TSTP Solution File: SET930+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET930+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n020.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 15:10:42 EDT 2023
% Result : Theorem 3.70s 1.12s
% Output : CNFRefutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 71 ( 21 unt; 0 def)
% Number of atoms : 183 ( 105 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 207 ( 95 ~; 72 |; 35 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 126 ( 2 sgn; 66 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<=> ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(f7,axiom,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
<=> ( ~ in(X1,X2)
& ~ in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_zfmisc_1) ).
fof(f8,axiom,
! [X0,X1,X2] :
( empty_set = set_difference(unordered_pair(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1,X2] :
~ ( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
& empty_set != set_difference(unordered_pair(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
& empty_set != set_difference(unordered_pair(X0,X1),X2) ),
inference(negated_conjecture,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f12,plain,
? [X0,X1,X2] :
( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
& empty_set != set_difference(unordered_pair(X0,X1),X2) ),
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| ( X0 != X1
& ~ in(X1,X2) )
| in(X0,X2) )
& ( ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) )
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| ( X0 != X1
& ~ in(X1,X2) )
| in(X0,X2) )
& ( ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) )
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ) ),
inference(flattening,[],[f13]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
| in(X1,X2)
| in(X0,X2) )
& ( ( ~ in(X1,X2)
& ~ in(X0,X2) )
| unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
| in(X1,X2)
| in(X0,X2) )
& ( ( ~ in(X1,X2)
& ~ in(X0,X2) )
| unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( empty_set = set_difference(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) )
& ( ( in(X1,X2)
& in(X0,X2) )
| empty_set != set_difference(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( empty_set = set_difference(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) )
& ( ( in(X1,X2)
& in(X0,X2) )
| empty_set != set_difference(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
( ? [X0,X1,X2] :
( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
& empty_set != set_difference(unordered_pair(X0,X1),X2) )
=> ( unordered_pair(sK2,sK3) != set_difference(unordered_pair(sK2,sK3),sK4)
& set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK3)
& set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2)
& empty_set != set_difference(unordered_pair(sK2,sK3),sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
( unordered_pair(sK2,sK3) != set_difference(unordered_pair(sK2,sK3),sK4)
& set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK3)
& set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2)
& empty_set != set_difference(unordered_pair(sK2,sK3),sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f12,f23]) ).
fof(f25,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f26,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
! [X2,X0,X1] :
( X0 = X1
| in(X1,X2)
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f30,plain,
! [X2,X0,X1] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| ~ in(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f31,plain,
! [X2,X0,X1] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| X0 != X1
| in(X0,X2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ in(X0,X2)
| unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
| in(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X2,X0,X1] :
( empty_set = set_difference(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
empty_set != set_difference(unordered_pair(sK2,sK3),sK4),
inference(cnf_transformation,[],[f24]) ).
fof(f41,plain,
set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2),
inference(cnf_transformation,[],[f24]) ).
fof(f42,plain,
set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK3),
inference(cnf_transformation,[],[f24]) ).
fof(f43,plain,
unordered_pair(sK2,sK3) != set_difference(unordered_pair(sK2,sK3),sK4),
inference(cnf_transformation,[],[f24]) ).
fof(f44,plain,
! [X2,X1] :
( singleton(X1) = set_difference(unordered_pair(X1,X1),X2)
| in(X1,X2) ),
inference(equality_resolution,[],[f31]) ).
cnf(c_49,plain,
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f25]) ).
cnf(c_50,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f26]) ).
cnf(c_52,plain,
( set_difference(unordered_pair(X0,X0),X1) = singleton(X0)
| in(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
cnf(c_53,plain,
( ~ in(X0,X1)
| set_difference(unordered_pair(X2,X0),X1) = singleton(X2)
| in(X2,X1) ),
inference(cnf_transformation,[],[f30]) ).
cnf(c_54,plain,
( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
| X0 = X1
| in(X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
cnf(c_55,plain,
( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f28]) ).
cnf(c_58,plain,
( set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1)
| in(X0,X2)
| in(X1,X2) ),
inference(cnf_transformation,[],[f36]) ).
cnf(c_60,plain,
( set_difference(unordered_pair(X0,X1),X2) != unordered_pair(X0,X1)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f34]) ).
