TSTP Solution File: SET734+4 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET734+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n004.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 15:09:24 EDT 2023
% Result : Theorem 3.06s 1.17s
% Output : CNFRefutation 3.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 8 unt; 0 def)
% Number of atoms : 199 ( 8 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 229 ( 84 ~; 70 |; 51 &)
% ( 8 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-5 aty)
% Number of variables : 197 ( 0 sgn; 130 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X9,X5,X0,X1,X10,X2,X11] :
( ( member(X11,X10)
& member(X2,X0) )
=> ( apply(compose_function(X9,X5,X0,X1,X10),X2,X11)
<=> ? [X4] :
( apply(X9,X4,X11)
& apply(X5,X2,X4)
& member(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_function) ).
fof(f16,axiom,
! [X5,X0] :
( identity(X5,X0)
<=> ! [X2] :
( member(X2,X0)
=> apply(X5,X2,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
fof(f18,axiom,
! [X5,X0,X1] :
( surjective(X5,X0,X1)
<=> ! [X4] :
( member(X4,X1)
=> ? [X3] :
( apply(X5,X3,X4)
& member(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjective) ).
fof(f29,conjecture,
! [X5,X9,X0,X1] :
( ( identity(compose_function(X9,X5,X1,X0,X1),X1)
& maps(X5,X1,X0)
& maps(X9,X0,X1) )
=> surjective(X9,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII25) ).
fof(f30,negated_conjecture,
~ ! [X5,X9,X0,X1] :
( ( identity(compose_function(X9,X5,X1,X0,X1),X1)
& maps(X5,X1,X0)
& maps(X9,X0,X1) )
=> surjective(X9,X0,X1) ),
inference(negated_conjecture,[],[f29]) ).
fof(f42,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( member(X6,X4)
& member(X5,X2) )
=> ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) ) ) ),
inference(rectify,[],[f14]) ).
fof(f44,plain,
! [X0,X1] :
( identity(X0,X1)
<=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
inference(rectify,[],[f16]) ).
fof(f46,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
<=> ! [X3] :
( member(X3,X2)
=> ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) ) ),
inference(rectify,[],[f18]) ).
fof(f57,plain,
~ ! [X0,X1,X2,X3] :
( ( identity(compose_function(X1,X0,X3,X2,X3),X3)
& maps(X0,X3,X2)
& maps(X1,X2,X3) )
=> surjective(X1,X2,X3) ),
inference(rectify,[],[f30]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ! [X3] :
( member(X3,X2)
=> ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) )
=> surjective(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f46]) ).
fof(f60,plain,
! [X0,X1] :
( identity(X0,X1)
=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
inference(unused_predicate_definition_removal,[],[f44]) ).
fof(f65,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) ) )
| ~ member(X6,X4)
| ~ member(X5,X2) ),
inference(ennf_transformation,[],[f42]) ).
fof(f66,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) ) )
| ~ member(X6,X4)
| ~ member(X5,X2) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
| ~ identity(X0,X1) ),
inference(ennf_transformation,[],[f60]) ).
fof(f68,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) )
& member(X3,X2) ) ),
inference(ennf_transformation,[],[f58]) ).
fof(f71,plain,
? [X0,X1,X2,X3] :
( ~ surjective(X1,X2,X3)
& identity(compose_function(X1,X0,X3,X2,X3),X3)
& maps(X0,X3,X2)
& maps(X1,X2,X3) ),
inference(ennf_transformation,[],[f57]) ).
fof(f72,plain,
? [X0,X1,X2,X3] :
( ~ surjective(X1,X2,X3)
& identity(compose_function(X1,X0,X3,X2,X3),X3)
& maps(X0,X3,X2)
& maps(X1,X2,X3) ),
inference(flattening,[],[f71]) ).
fof(f97,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ! [X7] :
( ~ apply(X0,X7,X6)
| ~ apply(X1,X5,X7)
| ~ member(X7,X3) ) )
& ( ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) )
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
| ~ member(X6,X4)
| ~ member(X5,X2) ),
inference(nnf_transformation,[],[f66]) ).
fof(f98,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ! [X7] :
( ~ apply(X0,X7,X6)
| ~ apply(X1,X5,X7)
| ~ member(X7,X3) ) )
& ( ? [X8] :
( apply(X0,X8,X6)
& apply(X1,X5,X8)
& member(X8,X3) )
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
| ~ member(X6,X4)
| ~ member(X5,X2) ),
inference(rectify,[],[f97]) ).
