%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG226+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 : 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 : Fri Sep 25 12:53:53 PM UTC 2026
% Result : Theorem 79.75s 13.18s
% Output : CNFRefutation 79.75s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f251ERROR: Could not build tree for root c_81519ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( ( m1_pboole(X1,X0)
& v2_relat_1(X1) )
=> ! [X2] :
( ( m1_pboole(X2,X0)
& v2_relat_1(X2) )
=> ( ( k7_relat_1(X1,k1_closure3(X0,X1)) = k7_relat_1(X2,k1_closure3(X0,X2))
& k1_closure3(X0,X1) = k1_closure3(X0,X2) )
=> r6_pboole(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_closure3) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( ( m1_pboole(X1,X0)
& v2_relat_1(X1) )
=> ! [X2] :
( ( m1_pboole(X2,X0)
& v2_relat_1(X2) )
=> ( ( k7_relat_1(X1,k1_closure3(X0,X1)) = k7_relat_1(X2,k1_closure3(X0,X2))
& k1_closure3(X0,X1) = k1_closure3(X0,X2) )
=> r6_pboole(X0,X1,X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f11,axiom,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f13,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(f14,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(f15,axiom,
! [X0,X1,X2] :
( X2 = k3_xboole_0(X0,X1)
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f21,axiom,
! [X0,X1] :
( v1_relat_1(X0)
=> v1_relat_1(k7_relat_1(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f22,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(f28,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f29,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X2,X0)
& m1_pboole(X1,X0)
& v2_relat_1(X1)
& ~ v1_xboole_0(X0) )
=> ~ v1_xboole_0(k1_funct_1(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_pboole) ).
fof(f30,axiom,
! [X0,X1] :
( ( v1_funct_1(X0)
& v1_relat_1(X0) )
=> ( v1_funct_1(k7_relat_1(X0,X1))
& v1_relat_1(k7_relat_1(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(f31,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(f49,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f51,axiom,
! [X0,X1] :
( m1_subset_1(X0,X1)
=> ( r2_hidden(X0,X1)
| v1_xboole_0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f54,axiom,
! [X0,X1,X2] :
( ( v1_funct_1(X2)
& v1_relat_1(X2) )
=> ( r2_hidden(X1,k1_relat_1(k7_relat_1(X2,X0)))
=> k1_funct_1(k7_relat_1(X2,X0),X1) = k1_funct_1(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funct_1) ).
fof(f57,axiom,
! [X0,X1] :
( v1_relat_1(X1)
=> k1_relat_1(k7_relat_1(X1,X0)) = k3_xboole_0(k1_relat_1(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_relat_1) ).
fof(f58,axiom,
! [X0] :
( ( v1_funct_1(X0)
& v1_relat_1(X0) )
=> ! [X1] :
( ( v1_funct_1(X1)
& v1_relat_1(X1) )
=> ( ( ! [X2] :
( r2_hidden(X2,k1_relat_1(X0))
=> k1_funct_1(X0,X2) = k1_funct_1(X1,X2) )
& k1_relat_1(X0) = k1_relat_1(X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_1) ).
fof(f66,plain,
? [X0] :
( ~ v1_xboole_0(X0)
& ? [X1] :
( m1_pboole(X1,X0)
& v2_relat_1(X1)
& ? [X2] :
( m1_pboole(X2,X0)
& v2_relat_1(X2)
& k7_relat_1(X1,k1_closure3(X0,X1)) = k7_relat_1(X2,k1_closure3(X0,X2))
& k1_closure3(X0,X1) = k1_closure3(X0,X2)
& ~ r6_pboole(X0,X1,X2) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f67,plain,
? [X0] :
( ~ v1_xboole_0(X0)
& ? [X1] :
( m1_pboole(X1,X0)
& v2_relat_1(X1)
& ? [X2] :
( m1_pboole(X2,X0)
& v2_relat_1(X2)
& k7_relat_1(X1,k1_closure3(X0,X1)) = k7_relat_1(X2,k1_closure3(X0,X2))
& k1_closure3(X0,X1) = k1_closure3(X0,X2)
& ~ r6_pboole(X0,X1,X2) ) ) ),
inference(flattening,[],[f66]) ).
fof(f78,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,[],[f13]) ).
fof(f79,plain,
! [X0,X1] :
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| ( m1_pboole(X1,X0)
<=> k1_relat_1(X1) = X0 ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f80,plain,
! [X0,X1] :
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| ( m1_pboole(X1,X0)
<=> k1_relat_1(X1) = X0 ) ),
inference(flattening,[],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( ~ v1_relat_1(X0)
| v1_relat_1(k7_relat_1(X0,X1)) ),
inference(ennf_transformation,[],[f21]) ).
fof(f82,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| ( v1_funct_1(X1)
& v1_relat_1(X1) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,X0)
| ~ m1_pboole(X1,X0)
| ~ v2_relat_1(X1)
| v1_xboole_0(X0)
| ~ v1_xboole_0(k1_funct_1(X1,X2)) ),
inference(ennf_transformation,[],[f29]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ~ m1_subset_1(X2,X0)
| ~ m1_pboole(X1,X0)
| ~ v2_relat_1(X1)
| v1_xboole_0(X0)
| ~ v1_xboole_0(k1_funct_1(X1,X2)) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0,X1] :
( ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| ( v1_funct_1(k7_relat_1(X0,X1))
& v1_relat_1(k7_relat_1(X0,X1)) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f88,plain,
! [X0,X1] :
( ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| ( v1_funct_1(k7_relat_1(X0,X1))
& v1_relat_1(k7_relat_1(X0,X1)) ) ),
inference(flattening,[],[f87]) ).
fof(f89,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,[],[f31]) ).
fof(f90,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,[],[f89]) ).
fof(f99,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f100,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f51]) ).
fof(f101,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(flattening,[],[f100]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ~ v1_funct_1(X2)
| ~ v1_relat_1(X2)
| ~ r2_hidden(X1,k1_relat_1(k7_relat_1(X2,X0)))
| k1_funct_1(k7_relat_1(X2,X0),X1) = k1_funct_1(X2,X1) ),
inference(ennf_transformation,[],[f54]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ~ v1_funct_1(X2)
| ~ v1_relat_1(X2)
| ~ r2_hidden(X1,k1_relat_1(k7_relat_1(X2,X0)))
| k1_funct_1(k7_relat_1(X2,X0),X1) = k1_funct_1(X2,X1) ),
inference(flattening,[],[f104]) ).
