TSTP Solution File: SET606+3 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET606+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n017.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 : Fri May 3 03:00:56 EDT 2024
% Result : Theorem 4.13s 1.24s
% Output : CNFRefutation 4.13s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
<=> member(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_equal) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(f3,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f5,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f9,conjecture,
! [X0,X1] : difference(X0,X1) = difference(X0,intersection(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_difference_into_intersection) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] : difference(X0,X1) = difference(X0,intersection(X0,X1)),
inference(negated_conjecture,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( member(X2,X0)
<~> member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f13,plain,
? [X0,X1] : difference(X0,X1) != difference(X0,intersection(X0,X1)),
inference(ennf_transformation,[],[f10]) ).
fof(f14,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f15,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) )
=> ( ( ~ member(sK0(X0,X1),X1)
| ~ member(sK0(X0,X1),X0) )
& ( member(sK0(X0,X1),X1)
| member(sK0(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ member(sK0(X0,X1),X1)
| ~ member(sK0(X0,X1),X0) )
& ( member(sK0(X0,X1),X1)
| member(sK0(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f14,f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) )
& ( ( ~ member(X2,X1)
& member(X2,X0) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) )
& ( ( ~ member(X2,X1)
& member(X2,X0) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f22,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f21]) ).
fof(f27,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,[],[f12]) ).
fof(f28,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,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f28,f29]) ).
fof(f31,plain,
( ? [X0,X1] : difference(X0,X1) != difference(X0,intersection(X0,X1))
=> difference(sK3,sK4) != difference(sK3,intersection(sK3,sK4)) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
difference(sK3,sK4) != difference(sK3,intersection(sK3,sK4)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f13,f31]) ).
fof(f33,plain,
! [X0,X1] :
( X0 = X1
| member(sK0(X0,X1),X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f34,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sK0(X0,X1),X1)
| ~ member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f36,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f37,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f38,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f40,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f43,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f44,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f50,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f51,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f53,plain,
difference(sK3,sK4) != difference(sK3,intersection(sK3,sK4)),
inference(cnf_transformation,[],[f32]) ).
cnf(c_49,plain,
( ~ member(sK0(X0,X1),X0)
| ~ member(sK0(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f34]) ).
cnf(c_50,plain,
( X0 = X1
| member(sK0(X0,X1),X0)
| member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f33]) ).
cnf(c_51,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f37]) ).
cnf(c_52,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f36]) ).
cnf(c_54,plain,
( ~ member(X0,X1)
| member(X0,difference(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f40]) ).
cnf(c_55,plain,
( ~ member(X0,difference(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_56,plain,
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
cnf(c_57,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f43]) ).
cnf(c_60,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f44]) ).
cnf(c_63,plain,
( ~ member(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
cnf(c_64,plain,
( member(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
cnf(c_67,negated_conjecture,
difference(sK3,intersection(sK3,sK4)) != difference(sK3,sK4),
inference(cnf_transformation,[],[f53]) ).
cnf(c_387,plain,
intersection(sK3,sK4) = sP0_iProver_def,
definition ).
cnf(c_388,plain,
difference(sK3,sP0_iProver_def) = sP1_iProver_def,
definition ).
cnf(c_389,plain,
difference(sK3,sK4) = sP2_iProver_def,
definition ).
cnf(c_390,negated_conjecture,
sP1_iProver_def != sP2_iProver_def,
inference(demodulation,[status(thm)],[c_67,c_389,c_387,c_388]) ).
cnf(c_635,plain,
( ~ member(X0,sP0_iProver_def)
| member(X0,sK4) ),
inference(superposition,[status(thm)],[c_387,c_52]) ).
cnf(c_648,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X2,X1)) ),
inference(superposition,[status(thm)],[c_60,c_51]) ).
cnf(c_678,plain,
( member(sK2(difference(X0,X1),X2),X0)
| subset(difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_64,c_56]) ).
cnf(c_679,plain,
( ~ member(X0,sP2_iProver_def)
| member(X0,sK3) ),
inference(superposition,[status(thm)],[c_389,c_56]) ).
