TSTP Solution File: ALG226+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : ALG226+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 02:04:22 EDT 2024
% Result : Theorem 184.47s 24.92s
% Output : CNFRefutation 184.47s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% 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/sandbox/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,[],[f1]) ).
fof(f11,axiom,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f13,axiom,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( k1_closure3(X0,X1) = X2
<=> a_2_0_closure3(X0,X1) = X2 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',d3_pboole) ).
fof(f15,axiom,
! [X0,X1,X2] :
( k3_xboole_0(X0,X1) = X2
<=> ! [X3] :
( r2_hidden(X3,X2)
<=> ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f22,axiom,
! [X0,X1] :
( m1_pboole(X1,X0)
=> ( v1_funct_1(X1)
& v1_relat_1(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_pboole) ).
fof(f28,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fc2_pboole) ).
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_xboole_0 != k1_funct_1(X2,X3)
& X0 = X3
& m1_subset_1(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_closure3) ).
fof(f33,axiom,
! [X0,X1] : k3_xboole_0(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f49,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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(X1,X2) = k1_funct_1(X0,X2) )
& k1_relat_1(X1) = k1_relat_1(X0) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_1) ).
fof(f59,plain,
! [X0] : k3_xboole_0(X0,X0) = X0,
inference(rectify,[],[f33]) ).
fof(f66,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ r6_pboole(X0,X1,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)
& m1_pboole(X2,X0)
& v2_relat_1(X2) )
& m1_pboole(X1,X0)
& v2_relat_1(X1) )
& ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f67,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ r6_pboole(X0,X1,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)
& m1_pboole(X2,X0)
& v2_relat_1(X2) )
& m1_pboole(X1,X0)
& v2_relat_1(X1) )
& ~ v1_xboole_0(X0) ),
inference(flattening,[],[f66]) ).
fof(f78,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( k1_closure3(X0,X1) = X2
<=> a_2_0_closure3(X0,X1) = X2 )
| ~ m1_pboole(X1,X0) )
| v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f79,plain,
! [X0,X1] :
( ( m1_pboole(X1,X0)
<=> k1_relat_1(X1) = X0 )
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f80,plain,
! [X0,X1] :
( ( m1_pboole(X1,X0)
<=> k1_relat_1(X1) = X0 )
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X1) ),
inference(flattening,[],[f79]) ).
fof(f82,plain,
! [X0,X1] :
( ( v1_funct_1(X1)
& v1_relat_1(X1) )
| ~ m1_pboole(X1,X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ~ v1_xboole_0(k1_funct_1(X1,X2))
| ~ m1_subset_1(X2,X0)
| ~ m1_pboole(X1,X0)
| ~ v2_relat_1(X1)
| v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ~ v1_xboole_0(k1_funct_1(X1,X2))
| ~ m1_subset_1(X2,X0)
| ~ m1_pboole(X1,X0)
| ~ v2_relat_1(X1)
| v1_xboole_0(X0) ),
inference(flattening,[],[f85]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
<=> ? [X3] :
( k1_xboole_0 != k1_funct_1(X2,X3)
& X0 = X3
& m1_subset_1(X3,X1) ) )
| ~ m1_pboole(X2,X1)
| v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
<=> ? [X3] :
( k1_xboole_0 != k1_funct_1(X2,X3)
& X0 = X3
& m1_subset_1(X3,X1) ) )
| ~ m1_pboole(X2,X1)
| v1_xboole_0(X1) ),
inference(flattening,[],[f89]) ).
fof(f99,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f100,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f51]) ).
fof(f101,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(flattening,[],[f100]) ).
fof(f104,plain,
! [X0,X1,X2] :
( k1_funct_1(k7_relat_1(X2,X0),X1) = k1_funct_1(X2,X1)
| ~ r2_hidden(X1,k1_relat_1(k7_relat_1(X2,X0)))
| ~ v1_funct_1(X2)
| ~ v1_relat_1(X2) ),
inference(ennf_transformation,[],[f54]) ).
fof(f105,plain,
! [X0,X1,X2] :
( k1_funct_1(k7_relat_1(X2,X0),X1) = k1_funct_1(X2,X1)
| ~ r2_hidden(X1,k1_relat_1(k7_relat_1(X2,X0)))
| ~ v1_funct_1(X2)
| ~ v1_relat_1(X2) ),
inference(flattening,[],[f104]) ).
fof(f108,plain,
! [X0,X1] :
( k1_relat_1(k7_relat_1(X1,X0)) = k3_xboole_0(k1_relat_1(X1),X0)
| ~ v1_relat_1(X1) ),
inference(ennf_transformation,[],[f57]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ? [X2] :
( k1_funct_1(X1,X2) != k1_funct_1(X0,X2)
& r2_hidden(X2,k1_relat_1(X0)) )
| k1_relat_1(X1) != k1_relat_1(X0)
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X1) )
| ~ v1_funct_1(X0)
| ~ v1_relat_1(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f110,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ? [X2] :
( k1_funct_1(X1,X2) != k1_funct_1(X0,X2)
& r2_hidden(X2,k1_relat_1(X0)) )
| k1_relat_1(X1) != k1_relat_1(X0)
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X1) )
| ~ v1_funct_1(X0)
| ~ v1_relat_1(X0) ),
inference(flattening,[],[f109]) ).