fof(f108,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| k1_relat_1(k7_relat_1(X1,X0)) = k3_xboole_0(k1_relat_1(X1),X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f109,plain,
! [X0] :
( ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| ! [X1] :
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| ? [X2] :
( r2_hidden(X2,k1_relat_1(X0))
& k1_funct_1(X1,X2) != k1_funct_1(X0,X2) )
| k1_relat_1(X1) != k1_relat_1(X0)
| X0 = X1 ) ),
inference(ennf_transformation,[],[f58]) ).
fof(f110,plain,
! [X0] :
( ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| ! [X1] :
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| ? [X2] :
( r2_hidden(X2,k1_relat_1(X0))
& k1_funct_1(X1,X2) != k1_funct_1(X0,X2) )
| k1_relat_1(X1) != k1_relat_1(X0)
| X0 = X1 ) ),
inference(flattening,[],[f109]) ).
fof(f111,plain,
( ~ v1_xboole_0(sK0)
& m1_pboole(sK1,sK0)
& v2_relat_1(sK1)
& m1_pboole(sK2,sK0)
& v2_relat_1(sK2)
& k7_relat_1(sK1,k1_closure3(sK0,sK1)) = k7_relat_1(sK2,k1_closure3(sK0,sK2))
& k1_closure3(sK0,sK1) = k1_closure3(sK0,sK2)
& ~ r6_pboole(sK0,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f67]) ).
fof(f115,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,[],[f78]) ).
fof(f116,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,[],[f80]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ( k3_xboole_0(X0,X1) != X2
| ! [X3] :
( ( ~ r2_hidden(X3,X2)
| ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) )
& ( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0)
| r2_hidden(X3,X2) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) )
& ( ~ r2_hidden(X3,X2)
| ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) ) )
| X2 = k3_xboole_0(X0,X1) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f118,plain,
! [X0,X1,X2] :
( ( k3_xboole_0(X0,X1) != X2
| ! [X3] :
( ( ~ r2_hidden(X3,X2)
| ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) )
& ( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0)
| r2_hidden(X3,X2) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) )
& ( ~ r2_hidden(X3,X2)
| ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) ) )
| X2 = k3_xboole_0(X0,X1) ) ),
inference(flattening,[],[f117]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ( k3_xboole_0(X0,X1) != X2
| ! [X4] :
( ( ~ r2_hidden(X4,X2)
| ( r2_hidden(X4,X1)
& r2_hidden(X4,X0) ) )
& ( ~ r2_hidden(X4,X1)
| ~ r2_hidden(X4,X0)
| r2_hidden(X4,X2) ) ) )
& ( ? [X3] :
( ( r2_hidden(X3,X2)
| ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) )
& ( ~ r2_hidden(X3,X2)
| ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0) ) )
| X2 = k3_xboole_0(X0,X1) ) ),
inference(rectify,[],[f118]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ( k3_xboole_0(X0,X1) != X2
| ! [X4] :
( ( ~ r2_hidden(X4,X2)
| ( r2_hidden(X4,X1)
& r2_hidden(X4,X0) ) )
& ( ~ r2_hidden(X4,X1)
| ~ r2_hidden(X4,X0)
| r2_hidden(X4,X2) ) ) )
& ( ( ( r2_hidden(sK4(X0,X1,X2),X2)
| ( r2_hidden(sK4(X0,X1,X2),X1)
& r2_hidden(sK4(X0,X1,X2),X0) ) )
& ( ~ r2_hidden(sK4(X0,X1,X2),X2)
| ~ r2_hidden(sK4(X0,X1,X2),X1)
| ~ r2_hidden(sK4(X0,X1,X2),X0) ) )
| X2 = k3_xboole_0(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f119]) ).
fof(f123,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,[],[f90]) ).
fof(f124,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,[],[f123]) ).
fof(f125,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,sK7(X0,X1,X2))
& sK7(X0,X1,X2) = X0
& m1_subset_1(sK7(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,[sK7]),skolemize(X4,sK7(X0,X1,X2))],[f124]) ).
fof(f144,plain,
! [X0] :
( ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| ! [X1] :
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| ( r2_hidden(sK22(X0,X1),k1_relat_1(X0))
& k1_funct_1(X1,sK22(X0,X1)) != k1_funct_1(X0,sK22(X0,X1)) )
| k1_relat_1(X1) != k1_relat_1(X0)
| X0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(X2,sK22(X0,X1))],[f110]) ).
fof(f145,plain,
~ v1_xboole_0(sK0),
inference(cnf_transformation,[],[f111]) ).
fof(f146,plain,
m1_pboole(sK1,sK0),
inference(cnf_transformation,[],[f111]) ).
fof(f147,plain,
v2_relat_1(sK1),
inference(cnf_transformation,[],[f111]) ).
fof(f148,plain,
m1_pboole(sK2,sK0),
inference(cnf_transformation,[],[f111]) ).
fof(f149,plain,
v2_relat_1(sK2),
inference(cnf_transformation,[],[f111]) ).
fof(f150,plain,
k7_relat_1(sK1,k1_closure3(sK0,sK1)) = k7_relat_1(sK2,k1_closure3(sK0,sK2)),
inference(cnf_transformation,[],[f111]) ).
fof(f151,plain,
k1_closure3(sK0,sK1) = k1_closure3(sK0,sK2),
inference(cnf_transformation,[],[f111]) ).
fof(f152,plain,
~ r6_pboole(sK0,sK1,sK2),
inference(cnf_transformation,[],[f111]) ).
fof(f160,plain,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f164,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,[],[f115]) ).
fof(f166,plain,
! [X0,X1] :
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| ~ m1_pboole(X1,X0)
| k1_relat_1(X1) = X0 ),
inference(cnf_transformation,[],[f116]) ).
fof(f167,plain,
! [X0,X1] :
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| k1_relat_1(X1) != X0
| m1_pboole(X1,X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f170,plain,
! [X2,X0,X1,X4] :
( k3_xboole_0(X0,X1) != X2
| ~ r2_hidden(X4,X1)
| ~ r2_hidden(X4,X0)
| r2_hidden(X4,X2) ),
inference(cnf_transformation,[],[f120]) ).
fof(f174,plain,
! [X0,X1] :
( ~ v1_relat_1(X0)
| v1_relat_1(k7_relat_1(X0,X1)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f175,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| v1_funct_1(X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f176,plain,
! [X0,X1] :
( ~ m1_pboole(X1,X0)
| v1_relat_1(X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f181,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f28]) ).
