TSTP Solution File: SET624+3 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET624+3 : TPTP v8.1.2. 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 : Thu Aug 31 15:08:45 EDT 2023
% Result : Theorem 3.76s 1.17s
% Output : CNFRefutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 69 ( 8 unt; 0 def)
% Number of atoms : 199 ( 3 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 228 ( 98 ~; 99 |; 23 &)
% ( 4 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 106 ( 4 sgn; 51 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(f3,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f4,axiom,
! [X0,X1] :
( intersect(X0,X1)
=> intersect(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_intersect) ).
fof(f6,conjecture,
! [X0,X1,X2] :
( intersect(X0,union(X1,X2))
<=> ( intersect(X0,X2)
| intersect(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersect_with_union) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( intersect(X0,union(X1,X2))
<=> ( intersect(X0,X2)
| intersect(X0,X1) ) ),
inference(negated_conjecture,[],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( intersect(X1,X0)
| ~ intersect(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f9,plain,
? [X0,X1,X2] :
( intersect(X0,union(X1,X2))
<~> ( intersect(X0,X2)
| intersect(X0,X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f10,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(f11,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,[],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) )
& ( ? [X2] :
( member(X2,X1)
& member(X2,X0) )
| ~ intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f13,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) )
& ( ? [X3] :
( member(X3,X1)
& member(X3,X0) )
| ~ intersect(X0,X1) ) ),
inference(rectify,[],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X1)
& member(X3,X0) )
=> ( member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) )
& ( ( member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) )
| ~ intersect(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14]) ).
fof(f20,plain,
? [X0,X1,X2] :
( ( ( ~ intersect(X0,X2)
& ~ intersect(X0,X1) )
| ~ intersect(X0,union(X1,X2)) )
& ( intersect(X0,X2)
| intersect(X0,X1)
| intersect(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f21,plain,
? [X0,X1,X2] :
( ( ( ~ intersect(X0,X2)
& ~ intersect(X0,X1) )
| ~ intersect(X0,union(X1,X2)) )
& ( intersect(X0,X2)
| intersect(X0,X1)
| intersect(X0,union(X1,X2)) ) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
( ? [X0,X1,X2] :
( ( ( ~ intersect(X0,X2)
& ~ intersect(X0,X1) )
| ~ intersect(X0,union(X1,X2)) )
& ( intersect(X0,X2)
| intersect(X0,X1)
| intersect(X0,union(X1,X2)) ) )
=> ( ( ( ~ intersect(sK2,sK4)
& ~ intersect(sK2,sK3) )
| ~ intersect(sK2,union(sK3,sK4)) )
& ( intersect(sK2,sK4)
| intersect(sK2,sK3)
| intersect(sK2,union(sK3,sK4)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
( ( ( ~ intersect(sK2,sK4)
& ~ intersect(sK2,sK3) )
| ~ intersect(sK2,union(sK3,sK4)) )
& ( intersect(sK2,sK4)
| intersect(sK2,sK3)
| intersect(sK2,union(sK3,sK4)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f21,f22]) ).
fof(f24,plain,
! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f25,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f27,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X0,X1] :
( member(sK0(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X2,X0,X1] :
( intersect(X0,X1)
| ~ member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f31,plain,
! [X0,X1] :
( intersect(X1,X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f36,plain,
( intersect(sK2,sK4)
| intersect(sK2,sK3)
| intersect(sK2,union(sK3,sK4)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f37,plain,
( ~ intersect(sK2,sK3)
| ~ intersect(sK2,union(sK3,sK4)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f38,plain,
( ~ intersect(sK2,sK4)
| ~ intersect(sK2,union(sK3,sK4)) ),
inference(cnf_transformation,[],[f23]) ).
cnf(c_50,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f25]) ).
cnf(c_51,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[],[f24]) ).
cnf(c_52,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| intersect(X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
cnf(c_53,plain,
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f28]) ).
cnf(c_54,plain,
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f27]) ).
cnf(c_55,plain,
union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f30]) ).
cnf(c_56,plain,
( ~ intersect(X0,X1)
| intersect(X1,X0) ),
inference(cnf_transformation,[],[f31]) ).
cnf(c_59,negated_conjecture,
( ~ intersect(sK2,union(sK3,sK4))
| ~ intersect(sK2,sK4) ),
inference(cnf_transformation,[],[f38]) ).
