TSTP Solution File: SET587+3 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET587+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n007.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 15:08:26 EDT 2023
% Result : Theorem 3.23s 1.16s
% Output : CNFRefutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 7 unt; 0 def)
% Number of atoms : 163 ( 27 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 173 ( 66 ~; 73 |; 21 &)
% ( 6 <=>; 5 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 114 ( 4 sgn; 61 !; 12 ?)
% 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,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,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) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_difference_empty_set) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( difference(X0,X1) = empty_set
<=> subset(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,[],[f4]) ).
fof(f13,plain,
? [X0,X1] :
( difference(X0,X1) = empty_set
<~> subset(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,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) )
& ( ( ~ member(X2,X1)
& member(X2,X0) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f18,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,[],[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,[],[f12]) ).
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(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f20,f21]) ).
fof(f29,plain,
? [X0,X1] :
( ( ~ subset(X0,X1)
| difference(X0,X1) != empty_set )
& ( subset(X0,X1)
| difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f30,plain,
( ? [X0,X1] :
( ( ~ subset(X0,X1)
| difference(X0,X1) != empty_set )
& ( subset(X0,X1)
| difference(X0,X1) = empty_set ) )
=> ( ( ~ subset(sK3,sK4)
| empty_set != difference(sK3,sK4) )
& ( subset(sK3,sK4)
| empty_set = difference(sK3,sK4) ) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
( ( ~ subset(sK3,sK4)
| empty_set != difference(sK3,sK4) )
& ( subset(sK3,sK4)
| empty_set = difference(sK3,sK4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f29,f30]) ).
fof(f32,plain,
! [X0,X1] :
( X0 = X1
| member(sK0(X0,X1),X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f34,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f36,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f37,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f38,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f49,plain,
( subset(sK3,sK4)
| empty_set = difference(sK3,sK4) ),
inference(cnf_transformation,[],[f31]) ).
fof(f50,plain,
( ~ subset(sK3,sK4)
| empty_set != difference(sK3,sK4) ),
inference(cnf_transformation,[],[f31]) ).
cnf(c_50,plain,
( X0 = X1
| member(sK0(X0,X1),X0)
| member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f32]) ).
cnf(c_51,plain,
( ~ member(X0,X1)
| member(X0,difference(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f36]) ).
cnf(c_52,plain,
( ~ member(X0,difference(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f35]) ).
cnf(c_53,plain,
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
cnf(c_54,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[],[f37]) ).
cnf(c_55,plain,
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
cnf(c_56,plain,
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_57,plain,
( ~ member(X0,X1)
| ~ subset(X1,X2)
| member(X0,X2) ),
inference(cnf_transformation,[],[f38]) ).
cnf(c_64,negated_conjecture,
( difference(sK3,sK4) != empty_set
| ~ subset(sK3,sK4) ),
inference(cnf_transformation,[],[f50]) ).
cnf(c_65,negated_conjecture,
( difference(sK3,sK4) = empty_set
| subset(sK3,sK4) ),
inference(cnf_transformation,[],[f49]) ).
cnf(c_797,plain,
( member(sK1(difference(X0,X1),X2),X0)
| subset(difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_56,c_53]) ).
cnf(c_865,plain,
( X0 = empty_set
| member(sK0(X0,empty_set),X0) ),
inference(superposition,[status(thm)],[c_50,c_54]) ).
cnf(c_910,plain,
( ~ subset(X0,X1)
| X0 = empty_set
| member(sK0(X0,empty_set),X1) ),
inference(superposition,[status(thm)],[c_865,c_57]) ).
cnf(c_911,plain,
( ~ member(sK0(difference(X0,X1),empty_set),X1)
| difference(X0,X1) = empty_set ),
inference(superposition,[status(thm)],[c_865,c_52]) ).
cnf(c_946,plain,
( ~ subset(X0,X1)
| member(sK1(difference(X0,X2),X3),X1)
| subset(difference(X0,X2),X3) ),
inference(superposition,[status(thm)],[c_797,c_57]) ).