fof(f182,plain,
! [X2,X0,X1] :
( ~ m1_subset_1(X2,X0)
| ~ m1_pboole(X1,X0)
| ~ v2_relat_1(X1)
| v1_xboole_0(X0)
| ~ v1_xboole_0(k1_funct_1(X1,X2)) ),
inference(cnf_transformation,[],[f86]) ).
fof(f183,plain,
! [X0,X1] :
( ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| v1_funct_1(k7_relat_1(X0,X1)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f188,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,[],[f125]) ).
fof(f230,plain,
! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f232,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f236,plain,
! [X2,X0,X1] :
( ~ v1_funct_1(X2)
| ~ v1_relat_1(X2)
| ~ r2_hidden(X1,k1_relat_1(k7_relat_1(X2,X0)))
| k1_funct_1(k7_relat_1(X2,X0),X1) = k1_funct_1(X2,X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f239,plain,
! [X0,X1] :
( ~ v1_relat_1(X1)
| k1_relat_1(k7_relat_1(X1,X0)) = k3_xboole_0(k1_relat_1(X1),X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f240,plain,
! [X0,X1] :
( ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| r2_hidden(sK22(X0,X1),k1_relat_1(X0))
| k1_relat_1(X1) != k1_relat_1(X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f144]) ).
fof(f241,plain,
! [X0,X1] :
( ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| k1_funct_1(X1,sK22(X0,X1)) != k1_funct_1(X0,sK22(X0,X1))
| k1_relat_1(X1) != k1_relat_1(X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f144]) ).
fof(f243,plain,
! [X0,X1] :
( v1_xboole_0(X0)
| ~ m1_pboole(X1,X0)
| k1_closure3(X0,X1) = a_2_0_closure3(X0,X1) ),
inference(equality_resolution,[],[f164]) ).
fof(f244,plain,
! [X1] :
( ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| m1_pboole(X1,k1_relat_1(X1)) ),
inference(equality_resolution,[],[f167]) ).
fof(f245,plain,
! [X0,X1,X4] :
( ~ r2_hidden(X4,X1)
| ~ r2_hidden(X4,X0)
| r2_hidden(X4,k3_xboole_0(X0,X1)) ),
inference(equality_resolution,[],[f170]) ).
fof(f248,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,[],[f188]) ).
tcf(c_49,negated_conjecture,
~ r6_pboole(sK0,sK1,sK2),
inference(cnf_transformation,[],[f152]) ).
tcf(c_50,negated_conjecture,
k1_closure3(sK0,sK1) = k1_closure3(sK0,sK2),
inference(cnf_transformation,[],[f151]) ).
tcf(c_51,negated_conjecture,
k7_relat_1(sK1,k1_closure3(sK0,sK1)) = k7_relat_1(sK2,k1_closure3(sK0,sK2)),
inference(cnf_transformation,[],[f150]) ).
tcf(c_52,negated_conjecture,
v2_relat_1(sK2),
inference(cnf_transformation,[],[f149]) ).
tcf(c_53,negated_conjecture,
m1_pboole(sK2,sK0),
inference(cnf_transformation,[],[f148]) ).
tcf(c_54,negated_conjecture,
v2_relat_1(sK1),
inference(cnf_transformation,[],[f147]) ).
tcf(c_55,negated_conjecture,
m1_pboole(sK1,sK0),
inference(cnf_transformation,[],[f146]) ).
tcf(c_56,negated_conjecture,
~ v1_xboole_0(sK0),
inference(cnf_transformation,[],[f145]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
inference(cnf_transformation,[],[f160]) ).
tcf(c_67,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,[],[f243]) ).
tcf(c_68,plain,
! [X0: $i] :
( m1_pboole(X0,k1_relat_1(X0))
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(cnf_transformation,[],[f244]) ).
tcf(c_69,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,[],[f166]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( r2_hidden(X0,k3_xboole_0(X2,X1))
| ~ r2_hidden(X0,X2)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f245]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( v1_relat_1(k7_relat_1(X0,X1))
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( v1_relat_1(X0)
| ~ m1_pboole(X0,X1) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( v1_funct_1(X0)
| ~ m1_pboole(X0,X1) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_83,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f181]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_xboole_0(X2)
| ~ v2_relat_1(X0)
| ~ m1_subset_1(X1,X2)
| ~ m1_pboole(X0,X2)
| ~ v1_xboole_0(k1_funct_1(X0,X1)) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( v1_funct_1(k7_relat_1(X0,X1))
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_87,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,[],[f248]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i] :
( r6_pboole(X1,X0,X0)
| ~ m1_pboole(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f230]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| r2_hidden(X0,X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( k1_funct_1(k7_relat_1(X1,X2),X0) = k1_funct_1(X1,X0) )
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X1)
| ~ r2_hidden(X0,k1_relat_1(k7_relat_1(X1,X2))) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i] :
( ( k3_xboole_0(k1_relat_1(X0),X1) = k1_relat_1(k7_relat_1(X0,X1)) )
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f239]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X1)
| ~ v1_funct_1(X0)
| ( k1_relat_1(X0) != k1_relat_1(X1) )
| ( k1_funct_1(X0,sK22(X0,X1)) != k1_funct_1(X1,sK22(X0,X1)) ) ),
inference(cnf_transformation,[],[f241]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i] :
( r2_hidden(sK22(X1,X0),k1_relat_1(X1))
| ( X0 = X1 )
| ~ v1_relat_1(X1)
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X1)
| ~ v1_funct_1(X0)
| ( k1_relat_1(X0) != k1_relat_1(X1) ) ),
inference(cnf_transformation,[],[f240]) ).
tcf(c_242,plain,
! [X0: $i,X1: $i] :
( ( k1_relat_1(X0) = X1 )
| ~ m1_pboole(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_69,c_78,c_77,c_69]) ).
tcf(c_635,plain,
k7_relat_1(sK1,k1_closure3(sK0,sK1)) = k7_relat_1(sK2,k1_closure3(sK0,sK1)),
inference(light_normalisation,[status(thm)],[c_51,c_50]) ).
tcf(c_2058,plain,
! [X0: $i,X1: $i] :
( ( k1_relat_1(X0) = X1 )
| ~ m1_pboole(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_242]) ).
tcf(c_3824,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_3827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( r6_pboole(X0,X2,X4)
| ~ r6_pboole(X1,X3,X5)
| ( X4 != X5 )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3831,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( m1_pboole(X0,X2)
| ~ m1_pboole(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3832,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X0)
| ~ v1_xboole_0(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_4902,plain,
( v1_relat_1(sK2)
| ~ m1_pboole(sK2,sK0) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_4903,plain,
( v1_relat_1(sK1)
| ~ m1_pboole(sK1,sK0) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_4911,plain,
( ( k1_relat_1(sK2) = sK0 )
| ~ m1_pboole(sK2,sK0) ),
inference(instantiation,[status(thm)],[c_2058]) ).
