TSTP Solution File: SET701+4 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET701+4 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n028.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 : Mon Jun 24 14:35:28 EDT 2024
% Result : Theorem 68.65s 10.20s
% Output : CNFRefutation 68.65s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f4,axiom,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
fof(f7,axiom,
! [X1,X0,X3] :
( member(X1,difference(X3,X0))
<=> ( ~ member(X1,X0)
& member(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).
fof(f12,conjecture,
! [X0,X1,X5,X3] :
( ( subset(X1,X3)
& subset(X0,X3) )
=> ( subset(X0,X1)
<=> subset(intersection(X0,difference(X3,X1)),intersection(X5,difference(X3,X5))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI35) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X5,X3] :
( ( subset(X1,X3)
& subset(X0,X3) )
=> ( subset(X0,X1)
<=> subset(intersection(X0,difference(X3,X1)),intersection(X5,difference(X3,X5))) ) ),
inference(negated_conjecture,[],[f12]) ).
fof(f15,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X2)
& member(X0,X1) ) ),
inference(rectify,[],[f4]) ).
fof(f18,plain,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( ~ member(X0,X1)
& member(X0,X2) ) ),
inference(rectify,[],[f7]) ).
fof(f23,plain,
~ ! [X0,X1,X2,X3] :
( ( subset(X1,X3)
& subset(X0,X3) )
=> ( subset(X0,X1)
<=> subset(intersection(X0,difference(X3,X1)),intersection(X2,difference(X3,X2))) ) ),
inference(rectify,[],[f13]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f26,plain,
? [X0,X1,X2,X3] :
( ( subset(X0,X1)
<~> subset(intersection(X0,difference(X3,X1)),intersection(X2,difference(X3,X2))) )
& subset(X1,X3)
& subset(X0,X3) ),
inference(ennf_transformation,[],[f23]) ).
fof(f27,plain,
? [X0,X1,X2,X3] :
( ( subset(X0,X1)
<~> subset(intersection(X0,difference(X3,X1)),intersection(X2,difference(X3,X2))) )
& subset(X1,X3)
& subset(X0,X3) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f29,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f29,f30]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) )
& ( ( member(X0,X2)
& member(X0,X1) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) )
& ( ( member(X0,X2)
& member(X0,X1) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f33]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) )
& ( ( ~ member(X0,X1)
& member(X0,X2) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) )
& ( ( ~ member(X0,X1)
& member(X0,X2) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f37]) ).
fof(f50,plain,
? [X0,X1,X2,X3] :
( ( ~ subset(intersection(X0,difference(X3,X1)),intersection(X2,difference(X3,X2)))
| ~ subset(X0,X1) )
& ( subset(intersection(X0,difference(X3,X1)),intersection(X2,difference(X3,X2)))
| subset(X0,X1) )
& subset(X1,X3)
& subset(X0,X3) ),
inference(nnf_transformation,[],[f27]) ).
fof(f51,plain,
? [X0,X1,X2,X3] :
( ( ~ subset(intersection(X0,difference(X3,X1)),intersection(X2,difference(X3,X2)))
| ~ subset(X0,X1) )
& ( subset(intersection(X0,difference(X3,X1)),intersection(X2,difference(X3,X2)))
| subset(X0,X1) )
& subset(X1,X3)
& subset(X0,X3) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
( ? [X0,X1,X2,X3] :
( ( ~ subset(intersection(X0,difference(X3,X1)),intersection(X2,difference(X3,X2)))
| ~ subset(X0,X1) )
& ( subset(intersection(X0,difference(X3,X1)),intersection(X2,difference(X3,X2)))
| subset(X0,X1) )
& subset(X1,X3)
& subset(X0,X3) )
=> ( ( ~ subset(intersection(sK3,difference(sK6,sK4)),intersection(sK5,difference(sK6,sK5)))
| ~ subset(sK3,sK4) )
& ( subset(intersection(sK3,difference(sK6,sK4)),intersection(sK5,difference(sK6,sK5)))
| subset(sK3,sK4) )
& subset(sK4,sK6)
& subset(sK3,sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
( ( ~ subset(intersection(sK3,difference(sK6,sK4)),intersection(sK5,difference(sK6,sK5)))
| ~ subset(sK3,sK4) )
& ( subset(intersection(sK3,difference(sK6,sK4)),intersection(sK5,difference(sK6,sK5)))
| subset(sK3,sK4) )
& subset(sK4,sK6)
& subset(sK3,sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f51,f52]) ).