fof(f111,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ~ r6_pboole(X0,X1,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)
& m1_pboole(X2,X0)
& v2_relat_1(X2) )
& m1_pboole(X1,X0)
& v2_relat_1(X1) )
& ~ v1_xboole_0(X0) )
=> ( ? [X1] :
( ? [X2] :
( ~ r6_pboole(sK0,X1,X2)
& k7_relat_1(X1,k1_closure3(sK0,X1)) = k7_relat_1(X2,k1_closure3(sK0,X2))
& k1_closure3(sK0,X1) = k1_closure3(sK0,X2)
& m1_pboole(X2,sK0)
& v2_relat_1(X2) )
& m1_pboole(X1,sK0)
& v2_relat_1(X1) )
& ~ v1_xboole_0(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f112,plain,
( ? [X1] :
( ? [X2] :
( ~ r6_pboole(sK0,X1,X2)
& k7_relat_1(X1,k1_closure3(sK0,X1)) = k7_relat_1(X2,k1_closure3(sK0,X2))
& k1_closure3(sK0,X1) = k1_closure3(sK0,X2)
& m1_pboole(X2,sK0)
& v2_relat_1(X2) )
& m1_pboole(X1,sK0)
& v2_relat_1(X1) )
=> ( ? [X2] :
( ~ r6_pboole(sK0,sK1,X2)
& k7_relat_1(X2,k1_closure3(sK0,X2)) = k7_relat_1(sK1,k1_closure3(sK0,sK1))
& k1_closure3(sK0,X2) = k1_closure3(sK0,sK1)
& m1_pboole(X2,sK0)
& v2_relat_1(X2) )
& m1_pboole(sK1,sK0)
& v2_relat_1(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f113,plain,
( ? [X2] :
( ~ r6_pboole(sK0,sK1,X2)
& k7_relat_1(X2,k1_closure3(sK0,X2)) = k7_relat_1(sK1,k1_closure3(sK0,sK1))
& k1_closure3(sK0,X2) = k1_closure3(sK0,sK1)
& m1_pboole(X2,sK0)
& v2_relat_1(X2) )
=> ( ~ r6_pboole(sK0,sK1,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)
& m1_pboole(sK2,sK0)
& v2_relat_1(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f114,plain,
( ~ r6_pboole(sK0,sK1,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)
& m1_pboole(sK2,sK0)
& v2_relat_1(sK2)
& m1_pboole(sK1,sK0)
& v2_relat_1(sK1)
& ~ v1_xboole_0(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f67,f113,f112,f111]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( k1_closure3(X0,X1) = X2
| a_2_0_closure3(X0,X1) != X2 )
& ( a_2_0_closure3(X0,X1) = X2
| k1_closure3(X0,X1) != X2 ) )
| ~ m1_pboole(X1,X0) )
| v1_xboole_0(X0) ),
inference(nnf_transformation,[],[f78]) ).
fof(f120,plain,
! [X0,X1] :
( ( ( m1_pboole(X1,X0)
| k1_relat_1(X1) != X0 )
& ( k1_relat_1(X1) = X0
| ~ m1_pboole(X1,X0) ) )
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X1) ),
inference(nnf_transformation,[],[f80]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ( k3_xboole_0(X0,X1) = X2
| ? [X3] :
( ( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X2) )
& ( ( 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,X1)
& r2_hidden(X3,X0) )
| ~ r2_hidden(X3,X2) ) )
| k3_xboole_0(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ( k3_xboole_0(X0,X1) = X2
| ? [X3] :
( ( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X2) )
& ( ( 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,X1)
& r2_hidden(X3,X0) )
| ~ r2_hidden(X3,X2) ) )
| k3_xboole_0(X0,X1) != X2 ) ),
inference(flattening,[],[f121]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ( k3_xboole_0(X0,X1) = X2
| ? [X3] :
( ( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X2) )
& ( ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) )
| r2_hidden(X3,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) ) )
| k3_xboole_0(X0,X1) != X2 ) ),
inference(rectify,[],[f122]) ).
fof(f124,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X3,X0)
| ~ r2_hidden(X3,X2) )
& ( ( r2_hidden(X3,X1)
& r2_hidden(X3,X0) )
| r2_hidden(X3,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) )
| r2_hidden(sK4(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f125,plain,
! [X0,X1,X2] :
( ( k3_xboole_0(X0,X1) = 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) )
| r2_hidden(sK4(X0,X1,X2),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) ) )
| k3_xboole_0(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f123,f124]) ).
fof(f130,plain,
! [X0,X1,X2] :
( ( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
| ! [X3] :
( k1_xboole_0 = k1_funct_1(X2,X3)
| 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)) ) )
| ~ m1_pboole(X2,X1)
| v1_xboole_0(X1) ),
inference(nnf_transformation,[],[f90]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
| ! [X3] :
( k1_xboole_0 = k1_funct_1(X2,X3)
| X0 != X3
| ~ m1_subset_1(X3,X1) ) )
& ( ? [X4] :
( k1_xboole_0 != k1_funct_1(X2,X4)
& X0 = X4
& m1_subset_1(X4,X1) )
| ~ r2_hidden(X0,a_2_0_closure3(X1,X2)) ) )
| ~ m1_pboole(X2,X1)
| v1_xboole_0(X1) ),
inference(rectify,[],[f130]) ).
fof(f132,plain,
! [X0,X1,X2] :
( ? [X4] :
( k1_xboole_0 != k1_funct_1(X2,X4)
& X0 = X4
& m1_subset_1(X4,X1) )
=> ( k1_xboole_0 != k1_funct_1(X2,sK7(X0,X1,X2))
& sK7(X0,X1,X2) = X0
& m1_subset_1(sK7(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f133,plain,
! [X0,X1,X2] :
( ( ( r2_hidden(X0,a_2_0_closure3(X1,X2))
| ! [X3] :
( k1_xboole_0 = k1_funct_1(X2,X3)
| X0 != X3
| ~ m1_subset_1(X3,X1) ) )
& ( ( k1_xboole_0 != k1_funct_1(X2,sK7(X0,X1,X2))
& sK7(X0,X1,X2) = X0
& m1_subset_1(sK7(X0,X1,X2),X1) )
| ~ r2_hidden(X0,a_2_0_closure3(X1,X2)) ) )
| ~ m1_pboole(X2,X1)
| v1_xboole_0(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f131,f132]) ).
fof(f166,plain,
! [X0,X1] :
( ? [X2] :
( k1_funct_1(X1,X2) != k1_funct_1(X0,X2)
& r2_hidden(X2,k1_relat_1(X0)) )
=> ( k1_funct_1(X1,sK22(X0,X1)) != k1_funct_1(X0,sK22(X0,X1))
& r2_hidden(sK22(X0,X1),k1_relat_1(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f167,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ( k1_funct_1(X1,sK22(X0,X1)) != k1_funct_1(X0,sK22(X0,X1))
& r2_hidden(sK22(X0,X1),k1_relat_1(X0)) )
| k1_relat_1(X1) != k1_relat_1(X0)
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X1) )
| ~ v1_funct_1(X0)
| ~ v1_relat_1(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f110,f166]) ).
fof(f168,plain,
~ v1_xboole_0(sK0),
inference(cnf_transformation,[],[f114]) ).
fof(f169,plain,
v2_relat_1(sK1),
inference(cnf_transformation,[],[f114]) ).
fof(f170,plain,
m1_pboole(sK1,sK0),
inference(cnf_transformation,[],[f114]) ).
