TSTP Solution File: SET994+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET994+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n011.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 03:02:12 EDT 2024
% Result : Theorem 4.03s 1.17s
% Output : CNFRefutation 4.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of formulae : 92 ( 36 unt; 0 def)
% Number of atoms : 266 ( 98 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 293 ( 119 ~; 111 |; 45 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 116 ( 4 sgn 68 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f8,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f9,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f10,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f20,axiom,
! [X0] :
? [X1] :
( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = n0 )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_funct_1__e4_14__funct_1) ).
fof(f21,axiom,
! [X0] :
? [X1] :
( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = n1 )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_funct_1__e7_14__funct_1) ).
fof(f22,axiom,
empty(n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',spc0_boole) ).
fof(f23,axiom,
~ empty(n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',spc1_boole) ).
fof(f24,conjecture,
! [X0] :
( ! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( ( relation_dom(X2) = X0
& relation_dom(X1) = X0 )
=> X1 = X2 ) ) )
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_funct_1) ).
fof(f25,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( ( relation_dom(X2) = X0
& relation_dom(X1) = X0 )
=> X1 = X2 ) ) )
=> empty_set = X0 ),
inference(negated_conjecture,[],[f24]) ).
fof(f27,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f31,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f41,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f42,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f45,plain,
! [X0] :
? [X1] :
( ! [X2] :
( apply(X1,X2) = n0
| ~ in(X2,X0) )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f46,plain,
! [X0] :
? [X1] :
( ! [X2] :
( apply(X1,X2) = n1
| ~ in(X2,X0) )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f47,plain,
? [X0] :
( empty_set != X0
& ! [X1] :
( ! [X2] :
( X1 = X2
| relation_dom(X2) != X0
| relation_dom(X1) != X0
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f48,plain,
? [X0] :
( empty_set != X0
& ! [X1] :
( ! [X2] :
( X1 = X2
| relation_dom(X2) != X0
| relation_dom(X1) != X0
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ) ),
inference(flattening,[],[f47]) ).
fof(f50,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f51,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f50]) ).
fof(f56,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f59,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK0(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
! [X0] : element(sK0(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f4,f59]) ).
fof(f77,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( apply(X1,X2) = n0
| ~ in(X2,X0) )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) )
=> ( ! [X2] :
( n0 = apply(sK9(X0),X2)
| ~ in(X2,X0) )
& relation_dom(sK9(X0)) = X0
& function(sK9(X0))
& relation(sK9(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
! [X0] :
( ! [X2] :
( n0 = apply(sK9(X0),X2)
| ~ in(X2,X0) )
& relation_dom(sK9(X0)) = X0
& function(sK9(X0))
& relation(sK9(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f45,f77]) ).
fof(f79,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( apply(X1,X2) = n1
| ~ in(X2,X0) )
& relation_dom(X1) = X0
& function(X1)
& relation(X1) )
=> ( ! [X2] :
( n1 = apply(sK10(X0),X2)
| ~ in(X2,X0) )
& relation_dom(sK10(X0)) = X0
& function(sK10(X0))
& relation(sK10(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
! [X0] :
( ! [X2] :
( n1 = apply(sK10(X0),X2)
| ~ in(X2,X0) )
& relation_dom(sK10(X0)) = X0
& function(sK10(X0))
& relation(sK10(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f46,f79]) ).
fof(f81,plain,
( ? [X0] :
( empty_set != X0
& ! [X1] :
( ! [X2] :
( X1 = X2
| relation_dom(X2) != X0
| relation_dom(X1) != X0
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ) )
=> ( empty_set != sK11
& ! [X1] :
( ! [X2] :
( X1 = X2
| relation_dom(X2) != sK11
| relation_dom(X1) != sK11
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
( empty_set != sK11
& ! [X1] :
( ! [X2] :
( X1 = X2
| relation_dom(X2) != sK11
| relation_dom(X1) != sK11
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f48,f81]) ).
fof(f86,plain,
! [X0] : element(sK0(X0),X0),
inference(cnf_transformation,[],[f60]) ).
fof(f91,plain,
empty(empty_set),
inference(cnf_transformation,[],[f8]) ).
fof(f93,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f94,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f110,plain,
! [X0] : relation(sK9(X0)),
inference(cnf_transformation,[],[f78]) ).
fof(f111,plain,
! [X0] : function(sK9(X0)),
inference(cnf_transformation,[],[f78]) ).
fof(f112,plain,
! [X0] : relation_dom(sK9(X0)) = X0,
inference(cnf_transformation,[],[f78]) ).
fof(f113,plain,
! [X2,X0] :
( n0 = apply(sK9(X0),X2)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f114,plain,
! [X0] : relation(sK10(X0)),
inference(cnf_transformation,[],[f80]) ).
