TSTP Solution File: SET731+4 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET731+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n020.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 15:09:23 EDT 2023
% Result : Theorem 3.63s 1.19s
% Output : CNFRefutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 8 unt; 0 def)
% Number of atoms : 194 ( 17 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 232 ( 85 ~; 68 |; 57 &)
% ( 9 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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; 5 con; 0-3 aty)
% Number of variables : 156 ( 0 sgn; 94 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',surjective) ).
fof(f22,axiom,
! [X5,X0,X4] :
( member(X4,image2(X5,X0))
<=> ? [X2] :
( apply(X5,X2,X4)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image2) ).
fof(f29,conjecture,
! [X5,X9,X0,X1,X10] :
( ( ! [X2,X4] :
( ( member(X4,X10)
& member(X2,X0) )
=> ( apply(X9,X2,X4)
<=> apply(X5,X2,X4) ) )
& image2(X5,X0) = X10
& subset(X10,X1)
& maps(X5,X0,X1) )
=> surjective(X9,X0,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII22) ).
fof(f30,negated_conjecture,
~ ! [X5,X9,X0,X1,X10] :
( ( ! [X2,X4] :
( ( member(X4,X10)
& member(X2,X0) )
=> ( apply(X9,X2,X4)
<=> apply(X5,X2,X4) ) )
& image2(X5,X0) = X10
& subset(X10,X1)
& maps(X5,X0,X1) )
=> surjective(X9,X0,X10) ),
inference(negated_conjecture,[],[f29]) ).
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(f50,plain,
! [X0,X1,X2] :
( member(X2,image2(X0,X1))
<=> ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1) ) ),
inference(rectify,[],[f22]) ).
fof(f57,plain,
~ ! [X0,X1,X2,X3,X4] :
( ( ! [X5,X6] :
( ( member(X6,X4)
& member(X5,X2) )
=> ( apply(X1,X5,X6)
<=> apply(X0,X5,X6) ) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3) )
=> surjective(X1,X2,X4) ),
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(f66,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(f69,plain,
? [X0,X1,X2,X3,X4] :
( ~ surjective(X1,X2,X4)
& ! [X5,X6] :
( ( apply(X1,X5,X6)
<=> apply(X0,X5,X6) )
| ~ member(X6,X4)
| ~ member(X5,X2) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3) ),
inference(ennf_transformation,[],[f57]) ).
fof(f70,plain,
? [X0,X1,X2,X3,X4] :
( ~ surjective(X1,X2,X4)
& ! [X5,X6] :
( ( apply(X1,X5,X6)
<=> apply(X0,X5,X6) )
| ~ member(X6,X4)
| ~ member(X5,X2) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3) ),
inference(flattening,[],[f69]) ).
fof(f99,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(f100,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])],[f66,f99]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) ) )
& ( ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) ) )
& ( ? [X4] :
( apply(X0,X4,X2)
& member(X4,X1) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(rectify,[],[f102]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ? [X4] :
( apply(X0,X4,X2)
& member(X4,X1) )
=> ( apply(X0,sK6(X0,X1,X2),X2)
& member(sK6(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) ) )
& ( ( apply(X0,sK6(X0,X1,X2),X2)
& member(sK6(X0,X1,X2),X1) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f103,f104]) ).
fof(f120,plain,
? [X0,X1,X2,X3,X4] :
( ~ surjective(X1,X2,X4)
& ! [X5,X6] :
( ( ( apply(X1,X5,X6)
| ~ apply(X0,X5,X6) )
& ( apply(X0,X5,X6)
| ~ apply(X1,X5,X6) ) )
| ~ member(X6,X4)
| ~ member(X5,X2) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3) ),
inference(nnf_transformation,[],[f70]) ).
