TSTP Solution File: SEU219+2 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU219+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n010.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 17:04:50 EDT 2023
% Result : Theorem 7.55s 1.66s
% Output : CNFRefutation 7.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 12 unt; 0 def)
% Number of atoms : 290 ( 107 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 389 ( 154 ~; 141 |; 74 &)
% ( 5 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 73 ( 0 sgn; 55 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> relation_inverse(X0) = function_inverse(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_funct_1) ).
fof(f50,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f174,axiom,
! [X0] :
( relation(X0)
=> ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
fof(f200,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
=> ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
=> ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
& relation_rng(X0) = relation_dom(X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f202,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f203,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) ) ) ),
inference(negated_conjecture,[],[f202]) ).
fof(f274,plain,
! [X0] :
( relation_inverse(X0) = function_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f275,plain,
! [X0] :
( relation_inverse(X0) = function_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f274]) ).
fof(f276,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f277,plain,
! [X0] :
( ( function(function_inverse(X0))
& relation(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f276]) ).
fof(f381,plain,
! [X0] :
( ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f174]) ).
fof(f404,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f200]) ).
fof(f405,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f404]) ).
fof(f408,plain,
? [X0] :
( ( relation_dom(X0) != relation_rng(function_inverse(X0))
| relation_rng(X0) != relation_dom(function_inverse(X0)) )
& one_to_one(X0)
& function(X0)
& relation(X0) ),
inference(ennf_transformation,[],[f203]) ).
fof(f409,plain,
? [X0] :
( ( relation_dom(X0) != relation_rng(function_inverse(X0))
| relation_rng(X0) != relation_dom(function_inverse(X0)) )
& one_to_one(X0)
& function(X0)
& relation(X0) ),
inference(flattening,[],[f408]) ).
fof(f438,plain,
! [X2,X3,X0,X1] :
( sP0(X2,X3,X0,X1)
<=> ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f439,plain,
! [X0] :
( ! [X1] :
( ( function_inverse(X0) = X1
<=> ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP0(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f405,f438]) ).
fof(f636,plain,
! [X0] :
( ! [X1] :
( ( ( function_inverse(X0) = X1
| ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP0(X2,X3,X0,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP0(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f439]) ).
fof(f637,plain,
! [X0] :
( ! [X1] :
( ( ( function_inverse(X0) = X1
| ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP0(X2,X3,X0,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X2,X3] :
( ( ( apply(X1,X2) = X3
& in(X2,relation_rng(X0)) )
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
& sP0(X2,X3,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f636]) ).
fof(f638,plain,
! [X0] :
( ! [X1] :
( ( ( function_inverse(X0) = X1
| ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP0(X2,X3,X0,X1) )
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X4,X5] :
( ( ( apply(X1,X4) = X5
& in(X4,relation_rng(X0)) )
| apply(X0,X5) != X4
| ~ in(X5,relation_dom(X0)) )
& sP0(X4,X5,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(rectify,[],[f637]) ).
fof(f639,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) )
& apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP0(X2,X3,X0,X1) )
=> ( ( ( sK72(X0,X1) != apply(X1,sK71(X0,X1))
| ~ in(sK71(X0,X1),relation_rng(X0)) )
& sK71(X0,X1) = apply(X0,sK72(X0,X1))
& in(sK72(X0,X1),relation_dom(X0)) )
| ~ sP0(sK71(X0,X1),sK72(X0,X1),X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f640,plain,
! [X0] :
( ! [X1] :
( ( ( function_inverse(X0) = X1
| ( ( sK72(X0,X1) != apply(X1,sK71(X0,X1))
| ~ in(sK71(X0,X1),relation_rng(X0)) )
& sK71(X0,X1) = apply(X0,sK72(X0,X1))
& in(sK72(X0,X1),relation_dom(X0)) )
| ~ sP0(sK71(X0,X1),sK72(X0,X1),X0,X1)
| relation_rng(X0) != relation_dom(X1) )
& ( ( ! [X4,X5] :
( ( ( apply(X1,X4) = X5
& in(X4,relation_rng(X0)) )
| apply(X0,X5) != X4
| ~ in(X5,relation_dom(X0)) )
& sP0(X4,X5,X0,X1) )
& relation_rng(X0) = relation_dom(X1) )
| function_inverse(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK71,sK72])],[f638,f639]) ).
