%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG225+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 : n006.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 12:53:52 PM UTC 2026
% Result : Theorem 3.77s 1.38s
% Output : CNFRefutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 17
% Syntax : Number of formulae : 117 ( 36 unt; 4 def)
% Number of atoms : 385 ( 94 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 371 ( 144 ~; 153 |; 45 &)
% ( 12 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 5 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 183 ( 0 sgn 170 !; 13 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( ( m1_pboole(X1,X0)
& v2_relat_1(X1) )
=> X1 = k1_funct_4(k1_pboole(X0),k7_relat_1(X1,k1_closure3(X0,X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_closure3) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( ( m1_pboole(X1,X0)
& v2_relat_1(X1) )
=> X1 = k1_funct_4(k1_pboole(X0),k7_relat_1(X1,k1_closure3(X0,X1))) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f13,axiom,
! [X0,X1] :
( m1_pboole(X1,X0)
=> ( v2_relat_1(X1)
<=> ! [X2] :
~ ( v1_xboole_0(k1_funct_1(X1,X2))
& r2_hidden(X2,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_pboole) ).
fof(f14,axiom,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( X2 = k1_closure3(X0,X1)
<=> X2 = a_2_0_closure3(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_closure3) ).
fof(f15,axiom,
! [X0,X1] :
( ( v1_funct_1(X1)
& v1_relat_1(X1) )
=> ( m1_pboole(X1,X0)
<=> k1_relat_1(X1) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pboole) ).
fof(f16,axiom,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( r2_hidden(X2,X0)
=> r2_hidden(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f17,axiom,
! [X0] : k1_pboole(X0) = k2_funcop_1(X0,k1_xboole_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_pboole) ).
fof(f21,axiom,
! [X0] : m1_pboole(k1_pboole(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_pboole) ).
fof(f27,axiom,
! [X0,X1] :
( m1_pboole(X1,X0)
=> ( v1_funct_1(X1)
& v1_relat_1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_pboole) ).
fof(f33,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f37,axiom,
! [X0,X1,X2] :
( ( m1_pboole(X2,X1)
& ~ v1_xboole_0(X1) )
=> ( r2_hidden(X0,a_2_0_closure3(X1,X2))
<=> ? [X3] :
( k1_funct_1(X2,X3) != k1_xboole_0
& X0 = X3
& m1_subset_1(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_closure3) ).
fof(f57,axiom,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( m1_pboole(X2,X0)
=> k1_funct_4(X1,X2) = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_closure3) ).
fof(f58,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f67,axiom,
! [X0,X1] :
( v1_relat_1(X1)
=> ( r1_tarski(k1_relat_1(X1),X0)
=> k7_relat_1(X1,X0) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t97_relat_1) ).
fof(f76,plain,
? [X0] :
( ~ v1_xboole_0(X0)
& ? [X1] :
( m1_pboole(X1,X0)
& v2_relat_1(X1)
& k1_funct_4(k1_pboole(X0),k7_relat_1(X1,k1_closure3(X0,X1))) != X1 ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f77,plain,
? [X0] :
( ~ v1_xboole_0(X0)
& ? [X1] :
( m1_pboole(X1,X0)
& v2_relat_1(X1)
& k1_funct_4(k1_pboole(X0),k7_relat_1(X1,k1_closure3(X0,X1))) != X1 ) ),
inference(flattening,[],[f76]) ).
fof(f88,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| ( v2_relat_1(X1)
<=> ! [X2] :
( ~ v1_xboole_0(k1_funct_1(X1,X2))
| ~ r2_hidden(X2,X0) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f89,plain,
! [X0] :
( v1_xboole_0(X0)
| ! [X1] :
( ~ m1_pboole(X1,X0)
| ! [X2] :
( X2 = k1_closure3(X0,X1)
<=> X2 = a_2_0_closure3(X0,X1) ) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f90,plain,
! [X0,X1] :
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| ( m1_pboole(X1,X0)
<=> k1_relat_1(X1) = X0 ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f91,plain,
! [X0,X1] :
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| ( m1_pboole(X1,X0)
<=> k1_relat_1(X1) = X0 ) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
<=> ! [X2] :
( ~ r2_hidden(X2,X0)
| r2_hidden(X2,X1) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f96,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| ( v1_funct_1(X1)
& v1_relat_1(X1) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ~ m1_pboole(X2,X1)
| v1_xboole_0(X1)
| ( r2_hidden(X0,a_2_0_closure3(X1,X2))
<=> ? [X3] :
( k1_funct_1(X2,X3) != k1_xboole_0
& X0 = X3
& m1_subset_1(X3,X1) ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ~ m1_pboole(X2,X1)
| v1_xboole_0(X1)
| ( r2_hidden(X0,a_2_0_closure3(X1,X2))
<=> ? [X3] :
( k1_funct_1(X2,X3) != k1_xboole_0
& X0 = X3
& m1_subset_1(X3,X1) ) ) ),
inference(flattening,[],[f101]) ).