tcf(c_4935,plain,
( r6_pboole(sK0,sK2,sK2)
| ~ m1_pboole(sK2,sK0) ),
inference(instantiation,[status(thm)],[c_128]) ).
tcf(c_4960,plain,
! [X0: $i] :
( v1_xboole_0(sK0)
| ( k1_closure3(sK0,X0) = a_2_0_closure3(sK0,X0) )
| ~ m1_pboole(X0,sK0) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_4990,plain,
! [X0: $i,X1: $i] :
( m1_pboole(X0,X1)
| ~ m1_pboole(sK1,sK0)
| ( X1 != sK0 )
| ( X0 != sK1 ) ),
inference(instantiation,[status(thm)],[c_3831]) ).
tcf(c_5005,plain,
v1_relat_1(sK1),
inference(superposition,[status(thm)],[c_55,c_77]) ).
tcf(c_5021,plain,
v1_funct_1(sK2),
inference(superposition,[status(thm)],[c_53,c_78]) ).
tcf(c_5022,plain,
v1_funct_1(sK1),
inference(superposition,[status(thm)],[c_55,c_78]) ).
tcf(c_5177,plain,
! [X0: $i] :
( v1_funct_1(k7_relat_1(sK1,X0))
| ~ v1_relat_1(sK1)
| ~ v1_funct_1(sK1) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_5179,plain,
! [X0: $i] :
( v1_relat_1(k7_relat_1(sK1,X0))
| ~ v1_relat_1(sK1) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_5187,plain,
! [X0: $i,X1: $i,X2: $i] :
( r6_pboole(X0,X1,X2)
| ~ r6_pboole(sK0,sK2,sK2)
| ( X2 != sK2 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(instantiation,[status(thm)],[c_3827]) ).
tcf(c_5242,plain,
! [X0: $i] :
( ( X0 = sK2 )
| ~ v1_relat_1(sK2)
| ~ v1_funct_1(sK2)
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0)
| ( k1_relat_1(X0) != k1_relat_1(sK2) )
| ( k1_funct_1(X0,sK22(X0,sK2)) != k1_funct_1(sK2,sK22(X0,sK2)) ) ),
inference(instantiation,[status(thm)],[c_142]) ).
tcf(c_5313,plain,
! [X0: $i] : k3_xboole_0(k1_relat_1(sK1),X0) = k1_relat_1(k7_relat_1(sK1,X0)),
inference(superposition,[status(thm)],[c_5005,c_141]) ).
tcf(c_5384,plain,
( v1_xboole_0(sK0)
| ( k1_closure3(sK0,sK2) = a_2_0_closure3(sK0,sK2) )
| ~ m1_pboole(sK2,sK0) ),
inference(instantiation,[status(thm)],[c_4960]) ).
tcf(c_5385,plain,
( v1_xboole_0(sK0)
| ( k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1) )
| ~ m1_pboole(sK1,sK0) ),
inference(instantiation,[status(thm)],[c_4960]) ).
tcf(c_5406,plain,
sK2 = sK2,
inference(instantiation,[status(thm)],[c_3824]) ).
tcf(c_5422,plain,
! [X0: $i] :
( m1_pboole(sK1,X0)
| ~ m1_pboole(sK1,sK0)
| ( sK1 != sK1 )
| ( X0 != sK0 ) ),
inference(instantiation,[status(thm)],[c_4990]) ).
tcf(c_5423,plain,
sK1 = sK1,
inference(instantiation,[status(thm)],[c_3824]) ).
tcf(c_5486,plain,
! [X0: $i] :
( m1_pboole(k7_relat_1(sK1,X0),k3_xboole_0(k1_relat_1(sK1),X0))
| ~ v1_relat_1(k7_relat_1(sK1,X0))
| ~ v1_funct_1(k7_relat_1(sK1,X0)) ),
inference(superposition,[status(thm)],[c_5313,c_68]) ).
tcf(c_5917,plain,
! [X0: $i] :
( v1_xboole_0(sK0)
| r2_hidden(X0,sK0)
| ~ m1_subset_1(X0,sK0) ),
inference(instantiation,[status(thm)],[c_134]) ).
tcf(c_6203,plain,
( v1_xboole_0(sK0)
| ( k1_closure3(sK0,sK2) = a_2_0_closure3(sK0,sK2) ) ),
inference(superposition,[status(thm)],[c_53,c_67]) ).
tcf(c_6204,plain,
( v1_xboole_0(sK0)
| ( k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1) ) ),
inference(superposition,[status(thm)],[c_55,c_67]) ).
tcf(c_6329,plain,
k1_closure3(sK0,sK2) = a_2_0_closure3(sK0,sK2),
inference(global_subsumption_just,[status(thm)],[c_6203,c_56,c_53,c_5384]) ).
tcf(c_6331,plain,
k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1),
inference(global_subsumption_just,[status(thm)],[c_6204,c_56,c_55,c_5385]) ).
tcf(c_6484,plain,
sK0 = sK0,
inference(instantiation,[status(thm)],[c_3824]) ).
tcf(c_6578,plain,
( m1_pboole(sK1,k1_relat_1(sK2))
| ~ m1_pboole(sK1,sK0)
| ( sK1 != sK1 )
| ( k1_relat_1(sK2) != sK0 ) ),
inference(instantiation,[status(thm)],[c_5422]) ).
tcf(c_6939,plain,
! [X0: $i] :
( v1_xboole_0(sK0)
| r2_hidden(X0,k1_closure3(sK0,sK2))
| ( k1_funct_1(sK2,X0) = k1_xboole_0 )
| ~ m1_pboole(sK2,sK0)
| ~ m1_subset_1(X0,sK0) ),
inference(superposition,[status(thm)],[c_6329,c_87]) ).
tcf(c_6940,plain,
! [X0: $i] :
( v1_xboole_0(sK0)
| r2_hidden(X0,k1_closure3(sK0,sK1))
| ( k1_funct_1(sK1,X0) = k1_xboole_0 )
| ~ m1_pboole(sK1,sK0)
| ~ m1_subset_1(X0,sK0) ),
inference(superposition,[status(thm)],[c_6331,c_87]) ).
tcf(c_6948,plain,
( r6_pboole(sK0,sK1,sK2)
| ~ r6_pboole(sK0,sK2,sK2)
| ( sK2 != sK2 )
| ( sK1 != sK2 )
| ( sK0 != sK0 ) ),
inference(instantiation,[status(thm)],[c_5187]) ).