fof(f115,plain,
! [X0] : function(sK10(X0)),
inference(cnf_transformation,[],[f80]) ).
fof(f116,plain,
! [X0] : relation_dom(sK10(X0)) = X0,
inference(cnf_transformation,[],[f80]) ).
fof(f117,plain,
! [X2,X0] :
( n1 = apply(sK10(X0),X2)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f118,plain,
empty(n0),
inference(cnf_transformation,[],[f22]) ).
fof(f119,plain,
~ empty(n1),
inference(cnf_transformation,[],[f23]) ).
fof(f120,plain,
! [X2,X1] :
( X1 = X2
| relation_dom(X2) != sK11
| relation_dom(X1) != sK11
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f121,plain,
empty_set != sK11,
inference(cnf_transformation,[],[f82]) ).
fof(f123,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f127,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f56]) ).
cnf(c_52,plain,
element(sK0(X0),X0),
inference(cnf_transformation,[],[f86]) ).
cnf(c_58,plain,
empty(empty_set),
inference(cnf_transformation,[],[f91]) ).
cnf(c_59,plain,
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f93]) ).
cnf(c_61,plain,
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f94]) ).
cnf(c_76,plain,
( ~ in(X0,X1)
| apply(sK9(X1),X0) = n0 ),
inference(cnf_transformation,[],[f113]) ).
cnf(c_77,plain,
relation_dom(sK9(X0)) = X0,
inference(cnf_transformation,[],[f112]) ).
cnf(c_78,plain,
function(sK9(X0)),
inference(cnf_transformation,[],[f111]) ).
cnf(c_79,plain,
relation(sK9(X0)),
inference(cnf_transformation,[],[f110]) ).
cnf(c_80,plain,
( ~ in(X0,X1)
| apply(sK10(X1),X0) = n1 ),
inference(cnf_transformation,[],[f117]) ).
cnf(c_81,plain,
relation_dom(sK10(X0)) = X0,
inference(cnf_transformation,[],[f116]) ).
cnf(c_82,plain,
function(sK10(X0)),
inference(cnf_transformation,[],[f115]) ).
cnf(c_83,plain,
relation(sK10(X0)),
inference(cnf_transformation,[],[f114]) ).
cnf(c_84,plain,
empty(n0),
inference(cnf_transformation,[],[f118]) ).
cnf(c_85,plain,
~ empty(n1),
inference(cnf_transformation,[],[f119]) ).
cnf(c_86,negated_conjecture,
empty_set != sK11,
inference(cnf_transformation,[],[f121]) ).
cnf(c_87,negated_conjecture,
( relation_dom(X0) != sK11
| relation_dom(X1) != sK11
| ~ function(X0)
| ~ function(X1)
| ~ relation(X0)
| ~ relation(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f120]) ).
cnf(c_89,plain,
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f123]) ).
cnf(c_93,plain,
( ~ empty(X0)
| X0 = empty_set ),
inference(cnf_transformation,[],[f127]) ).
cnf(c_613,negated_conjecture,
( relation_dom(X0) != sK11
| relation_dom(X1) != sK11
| ~ function(X0)
| ~ function(X1)
| ~ relation(X0)
| ~ relation(X1)
| X0 = X1 ),
inference(demodulation,[status(thm)],[c_87]) ).
cnf(c_614,negated_conjecture,
empty_set != sK11,
inference(demodulation,[status(thm)],[c_86]) ).
cnf(c_1084,plain,
( relation_dom(X0) != sK11
| X1 != sK11
| ~ function(sK10(X1))
| ~ relation(sK10(X1))
| ~ function(X0)
| ~ relation(X0)
| sK10(X1) = X0 ),
inference(superposition,[status(thm)],[c_81,c_613]) ).
cnf(c_1089,plain,
( relation_dom(X0) != sK11
| X1 != sK11
| ~ function(X0)
| ~ relation(X0)
| sK10(X1) = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[c_1084,c_83,c_82]) ).
cnf(c_1115,plain,
( X0 != sK11
| X1 != sK11
| ~ function(sK9(X0))
| ~ relation(sK9(X0))
| sK9(X0) = sK10(X1) ),
inference(superposition,[status(thm)],[c_77,c_1089]) ).
cnf(c_1121,plain,
( X0 != sK11
| X1 != sK11
| sK9(X0) = sK10(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1115,c_79,c_78]) ).
cnf(c_1140,plain,
( X0 != sK11
| sK10(X0) = sK9(sK11) ),
inference(equality_resolution,[status(thm)],[c_1121]) ).
cnf(c_1152,plain,
sK9(sK11) = sK10(sK11),
inference(equality_resolution,[status(thm)],[c_1140]) ).
