TSTP Solution File: SET175+3 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET175+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n002.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 03:00:11 EDT 2024
% Result : Theorem 3.12s 1.20s
% Output : CNFRefutation 3.12s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f4,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f6,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f9,conjecture,
! [X0,X1] : union(X0,intersection(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_absorbtion_for_union) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] : union(X0,intersection(X0,X1)) = X0,
inference(negated_conjecture,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f12,plain,
? [X0,X1] : union(X0,intersection(X0,X1)) != X0,
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f13]) ).
fof(f15,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(f16,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,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f18,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f17]) ).
fof(f19,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,[],[f11]) ).
fof(f20,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,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f22,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])],[f20,f21]) ).
fof(f27,plain,
( ? [X0,X1] : union(X0,intersection(X0,X1)) != X0
=> sK2 != union(sK2,intersection(sK2,sK3)) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
sK2 != union(sK2,intersection(sK2,sK3)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f12,f27]) ).
fof(f29,plain,
! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f31,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f32,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f37,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f38,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f41,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f42,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f48,plain,
sK2 != union(sK2,intersection(sK2,sK3)),
inference(cnf_transformation,[],[f28]) ).
cnf(c_49,plain,
( ~ member(X0,X1)
| member(X0,union(X2,X1)) ),
inference(cnf_transformation,[],[f31]) ).
cnf(c_51,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[],[f29]) ).
cnf(c_54,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
cnf(c_55,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f37]) ).
cnf(c_58,plain,
union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f38]) ).
cnf(c_60,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
cnf(c_61,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
cnf(c_66,negated_conjecture,
union(sK2,intersection(sK2,sK3)) != sK2,
inference(cnf_transformation,[],[f48]) ).
cnf(c_341,plain,
intersection(sK2,sK3) = sP0_iProver_def,
definition ).
cnf(c_342,plain,
union(sK2,sP0_iProver_def) = sP1_iProver_def,
definition ).
cnf(c_343,negated_conjecture,
sP1_iProver_def != sK2,
inference(demodulation,[status(thm)],[c_66,c_341,c_342]) ).
cnf(c_554,plain,
union(sP0_iProver_def,sK2) = sP1_iProver_def,
inference(demodulation,[status(thm)],[c_342,c_58]) ).
cnf(c_563,plain,
( ~ member(X0,sK2)
| member(X0,sP1_iProver_def) ),
inference(superposition,[status(thm)],[c_554,c_49]) ).
cnf(c_598,plain,
( ~ member(X0,sP0_iProver_def)
| member(X0,sK2) ),
inference(superposition,[status(thm)],[c_341,c_54]) ).
cnf(c_638,plain,
( member(sK0(sK2,X0),sP1_iProver_def)
| subset(sK2,X0) ),
inference(superposition,[status(thm)],[c_61,c_563]) ).
cnf(c_670,plain,
subset(sK2,sP1_iProver_def),
inference(superposition,[status(thm)],[c_638,c_60]) ).
cnf(c_692,plain,
( ~ subset(sK2,sP1_iProver_def)
| ~ subset(sP1_iProver_def,sK2)
| sP1_iProver_def = sK2 ),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_715,plain,
( ~ member(X0,sP1_iProver_def)
| member(X0,sK2)
| member(X0,sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_554,c_51]) ).
cnf(c_746,plain,
( ~ member(sK0(sP1_iProver_def,sK2),sK2)
| subset(sP1_iProver_def,sK2) ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_910,plain,
( member(X0,sK2)
| ~ member(X0,sP1_iProver_def) ),
inference(global_subsumption_just,[status(thm)],[c_715,c_598,c_715]) ).
cnf(c_911,plain,
( ~ member(X0,sP1_iProver_def)
| member(X0,sK2) ),
inference(renaming,[status(thm)],[c_910]) ).
cnf(c_917,plain,
( member(sK0(sP1_iProver_def,X0),sK2)
| subset(sP1_iProver_def,X0) ),
inference(superposition,[status(thm)],[c_61,c_911]) ).
cnf(c_932,plain,
( member(sK0(sP1_iProver_def,sK2),sK2)
| subset(sP1_iProver_def,sK2) ),
inference(instantiation,[status(thm)],[c_917]) ).
cnf(c_933,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_932,c_746,c_692,c_670,c_343]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET175+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n002.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 20:44:27 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.12/1.20 % SZS status Started for theBenchmark.p
% 3.12/1.20 % SZS status Theorem for theBenchmark.p
% 3.12/1.20
% 3.12/1.20 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.12/1.20
% 3.12/1.20 ------ iProver source info
% 3.12/1.20
% 3.12/1.20 git: date: 2024-05-02 19:28:25 +0000
% 3.12/1.20 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.12/1.20 git: non_committed_changes: false
% 3.12/1.20
% 3.12/1.20 ------ Parsing...
% 3.12/1.20 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.12/1.20
% 3.12/1.20 ------ 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
% 3.12/1.20
% 3.12/1.20 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.12/1.20
% 3.12/1.20 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.12/1.20 ------ Proving...
% 3.12/1.20 ------ Problem Properties
% 3.12/1.20
% 3.12/1.20
% 3.12/1.20 clauses 18
% 3.12/1.20 conjectures 1
% 3.12/1.20 EPR 4
% 3.12/1.20 Horn 15
% 3.12/1.20 unary 6
% 3.12/1.20 binary 6
% 3.12/1.20 lits 36
% 3.12/1.20 lits eq 8
% 3.12/1.20 fd_pure 0
% 3.12/1.20 fd_pseudo 0
% 3.12/1.20 fd_cond 0
% 3.12/1.20 fd_pseudo_cond 3
% 3.12/1.20 AC symbols 0
% 3.12/1.20
% 3.12/1.20 ------ Schedule dynamic 5 is on
% 3.12/1.20
% 3.12/1.20 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.12/1.20
% 3.12/1.20
% 3.12/1.20 ------
% 3.12/1.20 Current options:
% 3.12/1.20 ------
% 3.12/1.20
% 3.12/1.20
% 3.12/1.20
% 3.12/1.20
% 3.12/1.20 ------ Proving...
% 3.12/1.20
% 3.12/1.20
% 3.12/1.20 % SZS status Theorem for theBenchmark.p
% 3.12/1.20
% 3.12/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.12/1.20
% 3.12/1.20
%------------------------------------------------------------------------------