fof(f172,plain,
m1_pboole(sK2,sK0),
inference(cnf_transformation,[],[f114]) ).
fof(f173,plain,
k1_closure3(sK0,sK1) = k1_closure3(sK0,sK2),
inference(cnf_transformation,[],[f114]) ).
fof(f174,plain,
k7_relat_1(sK1,k1_closure3(sK0,sK1)) = k7_relat_1(sK2,k1_closure3(sK0,sK2)),
inference(cnf_transformation,[],[f114]) ).
fof(f175,plain,
~ r6_pboole(sK0,sK1,sK2),
inference(cnf_transformation,[],[f114]) ).
fof(f183,plain,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f187,plain,
! [X2,X0,X1] :
( a_2_0_closure3(X0,X1) = X2
| k1_closure3(X0,X1) != X2
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f189,plain,
! [X0,X1] :
( k1_relat_1(X1) = X0
| ~ m1_pboole(X1,X0)
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X1) ),
inference(cnf_transformation,[],[f120]) ).
fof(f192,plain,
! [X2,X0,X1,X4] :
( r2_hidden(X4,X1)
| ~ r2_hidden(X4,X2)
| k3_xboole_0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f125]) ).
fof(f193,plain,
! [X2,X0,X1,X4] :
( r2_hidden(X4,X2)
| ~ r2_hidden(X4,X1)
| ~ r2_hidden(X4,X0)
| k3_xboole_0(X0,X1) != X2 ),
inference(cnf_transformation,[],[f125]) ).
fof(f194,plain,
! [X2,X0,X1] :
( k3_xboole_0(X0,X1) = X2
| r2_hidden(sK4(X0,X1,X2),X0)
| r2_hidden(sK4(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f125]) ).
fof(f196,plain,
! [X2,X0,X1] :
( k3_xboole_0(X0,X1) = X2
| ~ r2_hidden(sK4(X0,X1,X2),X1)
| ~ r2_hidden(sK4(X0,X1,X2),X0)
| ~ r2_hidden(sK4(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f125]) ).
fof(f198,plain,
! [X0,X1] :
( v1_relat_1(X1)
| ~ m1_pboole(X1,X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f199,plain,
! [X0,X1] :
( v1_funct_1(X1)
| ~ m1_pboole(X1,X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f204,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f28]) ).
fof(f205,plain,
! [X2,X0,X1] :
( ~ v1_xboole_0(k1_funct_1(X1,X2))
| ~ m1_subset_1(X2,X0)
| ~ m1_pboole(X1,X0)
| ~ v2_relat_1(X1)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f208,plain,
! [X2,X0,X1] :
( m1_subset_1(sK7(X0,X1,X2),X1)
| ~ r2_hidden(X0,a_2_0_closure3(X1,X2))
| ~ m1_pboole(X2,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f209,plain,
! [X2,X0,X1] :
( sK7(X0,X1,X2) = X0
| ~ r2_hidden(X0,a_2_0_closure3(X1,X2))
| ~ m1_pboole(X2,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f211,plain,
! [X2,X3,X0,X1] :
( r2_hidden(X0,a_2_0_closure3(X1,X2))
| k1_xboole_0 = k1_funct_1(X2,X3)
| X0 != X3
| ~ m1_subset_1(X3,X1)
| ~ m1_pboole(X2,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f216,plain,
! [X0] : k3_xboole_0(X0,X0) = X0,
inference(cnf_transformation,[],[f59]) ).
fof(f253,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f255,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f259,plain,
! [X2,X0,X1] :
( k1_funct_1(k7_relat_1(X2,X0),X1) = k1_funct_1(X2,X1)
| ~ r2_hidden(X1,k1_relat_1(k7_relat_1(X2,X0)))
| ~ v1_funct_1(X2)
| ~ v1_relat_1(X2) ),
inference(cnf_transformation,[],[f105]) ).
fof(f262,plain,
! [X0,X1] :
( k1_relat_1(k7_relat_1(X1,X0)) = k3_xboole_0(k1_relat_1(X1),X0)
| ~ v1_relat_1(X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f263,plain,
! [X0,X1] :
( X0 = X1
| r2_hidden(sK22(X0,X1),k1_relat_1(X0))
| k1_relat_1(X1) != k1_relat_1(X0)
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X0)
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f264,plain,
! [X0,X1] :
( X0 = X1
| k1_funct_1(X1,sK22(X0,X1)) != k1_funct_1(X0,sK22(X0,X1))
| k1_relat_1(X1) != k1_relat_1(X0)
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| ~ v1_funct_1(X0)
| ~ v1_relat_1(X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f266,plain,
! [X0,X1] :
( k1_closure3(X0,X1) = a_2_0_closure3(X0,X1)
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X0) ),
inference(equality_resolution,[],[f187]) ).
fof(f268,plain,
! [X0,X1,X4] :
( r2_hidden(X4,k3_xboole_0(X0,X1))
| ~ r2_hidden(X4,X1)
| ~ r2_hidden(X4,X0) ),
inference(equality_resolution,[],[f193]) ).
fof(f269,plain,
! [X0,X1,X4] :
( r2_hidden(X4,X1)
| ~ r2_hidden(X4,k3_xboole_0(X0,X1)) ),
inference(equality_resolution,[],[f192]) ).
fof(f271,plain,
! [X2,X3,X1] :
( r2_hidden(X3,a_2_0_closure3(X1,X2))
| k1_xboole_0 = k1_funct_1(X2,X3)
| ~ m1_subset_1(X3,X1)
| ~ m1_pboole(X2,X1)
| v1_xboole_0(X1) ),
inference(equality_resolution,[],[f211]) ).
cnf(c_49,negated_conjecture,
~ r6_pboole(sK0,sK1,sK2),
inference(cnf_transformation,[],[f175]) ).
cnf(c_50,negated_conjecture,
k7_relat_1(sK1,k1_closure3(sK0,sK1)) = k7_relat_1(sK2,k1_closure3(sK0,sK2)),
inference(cnf_transformation,[],[f174]) ).
cnf(c_51,negated_conjecture,
k1_closure3(sK0,sK1) = k1_closure3(sK0,sK2),
inference(cnf_transformation,[],[f173]) ).
cnf(c_52,negated_conjecture,
m1_pboole(sK2,sK0),
inference(cnf_transformation,[],[f172]) ).
