%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : TOP028+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n019.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 03:55:02 PM UTC 2026
% Result : Theorem 0.94s 1.28s
% Output : CNFRefutation 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 97 ( 13 unt; 3 def)
% Number of atoms : 531 ( 19 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 651 ( 247 ~; 244 |; 146 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 25 ( 23 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 143 ( 0 sgn 132 !; 11 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( l1_pre_topc(X0)
& v2_pre_topc(X0)
& ~ v3_struct_0(X0) )
=> ? [X1] :
( v1_tsp_2(X1,X0)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_tsp_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l1_pre_topc(X0)
& v2_pre_topc(X0)
& ~ v3_struct_0(X0) )
=> ? [X1] :
( v1_tsp_2(X1,X0)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f24,axiom,
! [X0] :
( ( l1_pre_topc(X0)
& v2_pre_topc(X0) )
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
=> ( ( v3_tops_1(X1,X0)
& v3_pre_topc(X1,X0) )
=> ( v3_tops_1(X1,X0)
& v2_tops_1(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& v4_pre_topc(X1,X0)
& v3_pre_topc(X1,X0)
& v1_xboole_0(X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_tops_1) ).
fof(f50,axiom,
! [X0] :
( ( l1_pre_topc(X0)
& v2_pre_topc(X0) )
=> ? [X1] :
( v3_tops_1(X1,X0)
& v2_tops_1(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& v4_pre_topc(X1,X0)
& v3_pre_topc(X1,X0)
& v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_tops_1) ).
fof(f54,axiom,
! [X0] :
( ( l1_pre_topc(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
=> ( v3_tex_2(X1,X0)
=> v1_tsp_1(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_tsp_1) ).
fof(f57,axiom,
! [X0] :
( ( l1_pre_topc(X0)
& v2_pre_topc(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
& v1_xboole_0(X1) )
=> v3_tex_2(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_tex_2) ).
fof(f64,axiom,
! [X0] :
( ( l1_pre_topc(X0)
& v2_pre_topc(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
=> ~ ( ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
=> ~ ( v1_tsp_2(X2,X0)
& r1_tarski(X1,X2) ) )
& v1_tsp_1(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tsp_2) ).
fof(f82,plain,
? [X0] :
( l1_pre_topc(X0)
& v2_pre_topc(X0)
& ~ v3_struct_0(X0)
& ! [X1] :
( ~ v1_tsp_2(X1,X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f83,plain,
? [X0] :
( l1_pre_topc(X0)
& v2_pre_topc(X0)
& ~ v3_struct_0(X0)
& ! [X1] :
( ~ v1_tsp_2(X1,X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ) ),
inference(flattening,[],[f82]) ).
fof(f105,plain,
! [X0] :
( ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v3_tops_1(X1,X0)
| ~ v3_pre_topc(X1,X0)
| ( v3_tops_1(X1,X0)
& v2_tops_1(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& v4_pre_topc(X1,X0)
& v3_pre_topc(X1,X0)
& v1_xboole_0(X1) ) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f106,plain,
! [X0] :
( ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v3_tops_1(X1,X0)
| ~ v3_pre_topc(X1,X0)
| ( v3_tops_1(X1,X0)
& v2_tops_1(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& v4_pre_topc(X1,X0)
& v3_pre_topc(X1,X0)
& v1_xboole_0(X1) ) ) ),
inference(flattening,[],[f105]) ).
fof(f126,plain,
! [X0] :
( ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| ? [X1] :
( v3_tops_1(X1,X0)
& v2_tops_1(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& v4_pre_topc(X1,X0)
& v3_pre_topc(X1,X0)
& v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ) ),
inference(ennf_transformation,[],[f50]) ).
fof(f127,plain,
! [X0] :
( ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| ? [X1] :
( v3_tops_1(X1,X0)
& v2_tops_1(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& v4_pre_topc(X1,X0)
& v3_pre_topc(X1,X0)
& v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ) ),
inference(flattening,[],[f126]) ).