fof(f110,plain,
! [X0] :
( v1_xboole_0(X0)
| ! [X1] :
( ~ m1_pboole(X1,X0)
| ! [X2] :
( ~ m1_pboole(X2,X0)
| k1_funct_4(X1,X2) = X2 ) ) ),
inference(ennf_transformation,[],[f57]) ).
fof(f111,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f58]) ).
fof(f121,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| ~ r1_tarski(k1_relat_1(X1),X0)
| k7_relat_1(X1,X0) = X1 ),
inference(ennf_transformation,[],[f67]) ).
fof(f122,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| ~ r1_tarski(k1_relat_1(X1),X0)
| k7_relat_1(X1,X0) = X1 ),
inference(flattening,[],[f121]) ).
fof(f123,plain,
( ~ v1_xboole_0(sK0)
& m1_pboole(sK1,sK0)
& v2_relat_1(sK1)
& sK1 != k1_funct_4(k1_pboole(sK0),k7_relat_1(sK1,k1_closure3(sK0,sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f77]) ).
fof(f126,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| ( ( ~ v2_relat_1(X1)
| ! [X2] :
( ~ v1_xboole_0(k1_funct_1(X1,X2))
| ~ r2_hidden(X2,X0) ) )
& ( ? [X2] :
( v1_xboole_0(k1_funct_1(X1,X2))
& r2_hidden(X2,X0) )
| v2_relat_1(X1) ) ) ),
inference(nnf_transformation,[],[f88]) ).
fof(f127,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| ( ( ~ v2_relat_1(X1)
| ! [X3] :
( ~ v1_xboole_0(k1_funct_1(X1,X3))
| ~ r2_hidden(X3,X0) ) )
& ( ? [X2] :
( v1_xboole_0(k1_funct_1(X1,X2))
& r2_hidden(X2,X0) )
| v2_relat_1(X1) ) ) ),
inference(rectify,[],[f126]) ).
fof(f128,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| ( ( ~ v2_relat_1(X1)
| ! [X3] :
( ~ v1_xboole_0(k1_funct_1(X1,X3))
| ~ r2_hidden(X3,X0) ) )
& ( ( v1_xboole_0(k1_funct_1(X1,sK2(X0,X1)))
& r2_hidden(sK2(X0,X1),X0) )
| v2_relat_1(X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f127]) ).
fof(f129,plain,
! [X0] :
( v1_xboole_0(X0)
| ! [X1] :
( ~ m1_pboole(X1,X0)
| ! [X2] :
( ( k1_closure3(X0,X1) != X2
| X2 = a_2_0_closure3(X0,X1) )
& ( a_2_0_closure3(X0,X1) != X2
| X2 = k1_closure3(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f89]) ).
fof(f130,plain,
! [X0,X1] :
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| ( ( ~ m1_pboole(X1,X0)
| k1_relat_1(X1) = X0 )
& ( k1_relat_1(X1) != X0
| m1_pboole(X1,X0) ) ) ),
inference(nnf_transformation,[],[f91]) ).
fof(f131,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,[],[f92]) ).
fof(f132,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,[],[f131]) ).
fof(f133,plain,
! [X0,X1] :
( ( ~ r1_tarski(X0,X1)
| ! [X3] :
( ~ r2_hidden(X3,X0)
| r2_hidden(X3,X1) ) )
& ( ( r2_hidden(sK3(X0,X1),X0)
& ~ r2_hidden(sK3(X0,X1),X1) )
| r1_tarski(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f132]) ).
fof(f136,plain,
! [X0,X1,X2] :
( ~ m1_pboole(X2,X1)
| v1_xboole_0(X1)
| ( ( ~ r2_hidden(X0,a_2_0_closure3(X1,X2))
| ? [X3] :
( k1_funct_1(X2,X3) != k1_xboole_0
& X0 = X3
& m1_subset_1(X3,X1) ) )
& ( ! [X3] :
( k1_xboole_0 = k1_funct_1(X2,X3)
| X0 != X3
| ~ m1_subset_1(X3,X1) )
| r2_hidden(X0,a_2_0_closure3(X1,X2)) ) ) ),
inference(nnf_transformation,[],[f102]) ).