fof(f54,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f55,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f56,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f59,plain,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f60,plain,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f61,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f67,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f68,plain,
! [X2,X0,X1] :
( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f38]) ).
fof(f80,plain,
subset(sK3,sK6),
inference(cnf_transformation,[],[f53]) ).
fof(f82,plain,
( subset(intersection(sK3,difference(sK6,sK4)),intersection(sK5,difference(sK6,sK5)))
| subset(sK3,sK4) ),
inference(cnf_transformation,[],[f53]) ).
fof(f83,plain,
( ~ subset(intersection(sK3,difference(sK6,sK4)),intersection(sK5,difference(sK6,sK5)))
| ~ subset(sK3,sK4) ),
inference(cnf_transformation,[],[f53]) ).
cnf(c_49,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
cnf(c_50,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
cnf(c_51,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f54]) ).
cnf(c_54,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f61]) ).
cnf(c_55,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f60]) ).
cnf(c_56,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
cnf(c_61,plain,
( ~ member(X0,X1)
| member(X0,difference(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f68]) ).
cnf(c_62,plain,
( ~ member(X0,difference(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f67]) ).
cnf(c_75,negated_conjecture,
( ~ subset(intersection(sK3,difference(sK6,sK4)),intersection(sK5,difference(sK6,sK5)))
| ~ subset(sK3,sK4) ),
inference(cnf_transformation,[],[f83]) ).
cnf(c_76,negated_conjecture,
( subset(intersection(sK3,difference(sK6,sK4)),intersection(sK5,difference(sK6,sK5)))
| subset(sK3,sK4) ),
inference(cnf_transformation,[],[f82]) ).
cnf(c_78,negated_conjecture,
subset(sK3,sK6),
inference(cnf_transformation,[],[f80]) ).
cnf(c_443,plain,
difference(sK6,sK4) = sP0_iProver_def,
definition ).
cnf(c_444,plain,
intersection(sK3,sP0_iProver_def) = sP1_iProver_def,
definition ).
cnf(c_445,plain,
difference(sK6,sK5) = sP2_iProver_def,
definition ).
cnf(c_446,plain,
intersection(sK5,sP2_iProver_def) = sP3_iProver_def,
definition ).
cnf(c_449,negated_conjecture,
( subset(sK3,sK4)
| subset(sP1_iProver_def,sP3_iProver_def) ),
inference(demodulation,[status(thm)],[c_76,c_445,c_446,c_443,c_444]) ).
cnf(c_450,negated_conjecture,
( ~ subset(sK3,sK4)
| ~ subset(sP1_iProver_def,sP3_iProver_def) ),
inference(demodulation,[status(thm)],[c_75]) ).
cnf(c_1081,plain,
( ~ member(X0,sP3_iProver_def)
| member(X0,sP2_iProver_def) ),
inference(superposition,[status(thm)],[c_446,c_55]) ).
cnf(c_1127,plain,
( ~ member(X0,sP3_iProver_def)
| member(X0,sK5) ),
inference(superposition,[status(thm)],[c_446,c_56]) ).
cnf(c_1304,plain,
( ~ member(X0,sK5)
| ~ member(X0,sP2_iProver_def) ),
inference(superposition,[status(thm)],[c_445,c_62]) ).
cnf(c_1739,plain,
( ~ member(X0,sP1_iProver_def)
| member(X0,sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_444,c_55]) ).
cnf(c_1740,plain,
( ~ member(X0,sP3_iProver_def)
| member(X0,sP2_iProver_def) ),
inference(superposition,[status(thm)],[c_446,c_55]) ).