cnf(c_680,plain,
( ~ member(X0,sP1_iProver_def)
| member(X0,sK3) ),
inference(superposition,[status(thm)],[c_388,c_56]) ).
cnf(c_700,plain,
( ~ member(X0,sK4)
| ~ member(X0,sP2_iProver_def) ),
inference(superposition,[status(thm)],[c_389,c_55]) ).
cnf(c_701,plain,
( ~ member(X0,sP0_iProver_def)
| ~ member(X0,sP1_iProver_def) ),
inference(superposition,[status(thm)],[c_388,c_55]) ).
cnf(c_715,plain,
( member(sK2(sP0_iProver_def,X0),sK4)
| subset(sP0_iProver_def,X0) ),
inference(superposition,[status(thm)],[c_64,c_635]) ).
cnf(c_764,plain,
( ~ member(sK2(sP0_iProver_def,X0),sP2_iProver_def)
| subset(sP0_iProver_def,X0) ),
inference(superposition,[status(thm)],[c_715,c_700]) ).
cnf(c_784,plain,
( ~ member(X0,sK3)
| member(X0,sK4)
| member(X0,sP2_iProver_def) ),
inference(superposition,[status(thm)],[c_389,c_54]) ).
cnf(c_785,plain,
( ~ member(X0,sK3)
| member(X0,sP0_iProver_def)
| member(X0,sP1_iProver_def) ),
inference(superposition,[status(thm)],[c_388,c_54]) ).
cnf(c_788,plain,
( ~ member(sK2(X0,difference(X1,X2)),X1)
| member(sK2(X0,difference(X1,X2)),X2)
| subset(X0,difference(X1,X2)) ),
inference(superposition,[status(thm)],[c_54,c_63]) ).
cnf(c_830,plain,
( ~ member(sK0(sP1_iProver_def,sP2_iProver_def),sP1_iProver_def)
| ~ member(sK0(sP1_iProver_def,sP2_iProver_def),sP2_iProver_def)
| sP1_iProver_def = sP2_iProver_def ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_831,plain,
( sP1_iProver_def = sP2_iProver_def
| member(sK0(sP1_iProver_def,sP2_iProver_def),sP1_iProver_def)
| member(sK0(sP1_iProver_def,sP2_iProver_def),sP2_iProver_def) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_865,plain,
( X0 = sP2_iProver_def
| member(sK0(X0,sP2_iProver_def),X0)
| member(sK0(X0,sP2_iProver_def),sK3) ),
inference(superposition,[status(thm)],[c_50,c_679]) ).
cnf(c_1452,plain,
( ~ member(X0,sK3)
| ~ member(X0,sK4)
| member(X0,sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_387,c_648]) ).
cnf(c_1758,plain,
subset(difference(X0,X1),X0),
inference(superposition,[status(thm)],[c_678,c_63]) ).
cnf(c_1880,plain,
( ~ subset(X0,difference(X0,X1))
| difference(X0,X1) = X0 ),
inference(superposition,[status(thm)],[c_1758,c_57]) ).
cnf(c_2180,plain,
( member(sK2(X0,difference(X0,X1)),X1)
| subset(X0,difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_64,c_788]) ).
cnf(c_3801,plain,
subset(sP0_iProver_def,difference(sP0_iProver_def,sP2_iProver_def)),
inference(superposition,[status(thm)],[c_2180,c_764]) ).
cnf(c_4006,plain,
difference(sP0_iProver_def,sP2_iProver_def) = sP0_iProver_def,
inference(superposition,[status(thm)],[c_3801,c_1880]) ).
cnf(c_4095,plain,
( ~ member(X0,sP0_iProver_def)
| ~ member(X0,sP2_iProver_def) ),
inference(superposition,[status(thm)],[c_4006,c_55]) ).
cnf(c_5378,plain,
( sP1_iProver_def = sP2_iProver_def
| member(sK0(sP1_iProver_def,sP2_iProver_def),sK3) ),
inference(superposition,[status(thm)],[c_865,c_680]) ).
cnf(c_5383,plain,
member(sK0(sP1_iProver_def,sP2_iProver_def),sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_5378,c_390]) ).
