TSTP Solution File: SET603+4 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET603+4 : 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 : Fri May 3 03:00:55 EDT 2024
% Result : Theorem 7.29s 1.75s
% Output : CNFRefutation 7.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 13 unt; 0 def)
% Number of atoms : 119 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 130 ( 58 ~; 47 |; 16 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 76 ( 2 sgn 55 !; 5 ?)
% 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(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
fof(f6,axiom,
! [X2] : ~ member(X2,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
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,
! [X3] : equal_set(difference(X3,empty_set),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI30) ).
fof(f13,negated_conjecture,
~ ! [X3] : equal_set(difference(X3,empty_set),X3),
inference(negated_conjecture,[],[f12]) ).
fof(f17,plain,
! [X0] : ~ member(X0,empty_set),
inference(rectify,[],[f6]) ).
fof(f18,plain,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( ~ member(X0,X1)
& member(X0,X2) ) ),
inference(rectify,[],[f7]) ).
fof(f23,plain,
~ ! [X0] : equal_set(difference(X0,empty_set),X0),
inference(rectify,[],[f13]) ).
fof(f24,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f26,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f27,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(flattening,[],[f26]) ).
fof(f29,plain,
? [X0] : ~ equal_set(difference(X0,empty_set),X0),
inference(ennf_transformation,[],[f23]) ).
fof(f30,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,[],[f25]) ).
fof(f31,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,[],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f33,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])],[f31,f32]) ).
fof(f39,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(f40,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,[],[f39]) ).
fof(f52,plain,
( ? [X0] : ~ equal_set(difference(X0,empty_set),X0)
=> ~ equal_set(difference(sK3,empty_set),sK3) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
~ equal_set(difference(sK3,empty_set),sK3),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f29,f52]) ).
fof(f55,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f56,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f57,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f66,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f17]) ).
fof(f67,plain,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f69,plain,
! [X2,X0,X1] :
( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f81,plain,
~ equal_set(difference(sK3,empty_set),sK3),
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_52,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
cnf(c_61,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[],[f66]) ).
cnf(c_62,plain,
( ~ member(X0,X1)
| member(X0,difference(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f69]) ).
cnf(c_64,plain,
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
cnf(c_76,negated_conjecture,
~ equal_set(difference(sK3,empty_set),sK3),
inference(cnf_transformation,[],[f81]) ).
cnf(c_422,plain,
( difference(sK3,empty_set) != X0
| X1 != sK3
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_52,c_76]) ).
cnf(c_423,plain,
( ~ subset(difference(sK3,empty_set),sK3)
| ~ subset(sK3,difference(sK3,empty_set)) ),
inference(unflattening,[status(thm)],[c_422]) ).
cnf(c_1437,plain,
( ~ member(sK0(difference(sK3,empty_set),sK3),sK3)
| subset(difference(sK3,empty_set),sK3) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_1492,plain,
( member(sK0(difference(sK3,empty_set),sK3),difference(sK3,empty_set))
| subset(difference(sK3,empty_set),sK3) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_1858,plain,
( member(sK0(sK3,difference(sK3,empty_set)),sK3)
| subset(sK3,difference(sK3,empty_set)) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_1859,plain,
( ~ member(sK0(sK3,difference(sK3,empty_set)),difference(sK3,empty_set))
| subset(sK3,difference(sK3,empty_set)) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_1951,plain,
( ~ member(sK0(sK3,difference(sK3,empty_set)),sK3)
| member(sK0(sK3,difference(sK3,empty_set)),difference(sK3,X0))
| member(sK0(sK3,difference(sK3,empty_set)),X0) ),
inference(instantiation,[status(thm)],[c_62]) ).
cnf(c_1958,plain,
( ~ member(sK0(sK3,difference(sK3,empty_set)),sK3)
| member(sK0(sK3,difference(sK3,empty_set)),difference(sK3,empty_set))
| member(sK0(sK3,difference(sK3,empty_set)),empty_set) ),
inference(instantiation,[status(thm)],[c_1951]) ).
cnf(c_2089,plain,
( ~ member(sK0(difference(sK3,empty_set),sK3),difference(sK3,empty_set))
| member(sK0(difference(sK3,empty_set),sK3),sK3) ),
inference(instantiation,[status(thm)],[c_64]) ).
cnf(c_8193,plain,
~ member(sK0(sK3,difference(sK3,empty_set)),empty_set),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_11638,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_8193,c_2089,c_1958,c_1858,c_1859,c_1492,c_1437,c_423]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET603+4 : TPTP v8.1.2. Released v2.2.0.
% 0.08/0.14 % Command : run_iprover %s %d THM
% 0.15/0.35 % Computer : n028.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 2 20:52:48 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.22/0.48 Running first-order theorem proving
% 0.22/0.48 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
% 7.29/1.75 % SZS status Started for theBenchmark.p
% 7.29/1.75 % SZS status Theorem for theBenchmark.p
% 7.29/1.75
% 7.29/1.75 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.29/1.75
% 7.29/1.75 ------ iProver source info
% 7.29/1.75
% 7.29/1.75 git: date: 2024-05-02 19:28:25 +0000
% 7.29/1.75 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.29/1.75 git: non_committed_changes: false
% 7.29/1.75
% 7.29/1.75 ------ Parsing...
% 7.29/1.75 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.29/1.75
% 7.29/1.75 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 7.29/1.75
% 7.29/1.75 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.29/1.75
% 7.29/1.75 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.29/1.75 ------ Proving...
% 7.29/1.75 ------ Problem Properties
% 7.29/1.75
% 7.29/1.75
% 7.29/1.75 clauses 27
% 7.29/1.75 conjectures 0
% 7.29/1.75 EPR 2
% 7.29/1.75 Horn 22
% 7.29/1.75 unary 4
% 7.29/1.75 binary 16
% 7.29/1.75 lits 57
% 7.29/1.75 lits eq 3
% 7.29/1.75 fd_pure 0
% 7.29/1.75 fd_pseudo 0
% 7.29/1.75 fd_cond 0
% 7.29/1.75 fd_pseudo_cond 2
% 7.29/1.75 AC symbols 0
% 7.29/1.75
% 7.29/1.75 ------ Schedule dynamic 5 is on
% 7.29/1.75
% 7.29/1.75 ------ no conjectures: strip conj schedule
% 7.29/1.75
% 7.29/1.75 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 7.29/1.75
% 7.29/1.75
% 7.29/1.75 ------
% 7.29/1.75 Current options:
% 7.29/1.75 ------
% 7.29/1.75
% 7.29/1.75
% 7.29/1.75
% 7.29/1.75
% 7.29/1.75 ------ Proving...
% 7.29/1.75
% 7.29/1.75
% 7.29/1.75 % SZS status Theorem for theBenchmark.p
% 7.29/1.75
% 7.29/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.29/1.75
% 7.29/1.76
%------------------------------------------------------------------------------