tcf(c_7310,plain,
v1_relat_1(sK2),
inference(superposition,[status(thm)],[c_53,c_77]) ).
tcf(c_7311,plain,
v1_relat_1(sK1),
inference(superposition,[status(thm)],[c_55,c_77]) ).
tcf(c_7448,plain,
k1_relat_1(sK2) = sK0,
inference(superposition,[status(thm)],[c_53,c_2058]) ).
tcf(c_7449,plain,
k1_relat_1(sK1) = sK0,
inference(superposition,[status(thm)],[c_55,c_2058]) ).
tcf(c_7664,plain,
! [X0: $i] : k3_xboole_0(k1_relat_1(sK2),X0) = k1_relat_1(k7_relat_1(sK2,X0)),
inference(superposition,[status(thm)],[c_7310,c_141]) ).
tcf(c_7665,plain,
! [X0: $i] : k3_xboole_0(k1_relat_1(sK1),X0) = k1_relat_1(k7_relat_1(sK1,X0)),
inference(superposition,[status(thm)],[c_7311,c_141]) ).
tcf(c_7668,plain,
( v1_xboole_0(sK0)
| ( k1_closure3(sK0,sK2) = a_2_0_closure3(sK0,sK2) ) ),
inference(superposition,[status(thm)],[c_53,c_67]) ).
tcf(c_7669,plain,
( v1_xboole_0(sK0)
| ( k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1) ) ),
inference(superposition,[status(thm)],[c_55,c_67]) ).
tcf(c_7685,plain,
k1_closure3(sK0,sK2) = a_2_0_closure3(sK0,sK2),
inference(global_subsumption_just,[status(thm)],[c_7668,c_56,c_53,c_5384]) ).
tcf(c_7687,plain,
k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1),
inference(global_subsumption_just,[status(thm)],[c_7669,c_56,c_55,c_5385]) ).
tcf(c_8169,plain,
! [X0: $i] :
( ( k1_relat_1(X0) = k1_relat_1(sK2) )
| ~ m1_pboole(X0,k1_relat_1(sK2)) ),
inference(instantiation,[status(thm)],[c_2058]) ).
tcf(c_8254,plain,
! [X0: $i] :
( v1_xboole_0(sK0)
| r2_hidden(X0,k1_closure3(sK0,sK2))
| ( k1_funct_1(sK2,X0) = k1_xboole_0 )
| ~ m1_pboole(sK2,sK0)
| ~ m1_subset_1(X0,sK0) ),
inference(superposition,[status(thm)],[c_7685,c_87]) ).
tcf(c_8255,plain,
! [X0: $i] :
( v1_xboole_0(sK0)
| r2_hidden(X0,k1_closure3(sK0,sK1))
| ( k1_funct_1(sK1,X0) = k1_xboole_0 )
| ~ m1_pboole(sK1,sK0)
| ~ m1_subset_1(X0,sK0) ),
inference(superposition,[status(thm)],[c_7687,c_87]) ).
tcf(c_8397,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,sK0)
| ( k1_funct_1(sK2,X0) = k1_xboole_0 )
| r2_hidden(X0,k1_closure3(sK0,sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_8254,c_56,c_53,c_6939]) ).
tcf(c_8398,plain,
! [X0: $i] :
( r2_hidden(X0,k1_closure3(sK0,sK2))
| ( k1_funct_1(sK2,X0) = k1_xboole_0 )
| ~ m1_subset_1(X0,sK0) ),
inference(renaming,[status(thm)],[c_8397]) ).
tcf(c_8521,plain,
! [X0: $i,X1: $i] :
( ( k1_funct_1(k7_relat_1(sK2,X1),X0) = k1_funct_1(sK2,X0) )
| ~ v1_relat_1(sK2)
| ~ v1_funct_1(sK2)
| ~ r2_hidden(X0,k3_xboole_0(k1_relat_1(sK2),X1)) ),
inference(superposition,[status(thm)],[c_7664,c_138]) ).
tcf(c_8522,plain,
! [X0: $i,X1: $i] :
( ( k1_funct_1(k7_relat_1(sK1,X1),X0) = k1_funct_1(sK1,X0) )
| ~ v1_relat_1(sK1)
| ~ v1_funct_1(sK1)
| ~ r2_hidden(X0,k3_xboole_0(k1_relat_1(sK1),X1)) ),
inference(superposition,[status(thm)],[c_7665,c_138]) ).
tcf(c_8806,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,sK0)
| ( k1_funct_1(sK1,X0) = k1_xboole_0 )
| r2_hidden(X0,k1_closure3(sK0,sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_8255,c_56,c_55,c_6940]) ).
tcf(c_8807,plain,
! [X0: $i] :
( r2_hidden(X0,k1_closure3(sK0,sK1))
| ( k1_funct_1(sK1,X0) = k1_xboole_0 )
| ~ m1_subset_1(X0,sK0) ),
inference(renaming,[status(thm)],[c_8806]) ).
tcf(c_8888,plain,
! [X0: $i] :
( r2_hidden(sK22(X0,sK2),k1_relat_1(X0))
| ( X0 = sK2 )
| ~ v1_relat_1(sK2)
| ~ v1_funct_1(sK2)
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0)
| ( k1_relat_1(X0) != sK0 ) ),
inference(superposition,[status(thm)],[c_7448,c_143]) ).
tcf(c_9808,plain,
! [X0: $i] :
( r2_hidden(sK22(X0,sK2),k1_relat_1(X0))
| ( X0 = sK2 )
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0)
| ( k1_relat_1(X0) != sK0 ) ),
inference(global_subsumption_just,[status(thm)],[c_8888,c_53,c_4902,c_5021,c_8888]) ).
tcf(c_9812,plain,
( r2_hidden(sK22(sK1,sK2),k1_relat_1(sK1))
| ( sK1 = sK2 )
| ~ v1_relat_1(sK1)
| ~ v1_funct_1(sK1) ),
inference(superposition,[status(thm)],[c_7449,c_9808]) ).
tcf(c_15089,plain,
( ( sK1 = sK2 )
| ~ v1_relat_1(sK2)
| ~ v1_relat_1(sK1)
| ~ v1_funct_1(sK2)
| ~ v1_funct_1(sK1)
| ( k1_relat_1(sK1) != k1_relat_1(sK2) )
| ( k1_funct_1(sK1,sK22(sK1,sK2)) != k1_funct_1(sK2,sK22(sK1,sK2)) ) ),
inference(instantiation,[status(thm)],[c_5242]) ).
