TSTP Solution File: SEU135+2 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU135+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n025.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 17:03:57 EDT 2023
% Result : Theorem 7.59s 1.65s
% Output : CNFRefutation 7.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 7 unt; 0 def)
% Number of atoms : 243 ( 40 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 307 ( 116 ~; 135 |; 49 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 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 : 133 ( 5 sgn; 94 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
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(f38,conjecture,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f39,negated_conjecture,
~ ! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
inference(negated_conjecture,[],[f38]) ).
fof(f69,plain,
? [X0,X1] : set_union2(X0,X1) != set_union2(X0,set_difference(X1,X0)),
inference(ennf_transformation,[],[f39]) ).
fof(f84,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(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(flattening,[],[f84]) ).
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) ) ) )
& ( ! [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,[],[f85]) ).
fof(f87,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(f88,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])],[f86,f87]) ).
fof(f98,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(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(flattening,[],[f98]) ).
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) ) ) )
& ( ! [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,[],[f99]) ).
fof(f101,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(f102,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])],[f100,f101]) ).
fof(f113,plain,
( ? [X0,X1] : set_union2(X0,X1) != set_union2(X0,set_difference(X1,X0))
=> set_union2(sK8,sK9) != set_union2(sK8,set_difference(sK9,sK8)) ),
introduced(choice_axiom,[]) ).
fof(f114,plain,
set_union2(sK8,sK9) != set_union2(sK8,set_difference(sK9,sK8)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f69,f113]) ).
fof(f127,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f88]) ).
fof(f128,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f88]) ).
fof(f129,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f88]) ).
fof(f130,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| in(sK1(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X0)
| in(sK1(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f88]) ).
fof(f131,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ in(sK1(X0,X1,X2),X0)
| ~ in(sK1(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f88]) ).
fof(f132,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f88]) ).
fof(f142,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f102]) ).
fof(f144,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f102]) ).
fof(f176,plain,
set_union2(sK8,sK9) != set_union2(sK8,set_difference(sK9,sK8)),
inference(cnf_transformation,[],[f114]) ).
fof(f193,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f129]) ).
fof(f194,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f128]) ).
fof(f195,plain,
! [X0,X1,X4] :
( in(X4,X1)
| in(X4,X0)
| ~ in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f127]) ).
fof(f199,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f144]) ).
fof(f201,plain,
! [X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f142]) ).
cnf(c_57,plain,
( ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X2)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f132]) ).
cnf(c_58,plain,
( ~ in(sK1(X0,X1,X2),X0)
| ~ in(sK1(X0,X1,X2),X2)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f131]) ).
cnf(c_59,plain,
( set_union2(X0,X1) = X2
| in(sK1(X0,X1,X2),X0)
| in(sK1(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f130]) ).
cnf(c_60,plain,
( ~ in(X0,X1)
| in(X0,set_union2(X2,X1)) ),
inference(cnf_transformation,[],[f193]) ).
cnf(c_61,plain,
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(cnf_transformation,[],[f194]) ).
cnf(c_62,plain,
( ~ in(X0,set_union2(X1,X2))
| in(X0,X1)
| in(X0,X2) ),
inference(cnf_transformation,[],[f195]) ).
cnf(c_75,plain,
( ~ in(X0,X1)
| in(X0,set_difference(X1,X2))
| in(X0,X2) ),
inference(cnf_transformation,[],[f199]) ).
cnf(c_77,plain,
( ~ in(X0,set_difference(X1,X2))
| in(X0,X1) ),
inference(cnf_transformation,[],[f201]) ).
cnf(c_106,negated_conjecture,
set_union2(sK8,set_difference(sK9,sK8)) != set_union2(sK8,sK9),
inference(cnf_transformation,[],[f176]) ).