cnf(c_54,negated_conjecture,
m1_pboole(sK1,sK0),
inference(cnf_transformation,[],[f170]) ).
cnf(c_55,negated_conjecture,
v2_relat_1(sK1),
inference(cnf_transformation,[],[f169]) ).
cnf(c_56,negated_conjecture,
~ v1_xboole_0(sK0),
inference(cnf_transformation,[],[f168]) ).
cnf(c_62,plain,
k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
inference(cnf_transformation,[],[f183]) ).
cnf(c_67,plain,
( ~ m1_pboole(X0,X1)
| k1_closure3(X1,X0) = a_2_0_closure3(X1,X0)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f266]) ).
cnf(c_69,plain,
( ~ m1_pboole(X0,X1)
| ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| k1_relat_1(X0) = X1 ),
inference(cnf_transformation,[],[f189]) ).
cnf(c_70,plain,
( ~ r2_hidden(sK4(X0,X1,X2),X0)
| ~ r2_hidden(sK4(X0,X1,X2),X1)
| ~ r2_hidden(sK4(X0,X1,X2),X2)
| k3_xboole_0(X0,X1) = X2 ),
inference(cnf_transformation,[],[f196]) ).
cnf(c_72,plain,
( k3_xboole_0(X0,X1) = X2
| r2_hidden(sK4(X0,X1,X2),X0)
| r2_hidden(sK4(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f194]) ).
cnf(c_73,plain,
( ~ r2_hidden(X0,X1)
| ~ r2_hidden(X0,X2)
| r2_hidden(X0,k3_xboole_0(X2,X1)) ),
inference(cnf_transformation,[],[f268]) ).
cnf(c_74,plain,
( ~ r2_hidden(X0,k3_xboole_0(X1,X2))
| r2_hidden(X0,X2) ),
inference(cnf_transformation,[],[f269]) ).
cnf(c_77,plain,
( ~ m1_pboole(X0,X1)
| v1_funct_1(X0) ),
inference(cnf_transformation,[],[f199]) ).
cnf(c_78,plain,
( ~ m1_pboole(X0,X1)
| v1_relat_1(X0) ),
inference(cnf_transformation,[],[f198]) ).
cnf(c_83,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f204]) ).
cnf(c_84,plain,
( ~ v1_xboole_0(k1_funct_1(X0,X1))
| ~ m1_pboole(X0,X2)
| ~ m1_subset_1(X1,X2)
| ~ v2_relat_1(X0)
| v1_xboole_0(X2) ),
inference(cnf_transformation,[],[f205]) ).
cnf(c_87,plain,
( ~ m1_pboole(X0,X1)
| ~ m1_subset_1(X2,X1)
| k1_funct_1(X0,X2) = k1_xboole_0
| r2_hidden(X2,a_2_0_closure3(X1,X0))
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f271]) ).
cnf(c_89,plain,
( ~ r2_hidden(X0,a_2_0_closure3(X1,X2))
| ~ m1_pboole(X2,X1)
| sK7(X0,X1,X2) = X0
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f209]) ).
cnf(c_90,plain,
( ~ r2_hidden(X0,a_2_0_closure3(X1,X2))
| ~ m1_pboole(X2,X1)
| m1_subset_1(sK7(X0,X1,X2),X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f208]) ).
cnf(c_95,plain,
k3_xboole_0(X0,X0) = X0,
inference(cnf_transformation,[],[f216]) ).
cnf(c_128,plain,
( ~ m1_pboole(X0,X1)
| r6_pboole(X1,X0,X0) ),
inference(cnf_transformation,[],[f274]) ).
cnf(c_132,plain,
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f253]) ).
cnf(c_134,plain,
( ~ m1_subset_1(X0,X1)
| r2_hidden(X0,X1)
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f255]) ).
cnf(c_138,plain,
( ~ r2_hidden(X0,k1_relat_1(k7_relat_1(X1,X2)))
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X1)
| k1_funct_1(k7_relat_1(X1,X2),X0) = k1_funct_1(X1,X0) ),
inference(cnf_transformation,[],[f259]) ).
cnf(c_141,plain,
( ~ v1_relat_1(X0)
| k3_xboole_0(k1_relat_1(X0),X1) = k1_relat_1(k7_relat_1(X0,X1)) ),
inference(cnf_transformation,[],[f262]) ).
cnf(c_142,plain,
( k1_funct_1(X0,sK22(X0,X1)) != k1_funct_1(X1,sK22(X0,X1))
| k1_relat_1(X0) != k1_relat_1(X1)
| ~ v1_funct_1(X0)
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X0)
| ~ v1_relat_1(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f264]) ).
cnf(c_143,plain,
( k1_relat_1(X0) != k1_relat_1(X1)
| ~ v1_funct_1(X0)
| ~ v1_funct_1(X1)
| ~ v1_relat_1(X0)
| ~ v1_relat_1(X1)
| X0 = X1
| r2_hidden(sK22(X1,X0),k1_relat_1(X1)) ),
inference(cnf_transformation,[],[f263]) ).
cnf(c_184,plain,
( ~ m1_pboole(X0,X1)
| k1_relat_1(X0) = X1 ),
inference(global_subsumption_just,[status(thm)],[c_69,c_78,c_77,c_69]) ).
cnf(c_679,plain,
k7_relat_1(sK1,k1_closure3(sK0,sK1)) = k7_relat_1(sK2,k1_closure3(sK0,sK1)),
inference(light_normalisation,[status(thm)],[c_50,c_51]) ).
cnf(c_4304,plain,
k1_closure3(sK0,sK1) = sP0_iProver_def,
definition ).
cnf(c_4306,negated_conjecture,
~ v1_xboole_0(sK0),
inference(demodulation,[status(thm)],[c_56]) ).
cnf(c_4308,negated_conjecture,
m1_pboole(sK1,sK0),
inference(demodulation,[status(thm)],[c_54]) ).
cnf(c_4310,negated_conjecture,
m1_pboole(sK2,sK0),
inference(demodulation,[status(thm)],[c_52]) ).
cnf(c_4313,plain,
X0 = X0,
theory(equality) ).
cnf(c_4316,plain,
( X0 != X1
| X2 != X3
| X4 != X5
| ~ r6_pboole(X1,X3,X5)
| r6_pboole(X0,X2,X4) ),
theory(equality) ).