tcf(c_31986,plain,
( ( k1_relat_1(sK1) = k1_relat_1(sK2) )
| ~ m1_pboole(sK1,k1_relat_1(sK2)) ),
inference(instantiation,[status(thm)],[c_8169]) ).
tcf(c_54246,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(sK0)
| ~ v2_relat_1(X0)
| ~ m1_subset_1(X1,sK0)
| ~ m1_pboole(X0,sK0)
| ~ v1_xboole_0(k1_funct_1(X0,X1)) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_58982,plain,
! [X0: $i] :
( v1_xboole_0(sK0)
| ~ v2_relat_1(sK2)
| ~ m1_pboole(sK2,sK0)
| ~ m1_subset_1(X0,sK0)
| ~ v1_xboole_0(k1_funct_1(sK2,X0)) ),
inference(instantiation,[status(thm)],[c_54246]) ).
tcf(c_58984,plain,
! [X0: $i] :
( v1_xboole_0(sK0)
| ~ v2_relat_1(sK1)
| ~ m1_pboole(sK1,sK0)
| ~ m1_subset_1(X0,sK0)
| ~ v1_xboole_0(k1_funct_1(sK1,X0)) ),
inference(instantiation,[status(thm)],[c_54246]) ).
tcf(c_63496,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(k1_funct_1(sK2,X0))
| ~ v1_xboole_0(X1)
| ( k1_funct_1(sK2,X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_3832]) ).
tcf(c_63516,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(k1_funct_1(sK1,X0))
| ~ v1_xboole_0(X1)
| ( k1_funct_1(sK1,X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_3832]) ).
tcf(c_63627,plain,
v1_relat_1(sK2),
inference(superposition,[status(thm)],[c_53,c_77]) ).
tcf(c_63628,plain,
v1_relat_1(sK1),
inference(superposition,[status(thm)],[c_55,c_77]) ).
tcf(c_63839,plain,
k1_relat_1(sK2) = sK0,
inference(superposition,[status(thm)],[c_53,c_2058]) ).
tcf(c_63840,plain,
k1_relat_1(sK1) = sK0,
inference(superposition,[status(thm)],[c_55,c_2058]) ).
tcf(c_64045,plain,
! [X0: $i] : k3_xboole_0(k1_relat_1(sK2),X0) = k1_relat_1(k7_relat_1(sK2,X0)),
inference(superposition,[status(thm)],[c_63627,c_141]) ).
tcf(c_64046,plain,
! [X0: $i] : k3_xboole_0(k1_relat_1(sK1),X0) = k1_relat_1(k7_relat_1(sK1,X0)),
inference(superposition,[status(thm)],[c_63628,c_141]) ).
tcf(c_64049,plain,
( v1_xboole_0(sK0)
| ( k1_closure3(sK0,sK2) = a_2_0_closure3(sK0,sK2) ) ),
inference(superposition,[status(thm)],[c_53,c_67]) ).
tcf(c_64050,plain,
( v1_xboole_0(sK0)
| ( k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1) ) ),
inference(superposition,[status(thm)],[c_55,c_67]) ).
tcf(c_64100,plain,
k1_closure3(sK0,sK2) = a_2_0_closure3(sK0,sK2),
inference(global_subsumption_just,[status(thm)],[c_64049,c_56,c_53,c_5384]) ).
tcf(c_64102,plain,
k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1),
inference(global_subsumption_just,[status(thm)],[c_64050,c_56,c_55,c_5385]) ).
tcf(c_64106,plain,
! [X0: $i] :
( m1_pboole(k7_relat_1(sK1,X0),k3_xboole_0(k1_relat_1(sK1),X0))
| ~ v1_relat_1(k7_relat_1(sK1,X0))
| ~ v1_funct_1(k7_relat_1(sK1,X0)) ),
inference(superposition,[status(thm)],[c_64046,c_68]) ).
tcf(c_64367,plain,
! [X0: $i] :
( v1_xboole_0(sK0)
| r2_hidden(X0,k1_closure3(sK0,sK2))
| ( k1_funct_1(sK2,X0) = k1_xboole_0 )
| ~ m1_pboole(sK2,sK0)
| ~ m1_subset_1(X0,sK0) ),
inference(superposition,[status(thm)],[c_64100,c_87]) ).
tcf(c_64368,plain,
! [X0: $i] :
( v1_xboole_0(sK0)
| r2_hidden(X0,k1_closure3(sK0,sK1))
| ( k1_funct_1(sK1,X0) = k1_xboole_0 )
| ~ m1_pboole(sK1,sK0)
| ~ m1_subset_1(X0,sK0) ),
inference(superposition,[status(thm)],[c_64102,c_87]) ).
tcf(c_64444,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,sK0)
| ( k1_funct_1(sK2,X0) = k1_xboole_0 )
| r2_hidden(X0,k1_closure3(sK0,sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_64367,c_8398]) ).
tcf(c_64445,plain,
! [X0: $i] :
( r2_hidden(X0,k1_closure3(sK0,sK2))
| ( k1_funct_1(sK2,X0) = k1_xboole_0 )
| ~ m1_subset_1(X0,sK0) ),
inference(renaming,[status(thm)],[c_64444]) ).
tcf(c_64446,plain,
! [X0: $i] :
( r2_hidden(X0,k1_closure3(sK0,sK1))
| ( k1_funct_1(sK2,X0) = k1_xboole_0 )
| ~ m1_subset_1(X0,sK0) ),
inference(superposition,[status(thm)],[c_50,c_64445]) ).
tcf(c_64488,plain,
! [X0: $i,X1: $i] :
( ( k1_funct_1(k7_relat_1(sK2,X1),X0) = k1_funct_1(sK2,X0) )
| ~ v1_relat_1(sK2)
| ~ v1_funct_1(sK2)
| ~ r2_hidden(X0,k3_xboole_0(k1_relat_1(sK2),X1)) ),
inference(superposition,[status(thm)],[c_64045,c_138]) ).
tcf(c_64489,plain,
! [X0: $i,X1: $i] :
( ( k1_funct_1(k7_relat_1(sK1,X1),X0) = k1_funct_1(sK1,X0) )
| ~ v1_relat_1(sK1)
| ~ v1_funct_1(sK1)
| ~ r2_hidden(X0,k3_xboole_0(k1_relat_1(sK1),X1)) ),
inference(superposition,[status(thm)],[c_64046,c_138]) ).