fof(f137,plain,
! [X0,X1,X2] :
( ~ m1_pboole(X2,X1)
| v1_xboole_0(X1)
| ( ( ~ r2_hidden(X0,a_2_0_closure3(X1,X2))
| ? [X4] :
( k1_xboole_0 != k1_funct_1(X2,X4)
& X0 = X4
& m1_subset_1(X4,X1) ) )
& ( ! [X3] :
( k1_xboole_0 = k1_funct_1(X2,X3)
| X0 != X3
| ~ m1_subset_1(X3,X1) )
| r2_hidden(X0,a_2_0_closure3(X1,X2)) ) ) ),
inference(rectify,[],[f136]) ).
fof(f138,plain,
! [X0,X1,X2] :
( ~ m1_pboole(X2,X1)
| v1_xboole_0(X1)
| ( ( ~ r2_hidden(X0,a_2_0_closure3(X1,X2))
| ( k1_xboole_0 != k1_funct_1(X2,sK6(X0,X1,X2))
& sK6(X0,X1,X2) = X0
& m1_subset_1(sK6(X0,X1,X2),X1) ) )
& ( ! [X3] :
( k1_xboole_0 = k1_funct_1(X2,X3)
| X0 != X3
| ~ m1_subset_1(X3,X1) )
| r2_hidden(X0,a_2_0_closure3(X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X4,sK6(X0,X1,X2))],[f137]) ).
fof(f161,plain,
~ v1_xboole_0(sK0),
inference(cnf_transformation,[],[f123]) ).
fof(f162,plain,
m1_pboole(sK1,sK0),
inference(cnf_transformation,[],[f123]) ).
fof(f163,plain,
v2_relat_1(sK1),
inference(cnf_transformation,[],[f123]) ).
fof(f164,plain,
sK1 != k1_funct_4(k1_pboole(sK0),k7_relat_1(sK1,k1_closure3(sK0,sK1))),
inference(cnf_transformation,[],[f123]) ).
fof(f176,plain,
! [X3,X0,X1] :
( ~ m1_pboole(X1,X0)
| ~ v2_relat_1(X1)
| ~ v1_xboole_0(k1_funct_1(X1,X3))
| ~ r2_hidden(X3,X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f179,plain,
! [X2,X0,X1] :
( v1_xboole_0(X0)
| ~ m1_pboole(X1,X0)
| k1_closure3(X0,X1) != X2
| a_2_0_closure3(X0,X1) = X2 ),
inference(cnf_transformation,[],[f129]) ).
fof(f181,plain,
! [X0,X1] :
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| ~ m1_pboole(X1,X0)
| k1_relat_1(X1) = X0 ),
inference(cnf_transformation,[],[f130]) ).
fof(f184,plain,
! [X0,X1] :
( r2_hidden(sK3(X0,X1),X0)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f185,plain,
! [X0,X1] :
( ~ r2_hidden(sK3(X0,X1),X1)
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f186,plain,
! [X0] : k1_pboole(X0) = k2_funcop_1(X0,k1_xboole_0),
inference(cnf_transformation,[],[f17]) ).
fof(f189,plain,
! [X0] : m1_pboole(k1_pboole(X0),X0),
inference(cnf_transformation,[],[f21]) ).
fof(f191,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| v1_funct_1(X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f192,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| v1_relat_1(X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f199,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f33]) ).
fof(f209,plain,
! [X2,X3,X0,X1] :
( ~ m1_pboole(X2,X1)
| v1_xboole_0(X1)
| k1_xboole_0 = k1_funct_1(X2,X3)
| X0 != X3
| ~ m1_subset_1(X3,X1)
| r2_hidden(X0,a_2_0_closure3(X1,X2)) ),
inference(cnf_transformation,[],[f138]) ).
fof(f258,plain,
! [X2,X0,X1] :
( v1_xboole_0(X0)
| ~ m1_pboole(X1,X0)
| ~ m1_pboole(X2,X0)
| k1_funct_4(X1,X2) = X2 ),
inference(cnf_transformation,[],[f110]) ).
