plain,
? [X0] :
( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0)
& ~ r1_tarski(k4_autgroup(X0),k1_autgroup(X0)) ),
inference(ennf_transformation,[],[f2]) ).
fof(f73,plain,
? [X0] :
( l1_group_1(X0)
& v4_group_1(X0)
& v3_group_1(X0)
& v1_group_1(X0)
& ~ v3_struct_0(X0)
& ~ r1_tarski(k4_autgroup(X0),k1_autgroup(X0)) ),
inference(flattening,[],[f72]) ).
fof(f90,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( ~ r2_hidden(X2,X0)
| r2_hidden(X2,X1) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f93,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f15]) ).
fof(f94,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f19]) ).
fof(f96,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(flattening,[],[f95]) ).
fof(f97,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ~ m1_fraenkel(X2,X0,X1)
| ( v1_fraenkel(X2)
& ~ v1_xboole_0(X2) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f107,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f108,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(flattening,[],[f107]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ! [X3] :
( m2_fraenkel(X3,X0,X1,X2)
<=> m1_subset_1(X3,X2) ) ),
inference(flattening,[],[f113]) ).
fof(f115,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
| m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ),
inference(ennf_transformation,[],[f57]) ).
fof(f116,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
| m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ) ),
inference(flattening,[],[f115]) ).
fof(f117,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f58]) ).
fof(f118,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f59]) ).
fof(f119,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(flattening,[],[f118]) ).
fof(f126,plain,
( l1_group_1(sK0)
& v4_group_1(sK0)
& v3_group_1(sK0)
& v1_group_1(sK0)
& ~ v3_struct_0(sK0)
& ~ r1_tarski(k4_autgroup(sK0),k1_autgroup(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f73]) ).
fof(f127,plain,
! [X0,X1] :
( ( ~ r1_tarski(X0,X1)
| ! [X2] :
( ~ r2_hidden(X2,X0)
| r2_hidden(X2,X1) ) )
& ( ? [X2] :
( r2_hidden(X2,X0)
& ~ r2_hidden(X2,X1) )
| r1_tarski(X0,X1) ) ),
inference(nnf_transformation,[],[f90]) ).
fof(f128,plain,
! [X0,X1] :
( ( ~ r1_tarski(X0,X1)
| ! [X3] :
( ~ r2_hidden(X3,X0)
| r2_hidden(X3,X1) ) )
& ( ? [X2] :
( r2_hidden(X2,X0)
& ~ r2_hidden(X2,X1) )
| r1_tarski(X0,X1) ) ),
inference(rectify,[],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( ( ~ r1_tarski(X0,X1)
| ! [X3] :
( ~ r2_hidden(X3,X0)
| r2_hidden(X3,X1) ) )
& ( ( r2_hidden(sK1(X0,X1),X0)
& ~ r2_hidden(sK1(X0,X1),X1) )
| r1_tarski(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f128]) ).
fof(f151,plain,
! [X0,X1,X2] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ! [X3] :
( ( ~ m2_fraenkel(X3,X0,X1,X2)
| m1_subset_1(X3,X2) )
& ( ~ m1_subset_1(X3,X2)
| m2_fraenkel(X3,X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f114]) ).
fof(f154,plain,
l1_group_1(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f155,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f156,plain,
v3_group_1(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f157,plain,
v1_group_1(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f158,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f126]) ).
fof(f159,plain,
~ r1_tarski(k4_autgroup(sK0),k1_autgroup(sK0)),
inference(cnf_transformation,[],[f126]) ).
fof(f179,plain,
! [X0,X1] :
( r2_hidden(sK1(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f180,plain,
! [X0,X1] :
( ~ r2_hidden(sK1(X0,X1),X1)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f183,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f94]) ).
fof(f184,plain,
! [X0] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f96]) ).
fof(f185,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f187,plain,
! [X2,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| ~ v1_xboole_0(X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f204,plain,
! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f243,plain,
! [X2,X3,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ~ m2_fraenkel(X3,X0,X1,X2)
| m1_subset_1(X3,X2) ),
inference(cnf_transformation,[],[f151]) ).