fof(f99,plain,
! [X0,X1,X3,X5,X6] :
( ? [X8] :
( apply(X0,X8,X6)
& apply(X1,X5,X8)
& member(X8,X3) )
=> ( apply(X0,sK4(X0,X1,X3,X5,X6),X6)
& apply(X1,X5,sK4(X0,X1,X3,X5,X6))
& member(sK4(X0,X1,X3,X5,X6),X3) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ! [X7] :
( ~ apply(X0,X7,X6)
| ~ apply(X1,X5,X7)
| ~ member(X7,X3) ) )
& ( ( apply(X0,sK4(X0,X1,X3,X5,X6),X6)
& apply(X1,X5,sK4(X0,X1,X3,X5,X6))
& member(sK4(X0,X1,X3,X5,X6),X3) )
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
| ~ member(X6,X4)
| ~ member(X5,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f98,f99]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ? [X3] :
( ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) )
& member(X3,X2) )
=> ( ! [X4] :
( ~ apply(X0,X4,sK5(X0,X1,X2))
| ~ member(X4,X1) )
& member(sK5(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
| ( ! [X4] :
( ~ apply(X0,X4,sK5(X0,X1,X2))
| ~ member(X4,X1) )
& member(sK5(X0,X1,X2),X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f68,f101]) ).
fof(f122,plain,
( ? [X0,X1,X2,X3] :
( ~ surjective(X1,X2,X3)
& identity(compose_function(X1,X0,X3,X2,X3),X3)
& maps(X0,X3,X2)
& maps(X1,X2,X3) )
=> ( ~ surjective(sK11,sK12,sK13)
& identity(compose_function(sK11,sK10,sK13,sK12,sK13),sK13)
& maps(sK10,sK13,sK12)
& maps(sK11,sK12,sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f123,plain,
( ~ surjective(sK11,sK12,sK13)
& identity(compose_function(sK11,sK10,sK13,sK12,sK13),sK13)
& maps(sK10,sK13,sK12)
& maps(sK11,sK12,sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13])],[f72,f122]) ).
fof(f153,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( member(sK4(X0,X1,X3,X5,X6),X3)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ~ member(X6,X4)
| ~ member(X5,X2) ),
inference(cnf_transformation,[],[f100]) ).
fof(f155,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( apply(X0,sK4(X0,X1,X3,X5,X6),X6)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ~ member(X6,X4)
| ~ member(X5,X2) ),
inference(cnf_transformation,[],[f100]) ).
fof(f157,plain,
! [X2,X0,X1] :
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ~ identity(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f158,plain,
! [X2,X0,X1] :
( surjective(X0,X1,X2)
| member(sK5(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f102]) ).
fof(f159,plain,
! [X2,X0,X1,X4] :
( surjective(X0,X1,X2)
| ~ apply(X0,X4,sK5(X0,X1,X2))
| ~ member(X4,X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f178,plain,
identity(compose_function(sK11,sK10,sK13,sK12,sK13),sK13),
inference(cnf_transformation,[],[f123]) ).
fof(f179,plain,
~ surjective(sK11,sK12,sK13),
inference(cnf_transformation,[],[f123]) ).
cnf(c_79,plain,
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ~ member(X5,X2)
| ~ member(X6,X4)
| apply(X0,sK4(X0,X1,X3,X5,X6),X6) ),
inference(cnf_transformation,[],[f155]) ).
cnf(c_81,plain,
( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ~ member(X5,X2)
| ~ member(X6,X4)
| member(sK4(X0,X1,X3,X5,X6),X3) ),
inference(cnf_transformation,[],[f153]) ).
cnf(c_82,plain,
( ~ member(X0,X1)
| ~ identity(X2,X1)
| apply(X2,X0,X0) ),
inference(cnf_transformation,[],[f157]) ).
cnf(c_83,plain,
( ~ apply(X0,X1,sK5(X0,X2,X3))
| ~ member(X1,X2)
| surjective(X0,X2,X3) ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_84,plain,
( member(sK5(X0,X1,X2),X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f158]) ).
cnf(c_101,negated_conjecture,
~ surjective(sK11,sK12,sK13),
inference(cnf_transformation,[],[f179]) ).
cnf(c_102,negated_conjecture,
identity(compose_function(sK11,sK10,sK13,sK12,sK13),sK13),
inference(cnf_transformation,[],[f178]) ).
cnf(c_227,plain,
( member(sK5(X0,X1,X2),X2)
| surjective(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_84]) ).
cnf(c_636,plain,
( compose_function(sK11,sK10,sK13,sK12,sK13) != X1
| X0 != sK13
| ~ member(X2,X0)
| apply(X1,X2,X2) ),
inference(resolution_lifted,[status(thm)],[c_82,c_102]) ).
cnf(c_637,plain,
( ~ member(X0,sK13)
| apply(compose_function(sK11,sK10,sK13,sK12,sK13),X0,X0) ),
inference(unflattening,[status(thm)],[c_636]) ).