fof(f259,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f270,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| ~ r1_tarski(k1_relat_1(X1),X0)
| k7_relat_1(X1,X0) = X1 ),
inference(cnf_transformation,[],[f122]) ).
fof(f271,plain,
sK1 != k1_funct_4(k2_funcop_1(sK0,k1_xboole_0),k7_relat_1(sK1,k1_closure3(sK0,sK1))),
inference(definition_unfolding,[],[f164,f186]) ).
fof(f272,plain,
! [X0] : m1_pboole(k2_funcop_1(X0,k1_xboole_0),X0),
inference(definition_unfolding,[],[f189,f186]) ).
fof(f282,plain,
! [X0,X1] :
( v1_xboole_0(X0)
| ~ m1_pboole(X1,X0)
| k1_closure3(X0,X1) = a_2_0_closure3(X0,X1) ),
inference(equality_resolution,[],[f179]) ).
fof(f284,plain,
! [X2,X3,X1] :
( ~ m1_pboole(X2,X1)
| v1_xboole_0(X1)
| k1_xboole_0 = k1_funct_1(X2,X3)
| ~ m1_subset_1(X3,X1)
| r2_hidden(X3,a_2_0_closure3(X1,X2)) ),
inference(equality_resolution,[],[f209]) ).
tcf(c_49,negated_conjecture,
k1_funct_4(k2_funcop_1(sK0,k1_xboole_0),k7_relat_1(sK1,k1_closure3(sK0,sK1))) != sK1,
inference(cnf_transformation,[],[f271]) ).
tcf(c_50,negated_conjecture,
v2_relat_1(sK1),
inference(cnf_transformation,[],[f163]) ).
tcf(c_51,negated_conjecture,
m1_pboole(sK1,sK0),
inference(cnf_transformation,[],[f162]) ).
tcf(c_52,negated_conjecture,
~ v1_xboole_0(sK0),
inference(cnf_transformation,[],[f161]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ v2_relat_1(X0)
| ~ r2_hidden(X1,X2)
| ~ m1_pboole(X0,X2)
| ~ v1_xboole_0(k1_funct_1(X0,X1)) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| ( k1_closure3(X1,X0) = a_2_0_closure3(X1,X0) )
| ~ m1_pboole(X0,X1) ),
inference(cnf_transformation,[],[f282]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( ( k1_relat_1(X0) = X1 )
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0)
| ~ m1_pboole(X0,X1) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| ~ r2_hidden(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| r2_hidden(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_74,plain,
! [X0: $i] : m1_pboole(k2_funcop_1(X0,k1_xboole_0),X0),
inference(cnf_transformation,[],[f272]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( v1_relat_1(X0)
| ~ m1_pboole(X0,X1) ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( v1_funct_1(X0)
| ~ m1_pboole(X0,X1) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_84,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f199]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_xboole_0(X1)
| r2_hidden(X2,a_2_0_closure3(X1,X0))
| ( k1_funct_1(X0,X2) = k1_xboole_0 )
| ~ m1_subset_1(X2,X1)
| ~ m1_pboole(X0,X1) ),
inference(cnf_transformation,[],[f284]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_xboole_0(X1)
| ( k1_funct_4(X0,X2) = X2 )
| ~ m1_pboole(X2,X1)
| ~ m1_pboole(X0,X1) ),
inference(cnf_transformation,[],[f258]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f259]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i] :
( ( k7_relat_1(X0,X1) = X0 )
| ~ v1_relat_1(X0)
| ~ r1_tarski(k1_relat_1(X0),X1) ),
inference(cnf_transformation,[],[f270]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i] :
( ( k1_relat_1(X0) = X1 )
| ~ m1_pboole(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_68,c_77,c_76,c_68]) ).
tcf(c_2926,plain,
! [X0: $i,X1: $i] :
( ( k1_relat_1(X0) = X1 )
| ~ m1_pboole(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_198]) ).
tcf(c_5479,definition,
iPr_def_12 = k2_funcop_1(sK0,k1_xboole_0),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_5480,definition,
iPr_def_13 = k1_closure3(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_5481,definition,
iPr_def_14 = k7_relat_1(sK1,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_5482,definition,
iPr_def_15 = k1_funct_4(iPr_def_12,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_5483,negated_conjecture,
~ v1_xboole_0(sK0),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_5484,negated_conjecture,
m1_pboole(sK1,sK0),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_5485,negated_conjecture,
v2_relat_1(sK1),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_5486,negated_conjecture,
iPr_def_15 != sK1,
inference(demodulation,[status(thm)],[c_49,c_5480,c_5481,c_5479,c_5482]) ).