fof(f244,plain,
! [X2,X3,X0,X1] :
( ~ m1_fraenkel(X2,X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X3,X2)
| m2_fraenkel(X3,X0,X1,X2) ),
inference(cnf_transformation,[],[f151]) ).
fof(f248,plain,
! [X0,X1] :
( ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0)
| v3_struct_0(X0)
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
| m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0)) ),
inference(cnf_transformation,[],[f116]) ).
fof(f249,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f250,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_49,negated_conjecture,
~ r1_tarski(k4_autgroup(sK0),k1_autgroup(sK0)),
inference(cnf_transformation,[],[f159]) ).
tcf(c_50,negated_conjecture,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f158]) ).
tcf(c_51,negated_conjecture,
v1_group_1(sK0),
inference(cnf_transformation,[],[f157]) ).
tcf(c_52,negated_conjecture,
v3_group_1(sK0),
inference(cnf_transformation,[],[f156]) ).
tcf(c_53,negated_conjecture,
v4_group_1(sK0),
inference(cnf_transformation,[],[f155]) ).
tcf(c_54,negated_conjecture,
l1_group_1(sK0),
inference(cnf_transformation,[],[f154]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| ~ r2_hidden(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| r2_hidden(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_70,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_71,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v3_group_1(X0)
| ~ v1_group_1(X0) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_72,plain,
! [X0: $i] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ v1_xboole_0(X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_91,plain,
! [X0: $i] :
( v3_struct_0(X0)
| ~ l1_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[],[f204]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X2)
| m2_fraenkel(X3,X1,X2,X0)
| ~ m1_subset_1(X3,X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(cnf_transformation,[],[f244]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X2)
| m1_subset_1(X0,X3)
| ~ m1_fraenkel(X3,X1,X2)
| ~ m2_fraenkel(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f243]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k1_autgroup(X1))
| ~ l1_group_1(X1)
| ~ v4_group_1(X1)
| ~ v3_group_1(X1)
| ~ v1_group_1(X1)
| ~ m2_fraenkel(X0,u1_struct_0(X1),u1_struct_0(X1),k4_autgroup(X1)) ),
inference(cnf_transformation,[],[f248]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f249]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f250]) ).
tcf(c_151,plain,
( l1_struct_0(sK0)
| ~ l1_group_1(sK0) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_171,plain,
( v3_struct_0(sK0)
| ~ l1_struct_0(sK0)
| ~ v1_xboole_0(u1_struct_0(sK0)) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_189,plain,
( v3_struct_0(sK0)
| 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)
| ~ v1_group_1(sK0) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_190,plain,
( v3_struct_0(sK0)
| 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)
| ~ v1_group_1(sK0) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_232,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ m1_fraenkel(X0,X1,X2)
| ~ v1_xboole_0(X0) ),
inference(prop_impl_just,[status(thm)],[c_73]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ v1_xboole_0(X0)
| ~ m1_fraenkel(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_232]) ).
tcf(c_1249,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_fraenkel(k4_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v1_group_1(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_71]) ).
tcf(c_1250,plain,
( v3_struct_0(sK0)
| m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v1_group_1(sK0) ),
inference(unflattening,[status(thm)],[c_1249]) ).
tcf(c_1251,plain,
m1_fraenkel(k4_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)),
inference(global_subsumption_just,[status(thm)],[c_1250,c_54,c_53,c_52,c_51,c_50,c_189]) ).
tcf(c_1256,plain,
! [X0: $i] :
( v3_struct_0(X0)
| m1_fraenkel(k1_autgroup(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v1_group_1(X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_70]) ).
tcf(c_1257,plain,
( v3_struct_0(sK0)
| m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v1_group_1(sK0) ),
inference(unflattening,[status(thm)],[c_1256]) ).
