TSTP Solution File: SET931+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET931+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n013.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 2.09s 1.18s
% Output : CNFRefutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 61 ( 18 unt; 0 def)
% Number of atoms : 204 ( 174 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 229 ( 86 ~; 98 |; 38 &)
% ( 5 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 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 : 85 ( 13 sgn; 48 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
<=> ~ ( unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& singleton(X1) != X0
& empty_set != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l46_zfmisc_1) ).
fof(f6,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f7,axiom,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f8,conjecture,
! [X0,X1,X2] :
( empty_set = set_difference(X0,unordered_pair(X1,X2))
<=> ~ ( unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& singleton(X1) != X0
& empty_set != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2] :
( empty_set = set_difference(X0,unordered_pair(X1,X2))
<=> ~ ( unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& singleton(X1) != X0
& empty_set != X0 ) ),
inference(negated_conjecture,[],[f8]) ).
fof(f10,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f6]) ).
fof(f11,plain,
! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
<=> ( unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0 ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f12,plain,
? [X0,X1,X2] :
( empty_set = set_difference(X0,unordered_pair(X1,X2))
<~> ( unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0 ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( subset(X0,unordered_pair(X1,X2))
| ( unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& singleton(X1) != X0
& empty_set != X0 ) )
& ( unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( subset(X0,unordered_pair(X1,X2))
| ( unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& singleton(X1) != X0
& empty_set != X0 ) )
& ( unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f13]) ).
fof(f19,plain,
! [X0,X1] :
( ( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f20,plain,
? [X0,X1,X2] :
( ( ( unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& singleton(X1) != X0
& empty_set != X0 )
| empty_set != set_difference(X0,unordered_pair(X1,X2)) )
& ( unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0
| empty_set = set_difference(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f21,plain,
? [X0,X1,X2] :
( ( ( unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& singleton(X1) != X0
& empty_set != X0 )
| empty_set != set_difference(X0,unordered_pair(X1,X2)) )
& ( unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0
| empty_set = set_difference(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
( ? [X0,X1,X2] :
( ( ( unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& singleton(X1) != X0
& empty_set != X0 )
| empty_set != set_difference(X0,unordered_pair(X1,X2)) )
& ( unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0
| empty_set = set_difference(X0,unordered_pair(X1,X2)) ) )
=> ( ( ( sK2 != unordered_pair(sK3,sK4)
& sK2 != singleton(sK4)
& sK2 != singleton(sK3)
& empty_set != sK2 )
| empty_set != set_difference(sK2,unordered_pair(sK3,sK4)) )
& ( sK2 = unordered_pair(sK3,sK4)
| sK2 = singleton(sK4)
| sK2 = singleton(sK3)
| empty_set = sK2
| empty_set = set_difference(sK2,unordered_pair(sK3,sK4)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
( ( ( sK2 != unordered_pair(sK3,sK4)
& sK2 != singleton(sK4)
& sK2 != singleton(sK3)
& empty_set != sK2 )
| empty_set != set_difference(sK2,unordered_pair(sK3,sK4)) )
& ( sK2 = unordered_pair(sK3,sK4)
| sK2 = singleton(sK4)
| sK2 = singleton(sK3)
| empty_set = sK2
| empty_set = set_difference(sK2,unordered_pair(sK3,sK4)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f21,f22]) ).
fof(f26,plain,
! [X2,X0,X1] :
( unordered_pair(X1,X2) = X0
| singleton(X2) = X0
| singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X2,X0,X1] :
( subset(X0,unordered_pair(X1,X2))
| empty_set != X0 ),
inference(cnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X2,X0,X1] :
( subset(X0,unordered_pair(X1,X2))
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
! [X2,X0,X1] :
( subset(X0,unordered_pair(X1,X2))
| singleton(X2) != X0 ),
inference(cnf_transformation,[],[f14]) ).
fof(f33,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f34,plain,
! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f35,plain,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f36,plain,
( sK2 = unordered_pair(sK3,sK4)
| sK2 = singleton(sK4)
| sK2 = singleton(sK3)
| empty_set = sK2
| empty_set = set_difference(sK2,unordered_pair(sK3,sK4)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f37,plain,
( empty_set != sK2
| empty_set != set_difference(sK2,unordered_pair(sK3,sK4)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f38,plain,
( sK2 != singleton(sK3)
| empty_set != set_difference(sK2,unordered_pair(sK3,sK4)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f39,plain,
( sK2 != singleton(sK4)
| empty_set != set_difference(sK2,unordered_pair(sK3,sK4)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
( sK2 != unordered_pair(sK3,sK4)
| empty_set != set_difference(sK2,unordered_pair(sK3,sK4)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
! [X2,X1] : subset(singleton(X2),unordered_pair(X1,X2)),
inference(equality_resolution,[],[f29]) ).