fof(f641,plain,
( ? [X0] :
( ( relation_dom(X0) != relation_rng(function_inverse(X0))
| relation_rng(X0) != relation_dom(function_inverse(X0)) )
& one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( ( relation_dom(sK73) != relation_rng(function_inverse(sK73))
| relation_rng(sK73) != relation_dom(function_inverse(sK73)) )
& one_to_one(sK73)
& function(sK73)
& relation(sK73) ) ),
introduced(choice_axiom,[]) ).
fof(f642,plain,
( ( relation_dom(sK73) != relation_rng(function_inverse(sK73))
| relation_rng(sK73) != relation_dom(function_inverse(sK73)) )
& one_to_one(sK73)
& function(sK73)
& relation(sK73) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK73])],[f409,f641]) ).
fof(f808,plain,
! [X0] :
( relation_inverse(X0) = function_inverse(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f275]) ).
fof(f809,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f277]) ).
fof(f810,plain,
! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f277]) ).
fof(f973,plain,
! [X0] :
( relation_dom(X0) = relation_rng(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f381]) ).
fof(f1015,plain,
! [X0,X1] :
( relation_rng(X0) = relation_dom(X1)
| function_inverse(X0) != X1
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f640]) ).
fof(f1023,plain,
relation(sK73),
inference(cnf_transformation,[],[f642]) ).
fof(f1024,plain,
function(sK73),
inference(cnf_transformation,[],[f642]) ).
fof(f1025,plain,
one_to_one(sK73),
inference(cnf_transformation,[],[f642]) ).
fof(f1026,plain,
( relation_dom(sK73) != relation_rng(function_inverse(sK73))
| relation_rng(sK73) != relation_dom(function_inverse(sK73)) ),
inference(cnf_transformation,[],[f642]) ).
fof(f1288,plain,
! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f1015]) ).
cnf(c_196,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_inverse(X0) = function_inverse(X0) ),
inference(cnf_transformation,[],[f808]) ).
cnf(c_197,plain,
( ~ function(X0)
| ~ relation(X0)
| function(function_inverse(X0)) ),
inference(cnf_transformation,[],[f810]) ).
cnf(c_198,plain,
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f809]) ).
cnf(c_360,plain,
( ~ relation(X0)
| relation_rng(relation_inverse(X0)) = relation_dom(X0) ),
inference(cnf_transformation,[],[f973]) ).
cnf(c_408,plain,
( ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_dom(function_inverse(X0)) = relation_rng(X0) ),
inference(cnf_transformation,[],[f1288]) ).
cnf(c_410,negated_conjecture,
( relation_dom(function_inverse(sK73)) != relation_rng(sK73)
| relation_rng(function_inverse(sK73)) != relation_dom(sK73) ),
inference(cnf_transformation,[],[f1026]) ).
cnf(c_411,negated_conjecture,
one_to_one(sK73),
inference(cnf_transformation,[],[f1025]) ).
cnf(c_412,negated_conjecture,
function(sK73),
inference(cnf_transformation,[],[f1024]) ).
cnf(c_413,negated_conjecture,
relation(sK73),
inference(cnf_transformation,[],[f1023]) ).
cnf(c_715,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_dom(function_inverse(X0)) = relation_rng(X0) ),
inference(global_subsumption_just,[status(thm)],[c_408,c_198,c_197,c_408]) ).
cnf(c_998,plain,
( relation_rng(function_inverse(sK73)) != relation_dom(sK73)
| relation_dom(function_inverse(sK73)) != relation_rng(sK73) ),
inference(prop_impl_just,[status(thm)],[c_410]) ).
