%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG227+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 0.23s 1.29s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 41 ( 13 unt; 0 def)
% Number of atoms : 154 ( 56 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 181 ( 68 ~; 68 |; 29 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 73 ( 0 sgn 62 !; 11 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,X0)
=> ( ~ r2_hidden(X2,k1_closure3(X0,X1))
=> k1_funct_1(X1,X2) = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_closure3) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_pboole(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,X0)
=> ( ~ r2_hidden(X2,k1_closure3(X0,X1))
=> k1_funct_1(X1,X2) = k1_xboole_0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f8,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/sandbox/benchmark/theBenchmark.p',d3_closure3) ).
fof(f17,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/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_closure3) ).
fof(f39,plain,
? [X0] :
( ~ v1_xboole_0(X0)
& ? [X1] :
( m1_pboole(X1,X0)
& ? [X2] :
( m1_subset_1(X2,X0)
& ~ r2_hidden(X2,k1_closure3(X0,X1))
& k1_funct_1(X1,X2) != k1_xboole_0 ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f40,plain,
? [X0] :
( ~ v1_xboole_0(X0)
& ? [X1] :
( m1_pboole(X1,X0)
& ? [X2] :
( m1_subset_1(X2,X0)
& ~ r2_hidden(X2,k1_closure3(X0,X1))
& k1_funct_1(X1,X2) != k1_xboole_0 ) ) ),
inference(flattening,[],[f39]) ).
fof(f45,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,[],[f8]) ).
fof(f47,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,[],[f17]) ).
fof(f48,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,[],[f47]) ).
fof(f56,plain,
( ~ v1_xboole_0(sK0)
& m1_pboole(sK1,sK0)
& m1_subset_1(sK2,sK0)
& ~ r2_hidden(sK2,k1_closure3(sK0,sK1))
& k1_xboole_0 != k1_funct_1(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f40]) ).
fof(f57,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,[],[f45]) ).
fof(f60,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,[],[f48]) ).
fof(f61,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,[],[f60]) ).
fof(f62,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,sK5(X0,X1,X2))
& sK5(X0,X1,X2) = X0
& m1_subset_1(sK5(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,[sK5]),skolemize(X4,sK5(X0,X1,X2))],[f61]) ).
fof(f72,plain,
~ v1_xboole_0(sK0),
inference(cnf_transformation,[],[f56]) ).
fof(f73,plain,
m1_pboole(sK1,sK0),
inference(cnf_transformation,[],[f56]) ).
fof(f74,plain,
m1_subset_1(sK2,sK0),
inference(cnf_transformation,[],[f56]) ).
fof(f75,plain,
~ r2_hidden(sK2,k1_closure3(sK0,sK1)),
inference(cnf_transformation,[],[f56]) ).
fof(f76,plain,
k1_xboole_0 != k1_funct_1(sK1,sK2),
inference(cnf_transformation,[],[f56]) ).
fof(f82,plain,
! [X2,X0,X1] :
( v1_xboole_0(X0)
| ~ m1_pboole(X1,X0)
| a_2_0_closure3(X0,X1) != X2
| k1_closure3(X0,X1) = X2 ),
inference(cnf_transformation,[],[f57]) ).
fof(f91,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,[],[f62]) ).
fof(f112,plain,
! [X0,X1] :
( v1_xboole_0(X0)
| ~ m1_pboole(X1,X0)
| k1_closure3(X0,X1) = a_2_0_closure3(X0,X1) ),
inference(equality_resolution,[],[f82]) ).
fof(f114,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,[],[f91]) ).
tcf(c_49,negated_conjecture,
k1_funct_1(sK1,sK2) != k1_xboole_0,
inference(cnf_transformation,[],[f76]) ).
tcf(c_50,negated_conjecture,
~ r2_hidden(sK2,k1_closure3(sK0,sK1)),
inference(cnf_transformation,[],[f75]) ).