cnf(c_647,plain,
( X0 != sK11
| X1 != sK12
| X2 != sK13
| ~ apply(X0,X3,sK5(X0,X1,X2))
| ~ member(X3,X1) ),
inference(resolution_lifted,[status(thm)],[c_83,c_101]) ).
cnf(c_648,plain,
( ~ apply(sK11,X0,sK5(sK11,sK12,sK13))
| ~ member(X0,sK12) ),
inference(unflattening,[status(thm)],[c_647]) ).
cnf(c_656,plain,
( X0 != sK11
| X1 != sK12
| X2 != sK13
| member(sK5(X0,X1,X2),X2) ),
inference(resolution_lifted,[status(thm)],[c_227,c_101]) ).
cnf(c_657,plain,
member(sK5(sK11,sK12,sK13),sK13),
inference(unflattening,[status(thm)],[c_656]) ).
cnf(c_924,plain,
( ~ member(X0,sK13)
| apply(compose_function(sK11,sK10,sK13,sK12,sK13),X0,X0) ),
inference(prop_impl_just,[status(thm)],[c_637]) ).
cnf(c_932,plain,
( ~ apply(sK11,X0,sK5(sK11,sK12,sK13))
| ~ member(X0,sK12) ),
inference(prop_impl_just,[status(thm)],[c_648]) ).
cnf(c_3565,plain,
( ~ member(X0,sK13)
| member(sK4(sK11,sK10,sK12,X0,X0),sK12) ),
inference(resolution,[status(thm)],[c_81,c_924]) ).
cnf(c_3579,plain,
( ~ member(X0,sK13)
| apply(sK11,sK4(sK11,sK10,sK12,X0,X0),X0) ),
inference(resolution,[status(thm)],[c_79,c_924]) ).
cnf(c_3642,plain,
( ~ member(sK4(sK11,sK10,sK12,sK5(sK11,sK12,sK13),sK5(sK11,sK12,sK13)),sK12)
| ~ member(sK5(sK11,sK12,sK13),sK13) ),
inference(resolution,[status(thm)],[c_932,c_3579]) ).
cnf(c_3676,plain,
~ member(sK4(sK11,sK10,sK12,sK5(sK11,sK12,sK13),sK5(sK11,sK12,sK13)),sK12),
inference(global_subsumption_just,[status(thm)],[c_3642,c_657,c_3642]) ).
cnf(c_3682,plain,
~ member(sK5(sK11,sK12,sK13),sK13),
inference(resolution,[status(thm)],[c_3676,c_3565]) ).
cnf(c_3683,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3682,c_657]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET734+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n004.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 : Sat Aug 26 09:01:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.06/1.17 % SZS status Started for theBenchmark.p
% 3.06/1.17 % SZS status Theorem for theBenchmark.p
% 3.06/1.17
% 3.06/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.06/1.17
% 3.06/1.17 ------ iProver source info
% 3.06/1.17
% 3.06/1.17 git: date: 2023-05-31 18:12:56 +0000
% 3.06/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.06/1.17 git: non_committed_changes: false
% 3.06/1.17 git: last_make_outside_of_git: false
% 3.06/1.17
% 3.06/1.17 ------ Parsing...
% 3.06/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.06/1.17
% 3.06/1.17 ------ 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: 4 0s sf_e pe_s pe_e
% 3.06/1.17
% 3.06/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.06/1.17
% 3.06/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.06/1.17 ------ Proving...
% 3.06/1.17 ------ Problem Properties
% 3.06/1.17
% 3.06/1.17
% 3.06/1.17 clauses 55
% 3.06/1.17 conjectures 0
% 3.06/1.17 EPR 4
% 3.06/1.17 Horn 50
% 3.06/1.17 unary 5
% 3.06/1.17 binary 31
% 3.06/1.17 lits 140
% 3.06/1.17 lits eq 5
% 3.06/1.17 fd_pure 0
% 3.06/1.17 fd_pseudo 0
% 3.06/1.17 fd_cond 0
% 3.06/1.17 fd_pseudo_cond 4
% 3.06/1.17 AC symbols 0
% 3.06/1.17
% 3.06/1.17 ------ Input Options Time Limit: Unbounded
% 3.06/1.17
% 3.06/1.17
% 3.06/1.17 ------
% 3.06/1.17 Current options:
% 3.06/1.17 ------
% 3.06/1.17
% 3.06/1.17
% 3.06/1.17
% 3.06/1.17
% 3.06/1.17 ------ Proving...
% 3.06/1.17
% 3.06/1.17
% 3.06/1.17 % SZS status Theorem for theBenchmark.p
% 3.06/1.17
% 3.06/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.06/1.17
% 3.06/1.17
%------------------------------------------------------------------------------