TSTP Solution File: SEU045+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU045+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n019.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 17:03:31 EDT 2023
% Result : Theorem 0.49s 1.20s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 9 unt; 0 def)
% Number of atoms : 269 ( 41 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 339 ( 124 ~; 118 |; 71 &)
% ( 11 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 142 ( 7 sgn; 96 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f20,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(f33,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(relation_rng_restriction(X0,X2)))
=> apply(relation_rng_restriction(X0,X2),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_funct_1) ).
fof(f34,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(relation_rng_restriction(X0,X2)))
=> apply(relation_rng_restriction(X0,X2),X1) = apply(X2,X1) ) ),
inference(negated_conjecture,[],[f33]) ).
fof(f35,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X2,X3) = apply(X1,X3) )
& ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_1) ).
fof(f37,plain,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X2,X3) = apply(X1,X3) )
& ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) ) ) ) ) ) ),
inference(rectify,[],[f35]) ).
fof(f59,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f60,plain,
! [X0,X1] :
( ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f61,plain,
! [X0,X1] :
( ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f60]) ).
fof(f65,plain,
? [X0,X1,X2] :
( apply(relation_rng_restriction(X0,X2),X1) != apply(X2,X1)
& in(X1,relation_dom(relation_rng_restriction(X0,X2)))
& function(X2)
& relation(X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f66,plain,
? [X0,X1,X2] :
( apply(relation_rng_restriction(X0,X2),X1) != apply(X2,X1)
& in(X1,relation_dom(relation_rng_restriction(X0,X2)))
& function(X2)
& relation(X2) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) ) ) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f68,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) ) ) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X1,X2,X0] :
( sP0(X1,X2,X0)
<=> ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f70,plain,
! [X0,X2,X1] :
( ( relation_rng_restriction(X0,X2) = X1
<=> sP0(X1,X2,X0) )
| ~ sP1(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f71,plain,
! [X0,X1] :
( ! [X2] :
( sP1(X0,X2,X1)
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(definition_folding,[],[f68,f70,f69]) ).
fof(f94,plain,
( ? [X0,X1,X2] :
( apply(relation_rng_restriction(X0,X2),X1) != apply(X2,X1)
& in(X1,relation_dom(relation_rng_restriction(X0,X2)))
& function(X2)
& relation(X2) )
=> ( apply(relation_rng_restriction(sK13,sK15),sK14) != apply(sK15,sK14)
& in(sK14,relation_dom(relation_rng_restriction(sK13,sK15)))
& function(sK15)
& relation(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f95,plain,
( apply(relation_rng_restriction(sK13,sK15),sK14) != apply(sK15,sK14)
& in(sK14,relation_dom(relation_rng_restriction(sK13,sK15)))
& function(sK15)
& relation(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15])],[f66,f94]) ).
fof(f96,plain,
! [X0,X2,X1] :
( ( ( relation_rng_restriction(X0,X2) = X1
| ~ sP0(X1,X2,X0) )
& ( sP0(X1,X2,X0)
| relation_rng_restriction(X0,X2) != X1 ) )
| ~ sP1(X0,X2,X1) ),
inference(nnf_transformation,[],[f70]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ( ( relation_rng_restriction(X0,X1) = X2
| ~ sP0(X2,X1,X0) )
& ( sP0(X2,X1,X0)
| relation_rng_restriction(X0,X1) != X2 ) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f96]) ).
fof(f98,plain,
! [X1,X2,X0] :
( ( sP0(X1,X2,X0)
| ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
| ? [X4] :
( ( ~ in(apply(X2,X4),X0)
| ~ in(X4,relation_dom(X2))
| ~ in(X4,relation_dom(X1)) )
& ( ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) )
| in(X4,relation_dom(X1)) ) ) )
& ( ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& ! [X4] :
( ( in(X4,relation_dom(X1))
| ~ in(apply(X2,X4),X0)
| ~ in(X4,relation_dom(X2)) )
& ( ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) )
| ~ in(X4,relation_dom(X1)) ) ) )
| ~ sP0(X1,X2,X0) ) ),
inference(nnf_transformation,[],[f69]) ).