cnf(c_3199,plain,
( ~ in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_union2(sK8,sK9))
| ~ in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_difference(sK9,sK8))
| set_union2(sK8,set_difference(sK9,sK8)) = set_union2(sK8,sK9) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_3216,plain,
( ~ in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_union2(sK8,sK9))
| ~ in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK8)
| set_union2(sK8,set_difference(sK9,sK8)) = set_union2(sK8,sK9) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_3217,plain,
( set_union2(sK8,set_difference(sK9,sK8)) = set_union2(sK8,sK9)
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_union2(sK8,sK9))
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_difference(sK9,sK8))
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK8) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_3701,plain,
( ~ in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_union2(sK8,sK9))
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK8)
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK9) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_4574,plain,
( ~ in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_difference(sK9,sK8))
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK9) ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_7755,plain,
( ~ in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK8)
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_union2(sK8,X0)) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_16329,plain,
( ~ in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK9)
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_difference(sK9,X0))
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),X0) ),
inference(instantiation,[status(thm)],[c_75]) ).
cnf(c_16331,plain,
( ~ in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK9)
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_union2(X0,sK9)) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_24389,plain,
( ~ in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK8)
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_union2(sK8,sK9)) ),
inference(instantiation,[status(thm)],[c_7755]) ).
cnf(c_31916,plain,
( ~ in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK9)
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_union2(sK8,sK9)) ),
inference(instantiation,[status(thm)],[c_16331]) ).
cnf(c_45567,plain,
( ~ in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK9)
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),set_difference(sK9,sK8))
| in(sK1(sK8,set_difference(sK9,sK8),set_union2(sK8,sK9)),sK8) ),
inference(instantiation,[status(thm)],[c_16329]) ).
cnf(c_45568,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_45567,c_31916,c_24389,c_4574,c_3701,c_3217,c_3216,c_3199,c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU135+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.15/0.35 % Computer : n025.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Aug 23 19:58:21 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.46 Running first-order theorem proving
% 0.21/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.59/1.65 % SZS status Started for theBenchmark.p
% 7.59/1.65 % SZS status Theorem for theBenchmark.p
% 7.59/1.65
% 7.59/1.65 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.59/1.65
% 7.59/1.65 ------ iProver source info
% 7.59/1.65
% 7.59/1.65 git: date: 2023-05-31 18:12:56 +0000
% 7.59/1.65 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.59/1.65 git: non_committed_changes: false
% 7.59/1.65 git: last_make_outside_of_git: false
% 7.59/1.65
% 7.59/1.65 ------ Parsing...
% 7.59/1.65 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.59/1.65
% 7.59/1.65 ------ Preprocessing... sup_sim: 0 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
% 7.59/1.65
% 7.59/1.65 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.59/1.65
% 7.59/1.65 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.59/1.65 ------ Proving...
% 7.59/1.65 ------ Problem Properties
% 7.59/1.65
% 7.59/1.65
% 7.59/1.65 clauses 67
% 7.59/1.65 conjectures 1
% 7.59/1.65 EPR 16
% 7.59/1.65 Horn 53
% 7.59/1.65 unary 18
% 7.59/1.65 binary 28
% 7.59/1.65 lits 140
% 7.59/1.65 lits eq 31
% 7.59/1.65 fd_pure 0
% 7.59/1.65 fd_pseudo 0
% 7.59/1.65 fd_cond 3
% 7.59/1.65 fd_pseudo_cond 13
% 7.59/1.65 AC symbols 0
% 7.59/1.65
% 7.59/1.65 ------ Schedule dynamic 5 is on
% 7.59/1.65
% 7.59/1.65 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.59/1.65
% 7.59/1.65
% 7.59/1.65 ------
% 7.59/1.65 Current options:
% 7.59/1.65 ------
% 7.59/1.65
% 7.59/1.65
% 7.59/1.65
% 7.59/1.65
% 7.59/1.65 ------ Proving...
% 7.59/1.65
% 7.59/1.65
% 7.59/1.65 % SZS status Theorem for theBenchmark.p
% 7.59/1.65
% 7.59/1.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.59/1.65
% 7.59/1.65
%------------------------------------------------------------------------------