cnf(c_4321,plain,
( X0 != X1
| ~ v1_xboole_0(X1)
| v1_xboole_0(X0) ),
theory(equality) ).
cnf(c_5878,plain,
( k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1)
| v1_xboole_0(sK0) ),
inference(superposition,[status(thm)],[c_4308,c_67]) ).
cnf(c_5888,plain,
( a_2_0_closure3(sK0,sK1) = sP0_iProver_def
| v1_xboole_0(sK0) ),
inference(light_normalisation,[status(thm)],[c_5878,c_4304]) ).
cnf(c_5889,plain,
a_2_0_closure3(sK0,sK1) = sP0_iProver_def,
inference(forward_subsumption_resolution,[status(thm)],[c_5888,c_4306]) ).
cnf(c_6233,plain,
( ~ m1_pboole(sK2,sK0)
| r6_pboole(sK0,sK2,sK2) ),
inference(instantiation,[status(thm)],[c_128]) ).
cnf(c_6392,plain,
( ~ v1_xboole_0(k1_funct_1(X0,X1))
| ~ m1_pboole(X0,sK0)
| ~ m1_subset_1(X1,sK0)
| ~ v2_relat_1(X0)
| v1_xboole_0(sK0) ),
inference(instantiation,[status(thm)],[c_84]) ).
cnf(c_6667,plain,
( ~ m1_subset_1(X0,sK0)
| ~ m1_pboole(sK1,sK0)
| k1_funct_1(sK1,X0) = k1_xboole_0
| r2_hidden(X0,sP0_iProver_def)
| v1_xboole_0(sK0) ),
inference(superposition,[status(thm)],[c_5889,c_87]) ).
cnf(c_6675,plain,
( ~ m1_subset_1(X0,sK0)
| k1_funct_1(sK1,X0) = k1_xboole_0
| r2_hidden(X0,sP0_iProver_def) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6667,c_4306,c_4308]) ).
cnf(c_6952,plain,
( X0 != sK0
| X1 != sK2
| X2 != sK2
| ~ r6_pboole(sK0,sK2,sK2)
| r6_pboole(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_4316]) ).
cnf(c_7291,plain,
sK2 = sK2,
inference(instantiation,[status(thm)],[c_4313]) ).
cnf(c_7670,plain,
( ~ v1_xboole_0(k1_funct_1(sK1,X0))
| ~ m1_subset_1(X0,sK0)
| ~ m1_pboole(sK1,sK0)
| ~ v2_relat_1(sK1)
| v1_xboole_0(sK0) ),
inference(instantiation,[status(thm)],[c_6392]) ).
cnf(c_13629,plain,
sK0 = sK0,
inference(instantiation,[status(thm)],[c_4313]) ).
cnf(c_14631,plain,
( sK0 != sK0
| sK1 != sK2
| sK2 != sK2
| ~ r6_pboole(sK0,sK2,sK2)
| r6_pboole(sK0,sK1,sK2) ),
inference(instantiation,[status(thm)],[c_6952]) ).
cnf(c_49169,plain,
( k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1)
| v1_xboole_0(sK0) ),
inference(superposition,[status(thm)],[c_4308,c_67]) ).
cnf(c_49174,plain,
( a_2_0_closure3(sK0,sK1) = sP0_iProver_def
| v1_xboole_0(sK0) ),
inference(light_normalisation,[status(thm)],[c_49169,c_4304]) ).
cnf(c_49175,plain,
a_2_0_closure3(sK0,sK1) = sP0_iProver_def,
inference(forward_subsumption_resolution,[status(thm)],[c_49174,c_4306]) ).
cnf(c_49783,plain,
( k3_xboole_0(X0,X1) = X0
| r2_hidden(sK4(X0,X1,X0),X0) ),
inference(equality_factoring,[status(thm)],[c_72]) ).
cnf(c_50069,plain,
( ~ r2_hidden(X0,sP0_iProver_def)
| ~ m1_pboole(sK1,sK0)
| sK7(X0,sK0,sK1) = X0
| v1_xboole_0(sK0) ),
inference(superposition,[status(thm)],[c_49175,c_89]) ).
cnf(c_50072,plain,
( ~ r2_hidden(X0,sP0_iProver_def)
| sK7(X0,sK0,sK1) = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[c_50069,c_4306,c_4308]) ).
cnf(c_50282,plain,
( sK7(sK4(sP0_iProver_def,X0,sP0_iProver_def),sK0,sK1) = sK4(sP0_iProver_def,X0,sP0_iProver_def)
| k3_xboole_0(sP0_iProver_def,X0) = sP0_iProver_def ),
inference(superposition,[status(thm)],[c_49783,c_50072]) ).
cnf(c_63412,plain,
( ~ r2_hidden(sK4(sP0_iProver_def,X0,sP0_iProver_def),a_2_0_closure3(sK0,sK1))
| ~ m1_pboole(sK1,sK0)
| k3_xboole_0(sP0_iProver_def,X0) = sP0_iProver_def
| m1_subset_1(sK4(sP0_iProver_def,X0,sP0_iProver_def),sK0)
| v1_xboole_0(sK0) ),
inference(superposition,[status(thm)],[c_50282,c_90]) ).
cnf(c_63415,plain,
( ~ r2_hidden(sK4(sP0_iProver_def,X0,sP0_iProver_def),sP0_iProver_def)
| ~ m1_pboole(sK1,sK0)
| k3_xboole_0(sP0_iProver_def,X0) = sP0_iProver_def
| m1_subset_1(sK4(sP0_iProver_def,X0,sP0_iProver_def),sK0)
| v1_xboole_0(sK0) ),
inference(light_normalisation,[status(thm)],[c_63412,c_49175]) ).
cnf(c_63416,plain,
( ~ r2_hidden(sK4(sP0_iProver_def,X0,sP0_iProver_def),sP0_iProver_def)
| k3_xboole_0(sP0_iProver_def,X0) = sP0_iProver_def
| m1_subset_1(sK4(sP0_iProver_def,X0,sP0_iProver_def),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_63415,c_4306,c_4308]) ).
cnf(c_63480,plain,
( k3_xboole_0(sP0_iProver_def,X0) = sP0_iProver_def
| m1_subset_1(sK4(sP0_iProver_def,X0,sP0_iProver_def),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_63416,c_49783]) ).