cnf(c_61,plain,
( ~ in(X0,X1)
| ~ in(X2,X1)
| set_difference(unordered_pair(X2,X0),X1) = empty_set ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_64,negated_conjecture,
set_difference(unordered_pair(sK2,sK3),sK4) != unordered_pair(sK2,sK3),
inference(cnf_transformation,[],[f43]) ).
cnf(c_65,negated_conjecture,
set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK3),
inference(cnf_transformation,[],[f42]) ).
cnf(c_66,negated_conjecture,
set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2),
inference(cnf_transformation,[],[f41]) ).
cnf(c_67,negated_conjecture,
set_difference(unordered_pair(sK2,sK3),sK4) != empty_set,
inference(cnf_transformation,[],[f40]) ).
cnf(c_424,plain,
( ~ in(X0,X1)
| set_difference(unordered_pair(X1,X1),X0) = singleton(X1) ),
inference(superposition,[status(thm)],[c_52,c_49]) ).
cnf(c_443,plain,
( set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
| ~ in(X1,X2) ),
inference(superposition,[status(thm)],[c_50,c_55]) ).
cnf(c_451,plain,
( set_difference(unordered_pair(X0,X0),X1) = singleton(X0)
| set_difference(unordered_pair(X1,X1),X0) = singleton(X1) ),
inference(superposition,[status(thm)],[c_52,c_424]) ).
cnf(c_495,plain,
( set_difference(unordered_pair(X0,X0),X1) = unordered_pair(X0,X0)
| in(X0,X1) ),
inference(equality_factoring,[status(thm)],[c_58]) ).
cnf(c_582,plain,
( set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
| X0 = X1
| in(X0,X2) ),
inference(superposition,[status(thm)],[c_50,c_54]) ).
cnf(c_646,plain,
( ~ in(sK3,sK4)
| set_difference(unordered_pair(sK2,sK3),sK4) = singleton(sK2)
| in(sK2,sK4) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_665,plain,
( singleton(X0) != singleton(X0)
| set_difference(unordered_pair(X0,X0),X0) = singleton(X0) ),
inference(equality_factoring,[status(thm)],[c_451]) ).
cnf(c_667,plain,
set_difference(unordered_pair(X0,X0),X0) = singleton(X0),
inference(equality_resolution_simp,[status(thm)],[c_665]) ).
cnf(c_746,plain,
~ in(X0,X0),
inference(superposition,[status(thm)],[c_667,c_443]) ).
cnf(c_753,plain,
set_difference(unordered_pair(X0,X0),X0) = unordered_pair(X0,X0),
inference(superposition,[status(thm)],[c_495,c_746]) ).
cnf(c_756,plain,
( set_difference(unordered_pair(X0,X1),X1) = unordered_pair(X0,X1)
| in(X0,X1) ),
inference(superposition,[status(thm)],[c_58,c_746]) ).
cnf(c_757,plain,
unordered_pair(X0,X0) = singleton(X0),
inference(light_normalisation,[status(thm)],[c_753,c_667]) ).
cnf(c_767,plain,
( set_difference(singleton(X0),X1) = singleton(X0)
| in(X0,X1) ),
inference(demodulation,[status(thm)],[c_52,c_757]) ).
cnf(c_782,plain,
( set_difference(singleton(X0),X1) != singleton(X0)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_757,c_60]) ).
cnf(c_799,plain,
( ~ in(X0,X1)
| set_difference(unordered_pair(X0,X2),X1) = empty_set
| set_difference(singleton(X2),X1) = singleton(X2) ),
inference(superposition,[status(thm)],[c_767,c_61]) ).
cnf(c_815,plain,
( set_difference(unordered_pair(sK2,sK3),sK4) = unordered_pair(sK2,sK3)
| in(sK2,sK4)
| in(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_987,plain,
( set_difference(unordered_pair(X0,X1),X1) = unordered_pair(X0,X1)
| set_difference(unordered_pair(X0,X2),X1) = empty_set
| set_difference(singleton(X2),X1) = singleton(X2) ),
inference(superposition,[status(thm)],[c_756,c_799]) ).