fof(f132,plain,
! [X0] :
( ~ l1_pre_topc(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v3_tex_2(X1,X0)
| v1_tsp_1(X1,X0) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f133,plain,
! [X0] :
( ~ l1_pre_topc(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v3_tex_2(X1,X0)
| v1_tsp_1(X1,X0) ) ),
inference(flattening,[],[f132]) ).
fof(f137,plain,
! [X0] :
( ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_xboole_0(X1)
| v3_tex_2(X1,X0) ) ),
inference(ennf_transformation,[],[f57]) ).
fof(f138,plain,
! [X0] :
( ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_xboole_0(X1)
| v3_tex_2(X1,X0) ) ),
inference(flattening,[],[f137]) ).
fof(f146,plain,
! [X0] :
( ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
& v1_tsp_2(X2,X0)
& r1_tarski(X1,X2) )
| ~ v1_tsp_1(X1,X0) ) ),
inference(ennf_transformation,[],[f64]) ).
fof(f147,plain,
! [X0] :
( ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ? [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
& v1_tsp_2(X2,X0)
& r1_tarski(X1,X2) )
| ~ v1_tsp_1(X1,X0) ) ),
inference(flattening,[],[f146]) ).
fof(f152,plain,
( l1_pre_topc(sK2)
& v2_pre_topc(sK2)
& ~ v3_struct_0(sK2)
& ! [X1] :
( ~ v1_tsp_2(X1,sK2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK2))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f83]) ).
fof(f171,plain,
! [X0] :
( ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| v3_struct_0(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ( m1_subset_1(sK18(X0,X1),k1_zfmisc_1(u1_struct_0(X0)))
& v1_tsp_2(sK18(X0,X1),X0)
& r1_tarski(X1,sK18(X0,X1)) )
| ~ v1_tsp_1(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X2,sK18(X0,X1))],[f147]) ).
fof(f172,plain,
l1_pre_topc(sK2),
inference(cnf_transformation,[],[f152]) ).
fof(f173,plain,
v2_pre_topc(sK2),
inference(cnf_transformation,[],[f152]) ).
fof(f174,plain,
~ v3_struct_0(sK2),
inference(cnf_transformation,[],[f152]) ).
fof(f175,plain,
! [X1] :
( ~ v1_tsp_2(X1,sK2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK2))) ),
inference(cnf_transformation,[],[f152]) ).
fof(f218,plain,
! [X0,X1] :
( ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v3_tops_1(X1,X0)
| ~ v3_pre_topc(X1,X0)
| sP0(X1,X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f295,plain,
! [X0] :
( ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| sP1(X0) ),
inference(cnf_transformation,[],[f151]) ).
fof(f302,plain,
! [X0,X1] :
( ~ l1_pre_topc(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v3_tex_2(X1,X0)
| v1_tsp_1(X1,X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f305,plain,
! [X0,X1] :
( ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_xboole_0(X1)
| v3_tex_2(X1,X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f312,plain,
! [X0,X1] :
( ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| m1_subset_1(sK18(X0,X1),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_tsp_1(X1,X0) ),
inference(cnf_transformation,[],[f171]) ).
fof(f313,plain,
! [X0,X1] :
( ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| v3_struct_0(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v1_tsp_2(sK18(X0,X1),X0)
| ~ v1_tsp_1(X1,X0) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] :
( ~ v1_tsp_2(X0,sK2)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK2))) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_50,negated_conjecture,
~ v3_struct_0(sK2),
inference(cnf_transformation,[],[f174]) ).
tcf(c_51,negated_conjecture,
v2_pre_topc(sK2),
inference(cnf_transformation,[],[f173]) ).