tcf(c_64535,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,sK0)
| ( k1_funct_1(sK1,X0) = k1_xboole_0 )
| r2_hidden(X0,k1_closure3(sK0,sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_64368,c_8807]) ).
tcf(c_64536,plain,
! [X0: $i] :
( r2_hidden(X0,k1_closure3(sK0,sK1))
| ( k1_funct_1(sK1,X0) = k1_xboole_0 )
| ~ m1_subset_1(X0,sK0) ),
inference(renaming,[status(thm)],[c_64535]) ).
tcf(c_64592,plain,
! [X0: $i] :
( r2_hidden(sK22(X0,sK2),k1_relat_1(X0))
| ( X0 = sK2 )
| ~ v1_relat_1(sK2)
| ~ v1_funct_1(sK2)
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0)
| ( k1_relat_1(X0) != sK0 ) ),
inference(superposition,[status(thm)],[c_63839,c_143]) ).
tcf(c_64772,plain,
! [X0: $i] :
( r2_hidden(sK22(X0,sK2),k1_relat_1(X0))
| ( X0 = sK2 )
| ~ v1_relat_1(X0)
| ~ v1_funct_1(X0)
| ( k1_relat_1(X0) != sK0 ) ),
inference(global_subsumption_just,[status(thm)],[c_64592,c_9808]) ).
tcf(c_64775,plain,
( r2_hidden(sK22(sK1,sK2),k1_relat_1(sK1))
| ( sK1 = sK2 )
| ~ v1_relat_1(sK1)
| ~ v1_funct_1(sK1) ),
inference(superposition,[status(thm)],[c_63840,c_64772]) ).
tcf(c_64793,plain,
r2_hidden(sK22(sK1,sK2),k1_relat_1(sK1)),
inference(global_subsumption_just,[status(thm)],[c_64775,c_55,c_53,c_49,c_4903,c_4935,c_5022,c_5406,c_6484,c_6948,c_9812]) ).
tcf(c_64795,plain,
r2_hidden(sK22(sK1,sK2),sK0),
inference(superposition,[status(thm)],[c_63840,c_64793]) ).
tcf(c_64801,plain,
m1_subset_1(sK22(sK1,sK2),sK0),
inference(superposition,[status(thm)],[c_64795,c_132]) ).
tcf(c_66631,plain,
! [X0: $i] : m1_pboole(k7_relat_1(sK1,X0),k3_xboole_0(k1_relat_1(sK1),X0)),
inference(global_subsumption_just,[status(thm)],[c_64106,c_55,c_4903,c_5022,c_5179,c_5177,c_5486]) ).
tcf(c_66633,plain,
! [X0: $i] : m1_pboole(k7_relat_1(sK1,X0),k3_xboole_0(X0,k1_relat_1(sK1))),
inference(superposition,[status(thm)],[c_62,c_66631]) ).
tcf(c_69169,plain,
! [X0: $i] : k3_xboole_0(X0,k1_relat_1(sK1)) = k1_relat_1(k7_relat_1(sK1,X0)),
inference(superposition,[status(thm)],[c_66633,c_2058]) ).
tcf(c_69277,plain,
! [X0: $i] :
( v1_xboole_0(k1_funct_1(sK2,X0))
| ~ v1_xboole_0(k1_xboole_0)
| ( k1_funct_1(sK2,X0) != k1_xboole_0 ) ),
inference(instantiation,[status(thm)],[c_63496]) ).
tcf(c_69450,plain,
! [X0: $i] :
( v1_xboole_0(k1_funct_1(sK1,X0))
| ~ v1_xboole_0(k1_xboole_0)
| ( k1_funct_1(sK1,X0) != k1_xboole_0 ) ),
inference(instantiation,[status(thm)],[c_63516]) ).
tcf(c_69481,plain,
! [X0: $i] : k3_xboole_0(k1_relat_1(sK1),X0) = k3_xboole_0(X0,k1_relat_1(sK1)),
inference(superposition,[status(thm)],[c_69169,c_64046]) ).
tcf(c_69684,plain,
! [X0: $i] : k3_xboole_0(X0,sK0) = k3_xboole_0(sK0,X0),
inference(superposition,[status(thm)],[c_63840,c_69481]) ).
tcf(c_69764,plain,
! [X0: $i,X1: $i] :
( r2_hidden(X0,k3_xboole_0(sK0,X1))
| ~ r2_hidden(X0,sK0)
| ~ r2_hidden(X0,X1) ),
inference(superposition,[status(thm)],[c_69684,c_73]) ).
tcf(c_74932,plain,
! [X0: $i,X1: $i] :
( ( k1_funct_1(k7_relat_1(sK2,X1),X0) = k1_funct_1(sK2,X0) )
| ~ r2_hidden(X0,k3_xboole_0(k1_relat_1(sK2),X1)) ),
inference(global_subsumption_just,[status(thm)],[c_64488,c_53,c_4902,c_5021,c_8521]) ).
tcf(c_74995,plain,
! [X0: $i,X1: $i] :
( ( k1_funct_1(k7_relat_1(sK2,X1),X0) = k1_funct_1(sK2,X0) )
| ~ r2_hidden(X0,k3_xboole_0(sK0,X1)) ),
inference(superposition,[status(thm)],[c_63839,c_74932]) ).
tcf(c_75201,plain,
! [X0: $i,X1: $i] :
( ( k1_funct_1(k7_relat_1(sK2,X1),X0) = k1_funct_1(sK2,X0) )
| ~ r2_hidden(X0,sK0)
| ~ r2_hidden(X0,X1) ),
inference(superposition,[status(thm)],[c_69764,c_74995]) ).
tcf(c_76448,plain,
! [X0: $i] :
( ( k1_funct_1(sK1,X0) = k1_xboole_0 )
| ( k1_funct_1(k7_relat_1(sK2,k1_closure3(sK0,sK1)),X0) = k1_funct_1(sK2,X0) )
| ~ m1_subset_1(X0,sK0)
| ~ r2_hidden(X0,sK0) ),
inference(superposition,[status(thm)],[c_64536,c_75201]) ).
tcf(c_76449,plain,
! [X0: $i] :
( ( k1_funct_1(sK2,X0) = k1_xboole_0 )
| ( k1_funct_1(k7_relat_1(sK2,k1_closure3(sK0,sK1)),X0) = k1_funct_1(sK2,X0) )
| ~ m1_subset_1(X0,sK0)
| ~ r2_hidden(X0,sK0) ),
inference(superposition,[status(thm)],[c_64446,c_75201]) ).