tcf(c_6971,plain,
m1_pboole(iPr_def_12,sK0),
inference(superposition,[status(thm)],[c_5479,c_74]) ).
tcf(c_6976,plain,
v1_relat_1(sK1),
inference(superposition,[status(thm)],[c_5484,c_76]) ).
tcf(c_7064,plain,
! [X0: $i,X1: $i] :
( r1_tarski(X0,X1)
| m1_subset_1(sK3(X0,X1),X0) ),
inference(superposition,[status(thm)],[c_70,c_144]) ).
tcf(c_7114,plain,
k1_relat_1(sK1) = sK0,
inference(superposition,[status(thm)],[c_5484,c_2926]) ).
tcf(c_7460,plain,
( v1_xboole_0(sK0)
| ( k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1) ) ),
inference(superposition,[status(thm)],[c_5484,c_66]) ).
tcf(c_7468,plain,
( v1_xboole_0(sK0)
| ( a_2_0_closure3(sK0,sK1) = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_7460,c_5480]) ).
tcf(c_7469,plain,
a_2_0_closure3(sK0,sK1) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_7468,c_5483]) ).
tcf(c_7533,plain,
! [X0: $i] :
( ( k7_relat_1(sK1,X0) = sK1 )
| ~ v1_relat_1(sK1)
| ~ r1_tarski(sK0,X0) ),
inference(superposition,[status(thm)],[c_7114,c_155]) ).
tcf(c_7544,plain,
! [X0: $i] :
( ( k7_relat_1(sK1,X0) = sK1 )
| ~ r1_tarski(sK0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7533,c_6976]) ).
tcf(c_7704,plain,
! [X0: $i] :
( v1_xboole_0(sK0)
| ( k1_funct_4(iPr_def_12,X0) = X0 )
| ~ m1_pboole(X0,sK0) ),
inference(superposition,[status(thm)],[c_6971,c_143]) ).
tcf(c_7705,plain,
! [X0: $i] :
( ( k1_funct_4(iPr_def_12,X0) = X0 )
| ~ m1_pboole(X0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7704,c_5483]) ).
tcf(c_7787,plain,
k1_funct_4(iPr_def_12,sK1) = sK1,
inference(superposition,[status(thm)],[c_5484,c_7705]) ).
tcf(c_8154,plain,
! [X0: $i] :
( v1_xboole_0(sK0)
| r2_hidden(X0,iPr_def_13)
| ( k1_funct_1(sK1,X0) = k1_xboole_0 )
| ~ m1_pboole(sK1,sK0)
| ~ m1_subset_1(X0,sK0) ),
inference(superposition,[status(thm)],[c_7469,c_91]) ).
tcf(c_8163,plain,
! [X0: $i] :
( r2_hidden(X0,iPr_def_13)
| ( k1_funct_1(sK1,X0) = k1_xboole_0 )
| ~ m1_subset_1(X0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8154,c_5483,c_5484]) ).
tcf(c_8423,plain,
! [X0: $i] :
( r1_tarski(sK0,X0)
| r2_hidden(sK3(sK0,X0),iPr_def_13)
| ( k1_funct_1(sK1,sK3(sK0,X0)) = k1_xboole_0 ) ),
inference(superposition,[status(thm)],[c_7064,c_8163]) ).
tcf(c_8979,plain,
( r1_tarski(sK0,iPr_def_13)
| ( k1_funct_1(sK1,sK3(sK0,iPr_def_13)) = k1_xboole_0 ) ),
inference(superposition,[status(thm)],[c_8423,c_69]) ).
tcf(c_10748,plain,
( ( k7_relat_1(sK1,iPr_def_13) = sK1 )
| ( k1_funct_1(sK1,sK3(sK0,iPr_def_13)) = k1_xboole_0 ) ),
inference(superposition,[status(thm)],[c_8979,c_7544]) ).
tcf(c_10753,plain,
( ( sK1 = iPr_def_14 )
| ( k1_funct_1(sK1,sK3(sK0,iPr_def_13)) = k1_xboole_0 ) ),
inference(light_normalisation,[status(thm)],[c_10748,c_5481]) ).