tcf(c_52,negated_conjecture,
l1_pre_topc(sK2),
inference(cnf_transformation,[],[f172]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( sP0(X0,X1)
| ~ l1_pre_topc(X1)
| ~ v2_pre_topc(X1)
| ~ v3_tops_1(X0,X1)
| ~ v3_pre_topc(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_171,plain,
! [X0: $i] :
( sP1(X0)
| ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0) ),
inference(cnf_transformation,[],[f295]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v1_tsp_1(X0,X1)
| ~ l1_pre_topc(X1)
| ~ v3_tex_2(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f302]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v3_tex_2(X0,X1)
| ~ v1_xboole_0(X0)
| ~ l1_pre_topc(X1)
| ~ v2_pre_topc(X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f305]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v1_tsp_2(sK18(X1,X0),X1)
| ~ l1_pre_topc(X1)
| ~ v2_pre_topc(X1)
| ~ v1_tsp_1(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f313]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_subset_1(sK18(X1,X0),k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_pre_topc(X1)
| ~ v2_pre_topc(X1)
| ~ v1_tsp_1(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(cnf_transformation,[],[f312]) ).
tcf(c_1605,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X0)
| ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| ~ v1_tsp_1(X1,X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(sK2)))
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ( X0 != sK2 )
| ( sK18(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_189]) ).
tcf(c_1606,plain,
! [X0: $i] :
( v3_struct_0(sK2)
| ~ l1_pre_topc(sK2)
| ~ v2_pre_topc(sK2)
| ~ v1_tsp_1(X0,sK2)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK2)))
| ~ m1_subset_1(sK18(sK2,X0),k1_zfmisc_1(u1_struct_0(sK2))) ),
inference(unflattening,[status(thm)],[c_1605]) ).
tcf(c_1608,plain,
! [X0: $i] :
( ~ m1_subset_1(sK18(sK2,X0),k1_zfmisc_1(u1_struct_0(sK2)))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK2)))
| ~ v1_tsp_1(X0,sK2) ),
inference(global_subsumption_just,[status(thm)],[c_1606,c_52,c_51,c_50,c_1606]) ).
tcf(c_1609,plain,
! [X0: $i] :
( ~ v1_tsp_1(X0,sK2)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK2)))
| ~ m1_subset_1(sK18(sK2,X0),k1_zfmisc_1(u1_struct_0(sK2))) ),
inference(renaming,[status(thm)],[c_1608]) ).
tcf(c_1657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X3)
| v3_struct_0(X2)
| v1_tsp_1(X1,X3)
| ~ v1_xboole_0(X0)
| ~ l1_pre_topc(X3)
| ~ l1_pre_topc(X2)
| ~ v2_pre_topc(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X3)))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X2)))
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_181,c_178]) ).
tcf(c_1658,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| v1_tsp_1(X0,X1)
| ~ v1_xboole_0(X0)
| ~ l1_pre_topc(X1)
| ~ v2_pre_topc(X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(unflattening,[status(thm)],[c_1657]) ).
tcf(c_1795,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( v3_struct_0(X3)
| v3_struct_0(X2)
| m1_subset_1(sK18(X3,X1),k1_zfmisc_1(u1_struct_0(X3)))
| ~ v1_xboole_0(X0)
| ~ l1_pre_topc(X3)
| ~ l1_pre_topc(X2)
| ~ v2_pre_topc(X3)
| ~ v2_pre_topc(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X3)))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X2)))
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_1658,c_190]) ).
tcf(c_1796,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X1)
| m1_subset_1(sK18(X1,X0),k1_zfmisc_1(u1_struct_0(X1)))
| ~ v1_xboole_0(X0)
| ~ l1_pre_topc(X1)
| ~ v2_pre_topc(X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1))) ),
inference(unflattening,[status(thm)],[c_1795]) ).
tcf(c_1816,plain,
! [X0: $i,X1: $i,X2: $i] :
( v3_struct_0(X2)
| ~ v1_xboole_0(X0)
| ~ l1_pre_topc(X2)
| ~ v2_pre_topc(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(sK2)))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X2)))
| ~ m1_subset_1(sK18(sK2,X1),k1_zfmisc_1(u1_struct_0(sK2)))
| ( X2 != sK2 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_1658,c_1609]) ).