cnf(c_1249,plain,
( ~ empty(X0)
| relation_dom(X0) = empty_set ),
inference(superposition,[status(thm)],[c_61,c_93]) ).
cnf(c_1253,plain,
empty_set = n0,
inference(superposition,[status(thm)],[c_84,c_93]) ).
cnf(c_1266,plain,
( ~ in(X0,X1)
| apply(sK9(X1),X0) = empty_set ),
inference(demodulation,[status(thm)],[c_76,c_1253]) ).
cnf(c_1312,plain,
( ~ relation(sK10(X0))
| ~ empty(X0)
| empty(sK10(X0)) ),
inference(superposition,[status(thm)],[c_81,c_59]) ).
cnf(c_1314,plain,
( ~ empty(X0)
| empty(sK10(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1312,c_83]) ).
cnf(c_1326,plain,
( ~ empty(sK11)
| empty(sK9(sK11)) ),
inference(superposition,[status(thm)],[c_1152,c_1314]) ).
cnf(c_1350,plain,
( in(sK0(X0),X0)
| empty(X0) ),
inference(superposition,[status(thm)],[c_52,c_89]) ).
cnf(c_1417,plain,
( ~ empty(sK11)
| relation_dom(sK9(sK11)) = empty_set ),
inference(superposition,[status(thm)],[c_1326,c_1249]) ).
cnf(c_1439,plain,
( ~ empty(sK11)
| empty_set = sK11 ),
inference(demodulation,[status(thm)],[c_1417,c_77]) ).
cnf(c_1440,plain,
~ empty(sK11),
inference(forward_subsumption_resolution,[status(thm)],[c_1439,c_614]) ).
cnf(c_1464,plain,
( apply(sK10(X0),sK0(X0)) = n1
| empty(X0) ),
inference(superposition,[status(thm)],[c_1350,c_80]) ).
cnf(c_1465,plain,
( apply(sK9(X0),sK0(X0)) = empty_set
| empty(X0) ),
inference(superposition,[status(thm)],[c_1350,c_1266]) ).
cnf(c_1712,plain,
apply(sK10(sK11),sK0(sK11)) = n1,
inference(superposition,[status(thm)],[c_1464,c_1440]) ).
cnf(c_1713,plain,
apply(sK9(sK11),sK0(sK11)) = n1,
inference(light_normalisation,[status(thm)],[c_1712,c_1152]) ).
cnf(c_2163,plain,
apply(sK9(sK11),sK0(sK11)) = empty_set,
inference(superposition,[status(thm)],[c_1465,c_1440]) ).
cnf(c_2221,plain,
empty_set = n1,
inference(demodulation,[status(thm)],[c_1713,c_2163]) ).
cnf(c_2230,plain,
~ empty(empty_set),
inference(demodulation,[status(thm)],[c_85,c_2221]) ).
cnf(c_2231,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2230,c_58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET994+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n011.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 : Thu May 2 20:22:48 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 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
% 4.03/1.17 % SZS status Started for theBenchmark.p
% 4.03/1.17 % SZS status Theorem for theBenchmark.p
% 4.03/1.17
% 4.03/1.17 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.03/1.17
% 4.03/1.17 ------ iProver source info
% 4.03/1.17
% 4.03/1.17 git: date: 2024-05-02 19:28:25 +0000
% 4.03/1.17 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.03/1.17 git: non_committed_changes: false
% 4.03/1.17
% 4.03/1.17 ------ Parsing...
% 4.03/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.03/1.17
% 4.03/1.17 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 4.03/1.17
% 4.03/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.03/1.17
% 4.03/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.03/1.17 ------ Proving...
% 4.03/1.17 ------ Problem Properties
% 4.03/1.17
% 4.03/1.17
% 4.03/1.17 clauses 43
% 4.03/1.17 conjectures 2
% 4.03/1.17 EPR 22
% 4.03/1.17 Horn 41
% 4.03/1.17 unary 25
% 4.03/1.17 binary 12
% 4.03/1.17 lits 71
% 4.03/1.17 lits eq 10
% 4.03/1.17 fd_pure 0
% 4.03/1.17 fd_pseudo 0
% 4.03/1.17 fd_cond 1
% 4.03/1.17 fd_pseudo_cond 2
% 4.03/1.17 AC symbols 0
% 4.03/1.17
% 4.03/1.17 ------ Schedule dynamic 5 is on
% 4.03/1.17
% 4.03/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
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% 4.03/1.17 ------
% 4.03/1.17 Current options:
% 4.03/1.17 ------
% 4.03/1.17
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% 4.03/1.17 ------ Proving...
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% 4.03/1.17 % SZS status Theorem for theBenchmark.p
% 4.03/1.17
% 4.03/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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% 4.03/1.18
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