fof(f121,plain,
( ? [X0,X1,X2,X3,X4] :
( ~ surjective(X1,X2,X4)
& ! [X5,X6] :
( ( ( apply(X1,X5,X6)
| ~ apply(X0,X5,X6) )
& ( apply(X0,X5,X6)
| ~ apply(X1,X5,X6) ) )
| ~ member(X6,X4)
| ~ member(X5,X2) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3) )
=> ( ~ surjective(sK11,sK12,sK14)
& ! [X6,X5] :
( ( ( apply(sK11,X5,X6)
| ~ apply(sK10,X5,X6) )
& ( apply(sK10,X5,X6)
| ~ apply(sK11,X5,X6) ) )
| ~ member(X6,sK14)
| ~ member(X5,sK12) )
& sK14 = image2(sK10,sK12)
& subset(sK14,sK13)
& maps(sK10,sK12,sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f122,plain,
( ~ surjective(sK11,sK12,sK14)
& ! [X5,X6] :
( ( ( apply(sK11,X5,X6)
| ~ apply(sK10,X5,X6) )
& ( apply(sK10,X5,X6)
| ~ apply(sK11,X5,X6) ) )
| ~ member(X6,sK14)
| ~ member(X5,sK12) )
& sK14 = image2(sK10,sK12)
& subset(sK14,sK13)
& maps(sK10,sK12,sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13,sK14])],[f120,f121]) ).
fof(f156,plain,
! [X2,X0,X1] :
( surjective(X0,X1,X2)
| member(sK5(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f100]) ).
fof(f157,plain,
! [X2,X0,X1,X4] :
( surjective(X0,X1,X2)
| ~ apply(X0,X4,sK5(X0,X1,X2))
| ~ member(X4,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f160,plain,
! [X2,X0,X1] :
( member(sK6(X0,X1,X2),X1)
| ~ member(X2,image2(X0,X1)) ),
inference(cnf_transformation,[],[f105]) ).
fof(f161,plain,
! [X2,X0,X1] :
( apply(X0,sK6(X0,X1,X2),X2)
| ~ member(X2,image2(X0,X1)) ),
inference(cnf_transformation,[],[f105]) ).
fof(f176,plain,
sK14 = image2(sK10,sK12),
inference(cnf_transformation,[],[f122]) ).
fof(f178,plain,
! [X6,X5] :
( apply(sK11,X5,X6)
| ~ apply(sK10,X5,X6)
| ~ member(X6,sK14)
| ~ member(X5,sK12) ),
inference(cnf_transformation,[],[f122]) ).
fof(f179,plain,
~ surjective(sK11,sK12,sK14),
inference(cnf_transformation,[],[f122]) ).
cnf(c_82,plain,
( ~ apply(X0,X1,sK5(X0,X2,X3))
| ~ member(X1,X2)
| surjective(X0,X2,X3) ),
inference(cnf_transformation,[],[f157]) ).
cnf(c_83,plain,
( member(sK5(X0,X1,X2),X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f156]) ).
cnf(c_87,plain,
( ~ member(X0,image2(X1,X2))
| apply(X1,sK6(X1,X2,X0),X0) ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_88,plain,
( ~ member(X0,image2(X1,X2))
| member(sK6(X1,X2,X0),X2) ),
inference(cnf_transformation,[],[f160]) ).
cnf(c_100,negated_conjecture,
~ surjective(sK11,sK12,sK14),
inference(cnf_transformation,[],[f179]) ).
cnf(c_101,negated_conjecture,
( ~ apply(sK10,X0,X1)
| ~ member(X0,sK12)
| ~ member(X1,sK14)
| apply(sK11,X0,X1) ),
inference(cnf_transformation,[],[f178]) ).
cnf(c_103,negated_conjecture,
image2(sK10,sK12) = sK14,
inference(cnf_transformation,[],[f176]) ).
cnf(c_229,plain,
( member(sK5(X0,X1,X2),X2)
| surjective(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_83]) ).
cnf(c_924,plain,
( X0 != sK11
| X1 != sK12
| X2 != sK14
| ~ apply(X0,X3,sK5(X0,X1,X2))
| ~ member(X3,X1) ),
inference(resolution_lifted,[status(thm)],[c_82,c_100]) ).
cnf(c_925,plain,
( ~ apply(sK11,X0,sK5(sK11,sK12,sK14))
| ~ member(X0,sK12) ),
inference(unflattening,[status(thm)],[c_924]) ).
cnf(c_933,plain,
( X0 != sK11
| X1 != sK12
| X2 != sK14
| member(sK5(X0,X1,X2),X2) ),
inference(resolution_lifted,[status(thm)],[c_229,c_100]) ).