tcf(c_1817,plain,
! [X0: $i] :
( v3_struct_0(sK2)
| ~ l1_pre_topc(sK2)
| ~ v2_pre_topc(sK2)
| ~ v1_xboole_0(X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK2)))
| ~ m1_subset_1(sK18(sK2,X0),k1_zfmisc_1(u1_struct_0(sK2))) ),
inference(unflattening,[status(thm)],[c_1816]) ).
tcf(c_1819,plain,
! [X0: $i] :
( ~ m1_subset_1(sK18(sK2,X0),k1_zfmisc_1(u1_struct_0(sK2)))
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK2)))
| ~ v1_xboole_0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1817,c_52,c_51,c_50,c_1817]) ).
tcf(c_1820,plain,
! [X0: $i] :
( ~ v1_xboole_0(X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK2)))
| ~ m1_subset_1(sK18(sK2,X0),k1_zfmisc_1(u1_struct_0(sK2))) ),
inference(renaming,[status(thm)],[c_1819]) ).
tcf(c_2403,plain,
! [X0: $i,X1: $i] :
( v3_struct_0(X0)
| m1_subset_1(sK18(X0,X1),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_xboole_0(X1)
| ~ l1_pre_topc(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_1796]) ).
tcf(c_2404,plain,
! [X0: $i] :
( v3_struct_0(sK2)
| m1_subset_1(sK18(sK2,X0),k1_zfmisc_1(u1_struct_0(sK2)))
| ~ l1_pre_topc(sK2)
| ~ v1_xboole_0(X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK2))) ),
inference(unflattening,[status(thm)],[c_2403]) ).
tcf(c_2406,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK2)))
| ~ v1_xboole_0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_2404,c_52,c_50,c_1820,c_2404]) ).
tcf(c_2407,plain,
! [X0: $i] :
( ~ v1_xboole_0(X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK2))) ),
inference(renaming,[status(thm)],[c_2406]) ).
tcf(c_2870,definition,
iPr_def_23 = sK15(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_2890,plain,
! [X0: $i] :
( ~ v1_xboole_0(X0)
| ~ m1_subset_1(X0,iPr_def_12) ),
inference(demodulation,[status(thm)],[c_2407]) ).
fof(f148,definition,
! [X1,X0] :
( ~ sP0(X1,X0)
| ( v3_tops_1(X1,X0)
& v2_tops_1(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& v4_pre_topc(X1,X0)
& v3_pre_topc(X1,X0)
& v1_xboole_0(X1) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f149,plain,
! [X0] :
( ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| ! [X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v3_tops_1(X1,X0)
| ~ v3_pre_topc(X1,X0)
| sP0(X1,X0) ) ),
inference(definition_folding,[],[f106,f148]) ).
fof(f150,definition,
! [X0] :
( ~ sP1(X0)
| ? [X1] :
( v3_tops_1(X1,X0)
& v2_tops_1(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& v4_pre_topc(X1,X0)
& v3_pre_topc(X1,X0)
& v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f151,plain,
! [X0] :
( ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| sP1(X0) ),
inference(definition_folding,[],[f127,f150]) ).
fof(f153,plain,
! [X1,X0] :
( ~ sP0(X1,X0)
| ( v3_tops_1(X1,X0)
& v2_tops_1(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& v4_pre_topc(X1,X0)
& v3_pre_topc(X1,X0)
& v1_xboole_0(X1) ) ),
inference(nnf_transformation,[],[f148]) ).
fof(f154,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ( v3_tops_1(X0,X1)
& v2_tops_1(X0,X1)
& v5_membered(X0)
& v4_membered(X0)
& v3_membered(X0)
& v2_membered(X0)
& v1_membered(X0)
& v4_pre_topc(X0,X1)
& v3_pre_topc(X0,X1)
& v1_xboole_0(X0) ) ),
inference(rectify,[],[f153]) ).