cnf(c_1869,plain,
( member(sK0(sP1_iProver_def,X0),sP0_iProver_def)
| subset(sP1_iProver_def,X0) ),
inference(superposition,[status(thm)],[c_50,c_1739]) ).
cnf(c_1872,plain,
~ member(X0,sP3_iProver_def),
inference(global_subsumption_just,[status(thm)],[c_1740,c_1081,c_1127,c_1304]) ).
cnf(c_1911,plain,
( member(sK0(sK3,sK4),sK3)
| subset(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_1912,plain,
( ~ member(sK0(sK3,sK4),sK4)
| subset(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_1921,plain,
( ~ member(X0,sP1_iProver_def)
| member(X0,sK3) ),
inference(superposition,[status(thm)],[c_444,c_56]) ).
cnf(c_2140,plain,
( member(sK0(sP1_iProver_def,X0),sK3)
| subset(sP1_iProver_def,X0) ),
inference(superposition,[status(thm)],[c_50,c_1921]) ).
cnf(c_2758,plain,
( ~ member(X0,sK4)
| ~ member(X0,sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_443,c_62]) ).
cnf(c_3516,plain,
( ~ subset(X0,X1)
| member(sK0(X0,X2),X1)
| subset(X0,X2) ),
inference(superposition,[status(thm)],[c_50,c_51]) ).
cnf(c_3527,plain,
( ~ subset(sK3,X0)
| member(sK0(sP1_iProver_def,X1),X0)
| subset(sP1_iProver_def,X1) ),
inference(superposition,[status(thm)],[c_2140,c_51]) ).
cnf(c_4069,plain,
( ~ member(X0,sK6)
| member(X0,sK4)
| member(X0,sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_443,c_61]) ).
cnf(c_5566,plain,
( ~ member(X0,sK3)
| ~ member(X0,sP0_iProver_def)
| member(X0,sP1_iProver_def) ),
inference(superposition,[status(thm)],[c_444,c_54]) ).
cnf(c_6413,plain,
( ~ member(sK0(sP1_iProver_def,X0),sK4)
| subset(sP1_iProver_def,X0) ),
inference(superposition,[status(thm)],[c_1869,c_2758]) ).
cnf(c_13939,plain,
~ member(X0,sP3_iProver_def),
inference(global_subsumption_just,[status(thm)],[c_1740,c_1872]) ).
cnf(c_49393,plain,
( ~ member(sK0(sK3,sK4),sK3)
| ~ subset(sK3,X0)
| member(sK0(sK3,sK4),X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_49394,plain,
( ~ member(sK0(sK3,sK4),sK3)
| ~ subset(sK3,sK6)
| member(sK0(sK3,sK4),sK6) ),
inference(instantiation,[status(thm)],[c_49393]) ).
cnf(c_215551,plain,
( ~ subset(X0,sP3_iProver_def)
| subset(X0,X1) ),
inference(superposition,[status(thm)],[c_3516,c_13939]) ).
cnf(c_215560,plain,
( ~ subset(sP1_iProver_def,sK4)
| subset(sP1_iProver_def,X0) ),
inference(superposition,[status(thm)],[c_3516,c_6413]) ).
cnf(c_236383,plain,
( ~ subset(sK3,X0)
| subset(sP1_iProver_def,X0) ),
inference(superposition,[status(thm)],[c_3527,c_49]) ).
cnf(c_252023,plain,
( subset(sP1_iProver_def,sK4)
| subset(sP1_iProver_def,sP3_iProver_def) ),
inference(superposition,[status(thm)],[c_449,c_236383]) ).
cnf(c_263492,plain,
subset(sP1_iProver_def,sP3_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_252023,c_215560]) ).
cnf(c_263493,plain,
~ subset(sK3,sK4),
inference(backward_subsumption_resolution,[status(thm)],[c_450,c_263492]) ).
