TSTP Solution File: SEU201+2 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU201+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n007.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 17:04:38 EDT 2023
% Result : Theorem 17.51s 3.17s
% Output : CNFRefutation 17.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 13 unt; 0 def)
% Number of atoms : 193 ( 37 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 231 ( 88 ~; 99 |; 35 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 105 ( 1 sgn; 76 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f23,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f112,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
<=> ( in(X0,relation_rng(X2))
& in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_relat_1) ).
fof(f117,conjecture,
! [X0,X1] :
( relation(X1)
=> relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_relat_1) ).
fof(f118,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
inference(negated_conjecture,[],[f117]) ).
fof(f162,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f275,plain,
! [X0,X1,X2] :
( ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
<=> ( in(X0,relation_rng(X2))
& in(X0,X1) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f112]) ).
fof(f280,plain,
? [X0,X1] :
( relation_rng(relation_rng_restriction(X0,X1)) != set_intersection2(relation_rng(X1),X0)
& relation(X1) ),
inference(ennf_transformation,[],[f118]) ).
fof(f425,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f426,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f425]) ).
fof(f427,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f426]) ).
fof(f428,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( ~ in(sK27(X0,X1,X2),X1)
| ~ in(sK27(X0,X1,X2),X0)
| ~ in(sK27(X0,X1,X2),X2) )
& ( ( in(sK27(X0,X1,X2),X1)
& in(sK27(X0,X1,X2),X0) )
| in(sK27(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f429,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ( ( ~ in(sK27(X0,X1,X2),X1)
| ~ in(sK27(X0,X1,X2),X0)
| ~ in(sK27(X0,X1,X2),X2) )
& ( ( in(sK27(X0,X1,X2),X1)
& in(sK27(X0,X1,X2),X0) )
| in(sK27(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0) )
& ( ( in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f427,f428]) ).
fof(f493,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ in(X0,relation_rng(X2))
| ~ in(X0,X1) )
& ( ( in(X0,relation_rng(X2))
& in(X0,X1) )
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f275]) ).
fof(f494,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ in(X0,relation_rng(X2))
| ~ in(X0,X1) )
& ( ( in(X0,relation_rng(X2))
& in(X0,X1) )
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ) )
| ~ relation(X2) ),
inference(flattening,[],[f493]) ).
fof(f495,plain,
( ? [X0,X1] :
( relation_rng(relation_rng_restriction(X0,X1)) != set_intersection2(relation_rng(X1),X0)
& relation(X1) )
=> ( relation_rng(relation_rng_restriction(sK53,sK54)) != set_intersection2(relation_rng(sK54),sK53)
& relation(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f496,plain,
( relation_rng(relation_rng_restriction(sK53,sK54)) != set_intersection2(relation_rng(sK54),sK53)
& relation(sK54) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54])],[f280,f495]) ).
fof(f533,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f613,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| in(sK27(X0,X1,X2),X0)
| in(sK27(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f429]) ).
fof(f614,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| in(sK27(X0,X1,X2),X1)
| in(sK27(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f429]) ).
fof(f615,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ in(sK27(X0,X1,X2),X1)
| ~ in(sK27(X0,X1,X2),X0)
| ~ in(sK27(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f429]) ).
fof(f736,plain,
! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f494]) ).
fof(f737,plain,
! [X2,X0,X1] :
( in(X0,relation_rng(X2))
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f494]) ).
fof(f738,plain,
! [X2,X0,X1] :
( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ in(X0,relation_rng(X2))
| ~ in(X0,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f494]) ).
fof(f744,plain,
relation(sK54),
inference(cnf_transformation,[],[f496]) ).
fof(f745,plain,
relation_rng(relation_rng_restriction(sK53,sK54)) != set_intersection2(relation_rng(sK54),sK53),
inference(cnf_transformation,[],[f496]) ).
fof(f807,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f162]) ).
fof(f856,plain,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(definition_unfolding,[],[f533,f807,f807]) ).
fof(f892,plain,
! [X2,X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X2
| ~ in(sK27(X0,X1,X2),X1)
| ~ in(sK27(X0,X1,X2),X0)
| ~ in(sK27(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f615,f807]) ).
fof(f893,plain,
! [X2,X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X2
| in(sK27(X0,X1,X2),X1)
| in(sK27(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f614,f807]) ).