tcf(c_51,negated_conjecture,
m1_subset_1(sK2,sK0),
inference(cnf_transformation,[],[f74]) ).
tcf(c_52,negated_conjecture,
m1_pboole(sK1,sK0),
inference(cnf_transformation,[],[f73]) ).
tcf(c_53,negated_conjecture,
~ v1_xboole_0(sK0),
inference(cnf_transformation,[],[f72]) ).
tcf(c_56,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,[],[f112]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( v1_xboole_0(X1)
| r2_hidden(X0,a_2_0_closure3(X1,X2))
| ( k1_funct_1(X2,X0) = k1_xboole_0 )
| ~ m1_pboole(X2,X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_333,plain,
! [X0: $i,X1: $i] :
( v1_xboole_0(X1)
| ( k1_closure3(X1,X0) = a_2_0_closure3(X1,X0) )
| ( X1 != sK0 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_56]) ).
tcf(c_334,plain,
( v1_xboole_0(sK0)
| ( k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1) ) ),
inference(unflattening,[status(thm)],[c_333]) ).
tcf(c_335,plain,
k1_closure3(sK0,sK1) = a_2_0_closure3(sK0,sK1),
inference(global_subsumption_just,[status(thm)],[c_334,c_53,c_334]) ).
tcf(c_364,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)
| ( X1 != sK0 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_63]) ).
tcf(c_365,plain,
! [X0: $i] :
( v1_xboole_0(sK0)
| r2_hidden(X0,a_2_0_closure3(sK0,sK1))
| ( k1_funct_1(sK1,X0) = k1_xboole_0 )
| ~ m1_subset_1(X0,sK0) ),
inference(unflattening,[status(thm)],[c_364]) ).
tcf(c_367,plain,
! [X0: $i] :
( ~ m1_subset_1(X0,sK0)
| ( k1_funct_1(sK1,X0) = k1_xboole_0 )
| r2_hidden(X0,a_2_0_closure3(sK0,sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_365,c_53,c_365]) ).
tcf(c_368,plain,
! [X0: $i] :
( r2_hidden(X0,a_2_0_closure3(sK0,sK1))
| ( k1_funct_1(sK1,X0) = k1_xboole_0 )
| ~ m1_subset_1(X0,sK0) ),
inference(renaming,[status(thm)],[c_367]) ).
tcf(c_503,plain,
! [X0: $i] :
( r2_hidden(X0,a_2_0_closure3(sK0,sK1))
| ( k1_funct_1(sK1,X0) = k1_xboole_0 )
| ( sK0 != sK0 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_368]) ).
tcf(c_504,plain,
( r2_hidden(sK2,a_2_0_closure3(sK0,sK1))
| ( k1_funct_1(sK1,sK2) = k1_xboole_0 ) ),
inference(unflattening,[status(thm)],[c_503]) ).
tcf(c_783,plain,
~ r2_hidden(sK2,a_2_0_closure3(sK0,sK1)),
inference(demodulation,[status(thm)],[c_50,c_335]) ).
tcf(c_870,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_783,c_504,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG227+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 05:11:28 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 0.23/1.29 % SZS status Started for theBenchmark.p
% 0.23/1.29 % SZS status Theorem for theBenchmark.p
% 0.23/1.29
% 0.23/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.23/1.29
% 0.23/1.29 % ------ iProver source info
% 0.23/1.29
% 0.23/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.23/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.23/1.29 % git: non_committed_changes: false
% 0.23/1.29
% 0.23/1.29 % ------ Parsing...
% 0.23/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.23/1.29
% 0.23/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 14 0s sf_e pe_s pe:1:0s pe_e sup_sim: 1 sf_s rm: 4 0s sf_e pe_s %
% 0.23/1.29
% 0.23/1.29 % SZS status Theorem for theBenchmark.p
% 0.23/1.29
% 0.23/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.23/1.29
% 0.23/1.29
%------------------------------------------------------------------------------