tcf(c_76641,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,sK0)
| ( k1_funct_1(k7_relat_1(sK2,k1_closure3(sK0,sK1)),X0) = k1_funct_1(sK2,X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_76449,c_54,c_83,c_56,c_55,c_5917,c_58984,c_69450,c_76448]) ).
tcf(c_76642,plain,
! [X0: $i] :
( ( k1_funct_1(k7_relat_1(sK2,k1_closure3(sK0,sK1)),X0) = k1_funct_1(sK2,X0) )
| ~ m1_subset_1(X0,sK0) ),
inference(renaming,[status(thm)],[c_76641]) ).
tcf(c_76649,plain,
k1_funct_1(k7_relat_1(sK2,k1_closure3(sK0,sK1)),sK22(sK1,sK2)) = k1_funct_1(sK2,sK22(sK1,sK2)),
inference(superposition,[status(thm)],[c_64801,c_76642]) ).
tcf(c_76807,plain,
k1_funct_1(k7_relat_1(sK1,k1_closure3(sK0,sK1)),sK22(sK1,sK2)) = k1_funct_1(sK2,sK22(sK1,sK2)),
inference(superposition,[status(thm)],[c_635,c_76649]) ).
tcf(c_77645,plain,
! [X0: $i,X1: $i] :
( ( k1_funct_1(k7_relat_1(sK1,X1),X0) = k1_funct_1(sK1,X0) )
| ~ r2_hidden(X0,k3_xboole_0(k1_relat_1(sK1),X1)) ),
inference(global_subsumption_just,[status(thm)],[c_64489,c_55,c_4903,c_5022,c_8522]) ).
tcf(c_77708,plain,
! [X0: $i,X1: $i] :
( ( k1_funct_1(k7_relat_1(sK1,X1),X0) = k1_funct_1(sK1,X0) )
| ~ r2_hidden(X0,k3_xboole_0(sK0,X1)) ),
inference(superposition,[status(thm)],[c_63840,c_77645]) ).
tcf(c_77870,plain,
! [X0: $i,X1: $i] :
( ( k1_funct_1(k7_relat_1(sK1,X1),X0) = k1_funct_1(sK1,X0) )
| ~ r2_hidden(X0,sK0)
| ~ r2_hidden(X0,X1) ),
inference(superposition,[status(thm)],[c_69764,c_77708]) ).
tcf(c_80597,plain,
! [X0: $i] :
( ( k1_funct_1(sK2,X0) = k1_xboole_0 )
| ( k1_funct_1(k7_relat_1(sK1,k1_closure3(sK0,sK1)),X0) = k1_funct_1(sK1,X0) )
| ~ m1_subset_1(X0,sK0)
| ~ r2_hidden(X0,sK0) ),
inference(superposition,[status(thm)],[c_64446,c_77870]) ).
tcf(c_80840,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,sK0)
| ( k1_funct_1(k7_relat_1(sK1,k1_closure3(sK0,sK1)),X0) = k1_funct_1(sK1,X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_80597,c_52,c_83,c_56,c_53,c_5917,c_58982,c_69277,c_80597]) ).
tcf(c_80841,plain,
! [X0: $i] :
( ( k1_funct_1(k7_relat_1(sK1,k1_closure3(sK0,sK1)),X0) = k1_funct_1(sK1,X0) )
| ~ m1_subset_1(X0,sK0) ),
inference(renaming,[status(thm)],[c_80840]) ).
tcf(c_80848,plain,
k1_funct_1(k7_relat_1(sK1,k1_closure3(sK0,sK1)),sK22(sK1,sK2)) = k1_funct_1(sK1,sK22(sK1,sK2)),
inference(superposition,[status(thm)],[c_64801,c_80841]) ).
tcf(c_81518,plain,
k1_funct_1(sK1,sK22(sK1,sK2)) = k1_funct_1(sK2,sK22(sK1,sK2)),
inference(superposition,[status(thm)],[c_80848,c_76807]) ).
tcf(c_81519,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_81518,c_31986,c_15089,c_6948,c_6578,c_6484,c_5423,c_5406,c_5021,c_5022,c_4935,c_4911,c_4903,c_4902,c_49,c_53,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG226+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 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 05:11:05 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/0.34 Running first-order theorem proving
% 0.04/0.34 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
% 0.08/0.35
% 0.08/0.35 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.35
% 0.08/0.35 % Detected problem language: tptp
% 0.08/0.36 % Proving...
% 79.75/13.18 % SZS status Started for theBenchmark.p
% 79.75/13.18 % SZS status Theorem for theBenchmark.p
% 79.75/13.18
% 79.75/13.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 79.75/13.18
% 79.75/13.18 % ------ iProver source info
% 79.75/13.18
% 79.75/13.18 % git: date: 2026-07-19 20:42:38 +0200
% 79.75/13.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 79.75/13.18 % git: non_committed_changes: false
% 79.75/13.18
% 79.75/13.18 % ------ Parsing...
% 79.75/13.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 79.75/13.18
% 79.75/13.18 % ------ Preprocessing... sup_sim: 1 sf_s rm: 7 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 79.75/13.18
% 79.75/13.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 79.75/13.18
% 79.75/13.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 79.75/13.18 % ------ Proving...
% 79.75/13.18 % ------ Problem Properties
% 79.75/13.18
% 79.75/13.18 %
% 79.75/13.18 % clauses 85
% 79.75/13.18 % conjectures 7
% 79.75/13.18 % EPR 41
% 79.75/13.18 % Horn 71
% 79.75/13.18 % unary 41
% 79.75/13.18 % binary 13
% 79.75/13.18 % lits 189
% 79.75/13.18 % lits eq 28
% 79.75/13.18 % fd_pure 0
% 79.75/13.18 % fd_pseudo 0
% 79.75/13.18 % fd_cond 1
% 79.75/13.18 % fd_pseudo_cond 10
% 79.75/13.18 % AC symbols 0
% 79.75/13.18
% 79.75/13.18 % ------ Input Options Time Limit: Unbounded
% 79.75/13.18
% 79.75/13.18
% 79.75/13.18 % ------
% 79.75/13.18 % Current options:
% 79.75/13.18 % ------
% 79.75/13.18
% 79.75/13.18
% 79.75/13.18 %
% 79.75/13.18
% 79.75/13.18 % ------ Proving...
% 79.75/13.18 %
% 79.75/13.18
% 79.75/13.18 % SZS status Theorem for theBenchmark.p
% 79.75/13.18
% 79.75/13.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 79.75/13.18
% 79.75/13.18
%------------------------------------------------------------------------------