TSTP Solution File: SET930+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET930+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n018.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 14:36:37 EDT 2024
% Result : Theorem 16.77s 3.18s
% Output : CNFRefutation 16.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 15 unt; 0 def)
% Number of atoms : 128 ( 71 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 161 ( 75 ~; 47 |; 35 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 66 ( 0 sgn 46 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(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(f26,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
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(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]) ).
cnf(c_50,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f26]) ).
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_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_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_142,plain,
set_difference(unordered_pair(sK3,sK2),sK4) != empty_set,
inference(demodulation,[status(thm)],[c_67,c_50]) ).
cnf(c_144,plain,
set_difference(unordered_pair(sK3,sK2),sK4) != singleton(sK3),
inference(demodulation,[status(thm)],[c_65,c_50]) ).
cnf(c_145,plain,
set_difference(unordered_pair(sK3,sK2),sK4) != unordered_pair(sK3,sK2),
inference(demodulation,[status(thm)],[c_64,c_50]) ).
cnf(c_826,plain,
( set_difference(unordered_pair(sK3,sK2),sK4) = unordered_pair(sK3,sK2)
| in(sK2,sK4)
| in(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_908,plain,
( ~ in(sK2,sK4)
| set_difference(unordered_pair(X0,sK2),sK4) = singleton(X0)
| in(X0,sK4) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_1271,plain,
( ~ in(sK3,sK4)
| set_difference(unordered_pair(X0,sK3),sK4) = singleton(X0)
| in(X0,sK4) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_1272,plain,
( ~ in(sK3,sK4)
| set_difference(unordered_pair(sK2,sK3),sK4) = singleton(sK2)
| in(sK2,sK4) ),
inference(instantiation,[status(thm)],[c_1271]) ).
cnf(c_1277,plain,
( ~ in(X0,sK4)
| ~ in(sK3,sK4)
| set_difference(unordered_pair(sK3,X0),sK4) = empty_set ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_1278,plain,
( ~ in(sK2,sK4)
| ~ in(sK3,sK4)
| set_difference(unordered_pair(sK3,sK2),sK4) = empty_set ),
inference(instantiation,[status(thm)],[c_1277]) ).
cnf(c_7431,plain,
( ~ in(sK2,sK4)
| set_difference(unordered_pair(sK3,sK2),sK4) = singleton(sK3)
| in(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_908]) ).
cnf(c_7432,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_7431,c_1278,c_1272,c_826,c_145,c_144,c_142,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : SET930+1 : TPTP v8.2.0. Released v3.2.0.
% 0.03/0.14 % Command : run_iprover %s %d THM
% 0.13/0.36 % Computer : n018.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sun Jun 23 12:02:54 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.20/0.51 Running first-order theorem proving
% 0.20/0.51 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
% 16.77/3.18 % SZS status Started for theBenchmark.p
% 16.77/3.18 % SZS status Theorem for theBenchmark.p
% 16.77/3.18
% 16.77/3.18 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 16.77/3.18
% 16.77/3.18 ------ iProver source info
% 16.77/3.18
% 16.77/3.18 git: date: 2024-06-12 09:56:46 +0000
% 16.77/3.18 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 16.77/3.18 git: non_committed_changes: false
% 16.77/3.18
% 16.77/3.18 ------ Parsing...
% 16.77/3.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 16.77/3.18
% 16.77/3.18 ------ Preprocessing... sup_sim: 4 sf_s rm: 1 0s sf_e pe_s pe_e
% 16.77/3.18
% 16.77/3.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 16.77/3.18
% 16.77/3.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 16.77/3.18 ------ Proving...
% 16.77/3.18 ------ Problem Properties
% 16.77/3.18
% 16.77/3.18
% 16.77/3.18 clauses 19
% 16.77/3.18 conjectures 0
% 16.77/3.18 EPR 4
% 16.77/3.18 Horn 15
% 16.77/3.18 unary 8
% 16.77/3.18 binary 7
% 16.77/3.18 lits 34
% 16.77/3.18 lits eq 16
% 16.77/3.18 fd_pure 0
% 16.77/3.18 fd_pseudo 0
% 16.77/3.18 fd_cond 0
% 16.77/3.18 fd_pseudo_cond 1
% 16.77/3.18 AC symbols 0
% 16.77/3.18
% 16.77/3.18 ------ Input Options Time Limit: Unbounded
% 16.77/3.18
% 16.77/3.18
% 16.77/3.18 ------
% 16.77/3.18 Current options:
% 16.77/3.18 ------
% 16.77/3.18
% 16.77/3.18
% 16.77/3.18
% 16.77/3.18
% 16.77/3.18 ------ Proving...
% 16.77/3.18
% 16.77/3.18
% 16.77/3.18 % SZS status Theorem for theBenchmark.p
% 16.77/3.18
% 16.77/3.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 16.77/3.18
% 16.77/3.18
%------------------------------------------------------------------------------