TSTP Solution File: SEU136+2 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU136+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n021.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 : Thu Aug 31 17:03:58 EDT 2023
% Result : Theorem 7.44s 1.66s
% Output : CNFRefutation 7.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 13 unt; 0 def)
% Number of atoms : 244 ( 43 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 304 ( 116 ~; 132 |; 49 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 138 ( 4 sgn; 98 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f6,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f9,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f42,conjecture,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(f43,negated_conjecture,
~ ! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
inference(negated_conjecture,[],[f42]) ).
fof(f72,plain,
? [X0,X1] : set_difference(X0,X1) != set_difference(set_union2(X0,X1),X1),
inference(ennf_transformation,[],[f43]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f86]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK1(X0,X1,X2),X1)
& ~ in(sK1(X0,X1,X2),X0) )
| ~ in(sK1(X0,X1,X2),X2) )
& ( in(sK1(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X0)
| in(sK1(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ( ( ( ~ in(sK1(X0,X1,X2),X1)
& ~ in(sK1(X0,X1,X2),X0) )
| ~ in(sK1(X0,X1,X2),X2) )
& ( in(sK1(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X0)
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f87,f88]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f99]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) )
& ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f100]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( in(sK4(X0,X1,X2),X1)
| ~ in(sK4(X0,X1,X2),X0)
| ~ in(sK4(X0,X1,X2),X2) )
& ( ( ~ in(sK4(X0,X1,X2),X1)
& in(sK4(X0,X1,X2),X0) )
| in(sK4(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ( ( in(sK4(X0,X1,X2),X1)
| ~ in(sK4(X0,X1,X2),X0)
| ~ in(sK4(X0,X1,X2),X2) )
& ( ( ~ in(sK4(X0,X1,X2),X1)
& in(sK4(X0,X1,X2),X0) )
| in(sK4(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) )
& ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f101,f102]) ).
fof(f116,plain,
( ? [X0,X1] : set_difference(X0,X1) != set_difference(set_union2(X0,X1),X1)
=> set_difference(sK9,sK10) != set_difference(set_union2(sK9,sK10),sK10) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
set_difference(sK9,sK10) != set_difference(set_union2(sK9,sK10),sK10),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f72,f116]) ).
fof(f121,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f128,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f89]) ).
fof(f130,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f89]) ).
fof(f143,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f103]) ).
fof(f144,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f103]) ).
fof(f145,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f103]) ).
fof(f146,plain,
! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| in(sK4(X0,X1,X2),X0)
| in(sK4(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f103]) ).
fof(f147,plain,
! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| ~ in(sK4(X0,X1,X2),X1)
| in(sK4(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f103]) ).
fof(f148,plain,
! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| in(sK4(X0,X1,X2),X1)
| ~ in(sK4(X0,X1,X2),X0)
| ~ in(sK4(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f103]) ).
fof(f183,plain,
set_difference(sK9,sK10) != set_difference(set_union2(sK9,sK10),sK10),
inference(cnf_transformation,[],[f117]) ).
fof(f195,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f130]) ).
fof(f197,plain,
! [X0,X1,X4] :
( in(X4,X1)
| in(X4,X0)
| ~ in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f128]) ).
fof(f201,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f145]) ).
fof(f202,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f144]) ).
fof(f203,plain,
! [X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f143]) ).
cnf(c_50,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f121]) ).
cnf(c_60,plain,
( ~ in(X0,X1)
| in(X0,set_union2(X2,X1)) ),
inference(cnf_transformation,[],[f195]) ).
cnf(c_62,plain,
( ~ in(X0,set_union2(X1,X2))
| in(X0,X1)
| in(X0,X2) ),
inference(cnf_transformation,[],[f197]) ).
cnf(c_72,plain,
( ~ in(sK4(X0,X1,X2),X0)
| ~ in(sK4(X0,X1,X2),X2)
| set_difference(X0,X1) = X2
| in(sK4(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f148]) ).
cnf(c_73,plain,
( ~ in(sK4(X0,X1,X2),X1)
| set_difference(X0,X1) = X2
| in(sK4(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f147]) ).
cnf(c_74,plain,
( set_difference(X0,X1) = X2
| in(sK4(X0,X1,X2),X0)
| in(sK4(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f146]) ).
cnf(c_75,plain,
( ~ in(X0,X1)
| in(X0,set_difference(X1,X2))
| in(X0,X2) ),
inference(cnf_transformation,[],[f201]) ).
cnf(c_76,plain,
( ~ in(X0,set_difference(X1,X2))
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f202]) ).
cnf(c_77,plain,
( ~ in(X0,set_difference(X1,X2))
| in(X0,X1) ),
inference(cnf_transformation,[],[f203]) ).