fof(f894,plain,
! [X2,X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X2
| in(sK27(X0,X1,X2),X0)
| in(sK27(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f613,f807]) ).
fof(f938,plain,
relation_rng(relation_rng_restriction(sK53,sK54)) != set_difference(relation_rng(sK54),set_difference(relation_rng(sK54),sK53)),
inference(definition_unfolding,[],[f745,f807]) ).
cnf(c_54,plain,
set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(cnf_transformation,[],[f856]) ).
cnf(c_131,plain,
( ~ in(sK27(X0,X1,X2),X0)
| ~ in(sK27(X0,X1,X2),X1)
| ~ in(sK27(X0,X1,X2),X2)
| set_difference(X0,set_difference(X0,X1)) = X2 ),
inference(cnf_transformation,[],[f892]) ).
cnf(c_132,plain,
( set_difference(X0,set_difference(X0,X1)) = X2
| in(sK27(X0,X1,X2),X1)
| in(sK27(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f893]) ).
cnf(c_133,plain,
( set_difference(X0,set_difference(X0,X1)) = X2
| in(sK27(X0,X1,X2),X0)
| in(sK27(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f894]) ).
cnf(c_256,plain,
( ~ in(X0,relation_rng(X1))
| ~ in(X0,X2)
| ~ relation(X1)
| in(X0,relation_rng(relation_rng_restriction(X2,X1))) ),
inference(cnf_transformation,[],[f738]) ).
cnf(c_257,plain,
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2)
| in(X0,relation_rng(X2)) ),
inference(cnf_transformation,[],[f737]) ).
cnf(c_258,plain,
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2)
| in(X0,X1) ),
inference(cnf_transformation,[],[f736]) ).
cnf(c_264,negated_conjecture,
set_difference(relation_rng(sK54),set_difference(relation_rng(sK54),sK53)) != relation_rng(relation_rng_restriction(sK53,sK54)),
inference(cnf_transformation,[],[f938]) ).
cnf(c_265,negated_conjecture,
relation(sK54),
inference(cnf_transformation,[],[f744]) ).
cnf(c_3534,plain,
set_difference(sK53,set_difference(sK53,relation_rng(sK54))) != relation_rng(relation_rng_restriction(sK53,sK54)),
inference(demodulation,[status(thm)],[c_264,c_54]) ).
cnf(c_15734,plain,
( set_difference(sK53,set_difference(sK53,relation_rng(sK54))) = relation_rng(relation_rng_restriction(sK53,sK54))
| in(sK27(sK53,relation_rng(sK54),relation_rng(relation_rng_restriction(sK53,sK54))),relation_rng(relation_rng_restriction(sK53,sK54)))
| in(sK27(sK53,relation_rng(sK54),relation_rng(relation_rng_restriction(sK53,sK54))),relation_rng(sK54)) ),
inference(instantiation,[status(thm)],[c_132]) ).
cnf(c_15735,plain,
( set_difference(sK53,set_difference(sK53,relation_rng(sK54))) = relation_rng(relation_rng_restriction(sK53,sK54))
| in(sK27(sK53,relation_rng(sK54),relation_rng(relation_rng_restriction(sK53,sK54))),relation_rng(relation_rng_restriction(sK53,sK54)))
| in(sK27(sK53,relation_rng(sK54),relation_rng(relation_rng_restriction(sK53,sK54))),sK53) ),
inference(instantiation,[status(thm)],[c_133]) ).
cnf(c_16080,plain,
( ~ in(sK27(sK53,relation_rng(sK54),relation_rng(relation_rng_restriction(sK53,sK54))),relation_rng(relation_rng_restriction(sK53,sK54)))
| ~ in(sK27(sK53,relation_rng(sK54),relation_rng(relation_rng_restriction(sK53,sK54))),relation_rng(sK54))
| ~ in(sK27(sK53,relation_rng(sK54),relation_rng(relation_rng_restriction(sK53,sK54))),sK53)
| set_difference(sK53,set_difference(sK53,relation_rng(sK54))) = relation_rng(relation_rng_restriction(sK53,sK54)) ),
inference(instantiation,[status(thm)],[c_131]) ).