fof(f99,plain,
! [X1,X2,X0] :
( ( sP0(X1,X2,X0)
| ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
| ? [X4] :
( ( ~ in(apply(X2,X4),X0)
| ~ in(X4,relation_dom(X2))
| ~ in(X4,relation_dom(X1)) )
& ( ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) )
| in(X4,relation_dom(X1)) ) ) )
& ( ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& ! [X4] :
( ( in(X4,relation_dom(X1))
| ~ in(apply(X2,X4),X0)
| ~ in(X4,relation_dom(X2)) )
& ( ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) )
| ~ in(X4,relation_dom(X1)) ) ) )
| ~ sP0(X1,X2,X0) ) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( apply(X1,X3) != apply(X0,X3)
& in(X3,relation_dom(X0)) )
| ? [X4] :
( ( ~ in(apply(X1,X4),X2)
| ~ in(X4,relation_dom(X1))
| ~ in(X4,relation_dom(X0)) )
& ( ( in(apply(X1,X4),X2)
& in(X4,relation_dom(X1)) )
| in(X4,relation_dom(X0)) ) ) )
& ( ( ! [X5] :
( apply(X1,X5) = apply(X0,X5)
| ~ in(X5,relation_dom(X0)) )
& ! [X6] :
( ( in(X6,relation_dom(X0))
| ~ in(apply(X1,X6),X2)
| ~ in(X6,relation_dom(X1)) )
& ( ( in(apply(X1,X6),X2)
& in(X6,relation_dom(X1)) )
| ~ in(X6,relation_dom(X0)) ) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( ? [X3] :
( apply(X1,X3) != apply(X0,X3)
& in(X3,relation_dom(X0)) )
=> ( apply(X1,sK16(X0,X1)) != apply(X0,sK16(X0,X1))
& in(sK16(X0,X1),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(apply(X1,X4),X2)
| ~ in(X4,relation_dom(X1))
| ~ in(X4,relation_dom(X0)) )
& ( ( in(apply(X1,X4),X2)
& in(X4,relation_dom(X1)) )
| in(X4,relation_dom(X0)) ) )
=> ( ( ~ in(apply(X1,sK17(X0,X1,X2)),X2)
| ~ in(sK17(X0,X1,X2),relation_dom(X1))
| ~ in(sK17(X0,X1,X2),relation_dom(X0)) )
& ( ( in(apply(X1,sK17(X0,X1,X2)),X2)
& in(sK17(X0,X1,X2),relation_dom(X1)) )
| in(sK17(X0,X1,X2),relation_dom(X0)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( apply(X1,sK16(X0,X1)) != apply(X0,sK16(X0,X1))
& in(sK16(X0,X1),relation_dom(X0)) )
| ( ( ~ in(apply(X1,sK17(X0,X1,X2)),X2)
| ~ in(sK17(X0,X1,X2),relation_dom(X1))
| ~ in(sK17(X0,X1,X2),relation_dom(X0)) )
& ( ( in(apply(X1,sK17(X0,X1,X2)),X2)
& in(sK17(X0,X1,X2),relation_dom(X1)) )
| in(sK17(X0,X1,X2),relation_dom(X0)) ) ) )
& ( ( ! [X5] :
( apply(X1,X5) = apply(X0,X5)
| ~ in(X5,relation_dom(X0)) )
& ! [X6] :
( ( in(X6,relation_dom(X0))
| ~ in(apply(X1,X6),X2)
| ~ in(X6,relation_dom(X1)) )
& ( ( in(apply(X1,X6),X2)
& in(X6,relation_dom(X1)) )
| ~ in(X6,relation_dom(X0)) ) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17])],[f100,f102,f101]) ).
fof(f126,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f127,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f128,plain,
! [X0,X1] :
( function(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f149,plain,
relation(sK15),
inference(cnf_transformation,[],[f95]) ).
fof(f150,plain,
function(sK15),
inference(cnf_transformation,[],[f95]) ).
fof(f151,plain,
in(sK14,relation_dom(relation_rng_restriction(sK13,sK15))),
inference(cnf_transformation,[],[f95]) ).
fof(f152,plain,
apply(relation_rng_restriction(sK13,sK15),sK14) != apply(sK15,sK14),
inference(cnf_transformation,[],[f95]) ).
fof(f153,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| relation_rng_restriction(X0,X1) != X2
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f97]) ).
fof(f158,plain,
! [X2,X0,X1,X5] :
( apply(X1,X5) = apply(X0,X5)
| ~ in(X5,relation_dom(X0))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f103]) ).
fof(f165,plain,
! [X2,X0,X1] :
( sP1(X0,X2,X1)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f166,plain,
! [X0,X1] :
( sP0(relation_rng_restriction(X0,X1),X1,X0)
| ~ sP1(X0,X1,relation_rng_restriction(X0,X1)) ),
inference(equality_resolution,[],[f153]) ).
cnf(c_69,plain,
( ~ relation(X0)
| relation(relation_rng_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f126]) ).
cnf(c_70,plain,
( ~ relation(X0)
| ~ function(X0)
| function(relation_rng_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f128]) ).
cnf(c_71,plain,
( ~ relation(X0)
| ~ function(X0)
| relation(relation_rng_restriction(X1,X0)) ),
inference(cnf_transformation,[],[f127]) ).
cnf(c_92,negated_conjecture,
apply(relation_rng_restriction(sK13,sK15),sK14) != apply(sK15,sK14),
inference(cnf_transformation,[],[f152]) ).