cnf(c_60,negated_conjecture,
( ~ intersect(sK2,union(sK3,sK4))
| ~ intersect(sK2,sK3) ),
inference(cnf_transformation,[],[f37]) ).
cnf(c_61,negated_conjecture,
( intersect(sK2,union(sK3,sK4))
| intersect(sK2,sK4)
| intersect(sK2,sK3) ),
inference(cnf_transformation,[],[f36]) ).
cnf(c_355,plain,
( ~ member(X0,union(sK3,sK4))
| ~ member(X0,sK2)
| ~ intersect(sK2,sK3) ),
inference(resolution,[status(thm)],[c_52,c_60]) ).
cnf(c_385,plain,
( ~ member(X0,union(sK3,sK4))
| ~ member(X0,sK2)
| ~ member(X1,sK2)
| ~ member(X1,sK3) ),
inference(resolution,[status(thm)],[c_355,c_52]) ).
cnf(c_397,plain,
( ~ intersect(sK2,union(sK3,sK4))
| member(sK0(sK2,union(sK3,sK4)),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_426,plain,
( ~ intersect(sK2,union(sK3,sK4))
| member(sK0(sK2,union(sK3,sK4)),sK2) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_436,plain,
( intersect(sK2,union(sK4,sK3))
| intersect(sK2,sK4)
| intersect(sK2,sK3) ),
inference(superposition,[status(thm)],[c_55,c_61]) ).
cnf(c_439,plain,
( ~ intersect(sK2,sK3)
| member(sK0(sK2,sK3),sK2) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_454,plain,
( ~ member(X0,sK2)
| ~ member(X0,sK3)
| ~ member(X1,sK2)
| ~ member(X1,sK3) ),
inference(resolution,[status(thm)],[c_385,c_50]) ).
cnf(c_477,plain,
( ~ member(sK0(X0,X1),X2)
| ~ intersect(X0,X1)
| intersect(X2,X1) ),
inference(superposition,[status(thm)],[c_53,c_52]) ).
cnf(c_482,plain,
( ~ intersect(sK2,sK4)
| intersect(sK4,sK2) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_545,plain,
( ~ member(sK0(sK2,union(sK3,sK4)),union(sK3,sK4))
| member(sK0(sK2,union(sK3,sK4)),sK4)
| member(sK0(sK2,union(sK3,sK4)),sK3) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_557,plain,
( intersect(sK2,union(sK4,sK3))
| intersect(sK2,sK4)
| intersect(sK2,sK3) ),
inference(superposition,[status(thm)],[c_55,c_61]) ).
cnf(c_558,plain,
( ~ intersect(sK2,union(sK4,sK3))
| ~ intersect(sK2,sK3) ),
inference(superposition,[status(thm)],[c_55,c_60]) ).
cnf(c_590,plain,
( ~ member(sK0(sK2,union(sK3,sK4)),X0)
| ~ member(sK0(sK2,union(sK3,sK4)),sK2)
| intersect(X0,sK2) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_684,plain,
( ~ member(X0,sK2)
| ~ member(X0,sK3) ),
inference(factoring,[status(thm)],[c_454]) ).
cnf(c_690,plain,
( ~ member(sK0(X0,sK3),sK2)
| ~ intersect(X0,sK3) ),
inference(resolution,[status(thm)],[c_684,c_53]) ).
cnf(c_691,plain,
( ~ member(sK0(sK2,sK3),sK2)
| ~ intersect(sK2,sK3) ),
inference(instantiation,[status(thm)],[c_690]) ).
cnf(c_714,plain,
( intersect(sK2,sK4)
| intersect(sK2,union(sK4,sK3)) ),
inference(global_subsumption_just,[status(thm)],[c_557,c_436,c_439,c_691]) ).
cnf(c_715,plain,
( intersect(sK2,union(sK4,sK3))
| intersect(sK2,sK4) ),
inference(renaming,[status(thm)],[c_714]) ).
cnf(c_718,plain,
( ~ intersect(sK2,sK3)
| intersect(sK2,sK4) ),
inference(superposition,[status(thm)],[c_715,c_558]) ).
cnf(c_724,plain,
~ intersect(sK2,sK3),
inference(global_subsumption_just,[status(thm)],[c_718,c_439,c_691]) ).
