TSTP Solution File: SET587+3 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET587+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n021.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 : Mon Jun 24 14:34:55 EDT 2024
% Result : Theorem 3.69s 1.17s
% Output : CNFRefutation 3.69s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
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(f5,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_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(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(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(f23,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f24,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f23]) ).
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(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(f43,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
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_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_58,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f43]) ).
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_453,plain,
difference(sK3,sK4) = sP0_iProver_def,
definition ).
cnf(c_454,negated_conjecture,
( sP0_iProver_def = empty_set
| subset(sK3,sK4) ),
inference(demodulation,[status(thm)],[c_65,c_453]) ).
cnf(c_455,negated_conjecture,
( sP0_iProver_def != empty_set
| ~ subset(sK3,sK4) ),
inference(demodulation,[status(thm)],[c_64]) ).
cnf(c_800,plain,
subset(empty_set,X0),
inference(superposition,[status(thm)],[c_56,c_54]) ).
cnf(c_807,plain,
( ~ member(X0,sP0_iProver_def)
| member(X0,sK3) ),
inference(superposition,[status(thm)],[c_453,c_53]) ).
cnf(c_820,plain,
( ~ member(X0,sK3)
| member(X0,sK4)
| member(X0,sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_453,c_51]) ).
cnf(c_841,plain,
( ~ member(X0,sK4)
| ~ member(X0,sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_453,c_52]) ).
cnf(c_871,plain,
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(superposition,[status(thm)],[c_800,c_58]) ).
cnf(c_882,plain,
( member(sK1(sP0_iProver_def,X0),sK3)
| subset(sP0_iProver_def,X0) ),
inference(superposition,[status(thm)],[c_56,c_807]) ).
cnf(c_890,plain,
( ~ member(sK1(sP0_iProver_def,X0),sK4)
| subset(sP0_iProver_def,X0) ),
inference(superposition,[status(thm)],[c_56,c_841]) ).
cnf(c_904,plain,
( ~ subset(sK3,X0)
| member(sK1(sP0_iProver_def,X1),X0)
| subset(sP0_iProver_def,X1) ),
inference(superposition,[status(thm)],[c_882,c_57]) ).
cnf(c_932,plain,
( member(sK1(sK3,X0),sK4)
| member(sK1(sK3,X0),sP0_iProver_def)
| subset(sK3,X0) ),
inference(superposition,[status(thm)],[c_56,c_820]) ).
cnf(c_1600,plain,
( ~ subset(sK3,sK4)
| subset(sP0_iProver_def,X0) ),
inference(superposition,[status(thm)],[c_904,c_890]) ).
cnf(c_1675,plain,
( empty_set = sP0_iProver_def
| subset(sP0_iProver_def,X0) ),
inference(superposition,[status(thm)],[c_454,c_1600]) ).
cnf(c_1710,plain,
empty_set = sP0_iProver_def,
inference(superposition,[status(thm)],[c_1675,c_871]) ).
cnf(c_1721,plain,
~ member(X0,sP0_iProver_def),
inference(demodulation,[status(thm)],[c_54,c_1710]) ).
cnf(c_1722,plain,
( sP0_iProver_def != sP0_iProver_def
| ~ subset(sK3,sK4) ),
inference(demodulation,[status(thm)],[c_455,c_1710]) ).
cnf(c_1724,plain,
~ subset(sK3,sK4),
inference(equality_resolution_simp,[status(thm)],[c_1722]) ).
cnf(c_1793,plain,
( member(sK1(sK3,X0),sK4)
| subset(sK3,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_932,c_1721]) ).
cnf(c_1801,plain,
subset(sK3,sK4),
inference(superposition,[status(thm)],[c_1793,c_55]) ).
cnf(c_1802,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1801,c_1724]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET587+3 : TPTP v8.2.0. Released v2.2.0.
% 0.07/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Jun 23 11:34:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 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
% 3.69/1.17 % SZS status Started for theBenchmark.p
% 3.69/1.17 % SZS status Theorem for theBenchmark.p
% 3.69/1.17
% 3.69/1.17 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.69/1.17
% 3.69/1.17 ------ iProver source info
% 3.69/1.17
% 3.69/1.17 git: date: 2024-06-12 09:56:46 +0000
% 3.69/1.17 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 3.69/1.17 git: non_committed_changes: false
% 3.69/1.17
% 3.69/1.17 ------ Parsing...
% 3.69/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.69/1.17
% 3.69/1.17 ------ 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
% 3.69/1.17
% 3.69/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.69/1.17
% 3.69/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.69/1.17 ------ Proving...
% 3.69/1.17 ------ Problem Properties
% 3.69/1.17
% 3.69/1.17
% 3.69/1.17 clauses 16
% 3.69/1.17 conjectures 2
% 3.69/1.17 EPR 6
% 3.69/1.17 Horn 11
% 3.69/1.17 unary 3
% 3.69/1.17 binary 6
% 3.69/1.17 lits 36
% 3.69/1.17 lits eq 8
% 3.69/1.17 fd_pure 0
% 3.69/1.17 fd_pseudo 0
% 3.69/1.17 fd_cond 0
% 3.69/1.17 fd_pseudo_cond 5
% 3.69/1.17 AC symbols 0
% 3.69/1.17
% 3.69/1.17 ------ Schedule dynamic 5 is on
% 3.69/1.17
% 3.69/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.69/1.17
% 3.69/1.17
% 3.69/1.17 ------
% 3.69/1.17 Current options:
% 3.69/1.17 ------
% 3.69/1.17
% 3.69/1.17
% 3.69/1.17
% 3.69/1.17
% 3.69/1.17 ------ Proving...
% 3.69/1.17
% 3.69/1.17
% 3.69/1.17 % SZS status Theorem for theBenchmark.p
% 3.69/1.17
% 3.69/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.69/1.17
% 3.69/1.17
%------------------------------------------------------------------------------