cnf(c_263494,plain,
subset(sP1_iProver_def,X0),
inference(superposition,[status(thm)],[c_263492,c_215551]) ).
cnf(c_713679,plain,
( ~ member(sK0(sK3,sK4),sK3)
| ~ member(sK0(sK3,sK4),sP0_iProver_def)
| member(sK0(sK3,sK4),sP1_iProver_def) ),
inference(instantiation,[status(thm)],[c_5566]) ).
cnf(c_713681,plain,
( ~ member(sK0(sK3,sK4),sK6)
| member(sK0(sK3,sK4),sK4)
| member(sK0(sK3,sK4),sP0_iProver_def) ),
inference(instantiation,[status(thm)],[c_4069]) ).
cnf(c_714217,plain,
( ~ member(sK0(sK3,sK4),X0)
| ~ subset(X0,X1)
| member(sK0(sK3,sK4),X1) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_716270,plain,
( ~ member(sK0(sK3,sK4),X0)
| ~ subset(X0,sK4)
| member(sK0(sK3,sK4),sK4) ),
inference(instantiation,[status(thm)],[c_714217]) ).
cnf(c_718053,plain,
( ~ member(sK0(sK3,sK4),sP1_iProver_def)
| ~ subset(sP1_iProver_def,sK4)
| member(sK0(sK3,sK4),sK4) ),
inference(instantiation,[status(thm)],[c_716270]) ).
cnf(c_718054,plain,
subset(sP1_iProver_def,sK4),
inference(instantiation,[status(thm)],[c_263494]) ).
cnf(c_718055,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_718054,c_718053,c_713681,c_713679,c_263493,c_49394,c_1911,c_1912,c_78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET701+4 : TPTP v8.2.0. Released v2.2.0.
% 0.11/0.11 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Jun 23 12:00:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.45 Running first-order theorem proving
% 0.19/0.45 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 68.65/10.20 % SZS status Started for theBenchmark.p
% 68.65/10.20 % SZS status Theorem for theBenchmark.p
% 68.65/10.20
% 68.65/10.20 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 68.65/10.20
% 68.65/10.20 ------ iProver source info
% 68.65/10.20
% 68.65/10.20 git: date: 2024-06-12 09:56:46 +0000
% 68.65/10.20 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 68.65/10.20 git: non_committed_changes: false
% 68.65/10.20
% 68.65/10.20 ------ Parsing...
% 68.65/10.20 ------ Clausification by vclausify_rel & Parsing by iProver...
% 68.65/10.20
% 68.65/10.20 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 68.65/10.20
% 68.65/10.20 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 68.65/10.20
% 68.65/10.20 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 68.65/10.20 ------ Proving...
% 68.65/10.20 ------ Problem Properties
% 68.65/10.20
% 68.65/10.20
% 68.65/10.20 clauses 34
% 68.65/10.20 conjectures 4
% 68.65/10.20 EPR 6
% 68.65/10.20 Horn 28
% 68.65/10.20 unary 10
% 68.65/10.20 binary 17
% 68.65/10.20 lits 65
% 68.65/10.20 lits eq 7
% 68.65/10.20 fd_pure 0
% 68.65/10.20 fd_pseudo 0
% 68.65/10.20 fd_cond 0
% 68.65/10.20 fd_pseudo_cond 2
% 68.65/10.20 AC symbols 0
% 68.65/10.20
% 68.65/10.20 ------ Schedule dynamic 5 is on
% 68.65/10.20
% 68.65/10.20 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 68.65/10.20
% 68.65/10.20
% 68.65/10.20 ------
% 68.65/10.20 Current options:
% 68.65/10.20 ------
% 68.65/10.20
% 68.65/10.20
% 68.65/10.20
% 68.65/10.20
% 68.65/10.20 ------ Proving...
% 68.65/10.20
% 68.65/10.20
% 68.65/10.20 % SZS status Theorem for theBenchmark.p
% 68.65/10.20
% 68.65/10.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 68.65/10.20
% 68.65/10.20
%------------------------------------------------------------------------------