fof(f43,plain,
! [X2,X1] : subset(singleton(X1),unordered_pair(X1,X2)),
inference(equality_resolution,[],[f28]) ).
fof(f44,plain,
! [X2,X1] : subset(empty_set,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f27]) ).
cnf(c_52,plain,
subset(singleton(X0),unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f42]) ).
cnf(c_53,plain,
subset(singleton(X0),unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f43]) ).
cnf(c_54,plain,
subset(empty_set,unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f44]) ).
cnf(c_55,plain,
( ~ subset(X0,unordered_pair(X1,X2))
| unordered_pair(X1,X2) = X0
| singleton(X1) = X0
| singleton(X2) = X0
| X0 = empty_set ),
inference(cnf_transformation,[],[f26]) ).
cnf(c_58,plain,
subset(X0,X0),
inference(cnf_transformation,[],[f33]) ).
cnf(c_59,plain,
( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f35]) ).
cnf(c_60,plain,
( set_difference(X0,X1) != empty_set
| subset(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
cnf(c_61,negated_conjecture,
( set_difference(sK2,unordered_pair(sK3,sK4)) != empty_set
| unordered_pair(sK3,sK4) != sK2 ),
inference(cnf_transformation,[],[f40]) ).
cnf(c_62,negated_conjecture,
( set_difference(sK2,unordered_pair(sK3,sK4)) != empty_set
| singleton(sK4) != sK2 ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_63,negated_conjecture,
( set_difference(sK2,unordered_pair(sK3,sK4)) != empty_set
| singleton(sK3) != sK2 ),
inference(cnf_transformation,[],[f38]) ).
cnf(c_64,negated_conjecture,
( set_difference(sK2,unordered_pair(sK3,sK4)) != empty_set
| empty_set != sK2 ),
inference(cnf_transformation,[],[f37]) ).
cnf(c_65,negated_conjecture,
( set_difference(sK2,unordered_pair(sK3,sK4)) = empty_set
| unordered_pair(sK3,sK4) = sK2
| singleton(sK3) = sK2
| singleton(sK4) = sK2
| empty_set = sK2 ),
inference(cnf_transformation,[],[f36]) ).
cnf(c_988,plain,
set_difference(singleton(X0),unordered_pair(X1,X0)) = empty_set,
inference(superposition,[status(thm)],[c_52,c_59]) ).
cnf(c_989,plain,
set_difference(singleton(X0),unordered_pair(X0,X1)) = empty_set,
inference(superposition,[status(thm)],[c_53,c_59]) ).
cnf(c_990,plain,
set_difference(empty_set,unordered_pair(X0,X1)) = empty_set,
inference(superposition,[status(thm)],[c_54,c_59]) ).
cnf(c_991,plain,
set_difference(X0,X0) = empty_set,
inference(superposition,[status(thm)],[c_58,c_59]) ).
cnf(c_1002,plain,
( unordered_pair(sK3,sK4) = sK2
| singleton(sK3) = sK2
| singleton(sK4) = sK2
| empty_set = sK2
| subset(sK2,unordered_pair(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_65,c_60]) ).
cnf(c_1037,plain,
( unordered_pair(sK3,sK4) = sK2
| singleton(sK3) = sK2
| singleton(sK4) = sK2
| empty_set = sK2 ),
inference(superposition,[status(thm)],[c_1002,c_55]) ).
cnf(c_1064,plain,
( unordered_pair(sK3,sK4) != sK2
| set_difference(sK2,sK2) != empty_set
| singleton(sK3) = sK2
| singleton(sK4) = sK2
| empty_set = sK2 ),
inference(superposition,[status(thm)],[c_1037,c_61]) ).
cnf(c_1092,plain,
( unordered_pair(sK3,sK4) != sK2
| singleton(sK3) = sK2
| singleton(sK4) = sK2
| empty_set = sK2 ),
inference(forward_subsumption_resolution,[status(thm)],[c_1064,c_991]) ).