fof(f167,plain,
! [X0] :
( ~ sP1(X0)
| ? [X1] :
( v3_tops_1(X1,X0)
& v2_tops_1(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& v4_pre_topc(X1,X0)
& v3_pre_topc(X1,X0)
& v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ) ),
inference(nnf_transformation,[],[f150]) ).
fof(f168,plain,
! [X0] :
( ~ sP1(X0)
| ( v3_tops_1(sK15(X0),X0)
& v2_tops_1(sK15(X0),X0)
& v5_membered(sK15(X0))
& v4_membered(sK15(X0))
& v3_membered(sK15(X0))
& v2_membered(sK15(X0))
& v1_membered(sK15(X0))
& v4_pre_topc(sK15(X0),X0)
& v3_pre_topc(sK15(X0),X0)
& v1_xboole_0(sK15(X0))
& m1_subset_1(sK15(X0),k1_zfmisc_1(u1_struct_0(X0))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X1,sK15(X0))],[f167]) ).
fof(f217,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f284,plain,
! [X0] :
( ~ sP1(X0)
| v3_tops_1(sK15(X0),X0) ),
inference(cnf_transformation,[],[f168]) ).
fof(f292,plain,
! [X0] :
( ~ sP1(X0)
| v3_pre_topc(sK15(X0),X0) ),
inference(cnf_transformation,[],[f168]) ).
fof(f294,plain,
! [X0] :
( ~ sP1(X0)
| m1_subset_1(sK15(X0),k1_zfmisc_1(u1_struct_0(X0))) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X0)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_160,plain,
! [X0: $i] :
( m1_subset_1(sK15(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f294]) ).
tcf(c_162,plain,
! [X0: $i] :
( v3_pre_topc(sK15(X0),X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f292]) ).
tcf(c_170,plain,
! [X0: $i] :
( v3_tops_1(sK15(X0),X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f284]) ).
tcf(c_1720,plain,
! [X0: $i,X1: $i] :
( v3_pre_topc(sK15(X1),X1)
| ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_171,c_162]) ).
tcf(c_1721,plain,
! [X0: $i] :
( v3_pre_topc(sK15(X0),X0)
| ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0) ),
inference(unflattening,[status(thm)],[c_1720]) ).
tcf(c_1744,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(sK15(X1),k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_171,c_160]) ).
tcf(c_1745,plain,
! [X0: $i] :
( m1_subset_1(sK15(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0) ),
inference(unflattening,[status(thm)],[c_1744]) ).
tcf(c_2228,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X1,X2)
| ~ sP1(X0)
| ~ l1_pre_topc(X2)
| ~ v2_pre_topc(X2)
| ~ v3_pre_topc(X1,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))
| ( X0 != X2 )
| ( sK15(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_94,c_170]) ).
tcf(c_2229,plain,
! [X0: $i] :
( sP0(sK15(X0),X0)
| ~ sP1(X0)
| ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| ~ v3_pre_topc(sK15(X0),X0)
| ~ m1_subset_1(sK15(X0),k1_zfmisc_1(u1_struct_0(X0))) ),
inference(unflattening,[status(thm)],[c_2228]) ).
tcf(c_2231,plain,
! [X0: $i] :
( sP0(sK15(X0),X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0) ),
inference(global_subsumption_just,[status(thm)],[c_2229,c_171,c_1721,c_1745,c_2229]) ).
tcf(c_2232,plain,
! [X0: $i] :
( sP0(sK15(X0),X0)
| ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0) ),
inference(renaming,[status(thm)],[c_2231]) ).
tcf(c_2361,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_xboole_0(X1)
| ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| ( X0 != X2 )
| ( sK15(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_84,c_2232]) ).
tcf(c_2362,plain,
! [X0: $i] :
( v1_xboole_0(sK15(X0))
| ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0) ),
inference(unflattening,[status(thm)],[c_2361]) ).
tcf(c_2389,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(sK15(X1),k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_171,c_160]) ).
tcf(c_2390,plain,
! [X0: $i] :
( m1_subset_1(sK15(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_pre_topc(X0)
| ~ v2_pre_topc(X0) ),
inference(unflattening,[status(thm)],[c_2389]) ).