cnf(c_63483,plain,
( k3_xboole_0(sP0_iProver_def,X0) = sP0_iProver_def
| r2_hidden(sK4(sP0_iProver_def,X0,sP0_iProver_def),sK0)
| v1_xboole_0(sK0) ),
inference(superposition,[status(thm)],[c_63480,c_134]) ).
cnf(c_63486,plain,
( k3_xboole_0(sP0_iProver_def,X0) = sP0_iProver_def
| r2_hidden(sK4(sP0_iProver_def,X0,sP0_iProver_def),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_63483,c_4306]) ).
cnf(c_63532,plain,
( ~ r2_hidden(sK4(sP0_iProver_def,sK0,sP0_iProver_def),sP0_iProver_def)
| k3_xboole_0(sP0_iProver_def,sK0) = sP0_iProver_def ),
inference(superposition,[status(thm)],[c_63486,c_70]) ).
cnf(c_71320,plain,
k3_xboole_0(sP0_iProver_def,sK0) = sP0_iProver_def,
inference(forward_subsumption_resolution,[status(thm)],[c_63532,c_49783]) ).
cnf(c_71361,plain,
( ~ r2_hidden(X0,sP0_iProver_def)
| r2_hidden(X0,sK0) ),
inference(superposition,[status(thm)],[c_71320,c_74]) ).
cnf(c_114191,plain,
( k1_funct_1(sK1,X0) != X1
| ~ v1_xboole_0(X1)
| v1_xboole_0(k1_funct_1(sK1,X0)) ),
inference(instantiation,[status(thm)],[c_4321]) ).
cnf(c_114204,plain,
( ~ r2_hidden(X0,sK0)
| m1_subset_1(X0,sK0) ),
inference(instantiation,[status(thm)],[c_132]) ).
cnf(c_117179,plain,
( k1_funct_1(sK1,X0) != k1_xboole_0
| ~ v1_xboole_0(k1_xboole_0)
| v1_xboole_0(k1_funct_1(sK1,X0)) ),
inference(instantiation,[status(thm)],[c_114191]) ).
cnf(c_182383,plain,
k7_relat_1(sK1,sP0_iProver_def) = k7_relat_1(sK2,sP0_iProver_def),
inference(light_normalisation,[status(thm)],[c_679,c_4304]) ).
cnf(c_182395,plain,
k1_relat_1(sK2) = sK0,
inference(superposition,[status(thm)],[c_4310,c_184]) ).
cnf(c_182396,plain,
k1_relat_1(sK1) = sK0,
inference(superposition,[status(thm)],[c_4308,c_184]) ).
cnf(c_182404,plain,
v1_funct_1(sK2),
inference(superposition,[status(thm)],[c_4310,c_77]) ).
cnf(c_182405,plain,
v1_funct_1(sK1),
inference(superposition,[status(thm)],[c_4308,c_77]) ).
cnf(c_182413,plain,
v1_relat_1(sK2),
inference(superposition,[status(thm)],[c_4310,c_78]) ).
cnf(c_182414,plain,
v1_relat_1(sK1),
inference(superposition,[status(thm)],[c_4308,c_78]) ).
cnf(c_182733,plain,
( ~ r2_hidden(X0,X1)
| ~ r2_hidden(X0,X2)
| m1_subset_1(X0,k3_xboole_0(X2,X1)) ),
inference(superposition,[status(thm)],[c_73,c_132]) ).
cnf(c_182758,plain,
k3_xboole_0(k1_relat_1(sK2),X0) = k1_relat_1(k7_relat_1(sK2,X0)),
inference(superposition,[status(thm)],[c_182413,c_141]) ).
cnf(c_182759,plain,
k3_xboole_0(k1_relat_1(sK1),X0) = k1_relat_1(k7_relat_1(sK1,X0)),
inference(superposition,[status(thm)],[c_182414,c_141]) ).
cnf(c_182762,plain,
k1_relat_1(k7_relat_1(sK1,X0)) = k3_xboole_0(sK0,X0),
inference(light_normalisation,[status(thm)],[c_182759,c_182396]) ).
cnf(c_182763,plain,
k1_relat_1(k7_relat_1(sK2,X0)) = k3_xboole_0(sK0,X0),
inference(light_normalisation,[status(thm)],[c_182758,c_182395]) ).
cnf(c_182906,plain,
( k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1)
| v1_xboole_0(sK0) ),
inference(superposition,[status(thm)],[c_4308,c_67]) ).
cnf(c_182916,plain,
( a_2_0_closure3(sK0,sK1) = sP0_iProver_def
| v1_xboole_0(sK0) ),
inference(light_normalisation,[status(thm)],[c_182906,c_4304]) ).
cnf(c_182917,plain,
a_2_0_closure3(sK0,sK1) = sP0_iProver_def,
inference(forward_subsumption_resolution,[status(thm)],[c_182916,c_4306]) ).
cnf(c_183308,plain,
( k3_xboole_0(X0,X1) = X0
| r2_hidden(sK4(X0,X1,X0),X0) ),
inference(equality_factoring,[status(thm)],[c_72]) ).
cnf(c_183729,plain,
( ~ m1_subset_1(X0,sK0)
| ~ m1_pboole(sK1,sK0)
| k1_funct_1(sK1,X0) = k1_xboole_0
| r2_hidden(X0,sP0_iProver_def)
| v1_xboole_0(sK0) ),
inference(superposition,[status(thm)],[c_182917,c_87]) ).
cnf(c_183737,plain,
( ~ m1_subset_1(X0,sK0)
| k1_funct_1(sK1,X0) = k1_xboole_0
| r2_hidden(X0,sP0_iProver_def) ),
inference(forward_subsumption_resolution,[status(thm)],[c_183729,c_4306,c_4308]) ).
cnf(c_183898,plain,
( ~ m1_subset_1(X0,sK0)
| r2_hidden(X0,sP0_iProver_def) ),
inference(global_subsumption_just,[status(thm)],[c_183737,c_55,c_83,c_56,c_54,c_6675,c_7670,c_117179]) ).
cnf(c_184258,plain,
( ~ r2_hidden(X0,k3_xboole_0(sK0,X1))
| ~ v1_funct_1(sK2)
| ~ v1_relat_1(sK2)
| k1_funct_1(k7_relat_1(sK2,X1),X0) = k1_funct_1(sK2,X0) ),
inference(superposition,[status(thm)],[c_182763,c_138]) ).