cnf(c_1097,plain,
( singleton(sK3) = sK2
| singleton(sK4) = sK2
| empty_set = sK2 ),
inference(backward_subsumption_resolution,[status(thm)],[c_1037,c_1092]) ).
cnf(c_1112,plain,
( set_difference(sK2,unordered_pair(X0,sK4)) = empty_set
| singleton(sK3) = sK2
| empty_set = sK2 ),
inference(superposition,[status(thm)],[c_1097,c_988]) ).
cnf(c_1189,plain,
( singleton(sK4) != sK2
| singleton(sK3) = sK2
| empty_set = sK2 ),
inference(superposition,[status(thm)],[c_1112,c_62]) ).
cnf(c_1197,plain,
( singleton(sK3) = sK2
| empty_set = sK2 ),
inference(global_subsumption_just,[status(thm)],[c_1189,c_1097,c_1189]) ).
cnf(c_1203,plain,
( set_difference(sK2,unordered_pair(sK3,X0)) = empty_set
| empty_set = sK2 ),
inference(superposition,[status(thm)],[c_1197,c_989]) ).
cnf(c_1245,plain,
( singleton(sK3) != sK2
| empty_set = sK2 ),
inference(superposition,[status(thm)],[c_1203,c_63]) ).
cnf(c_1254,plain,
empty_set = sK2,
inference(global_subsumption_just,[status(thm)],[c_1245,c_1197,c_1245]) ).
cnf(c_1263,plain,
set_difference(sK2,unordered_pair(X0,X1)) = sK2,
inference(demodulation,[status(thm)],[c_990,c_1254]) ).
cnf(c_1271,plain,
( set_difference(sK2,unordered_pair(sK3,sK4)) != sK2
| sK2 != sK2 ),
inference(demodulation,[status(thm)],[c_64,c_1254]) ).
cnf(c_1276,plain,
set_difference(sK2,unordered_pair(sK3,sK4)) != sK2,
inference(equality_resolution_simp,[status(thm)],[c_1271]) ).
cnf(c_1277,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1276,c_1263]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET931+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 13:59:32 EDT 2023
% 0.12/0.34 % 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
% 2.09/1.18 % SZS status Started for theBenchmark.p
% 2.09/1.18 % SZS status Theorem for theBenchmark.p
% 2.09/1.18
% 2.09/1.18 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.09/1.18
% 2.09/1.18 ------ iProver source info
% 2.09/1.18
% 2.09/1.18 git: date: 2023-05-31 18:12:56 +0000
% 2.09/1.18 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.09/1.18 git: non_committed_changes: false
% 2.09/1.18 git: last_make_outside_of_git: false
% 2.09/1.18
% 2.09/1.18 ------ Parsing...
% 2.09/1.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.09/1.18
% 2.09/1.18 ------ 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
% 2.09/1.18
% 2.09/1.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.09/1.18
% 2.09/1.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.09/1.18 ------ Proving...
% 2.09/1.18 ------ Problem Properties
% 2.09/1.18
% 2.09/1.18
% 2.09/1.18 clauses 16
% 2.09/1.18 conjectures 5
% 2.09/1.18 EPR 4
% 2.09/1.18 Horn 14
% 2.09/1.18 unary 8
% 2.09/1.18 binary 6
% 2.09/1.18 lits 30
% 2.09/1.18 lits eq 20
% 2.09/1.18 fd_pure 0
% 2.09/1.18 fd_pseudo 0
% 2.09/1.18 fd_cond 0
% 2.09/1.18 fd_pseudo_cond 1
% 2.09/1.18 AC symbols 0
% 2.09/1.18
% 2.09/1.18 ------ Schedule dynamic 5 is on
% 2.09/1.18
% 2.09/1.18 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.09/1.18
% 2.09/1.18
% 2.09/1.18 ------
% 2.09/1.18 Current options:
% 2.09/1.18 ------
% 2.09/1.18
% 2.09/1.18
% 2.09/1.18
% 2.09/1.18
% 2.09/1.18 ------ Proving...
% 2.09/1.18
% 2.09/1.18
% 2.09/1.18 % SZS status Theorem for theBenchmark.p
% 2.09/1.18
% 2.09/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.09/1.19
% 2.09/1.19
%------------------------------------------------------------------------------