cnf(c_800,plain,
( ~ intersect(sK3,sK2)
| intersect(sK2,sK3) ),
inference(instantiation,[status(thm)],[c_56]) ).
cnf(c_994,plain,
( ~ member(sK0(sK2,union(sK3,sK4)),X0)
| ~ member(sK0(sK2,union(sK3,sK4)),sK4)
| intersect(X0,sK4) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_995,plain,
( ~ member(sK0(sK2,union(sK3,sK4)),sK2)
| ~ member(sK0(sK2,union(sK3,sK4)),sK4)
| intersect(sK2,sK4) ),
inference(instantiation,[status(thm)],[c_994]) ).
cnf(c_1522,plain,
( ~ member(sK0(sK2,union(sK3,sK4)),sK2)
| ~ member(sK0(sK2,union(sK3,sK4)),sK3)
| intersect(sK3,sK2) ),
inference(instantiation,[status(thm)],[c_590]) ).
cnf(c_1641,negated_conjecture,
~ intersect(sK2,union(sK3,sK4)),
inference(global_subsumption_just,[status(thm)],[c_59,c_59,c_397,c_426,c_545,c_724,c_800,c_995,c_1522]) ).
cnf(c_1649,plain,
~ intersect(sK2,union(sK4,sK3)),
inference(superposition,[status(thm)],[c_55,c_1641]) ).
cnf(c_1661,plain,
( ~ member(sK0(X0,X1),X2)
| ~ intersect(X0,X1)
| intersect(union(X2,X3),X1) ),
inference(superposition,[status(thm)],[c_50,c_477]) ).
cnf(c_1670,plain,
( ~ intersect(X0,X1)
| intersect(union(X0,X2),X1) ),
inference(superposition,[status(thm)],[c_54,c_1661]) ).
cnf(c_1826,plain,
( ~ intersect(X0,X1)
| intersect(X1,union(X0,X2)) ),
inference(superposition,[status(thm)],[c_1670,c_56]) ).
cnf(c_1882,plain,
~ intersect(sK4,sK2),
inference(superposition,[status(thm)],[c_1826,c_1649]) ).
cnf(c_1883,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1882,c_1641,c_724,c_482,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET624+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 14:13:52 EDT 2023
% 0.14/0.35 % 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
% 3.76/1.17 % SZS status Started for theBenchmark.p
% 3.76/1.17 % SZS status Theorem for theBenchmark.p
% 3.76/1.17
% 3.76/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.76/1.17
% 3.76/1.17 ------ iProver source info
% 3.76/1.17
% 3.76/1.17 git: date: 2023-05-31 18:12:56 +0000
% 3.76/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.76/1.17 git: non_committed_changes: false
% 3.76/1.17 git: last_make_outside_of_git: false
% 3.76/1.17
% 3.76/1.17 ------ Parsing...
% 3.76/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.76/1.17
% 3.76/1.17 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 3.76/1.17
% 3.76/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.76/1.17
% 3.76/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.76/1.17 ------ Proving...
% 3.76/1.17 ------ Problem Properties
% 3.76/1.17
% 3.76/1.17
% 3.76/1.17 clauses 13
% 3.76/1.17 conjectures 3
% 3.76/1.17 EPR 2
% 3.76/1.17 Horn 10
% 3.76/1.17 unary 1
% 3.76/1.17 binary 7
% 3.76/1.17 lits 30
% 3.76/1.17 lits eq 3
% 3.76/1.17 fd_pure 0
% 3.76/1.17 fd_pseudo 0
% 3.76/1.17 fd_cond 0
% 3.76/1.17 fd_pseudo_cond 2
% 3.76/1.17 AC symbols 0
% 3.76/1.17
% 3.76/1.17 ------ Input Options Time Limit: Unbounded
% 3.76/1.17
% 3.76/1.17
% 3.76/1.17 ------
% 3.76/1.17 Current options:
% 3.76/1.17 ------
% 3.76/1.17
% 3.76/1.17
% 3.76/1.17
% 3.76/1.17
% 3.76/1.17 ------ Proving...
% 3.76/1.17
% 3.76/1.17
% 3.76/1.17 % SZS status Theorem for theBenchmark.p
% 3.76/1.17
% 3.76/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.76/1.17
% 3.76/1.18
%------------------------------------------------------------------------------