tcf(c_11646,plain,
! [X0: $i] :
( ( sK1 = iPr_def_14 )
| ~ v1_xboole_0(k1_xboole_0)
| ~ v2_relat_1(sK1)
| ~ m1_pboole(sK1,X0)
| ~ r2_hidden(sK3(sK0,iPr_def_13),X0) ),
inference(superposition,[status(thm)],[c_10753,c_64]) ).
tcf(c_11647,plain,
! [X0: $i] :
( ( sK1 = iPr_def_14 )
| ~ m1_pboole(sK1,X0)
| ~ r2_hidden(sK3(sK0,iPr_def_13),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11646,c_84,c_5485]) ).
tcf(c_11908,plain,
( r1_tarski(sK0,iPr_def_13)
| ( sK1 = iPr_def_14 )
| ~ m1_pboole(sK1,sK0) ),
inference(superposition,[status(thm)],[c_70,c_11647]) ).
tcf(c_11914,plain,
( r1_tarski(sK0,iPr_def_13)
| ( sK1 = iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11908,c_5484]) ).
tcf(c_11979,plain,
( ( sK1 = iPr_def_14 )
| ( k7_relat_1(sK1,iPr_def_13) = sK1 ) ),
inference(superposition,[status(thm)],[c_11914,c_7544]) ).
tcf(c_11984,plain,
sK1 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_11979,c_5481]) ).
tcf(c_12036,plain,
k1_funct_4(iPr_def_12,iPr_def_14) = iPr_def_14,
inference(demodulation,[status(thm)],[c_7787,c_11984]) ).
tcf(c_12046,plain,
iPr_def_14 != iPr_def_15,
inference(demodulation,[status(thm)],[c_5486,c_11984]) ).
tcf(c_12052,plain,
iPr_def_14 = iPr_def_15,
inference(demodulation,[status(thm)],[c_5482,c_12036]) ).
tcf(c_12053,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_12052,c_12046]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG225+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.40 % Computer : n006.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Fri Sep 25 05:10:12 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.46 Running first-order theorem proving
% 0.15/0.46 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
% 0.15/0.48
% 0.15/0.48 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.48
% 0.15/0.48 % Detected problem language: tptp
% 0.23/0.49 % Proving...
% 3.77/1.38 % SZS status Started for theBenchmark.p
% 3.77/1.38 % SZS status Theorem for theBenchmark.p
% 3.77/1.38
% 3.77/1.38 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.77/1.38
% 3.77/1.38 % ------ iProver source info
% 3.77/1.38
% 3.77/1.38 % git: date: 2026-07-19 20:42:38 +0200
% 3.77/1.38 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.77/1.38 % git: non_committed_changes: false
% 3.77/1.38
% 3.77/1.38 % ------ Parsing...
% 3.77/1.38 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.77/1.38
% 3.77/1.38 % ------ Preprocessing... sup_sim: 0 sf_s rm: 8 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.77/1.38
% 3.77/1.38 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.77/1.38
% 3.77/1.38 % ------ Preprocessing... sf_s rm: 3 0s sf_e sf_s rm: 0 0s sf_e
% 3.77/1.38 % ------ Proving...
% 3.77/1.38 % ------ Problem Properties
% 3.77/1.38
% 3.77/1.38 %
% 3.77/1.38 % clauses 99
% 3.77/1.38 % conjectures 4
% 3.77/1.38 % EPR 44
% 3.77/1.38 % Horn 82
% 3.77/1.38 % unary 49
% 3.77/1.38 % binary 20
% 3.77/1.38 % lits 203
% 3.77/1.38 % lits eq 21
% 3.77/1.38 % fd_pure 0
% 3.77/1.38 % fd_pseudo 0
% 3.77/1.38 % fd_cond 1
% 3.77/1.38 % fd_pseudo_cond 5
% 3.77/1.38 % AC symbols 0
% 3.77/1.38
% 3.77/1.38 % ------ Schedule dynamic 5 is on
% 3.77/1.38
% 3.77/1.38 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.77/1.38
% 3.77/1.38
% 3.77/1.38 % ------
% 3.77/1.38 % Current options:
% 3.77/1.38 % ------
% 3.77/1.38
% 3.77/1.38
% 3.77/1.38 %
% 3.77/1.38
% 3.77/1.38 % ------ Proving...
% 3.77/1.38 %
% 3.77/1.38
% 3.77/1.38 % SZS status Theorem for theBenchmark.p
% 3.77/1.38
% 3.77/1.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.77/1.38
% 3.77/1.38
%------------------------------------------------------------------------------