cnf(c_112,negated_conjecture,
set_difference(set_union2(sK9,sK10),sK10) != set_difference(sK9,sK10),
inference(cnf_transformation,[],[f183]) ).
cnf(c_631,plain,
set_difference(set_union2(sK10,sK9),sK10) != set_difference(sK9,sK10),
inference(demodulation,[status(thm)],[c_112,c_50]) ).
cnf(c_2241,plain,
( ~ in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),sK10)
| set_difference(set_union2(sK10,sK9),sK10) = set_difference(sK9,sK10)
| in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),set_difference(sK9,sK10)) ),
inference(instantiation,[status(thm)],[c_73]) ).
cnf(c_2242,plain,
( ~ in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),set_union2(sK10,sK9))
| ~ in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),set_difference(sK9,sK10))
| set_difference(set_union2(sK10,sK9),sK10) = set_difference(sK9,sK10)
| in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),sK10) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_2337,plain,
( ~ in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),set_union2(sK10,sK9))
| in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),sK9)
| in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),sK10) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_2907,plain,
( ~ in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),set_difference(sK9,sK10))
| in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),sK9) ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_4870,plain,
( ~ in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),sK9)
| in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),set_difference(sK9,X0))
| in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),X0) ),
inference(instantiation,[status(thm)],[c_75]) ).
cnf(c_4872,plain,
( ~ in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),sK9)
| in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),set_union2(X0,sK9)) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_9727,plain,
( ~ in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),sK9)
| in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),set_difference(sK9,sK10))
| in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),sK10) ),
inference(instantiation,[status(thm)],[c_4870]) ).
cnf(c_9876,plain,
( ~ in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),sK9)
| in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),set_union2(sK10,sK9)) ),
inference(instantiation,[status(thm)],[c_4872]) ).
cnf(c_17277,plain,
( in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),set_union2(sK10,sK9))
| in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),set_difference(sK9,sK10)) ),
inference(resolution,[status(thm)],[c_74,c_631]) ).
cnf(c_18031,plain,
in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),set_difference(sK9,sK10)),
inference(global_subsumption_just,[status(thm)],[c_17277,c_631,c_2241,c_2337,c_9727,c_17277]) ).
cnf(c_18040,plain,
~ in(sK4(set_union2(sK10,sK9),sK10,set_difference(sK9,sK10)),sK10),
inference(resolution,[status(thm)],[c_18031,c_76]) ).
cnf(c_18042,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_18040,c_18031,c_9876,c_2907,c_2242,c_631]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU136+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n021.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 : Wed Aug 23 16:22:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.44/1.66 % SZS status Started for theBenchmark.p
% 7.44/1.66 % SZS status Theorem for theBenchmark.p
% 7.44/1.66
% 7.44/1.66 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.44/1.66
% 7.44/1.66 ------ iProver source info
% 7.44/1.66
% 7.44/1.66 git: date: 2023-05-31 18:12:56 +0000
% 7.44/1.66 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.44/1.66 git: non_committed_changes: false
% 7.44/1.66 git: last_make_outside_of_git: false
% 7.44/1.66
% 7.44/1.66 ------ Parsing...
% 7.44/1.66 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.44/1.66
% 7.44/1.66 ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 7.44/1.66
% 7.44/1.66 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.44/1.66
% 7.44/1.66 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.44/1.66 ------ Proving...
% 7.44/1.66 ------ Problem Properties
% 7.44/1.66
% 7.44/1.66
% 7.44/1.66 clauses 68
% 7.44/1.66 conjectures 0
% 7.44/1.66 EPR 16
% 7.44/1.66 Horn 54
% 7.44/1.66 unary 19
% 7.44/1.66 binary 28
% 7.44/1.66 lits 141
% 7.44/1.66 lits eq 32
% 7.44/1.66 fd_pure 0
% 7.44/1.66 fd_pseudo 0
% 7.44/1.66 fd_cond 3
% 7.44/1.66 fd_pseudo_cond 13
% 7.44/1.66 AC symbols 0
% 7.44/1.66
% 7.44/1.66 ------ Input Options Time Limit: Unbounded
% 7.44/1.66
% 7.44/1.66
% 7.44/1.66 ------
% 7.44/1.66 Current options:
% 7.44/1.66 ------
% 7.44/1.66
% 7.44/1.66
% 7.44/1.66
% 7.44/1.66
% 7.44/1.66 ------ Proving...
% 7.44/1.66
% 7.44/1.66
% 7.44/1.66 % SZS status Theorem for theBenchmark.p
% 7.44/1.66
% 7.44/1.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.44/1.66
% 7.44/1.66
%------------------------------------------------------------------------------