cnf(c_184259,plain,
( ~ r2_hidden(X0,k3_xboole_0(sK0,X1))
| ~ v1_funct_1(sK1)
| ~ v1_relat_1(sK1)
| k1_funct_1(k7_relat_1(sK1,X1),X0) = k1_funct_1(sK1,X0) ),
inference(superposition,[status(thm)],[c_182762,c_138]) ).
cnf(c_184262,plain,
( ~ r2_hidden(X0,k3_xboole_0(sK0,X1))
| k1_funct_1(k7_relat_1(sK1,X1),X0) = k1_funct_1(sK1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_184259,c_182414,c_182405]) ).
cnf(c_184265,plain,
( ~ r2_hidden(X0,k3_xboole_0(sK0,X1))
| k1_funct_1(k7_relat_1(sK2,X1),X0) = k1_funct_1(sK2,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_184258,c_182413,c_182404]) ).
cnf(c_184970,plain,
( ~ r2_hidden(X0,sK0)
| k1_funct_1(k7_relat_1(sK1,sK0),X0) = k1_funct_1(sK1,X0) ),
inference(superposition,[status(thm)],[c_95,c_184262]) ).
cnf(c_185038,plain,
( ~ r2_hidden(X0,sK0)
| k1_funct_1(k7_relat_1(sK2,sK0),X0) = k1_funct_1(sK2,X0) ),
inference(superposition,[status(thm)],[c_95,c_184265]) ).
cnf(c_193883,plain,
( k3_xboole_0(X0,X1) = X0
| m1_subset_1(sK4(X0,X1,X0),X0) ),
inference(superposition,[status(thm)],[c_183308,c_132]) ).
cnf(c_198435,plain,
( k3_xboole_0(sK0,X0) = sK0
| r2_hidden(sK4(sK0,X0,sK0),sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_193883,c_183898]) ).
cnf(c_203039,plain,
( ~ r2_hidden(sK4(sK0,sP0_iProver_def,sK0),sK0)
| k3_xboole_0(sK0,sP0_iProver_def) = sK0 ),
inference(superposition,[status(thm)],[c_198435,c_70]) ).
cnf(c_219743,plain,
( ~ r2_hidden(sK4(sK0,sP0_iProver_def,sK0),sK0)
| k3_xboole_0(sP0_iProver_def,sK0) = sK0 ),
inference(demodulation,[status(thm)],[c_203039,c_62]) ).
cnf(c_219751,plain,
( k3_xboole_0(sK0,sP0_iProver_def) = sK0
| k3_xboole_0(sP0_iProver_def,sK0) = sK0 ),
inference(superposition,[status(thm)],[c_183308,c_219743]) ).
cnf(c_225476,plain,
k3_xboole_0(sP0_iProver_def,sK0) = sK0,
inference(demodulation,[status(thm)],[c_219751,c_62]) ).
cnf(c_225524,plain,
( ~ r2_hidden(X0,sK0)
| ~ r2_hidden(X0,sP0_iProver_def)
| m1_subset_1(X0,sK0) ),
inference(superposition,[status(thm)],[c_225476,c_182733]) ).
cnf(c_227653,plain,
( ~ r2_hidden(X0,sP0_iProver_def)
| m1_subset_1(X0,sK0) ),
inference(global_subsumption_just,[status(thm)],[c_225524,c_71361,c_114204]) ).
cnf(c_227680,plain,
( k3_xboole_0(sP0_iProver_def,X0) = sP0_iProver_def
| m1_subset_1(sK4(sP0_iProver_def,X0,sP0_iProver_def),sK0) ),
inference(superposition,[status(thm)],[c_183308,c_227653]) ).
cnf(c_248877,plain,
( k3_xboole_0(sP0_iProver_def,X0) = sP0_iProver_def
| r2_hidden(sK4(sP0_iProver_def,X0,sP0_iProver_def),sK0)
| v1_xboole_0(sK0) ),
inference(superposition,[status(thm)],[c_227680,c_134]) ).
cnf(c_248931,plain,
( k3_xboole_0(sP0_iProver_def,X0) = sP0_iProver_def
| r2_hidden(sK4(sP0_iProver_def,X0,sP0_iProver_def),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_248877,c_4306]) ).
cnf(c_249194,plain,
( ~ r2_hidden(sK4(sP0_iProver_def,sK0,sP0_iProver_def),sP0_iProver_def)
| k3_xboole_0(sP0_iProver_def,sK0) = sP0_iProver_def ),
inference(superposition,[status(thm)],[c_248931,c_70]) ).
cnf(c_249196,plain,
( ~ r2_hidden(sK4(sP0_iProver_def,sK0,sP0_iProver_def),sP0_iProver_def)
| sK0 = sP0_iProver_def ),
inference(light_normalisation,[status(thm)],[c_249194,c_225476]) ).
cnf(c_249778,plain,
( k3_xboole_0(sP0_iProver_def,sK0) = sP0_iProver_def
| sK0 = sP0_iProver_def ),
inference(superposition,[status(thm)],[c_183308,c_249196]) ).
cnf(c_249779,plain,
sK0 = sP0_iProver_def,
inference(light_normalisation,[status(thm)],[c_249778,c_225476]) ).
cnf(c_250174,plain,
k1_relat_1(sK1) = sP0_iProver_def,
inference(demodulation,[status(thm)],[c_182396,c_249779]) ).
cnf(c_250175,plain,
k1_relat_1(sK2) = sP0_iProver_def,
inference(demodulation,[status(thm)],[c_182395,c_249779]) ).
cnf(c_253324,plain,
( ~ r2_hidden(X0,sP0_iProver_def)
| k1_funct_1(k7_relat_1(sK1,sP0_iProver_def),X0) = k1_funct_1(sK1,X0) ),
inference(light_normalisation,[status(thm)],[c_184970,c_249779]) ).
cnf(c_253512,plain,
( ~ r2_hidden(X0,sP0_iProver_def)
| k1_funct_1(k7_relat_1(sK1,sP0_iProver_def),X0) = k1_funct_1(sK2,X0) ),
inference(light_normalisation,[status(thm)],[c_185038,c_182383,c_249779]) ).
cnf(c_253896,plain,
( k1_relat_1(X0) != sP0_iProver_def
| ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| ~ v1_funct_1(sK1)
| ~ v1_relat_1(sK1)
| X0 = sK1
| r2_hidden(sK22(sK1,X0),k1_relat_1(sK1)) ),
inference(superposition,[status(thm)],[c_250174,c_143]) ).