cnf(c_1685,plain,
( ~ subset(difference(X0,X1),X1)
| difference(X0,X1) = empty_set ),
inference(superposition,[status(thm)],[c_910,c_911]) ).
cnf(c_3273,plain,
( ~ subset(X0,X1)
| subset(difference(X0,X2),X1) ),
inference(superposition,[status(thm)],[c_946,c_55]) ).
cnf(c_3467,plain,
( ~ subset(X0,X1)
| difference(X0,X1) = empty_set ),
inference(superposition,[status(thm)],[c_3273,c_1685]) ).
cnf(c_3634,plain,
difference(sK3,sK4) = empty_set,
inference(backward_subsumption_resolution,[status(thm)],[c_65,c_3467]) ).
cnf(c_3635,plain,
~ subset(sK3,sK4),
inference(backward_subsumption_resolution,[status(thm)],[c_64,c_3467]) ).
cnf(c_3693,plain,
( ~ member(X0,sK3)
| member(X0,empty_set)
| member(X0,sK4) ),
inference(superposition,[status(thm)],[c_3634,c_51]) ).
cnf(c_3707,plain,
( ~ member(X0,sK3)
| member(X0,sK4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3693,c_54]) ).
cnf(c_4136,plain,
( member(sK1(sK3,X0),sK4)
| subset(sK3,X0) ),
inference(superposition,[status(thm)],[c_56,c_3707]) ).
cnf(c_4277,plain,
subset(sK3,sK4),
inference(superposition,[status(thm)],[c_4136,c_55]) ).
cnf(c_4280,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4277,c_3635]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET587+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 08:31:41 EDT 2023
% 0.13/0.34 % 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
% 3.23/1.16 % SZS status Started for theBenchmark.p
% 3.23/1.16 % SZS status Theorem for theBenchmark.p
% 3.23/1.16
% 3.23/1.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.23/1.16
% 3.23/1.16 ------ iProver source info
% 3.23/1.16
% 3.23/1.16 git: date: 2023-05-31 18:12:56 +0000
% 3.23/1.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.23/1.16 git: non_committed_changes: false
% 3.23/1.16 git: last_make_outside_of_git: false
% 3.23/1.16
% 3.23/1.16 ------ Parsing...
% 3.23/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.23/1.16
% 3.23/1.16 ------ 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
% 3.23/1.16
% 3.23/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.23/1.16
% 3.23/1.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.23/1.16 ------ Proving...
% 3.23/1.16 ------ Problem Properties
% 3.23/1.16
% 3.23/1.16
% 3.23/1.16 clauses 15
% 3.23/1.16 conjectures 2
% 3.23/1.16 EPR 4
% 3.23/1.16 Horn 10
% 3.23/1.16 unary 2
% 3.23/1.16 binary 6
% 3.23/1.16 lits 35
% 3.23/1.16 lits eq 7
% 3.23/1.16 fd_pure 0
% 3.23/1.16 fd_pseudo 0
% 3.23/1.16 fd_cond 0
% 3.23/1.16 fd_pseudo_cond 5
% 3.23/1.16 AC symbols 0
% 3.23/1.16
% 3.23/1.16 ------ Schedule dynamic 5 is on
% 3.23/1.16
% 3.23/1.16 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.23/1.16
% 3.23/1.16
% 3.23/1.16 ------
% 3.23/1.16 Current options:
% 3.23/1.16 ------
% 3.23/1.16
% 3.23/1.16
% 3.23/1.16
% 3.23/1.16
% 3.23/1.16 ------ Proving...
% 3.23/1.16
% 3.23/1.16
% 3.23/1.16 % SZS status Theorem for theBenchmark.p
% 3.23/1.16
% 3.23/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.23/1.16
% 3.23/1.16
%------------------------------------------------------------------------------