cnf(c_1591,plain,
( set_difference(unordered_pair(sK2,sK4),sK4) = unordered_pair(sK2,sK4)
| set_difference(singleton(sK3),sK4) = singleton(sK3) ),
inference(superposition,[status(thm)],[c_987,c_67]) ).
cnf(c_1693,plain,
( unordered_pair(sK2,sK4) != singleton(sK4)
| set_difference(singleton(sK3),sK4) = singleton(sK3)
| sK2 = sK4
| in(sK2,sK4) ),
inference(superposition,[status(thm)],[c_1591,c_582]) ).
cnf(c_1695,plain,
( ~ in(sK2,sK4)
| set_difference(singleton(sK3),sK4) = singleton(sK3) ),
inference(superposition,[status(thm)],[c_1591,c_60]) ).
cnf(c_1742,plain,
set_difference(singleton(sK3),sK4) = singleton(sK3),
inference(global_subsumption_just,[status(thm)],[c_1695,c_66,c_64,c_646,c_815,c_1695]) ).
cnf(c_1745,plain,
~ in(sK3,sK4),
inference(superposition,[status(thm)],[c_1742,c_782]) ).
cnf(c_1827,plain,
in(sK2,sK4),
inference(global_subsumption_just,[status(thm)],[c_1693,c_64,c_815,c_1745]) ).
cnf(c_1837,plain,
( set_difference(unordered_pair(X0,sK2),sK4) = singleton(X0)
| in(X0,sK4) ),
inference(superposition,[status(thm)],[c_1827,c_53]) ).
cnf(c_2109,plain,
set_difference(unordered_pair(sK3,sK2),sK4) = singleton(sK3),
inference(superposition,[status(thm)],[c_1837,c_1745]) ).
cnf(c_2260,plain,
set_difference(unordered_pair(sK2,sK3),sK4) = singleton(sK3),
inference(demodulation,[status(thm)],[c_2109,c_50]) ).
cnf(c_2261,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2260,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET930+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : run_iprover %s %d THM
% 0.11/0.34 % Computer : n020.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Sat Aug 26 09:16:15 EDT 2023
% 0.11/0.34 % CPUTime :
% 0.18/0.46 Running first-order theorem proving
% 0.18/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.70/1.12 % SZS status Started for theBenchmark.p
% 3.70/1.12 % SZS status Theorem for theBenchmark.p
% 3.70/1.12
% 3.70/1.12 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.70/1.12
% 3.70/1.12 ------ iProver source info
% 3.70/1.12
% 3.70/1.12 git: date: 2023-05-31 18:12:56 +0000
% 3.70/1.12 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.70/1.12 git: non_committed_changes: false
% 3.70/1.12 git: last_make_outside_of_git: false
% 3.70/1.12
% 3.70/1.12 ------ Parsing...
% 3.70/1.12 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.70/1.12
% 3.70/1.12 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 3.70/1.12
% 3.70/1.12 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.70/1.12
% 3.70/1.12 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.70/1.12 ------ Proving...
% 3.70/1.12 ------ Problem Properties
% 3.70/1.12
% 3.70/1.12
% 3.70/1.12 clauses 19
% 3.70/1.12 conjectures 4
% 3.70/1.12 EPR 4
% 3.70/1.12 Horn 15
% 3.70/1.12 unary 8
% 3.70/1.12 binary 7
% 3.70/1.12 lits 34
% 3.70/1.12 lits eq 16
% 3.70/1.12 fd_pure 0
% 3.70/1.12 fd_pseudo 0
% 3.70/1.12 fd_cond 0
% 3.70/1.12 fd_pseudo_cond 1
% 3.70/1.12 AC symbols 0
% 3.70/1.12
% 3.70/1.12 ------ Schedule dynamic 5 is on
% 3.70/1.12
% 3.70/1.12 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.70/1.12
% 3.70/1.12
% 3.70/1.12 ------
% 3.70/1.12 Current options:
% 3.70/1.12 ------
% 3.70/1.12
% 3.70/1.12
% 3.70/1.12
% 3.70/1.12
% 3.70/1.12 ------ Proving...
% 3.70/1.12
% 3.70/1.12
% 3.70/1.12 % SZS status Theorem for theBenchmark.p
% 3.70/1.12
% 3.70/1.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.70/1.12
% 3.70/1.12
%------------------------------------------------------------------------------