tcf(c_1258,plain,
m1_fraenkel(k1_autgroup(sK0),u1_struct_0(sK0),u1_struct_0(sK0)),
inference(global_subsumption_just,[status(thm)],[c_1257,c_54,c_53,c_52,c_51,c_50,c_190]) ).
tcf(c_1263,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k1_autgroup(X0))
| ~ l1_group_1(X0)
| ~ v4_group_1(X0)
| ~ v1_group_1(X0)
| ~ m2_fraenkel(X1,u1_struct_0(X0),u1_struct_0(X0),k4_autgroup(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_135]) ).
tcf(c_1264,plain,
! [X0: $i] :
( v3_struct_0(sK0)
| m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ l1_group_1(sK0)
| ~ v4_group_1(sK0)
| ~ v1_group_1(sK0)
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(unflattening,[status(thm)],[c_1263]) ).
tcf(c_1266,plain,
! [X0: $i] :
( ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_1264,c_54,c_53,c_51,c_50,c_1264]) ).
tcf(c_1267,plain,
! [X0: $i] :
( m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(renaming,[status(thm)],[c_1266]) ).
tcf(c_3238,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X2)
| m2_fraenkel(X3,X1,X2,X0)
| ~ m1_subset_1(X3,X0)
| ( u1_struct_0(sK0) != X2 )
| ( u1_struct_0(sK0) != X1 )
| ( k4_autgroup(sK0) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_130,c_1251]) ).
tcf(c_3239,plain,
! [X0: $i] :
( v1_xboole_0(u1_struct_0(sK0))
| m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ m1_subset_1(X0,k4_autgroup(sK0)) ),
inference(unflattening,[status(thm)],[c_3238]) ).
tcf(c_3241,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,k4_autgroup(sK0))
| m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_3239,c_54,c_50,c_151,c_171,c_3239]) ).
tcf(c_3242,plain,
! [X0: $i] :
( m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k4_autgroup(sK0))
| ~ m1_subset_1(X0,k4_autgroup(sK0)) ),
inference(renaming,[status(thm)],[c_3241]) ).
tcf(c_3291,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ v1_xboole_0(X0)
| ( u1_struct_0(sK0) != X2 )
| ( u1_struct_0(sK0) != X1 )
| ( k1_autgroup(sK0) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_233,c_1258]) ).
tcf(c_3292,plain,
~ v1_xboole_0(k1_autgroup(sK0)),
inference(unflattening,[status(thm)],[c_3291]) ).
tcf(c_3450,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v1_xboole_0(X1)
| m1_subset_1(X3,X2)
| ~ m2_fraenkel(X3,X0,X1,X2)
| ( u1_struct_0(sK0) != X1 )
| ( u1_struct_0(sK0) != X0 )
| ( k1_autgroup(sK0) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_131,c_1258]) ).
tcf(c_3451,plain,
! [X0: $i] :
( v1_xboole_0(u1_struct_0(sK0))
| m1_subset_1(X0,k1_autgroup(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) ),
inference(unflattening,[status(thm)],[c_3450]) ).
tcf(c_3453,plain,
! [X0: $i] :
( ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0))
| m1_subset_1(X0,k1_autgroup(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_3451,c_54,c_50,c_151,c_171,c_3451]) ).
tcf(c_3454,plain,
! [X0: $i] :
( m1_subset_1(X0,k1_autgroup(sK0))
| ~ m2_fraenkel(X0,u1_struct_0(sK0),u1_struct_0(sK0),k1_autgroup(sK0)) ),
inference(renaming,[status(thm)],[c_3453]) ).
tcf(c_7656,plain,
! [X0: $i] :
( m1_subset_1(X0,iPr_def_11)
| ~ m2_fraenkel(X0,iPr_def_10,iPr_def_10,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_3454]) ).
tcf(c_7661,plain,
~ v1_xboole_0(iPr_def_11),
inference(demodulation,[status(thm)],[c_3292]) ).