tcf(c_2417,plain,
! [X0: $i] :
( m1_subset_1(sK15(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_pre_topc(X0)
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_2390]) ).
tcf(c_2418,plain,
( m1_subset_1(sK15(sK2),k1_zfmisc_1(u1_struct_0(sK2)))
| ~ l1_pre_topc(sK2) ),
inference(unflattening,[status(thm)],[c_2417]) ).
tcf(c_2419,plain,
m1_subset_1(sK15(sK2),k1_zfmisc_1(u1_struct_0(sK2))),
inference(global_subsumption_just,[status(thm)],[c_2418,c_52,c_2418]) ).
tcf(c_2424,plain,
! [X0: $i] :
( v1_xboole_0(sK15(X0))
| ~ l1_pre_topc(X0)
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_2362]) ).
tcf(c_2425,plain,
( v1_xboole_0(sK15(sK2))
| ~ l1_pre_topc(sK2) ),
inference(unflattening,[status(thm)],[c_2424]) ).
tcf(c_2426,plain,
v1_xboole_0(sK15(sK2)),
inference(global_subsumption_just,[status(thm)],[c_2425,c_52,c_2425]) ).
tcf(c_2888,plain,
v1_xboole_0(iPr_def_23),
inference(demodulation,[status(thm)],[c_2426,c_2870]) ).
tcf(c_2889,plain,
m1_subset_1(iPr_def_23,iPr_def_12),
inference(demodulation,[status(thm)],[c_2419]) ).
tcf(c_3414,plain,
~ v1_xboole_0(iPr_def_23),
inference(superposition,[status(thm)],[c_2889,c_2890]) ).
tcf(c_3415,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3414,c_2888]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP028+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n019.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 04:11:48 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 0.94/1.28 % SZS status Started for theBenchmark.p
% 0.94/1.28 % SZS status Theorem for theBenchmark.p
% 0.94/1.28
% 0.94/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.94/1.28
% 0.94/1.28 % ------ iProver source info
% 0.94/1.28
% 0.94/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 0.94/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.94/1.28 % git: non_committed_changes: false
% 0.94/1.28
% 0.94/1.28 % ------ Parsing...
% 0.94/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.94/1.28
% 0.94/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 65 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 16 0s sf_e pe_s pe_e %
% 0.94/1.28
% 0.94/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.94/1.28
% 0.94/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.94/1.28 % ------ Proving...
% 0.94/1.28 % ------ Problem Properties
% 0.94/1.28
% 0.94/1.28 %
% 0.94/1.28 % clauses 65
% 0.94/1.28 % conjectures 0
% 0.94/1.28 % EPR 28
% 0.94/1.28 % Horn 63
% 0.94/1.28 % unary 48
% 0.94/1.28 % binary 13
% 0.94/1.28 % lits 86
% 0.94/1.28 % lits eq 22
% 0.94/1.28 % fd_pure 0
% 0.94/1.28 % fd_pseudo 0
% 0.94/1.28 % fd_cond 1
% 0.94/1.28 % fd_pseudo_cond 1
% 0.94/1.28 % AC symbols 0
% 0.94/1.28
% 0.94/1.28 % ------ Schedule dynamic 5 is on
% 0.94/1.28
% 0.94/1.28 % ------ no conjectures: strip conj schedule
% 0.94/1.28
% 0.94/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.94/1.28
% 0.94/1.28
% 0.94/1.28 % ------
% 0.94/1.28 % Current options:
% 0.94/1.28 % ------
% 0.94/1.28
% 0.94/1.28
% 0.94/1.28 %
% 0.94/1.28
% 0.94/1.28 % ------ Proving...
% 0.94/1.28 %
% 0.94/1.28
% 0.94/1.28 % SZS status Theorem for theBenchmark.p
% 0.94/1.28
% 0.94/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.94/1.28
% 0.94/1.28
%------------------------------------------------------------------------------