cnf(c_999,plain,
( relation_dom(function_inverse(sK73)) != relation_rng(sK73)
| relation_rng(function_inverse(sK73)) != relation_dom(sK73) ),
inference(renaming,[status(thm)],[c_998]) ).
cnf(c_6108,plain,
( X0 != sK73
| ~ function(X0)
| ~ relation(X0)
| relation_dom(function_inverse(X0)) = relation_rng(X0) ),
inference(resolution_lifted,[status(thm)],[c_715,c_411]) ).
cnf(c_6109,plain,
( ~ function(sK73)
| ~ relation(sK73)
| relation_dom(function_inverse(sK73)) = relation_rng(sK73) ),
inference(unflattening,[status(thm)],[c_6108]) ).
cnf(c_6110,plain,
relation_dom(function_inverse(sK73)) = relation_rng(sK73),
inference(global_subsumption_just,[status(thm)],[c_6109,c_413,c_412,c_6109]) ).
cnf(c_6225,plain,
relation_rng(function_inverse(sK73)) != relation_dom(sK73),
inference(backward_subsumption_resolution,[status(thm)],[c_999,c_6110]) ).
cnf(c_20958,plain,
relation_rng(relation_inverse(sK73)) = relation_dom(sK73),
inference(superposition,[status(thm)],[c_413,c_360]) ).
cnf(c_35760,plain,
( ~ function(sK73)
| ~ relation(sK73)
| relation_inverse(sK73) = function_inverse(sK73) ),
inference(superposition,[status(thm)],[c_411,c_196]) ).
cnf(c_35770,plain,
relation_inverse(sK73) = function_inverse(sK73),
inference(forward_subsumption_resolution,[status(thm)],[c_35760,c_413,c_412]) ).
cnf(c_35835,plain,
relation_rng(function_inverse(sK73)) = relation_dom(sK73),
inference(demodulation,[status(thm)],[c_20958,c_35770]) ).
cnf(c_35837,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_35835,c_6225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU219+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.15/0.34 % Computer : n010.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Wed Aug 23 18:15:21 EDT 2023
% 0.15/0.34 % 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
% 7.55/1.66 % SZS status Started for theBenchmark.p
% 7.55/1.66 % SZS status Theorem for theBenchmark.p
% 7.55/1.66
% 7.55/1.66 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.55/1.66
% 7.55/1.66 ------ iProver source info
% 7.55/1.66
% 7.55/1.66 git: date: 2023-05-31 18:12:56 +0000
% 7.55/1.66 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.55/1.66 git: non_committed_changes: false
% 7.55/1.66 git: last_make_outside_of_git: false
% 7.55/1.66
% 7.55/1.66 ------ Parsing...
% 7.55/1.66 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.55/1.66
% 7.55/1.66 ------ Preprocessing... sup_sim: 41 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
% 7.55/1.66
% 7.55/1.66 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.55/1.66
% 7.55/1.66 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.55/1.66 ------ Proving...
% 7.55/1.66 ------ Problem Properties
% 7.55/1.66
% 7.55/1.66
% 7.55/1.66 clauses 360
% 7.55/1.66 conjectures 3
% 7.55/1.66 EPR 47
% 7.55/1.66 Horn 291
% 7.55/1.66 unary 58
% 7.55/1.66 binary 114
% 7.55/1.66 lits 989
% 7.55/1.66 lits eq 189
% 7.55/1.66 fd_pure 0
% 7.55/1.66 fd_pseudo 0
% 7.55/1.66 fd_cond 14
% 7.55/1.66 fd_pseudo_cond 73
% 7.55/1.66 AC symbols 0
% 7.55/1.66
% 7.55/1.66 ------ Schedule dynamic 5 is on
% 7.55/1.66
% 7.55/1.66 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
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% 7.55/1.66 ------
% 7.55/1.66 Current options:
% 7.55/1.66 ------
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% 7.55/1.66
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% 7.55/1.66 ------ Proving...
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% 7.55/1.66 % SZS status Theorem for theBenchmark.p
% 7.55/1.66
% 7.55/1.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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% 7.55/1.66
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