cnf(c_21287,plain,
( ~ in(sK27(sK53,relation_rng(sK54),relation_rng(relation_rng_restriction(sK53,sK54))),relation_rng(relation_rng_restriction(sK53,sK54)))
| ~ relation(sK54)
| in(sK27(sK53,relation_rng(sK54),relation_rng(relation_rng_restriction(sK53,sK54))),sK53) ),
inference(instantiation,[status(thm)],[c_258]) ).
cnf(c_21288,plain,
( ~ in(sK27(sK53,relation_rng(sK54),relation_rng(relation_rng_restriction(sK53,sK54))),relation_rng(relation_rng_restriction(sK53,sK54)))
| ~ relation(sK54)
| in(sK27(sK53,relation_rng(sK54),relation_rng(relation_rng_restriction(sK53,sK54))),relation_rng(sK54)) ),
inference(instantiation,[status(thm)],[c_257]) ).
cnf(c_34496,plain,
( ~ in(sK27(sK53,relation_rng(sK54),relation_rng(relation_rng_restriction(sK53,sK54))),relation_rng(X0))
| ~ in(sK27(sK53,relation_rng(sK54),relation_rng(relation_rng_restriction(sK53,sK54))),sK53)
| ~ relation(X0)
| in(sK27(sK53,relation_rng(sK54),relation_rng(relation_rng_restriction(sK53,sK54))),relation_rng(relation_rng_restriction(sK53,X0))) ),
inference(instantiation,[status(thm)],[c_256]) ).
cnf(c_64553,plain,
( ~ in(sK27(sK53,relation_rng(sK54),relation_rng(relation_rng_restriction(sK53,sK54))),relation_rng(sK54))
| ~ in(sK27(sK53,relation_rng(sK54),relation_rng(relation_rng_restriction(sK53,sK54))),sK53)
| ~ relation(sK54)
| in(sK27(sK53,relation_rng(sK54),relation_rng(relation_rng_restriction(sK53,sK54))),relation_rng(relation_rng_restriction(sK53,sK54))) ),
inference(instantiation,[status(thm)],[c_34496]) ).
cnf(c_64554,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_64553,c_21287,c_21288,c_16080,c_15735,c_15734,c_3534,c_265]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU201+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n007.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 16:01:54 EDT 2023
% 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 --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 17.51/3.17 % SZS status Started for theBenchmark.p
% 17.51/3.17 % SZS status Theorem for theBenchmark.p
% 17.51/3.17
% 17.51/3.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 17.51/3.17
% 17.51/3.17 ------ iProver source info
% 17.51/3.17
% 17.51/3.17 git: date: 2023-05-31 18:12:56 +0000
% 17.51/3.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 17.51/3.17 git: non_committed_changes: false
% 17.51/3.17 git: last_make_outside_of_git: false
% 17.51/3.17
% 17.51/3.17 ------ Parsing...
% 17.51/3.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 17.51/3.17
% 17.51/3.17 ------ Preprocessing... sup_sim: 36 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
% 17.51/3.17
% 17.51/3.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 17.51/3.17
% 17.51/3.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.51/3.17 ------ Proving...
% 17.51/3.17 ------ Problem Properties
% 17.51/3.17
% 17.51/3.17
% 17.51/3.17 clauses 289
% 17.51/3.17 conjectures 1
% 17.51/3.17 EPR 34
% 17.51/3.17 Horn 230
% 17.51/3.17 unary 46
% 17.51/3.17 binary 100
% 17.51/3.17 lits 753
% 17.51/3.17 lits eq 155
% 17.51/3.17 fd_pure 0
% 17.51/3.17 fd_pseudo 0
% 17.51/3.17 fd_cond 13
% 17.51/3.17 fd_pseudo_cond 62
% 17.51/3.17 AC symbols 0
% 17.51/3.17
% 17.51/3.17 ------ Schedule dynamic 5 is on
% 17.51/3.17
% 17.51/3.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 17.51/3.17
% 17.51/3.17
% 17.51/3.17 ------
% 17.51/3.17 Current options:
% 17.51/3.17 ------
% 17.51/3.17
% 17.51/3.17
% 17.51/3.17
% 17.51/3.17
% 17.51/3.17 ------ Proving...
% 17.51/3.17
% 17.51/3.17
% 17.51/3.17 % SZS status Theorem for theBenchmark.p
% 17.51/3.17
% 17.51/3.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.51/3.17
% 17.51/3.18
%------------------------------------------------------------------------------