cnf(c_253897,plain,
( k1_relat_1(X0) != sP0_iProver_def
| ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| ~ v1_funct_1(sK1)
| ~ v1_relat_1(sK1)
| X0 = sK1
| r2_hidden(sK22(sK1,X0),sP0_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_253896,c_250174]) ).
cnf(c_253898,plain,
( k1_relat_1(X0) != sP0_iProver_def
| ~ v1_funct_1(X0)
| ~ v1_relat_1(X0)
| X0 = sK1
| r2_hidden(sK22(sK1,X0),sP0_iProver_def) ),
inference(forward_subsumption_resolution,[status(thm)],[c_253897,c_182414,c_182405]) ).
cnf(c_272713,plain,
( ~ v1_funct_1(sK2)
| ~ v1_relat_1(sK2)
| sK1 = sK2
| r2_hidden(sK22(sK1,sK2),sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_250175,c_253898]) ).
cnf(c_272730,plain,
( sK1 = sK2
| r2_hidden(sK22(sK1,sK2),sP0_iProver_def) ),
inference(forward_subsumption_resolution,[status(thm)],[c_272713,c_182413,c_182404]) ).
cnf(c_272820,plain,
r2_hidden(sK22(sK1,sK2),sP0_iProver_def),
inference(global_subsumption_just,[status(thm)],[c_272730,c_52,c_49,c_6233,c_7291,c_13629,c_14631,c_272730]) ).
cnf(c_272827,plain,
k1_funct_1(k7_relat_1(sK1,sP0_iProver_def),sK22(sK1,sK2)) = k1_funct_1(sK2,sK22(sK1,sK2)),
inference(superposition,[status(thm)],[c_272820,c_253512]) ).
cnf(c_272828,plain,
k1_funct_1(k7_relat_1(sK1,sP0_iProver_def),sK22(sK1,sK2)) = k1_funct_1(sK1,sK22(sK1,sK2)),
inference(superposition,[status(thm)],[c_272820,c_253324]) ).
cnf(c_380010,plain,
k1_funct_1(sK1,sK22(sK1,sK2)) = k1_funct_1(sK2,sK22(sK1,sK2)),
inference(demodulation,[status(thm)],[c_272827,c_272828]) ).
cnf(c_380014,plain,
( k1_relat_1(sK1) != k1_relat_1(sK2)
| ~ v1_funct_1(sK1)
| ~ v1_funct_1(sK2)
| ~ v1_relat_1(sK1)
| ~ v1_relat_1(sK2)
| sK1 = sK2 ),
inference(superposition,[status(thm)],[c_380010,c_142]) ).
cnf(c_380024,plain,
( sP0_iProver_def != sP0_iProver_def
| ~ v1_funct_1(sK1)
| ~ v1_funct_1(sK2)
| ~ v1_relat_1(sK1)
| ~ v1_relat_1(sK2)
| sK1 = sK2 ),
inference(light_normalisation,[status(thm)],[c_380014,c_250174,c_250175]) ).
cnf(c_380025,plain,
( ~ v1_funct_1(sK1)
| ~ v1_funct_1(sK2)
| ~ v1_relat_1(sK1)
| ~ v1_relat_1(sK2)
| sK1 = sK2 ),
inference(equality_resolution_simp,[status(thm)],[c_380024]) ).
cnf(c_380026,plain,
sK1 = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_380025,c_182413,c_182414,c_182404,c_182405]) ).
cnf(c_380160,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_380026,c_14631,c_13629,c_7291,c_6233,c_49,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG226+1 : TPTP v8.1.2. Released v3.4.0.
% 0.03/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu May 2 22:42:32 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 184.47/24.92 % SZS status Started for theBenchmark.p
% 184.47/24.92 % SZS status Theorem for theBenchmark.p
% 184.47/24.92
% 184.47/24.92 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 184.47/24.92
% 184.47/24.92 ------ iProver source info
% 184.47/24.92
% 184.47/24.92 git: date: 2024-05-02 19:28:25 +0000
% 184.47/24.92 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 184.47/24.92 git: non_committed_changes: false
% 184.47/24.92
% 184.47/24.92 ------ Parsing...
% 184.47/24.92 ------ Clausification by vclausify_rel & Parsing by iProver...
% 184.47/24.92
% 184.47/24.92 ------ 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
% 184.47/24.92
% 184.47/24.92 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 184.47/24.92
% 184.47/24.92 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 184.47/24.92 ------ Proving...
% 184.47/24.92 ------ Problem Properties
% 184.47/24.92
% 184.47/24.92
% 184.47/24.92 clauses 87
% 184.47/24.92 conjectures 7
% 184.47/24.92 EPR 42
% 184.47/24.92 Horn 73
% 184.47/24.92 unary 43
% 184.47/24.92 binary 13
% 184.47/24.92 lits 191
% 184.47/24.92 lits eq 30
% 184.47/24.92 fd_pure 0
% 184.47/24.92 fd_pseudo 0
% 184.47/24.92 fd_cond 1
% 184.47/24.92 fd_pseudo_cond 10
% 184.47/24.92 AC symbols 0
% 184.47/24.92
% 184.47/24.92 ------ Schedule dynamic 5 is on
% 184.47/24.92
% 184.47/24.92 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 184.47/24.92
% 184.47/24.92
% 184.47/24.92 ------
% 184.47/24.92 Current options:
% 184.47/24.92 ------
% 184.47/24.92
% 184.47/24.92
% 184.47/24.92
% 184.47/24.92
% 184.47/24.92 ------ Proving...
% 184.47/24.92 Proof_search_loop: time out after: 7245 full_loop iterations
% 184.47/24.92
% 184.47/24.92 ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 184.47/24.92
% 184.47/24.92
% 184.47/24.92 ------
% 184.47/24.92 Current options:
% 184.47/24.92 ------
% 184.47/24.92
% 184.47/24.92
% 184.47/24.92
% 184.47/24.92
% 184.47/24.92 ------ Proving...
% 184.47/24.92
% 184.47/24.92
% 184.47/24.92 % SZS status Theorem for theBenchmark.p
% 184.47/24.92
% 184.47/24.92 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 184.47/24.93
% 184.47/24.93
%------------------------------------------------------------------------------