cnf(c_5526,plain,
( member(sK0(sP1_iProver_def,sP2_iProver_def),sP0_iProver_def)
| member(sK0(sP1_iProver_def,sP2_iProver_def),sP1_iProver_def) ),
inference(superposition,[status(thm)],[c_5383,c_785]) ).
cnf(c_5527,plain,
( member(sK0(sP1_iProver_def,sP2_iProver_def),sK4)
| member(sK0(sP1_iProver_def,sP2_iProver_def),sP2_iProver_def) ),
inference(superposition,[status(thm)],[c_5383,c_784]) ).
cnf(c_5684,plain,
( ~ member(sK0(sP1_iProver_def,sP2_iProver_def),sK3)
| member(sK0(sP1_iProver_def,sP2_iProver_def),sP0_iProver_def)
| member(sK0(sP1_iProver_def,sP2_iProver_def),sP2_iProver_def) ),
inference(superposition,[status(thm)],[c_5527,c_1452]) ).
cnf(c_5689,plain,
( member(sK0(sP1_iProver_def,sP2_iProver_def),sP0_iProver_def)
| member(sK0(sP1_iProver_def,sP2_iProver_def),sP2_iProver_def) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5684,c_5383]) ).
cnf(c_5692,plain,
member(sK0(sP1_iProver_def,sP2_iProver_def),sP0_iProver_def),
inference(global_subsumption_just,[status(thm)],[c_5689,c_390,c_830,c_5526,c_5689]) ).
cnf(c_5695,plain,
~ member(sK0(sP1_iProver_def,sP2_iProver_def),sP2_iProver_def),
inference(superposition,[status(thm)],[c_5692,c_4095]) ).
cnf(c_5696,plain,
~ member(sK0(sP1_iProver_def,sP2_iProver_def),sP1_iProver_def),
inference(superposition,[status(thm)],[c_5692,c_701]) ).
cnf(c_5702,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5695,c_5696,c_831,c_390]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET606+3 : TPTP v8.1.2. Released v2.2.0.
% 0.08/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu May 2 20:05:06 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 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
% 4.13/1.24 % SZS status Started for theBenchmark.p
% 4.13/1.24 % SZS status Theorem for theBenchmark.p
% 4.13/1.24
% 4.13/1.24 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.13/1.24
% 4.13/1.24 ------ iProver source info
% 4.13/1.24
% 4.13/1.24 git: date: 2024-05-02 19:28:25 +0000
% 4.13/1.24 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.13/1.24 git: non_committed_changes: false
% 4.13/1.24
% 4.13/1.24 ------ Parsing...
% 4.13/1.24 ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.13/1.24
% 4.13/1.24 ------ Preprocessing... sup_sim: 0 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
% 4.13/1.24
% 4.13/1.24 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.13/1.24
% 4.13/1.24 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.13/1.24 ------ Proving...
% 4.13/1.24 ------ Problem Properties
% 4.13/1.24
% 4.13/1.24
% 4.13/1.24 clauses 20
% 4.13/1.24 conjectures 1
% 4.13/1.24 EPR 4
% 4.13/1.24 Horn 16
% 4.13/1.24 unary 6
% 4.13/1.24 binary 6
% 4.13/1.24 lits 42
% 4.13/1.24 lits eq 10
% 4.13/1.24 fd_pure 0
% 4.13/1.24 fd_pseudo 0
% 4.13/1.24 fd_cond 0
% 4.13/1.24 fd_pseudo_cond 5
% 4.13/1.24 AC symbols 0
% 4.13/1.24
% 4.13/1.24 ------ Schedule dynamic 5 is on
% 4.13/1.24
% 4.13/1.24 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.13/1.24
% 4.13/1.24
% 4.13/1.24 ------
% 4.13/1.24 Current options:
% 4.13/1.24 ------
% 4.13/1.24
% 4.13/1.24
% 4.13/1.24
% 4.13/1.24
% 4.13/1.24 ------ Proving...
% 4.13/1.24
% 4.13/1.24
% 4.13/1.24 % SZS status Theorem for theBenchmark.p
% 4.13/1.24
% 4.13/1.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.13/1.24
% 4.13/1.24
%------------------------------------------------------------------------------