cnf(c_934,plain,
member(sK5(sK11,sK12,sK14),sK14),
inference(unflattening,[status(thm)],[c_933]) ).
cnf(c_1141,plain,
( ~ member(X0,sK12)
| ~ apply(sK11,X0,sK5(sK11,sK12,sK14)) ),
inference(prop_impl_just,[status(thm)],[c_925]) ).
cnf(c_1142,plain,
( ~ apply(sK11,X0,sK5(sK11,sK12,sK14))
| ~ member(X0,sK12) ),
inference(renaming,[status(thm)],[c_1141]) ).
cnf(c_4236,plain,
( ~ member(sK6(sK10,X0,X1),sK12)
| ~ member(X1,image2(sK10,X0))
| ~ member(X1,sK14)
| apply(sK11,sK6(sK10,X0,X1),X1) ),
inference(superposition,[status(thm)],[c_87,c_101]) ).
cnf(c_4450,plain,
( ~ member(sK6(sK10,X0,sK5(sK11,sK12,sK14)),sK12)
| ~ member(sK5(sK11,sK12,sK14),image2(sK10,X0))
| ~ member(sK5(sK11,sK12,sK14),sK14) ),
inference(superposition,[status(thm)],[c_4236,c_1142]) ).
cnf(c_4455,plain,
( ~ member(sK6(sK10,X0,sK5(sK11,sK12,sK14)),sK12)
| ~ member(sK5(sK11,sK12,sK14),image2(sK10,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4450,c_934]) ).
cnf(c_4863,plain,
~ member(sK5(sK11,sK12,sK14),image2(sK10,sK12)),
inference(superposition,[status(thm)],[c_88,c_4455]) ).
cnf(c_4864,plain,
~ member(sK5(sK11,sK12,sK14),sK14),
inference(light_normalisation,[status(thm)],[c_4863,c_103]) ).
cnf(c_4865,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4864,c_934]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET731+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.15/0.14 % Command : run_iprover %s %d THM
% 0.15/0.36 % Computer : n020.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 14:10:14 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.50 Running first-order theorem proving
% 0.22/0.50 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.63/1.19 % SZS status Started for theBenchmark.p
% 3.63/1.19 % SZS status Theorem for theBenchmark.p
% 3.63/1.19
% 3.63/1.19 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.63/1.19
% 3.63/1.19 ------ iProver source info
% 3.63/1.19
% 3.63/1.19 git: date: 2023-05-31 18:12:56 +0000
% 3.63/1.19 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.63/1.19 git: non_committed_changes: false
% 3.63/1.19 git: last_make_outside_of_git: false
% 3.63/1.19
% 3.63/1.19 ------ Parsing...
% 3.63/1.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.63/1.19
% 3.63/1.19 ------ 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: 3 0s sf_e pe_s pe_e
% 3.63/1.19
% 3.63/1.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.63/1.19
% 3.63/1.19 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.63/1.19 ------ Proving...
% 3.63/1.19 ------ Problem Properties
% 3.63/1.19
% 3.63/1.19
% 3.63/1.19 clauses 55
% 3.63/1.19 conjectures 4
% 3.63/1.19 EPR 6
% 3.63/1.19 Horn 50
% 3.63/1.19 unary 7
% 3.63/1.19 binary 28
% 3.63/1.19 lits 138
% 3.63/1.19 lits eq 5
% 3.63/1.19 fd_pure 0
% 3.63/1.19 fd_pseudo 0
% 3.63/1.19 fd_cond 0
% 3.63/1.19 fd_pseudo_cond 3
% 3.63/1.19 AC symbols 0
% 3.63/1.19
% 3.63/1.19 ------ Schedule dynamic 5 is on
% 3.63/1.19
% 3.63/1.19 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.63/1.19
% 3.63/1.19
% 3.63/1.19 ------
% 3.63/1.19 Current options:
% 3.63/1.19 ------
% 3.63/1.19
% 3.63/1.19
% 3.63/1.19
% 3.63/1.19
% 3.63/1.19 ------ Proving...
% 3.63/1.19
% 3.63/1.19
% 3.63/1.19 % SZS status Theorem for theBenchmark.p
% 3.63/1.19
% 3.63/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.63/1.19
% 3.63/1.20
%------------------------------------------------------------------------------