tcf(c_7668,plain,
! [X0: $i] :
( m2_fraenkel(X0,iPr_def_10,iPr_def_10,iPr_def_12)
| ~ m1_subset_1(X0,iPr_def_12) ),
inference(demodulation,[status(thm)],[c_3242]) ).
tcf(c_7669,plain,
! [X0: $i] :
( m2_fraenkel(X0,iPr_def_10,iPr_def_10,iPr_def_11)
| ~ m2_fraenkel(X0,iPr_def_10,iPr_def_10,iPr_def_12) ),
inference(demodulation,[status(thm)],[c_1267]) ).
tcf(c_7673,negated_conjecture,
~ r1_tarski(iPr_def_12,iPr_def_11),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_9597,plain,
! [X0: $i] :
( m2_fraenkel(X0,iPr_def_10,iPr_def_10,iPr_def_11)
| ~ m1_subset_1(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_7668,c_7669]) ).
tcf(c_9607,plain,
! [X0: $i] :
( m1_subset_1(X0,iPr_def_11)
| ~ m1_subset_1(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_9597,c_7656]) ).
tcf(c_9752,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| m1_subset_1(sK1(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_66,c_136]) ).
tcf(c_9873,plain,
! [X0: $i] :
( r1_tarski(iPr_def_12,X0)
| m1_subset_1(sK1(iPr_def_12,X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_9752,c_9607]) ).
tcf(c_9996,plain,
! [X0: $i] :
( v1_xboole_0(iPr_def_11)
| r1_tarski(iPr_def_12,X0)
| r2_hidden(sK1(iPr_def_12,X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_9873,c_137]) ).
tcf(c_9999,plain,
! [X0: $i] :
( r1_tarski(iPr_def_12,X0)
| r2_hidden(sK1(iPr_def_12,X0),iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9996,c_7661]) ).
tcf(c_10010,plain,
r1_tarski(iPr_def_12,iPr_def_11),
inference(superposition,[status(thm)],[c_9999,c_65]) ).
tcf(c_10011,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_10010,c_7673]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP623+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 15:17:24 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 4.50/1.27 % SZS status Started for theBenchmark.p
% 4.50/1.27 % SZS status Theorem for theBenchmark.p
% 4.50/1.27
% 4.50/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.50/1.27
% 4.50/1.27 % ------ iProver source info
% 4.50/1.27
% 4.50/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 4.50/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.50/1.27 % git: non_committed_changes: false
% 4.50/1.27
% 4.50/1.27 % ------ Parsing...
% 4.50/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.50/1.27
% 4.50/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 10 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e %
% 4.50/1.27
% 4.50/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.50/1.27
% 4.50/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.50/1.27 % ------ Proving...
% 4.50/1.27 % ------ Problem Properties
% 4.50/1.27
% 4.50/1.27 %
% 4.50/1.27 % clauses 118
% 4.50/1.27 % conjectures 4
% 4.50/1.27 % EPR 57
% 4.50/1.27 % Horn 107
% 4.50/1.27 % unary 56
% 4.50/1.27 % binary 41
% 4.50/1.27 % lits 211
% 4.50/1.27 % lits eq 12
% 4.50/1.27 % fd_pure 0
% 4.50/1.27 % fd_pseudo 0
% 4.50/1.27 % fd_cond 1
% 4.50/1.27 % fd_pseudo_cond 3
% 4.50/1.27 % AC symbols 0
% 4.50/1.27
% 4.50/1.27 % ------ Schedule dynamic 5 is on
% 4.50/1.27
% 4.50/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.50/1.27
% 4.50/1.27
% 4.50/1.27 % ------
% 4.50/1.27 % Current options:
% 4.50/1.27 % ------
% 4.50/1.27
% 4.50/1.27
% 4.50/1.27 %
% 4.50/1.27
% 4.50/1.27 % ------ Proving...
% 4.50/1.27 %
% 4.50/1.27
% 4.50/1.27 % SZS status Theorem for theBenchmark.p
% 4.50/1.27
% 4.50/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.50/1.27
% 4.50/1.27
%------------------------------------------------------------------------------