cnf(c_93,negated_conjecture,
in(sK14,relation_dom(relation_rng_restriction(sK13,sK15))),
inference(cnf_transformation,[],[f151]) ).
cnf(c_94,negated_conjecture,
function(sK15),
inference(cnf_transformation,[],[f150]) ).
cnf(c_95,negated_conjecture,
relation(sK15),
inference(cnf_transformation,[],[f149]) ).
cnf(c_97,plain,
( ~ sP1(X0,X1,relation_rng_restriction(X0,X1))
| sP0(relation_rng_restriction(X0,X1),X1,X0) ),
inference(cnf_transformation,[],[f166]) ).
cnf(c_104,plain,
( ~ sP0(X0,X1,X2)
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) = apply(X1,X3) ),
inference(cnf_transformation,[],[f158]) ).
cnf(c_108,plain,
( ~ relation(X0)
| ~ relation(X1)
| ~ function(X0)
| ~ function(X1)
| sP1(X2,X1,X0) ),
inference(cnf_transformation,[],[f165]) ).
cnf(c_135,plain,
( ~ relation(X0)
| relation(relation_rng_restriction(X1,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_71,c_69]) ).
cnf(c_590,plain,
( relation_rng_restriction(X0,X1) != X2
| X0 != X4
| X1 != X3
| ~ relation(X2)
| ~ relation(X3)
| ~ function(X2)
| ~ function(X3)
| sP0(relation_rng_restriction(X0,X1),X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_108,c_97]) ).
cnf(c_591,plain,
( ~ relation(relation_rng_restriction(X0,X1))
| ~ function(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ function(X1)
| sP0(relation_rng_restriction(X0,X1),X1,X0) ),
inference(unflattening,[status(thm)],[c_590]) ).
cnf(c_603,plain,
( ~ relation(X0)
| ~ function(X0)
| sP0(relation_rng_restriction(X1,X0),X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_591,c_70,c_135]) ).
cnf(c_3921,plain,
( ~ in(X0,relation_dom(relation_rng_restriction(X1,X2)))
| ~ relation(X2)
| ~ function(X2)
| apply(relation_rng_restriction(X1,X2),X0) = apply(X2,X0) ),
inference(superposition,[status(thm)],[c_603,c_104]) ).
cnf(c_4263,plain,
( ~ relation(sK15)
| ~ function(sK15)
| apply(relation_rng_restriction(sK13,sK15),sK14) = apply(sK15,sK14) ),
inference(superposition,[status(thm)],[c_93,c_3921]) ).
cnf(c_4270,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4263,c_92,c_94,c_95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU045+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.36 % Computer : n019.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 18:33:29 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.49/1.20 % SZS status Started for theBenchmark.p
% 0.49/1.20 % SZS status Theorem for theBenchmark.p
% 0.49/1.20
% 0.49/1.20 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.49/1.20
% 0.49/1.20 ------ iProver source info
% 0.49/1.20
% 0.49/1.20 git: date: 2023-05-31 18:12:56 +0000
% 0.49/1.20 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.49/1.20 git: non_committed_changes: false
% 0.49/1.20 git: last_make_outside_of_git: false
% 0.49/1.20
% 0.49/1.20 ------ Parsing...
% 0.49/1.20 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.49/1.20
% 0.49/1.20 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 0.49/1.20
% 0.49/1.20 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.49/1.20
% 0.49/1.20 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.49/1.20 ------ Proving...
% 0.49/1.20 ------ Problem Properties
% 0.49/1.20
% 0.49/1.20
% 0.49/1.20 clauses 54
% 0.49/1.20 conjectures 4
% 0.49/1.20 EPR 26
% 0.49/1.20 Horn 47
% 0.49/1.20 unary 25
% 0.49/1.20 binary 11
% 0.49/1.20 lits 113
% 0.49/1.20 lits eq 8
% 0.49/1.20 fd_pure 0
% 0.49/1.20 fd_pseudo 0
% 0.49/1.20 fd_cond 1
% 0.49/1.20 fd_pseudo_cond 2
% 0.49/1.20 AC symbols 0
% 0.49/1.20
% 0.49/1.20 ------ Schedule dynamic 5 is on
% 0.49/1.20
% 0.49/1.20 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.49/1.20
% 0.49/1.20
% 0.49/1.20 ------
% 0.49/1.20 Current options:
% 0.49/1.20 ------
% 0.49/1.20
% 0.49/1.20
% 0.49/1.20
% 0.49/1.20
% 0.49/1.20 ------ Proving...
% 0.49/1.20
% 0.49/1.20
% 0.49/1.20 % SZS status Theorem for theBenchmark.p
% 0.49/1.20
% 0.49/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.49/1.20
% 0.49/1.20
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