TSTP Solution File: SET597+3 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET597+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n025.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 15:08:30 EDT 2023
% Result : Theorem 0.50s 1.17s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 71 ( 18 unt; 0 def)
% Number of atoms : 257 ( 57 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 306 ( 120 ~; 126 |; 50 &)
% ( 3 <=>; 5 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 96 ( 2 sgn; 47 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : subset(X0,union(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_of_union) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset(union(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_subset) ).
fof(f5,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f6,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f7,axiom,
! [X0] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(f9,conjecture,
! [X0,X1,X2] :
( union(X1,X2) = X0
<=> ( ! [X3] :
( ( subset(X2,X3)
& subset(X1,X3) )
=> subset(X0,X3) )
& subset(X2,X0)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th56) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
( union(X1,X2) = X0
<=> ( ! [X3] :
( ( subset(X2,X3)
& subset(X1,X3) )
=> subset(X0,X3) )
& subset(X2,X0)
& subset(X1,X0) ) ),
inference(negated_conjecture,[],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( subset(union(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0,X1,X2] :
( subset(union(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(flattening,[],[f11]) ).
fof(f14,plain,
? [X0,X1,X2] :
( union(X1,X2) = X0
<~> ( ! [X3] :
( subset(X0,X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) )
& subset(X2,X0)
& subset(X1,X0) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f15,plain,
? [X0,X1,X2] :
( union(X1,X2) = X0
<~> ( ! [X3] :
( subset(X0,X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) )
& subset(X2,X0)
& subset(X1,X0) ) ),
inference(flattening,[],[f14]) ).
fof(f22,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f23,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f22]) ).
fof(f28,plain,
? [X0,X1,X2] :
( ( ? [X3] :
( ~ subset(X0,X3)
& subset(X2,X3)
& subset(X1,X3) )
| ~ subset(X2,X0)
| ~ subset(X1,X0)
| union(X1,X2) != X0 )
& ( ( ! [X3] :
( subset(X0,X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) )
& subset(X2,X0)
& subset(X1,X0) )
| union(X1,X2) = X0 ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f29,plain,
? [X0,X1,X2] :
( ( ? [X3] :
( ~ subset(X0,X3)
& subset(X2,X3)
& subset(X1,X3) )
| ~ subset(X2,X0)
| ~ subset(X1,X0)
| union(X1,X2) != X0 )
& ( ( ! [X3] :
( subset(X0,X3)
| ~ subset(X2,X3)
| ~ subset(X1,X3) )
& subset(X2,X0)
& subset(X1,X0) )
| union(X1,X2) = X0 ) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
? [X0,X1,X2] :
( ( ? [X3] :
( ~ subset(X0,X3)
& subset(X2,X3)
& subset(X1,X3) )
| ~ subset(X2,X0)
| ~ subset(X1,X0)
| union(X1,X2) != X0 )
& ( ( ! [X4] :
( subset(X0,X4)
| ~ subset(X2,X4)
| ~ subset(X1,X4) )
& subset(X2,X0)
& subset(X1,X0) )
| union(X1,X2) = X0 ) ),
inference(rectify,[],[f29]) ).
fof(f31,plain,
( ? [X0,X1,X2] :
( ( ? [X3] :
( ~ subset(X0,X3)
& subset(X2,X3)
& subset(X1,X3) )
| ~ subset(X2,X0)
| ~ subset(X1,X0)
| union(X1,X2) != X0 )
& ( ( ! [X4] :
( subset(X0,X4)
| ~ subset(X2,X4)
| ~ subset(X1,X4) )
& subset(X2,X0)
& subset(X1,X0) )
| union(X1,X2) = X0 ) )
=> ( ( ? [X3] :
( ~ subset(sK2,X3)
& subset(sK4,X3)
& subset(sK3,X3) )
| ~ subset(sK4,sK2)
| ~ subset(sK3,sK2)
| sK2 != union(sK3,sK4) )
& ( ( ! [X4] :
( subset(sK2,X4)
| ~ subset(sK4,X4)
| ~ subset(sK3,X4) )
& subset(sK4,sK2)
& subset(sK3,sK2) )
| sK2 = union(sK3,sK4) ) ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
( ? [X3] :
( ~ subset(sK2,X3)
& subset(sK4,X3)
& subset(sK3,X3) )
=> ( ~ subset(sK2,sK5)
& subset(sK4,sK5)
& subset(sK3,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
( ( ( ~ subset(sK2,sK5)
& subset(sK4,sK5)
& subset(sK3,sK5) )
| ~ subset(sK4,sK2)
| ~ subset(sK3,sK2)
| sK2 != union(sK3,sK4) )
& ( ( ! [X4] :
( subset(sK2,X4)
| ~ subset(sK4,X4)
| ~ subset(sK3,X4) )
& subset(sK4,sK2)
& subset(sK3,sK2) )
| sK2 = union(sK3,sK4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f30,f32,f31]) ).
fof(f34,plain,
! [X0,X1] : subset(X0,union(X0,X1)),
inference(cnf_transformation,[],[f1]) ).
fof(f35,plain,
! [X2,X0,X1] :
( subset(union(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f44,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f46,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f7]) ).
fof(f51,plain,
( subset(sK3,sK2)
| sK2 = union(sK3,sK4) ),
inference(cnf_transformation,[],[f33]) ).
fof(f52,plain,
( subset(sK4,sK2)
| sK2 = union(sK3,sK4) ),
inference(cnf_transformation,[],[f33]) ).
fof(f53,plain,
! [X4] :
( subset(sK2,X4)
| ~ subset(sK4,X4)
| ~ subset(sK3,X4)
| sK2 = union(sK3,sK4) ),
inference(cnf_transformation,[],[f33]) ).
fof(f54,plain,
( subset(sK3,sK5)
| ~ subset(sK4,sK2)
| ~ subset(sK3,sK2)
| sK2 != union(sK3,sK4) ),
inference(cnf_transformation,[],[f33]) ).
fof(f55,plain,
( subset(sK4,sK5)
| ~ subset(sK4,sK2)
| ~ subset(sK3,sK2)
| sK2 != union(sK3,sK4) ),
inference(cnf_transformation,[],[f33]) ).
fof(f56,plain,
( ~ subset(sK2,sK5)
| ~ subset(sK4,sK2)
| ~ subset(sK3,sK2)
| sK2 != union(sK3,sK4) ),
inference(cnf_transformation,[],[f33]) ).
cnf(c_49,plain,
subset(X0,union(X0,X1)),
inference(cnf_transformation,[],[f34]) ).
cnf(c_50,plain,
( ~ subset(X0,X1)
| ~ subset(X2,X1)
| subset(union(X0,X2),X1) ),
inference(cnf_transformation,[],[f35]) ).
cnf(c_57,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f44]) ).
cnf(c_60,plain,
union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f45]) ).
cnf(c_61,plain,
subset(X0,X0),
inference(cnf_transformation,[],[f46]) ).
cnf(c_64,negated_conjecture,
( union(sK3,sK4) != sK2
| ~ subset(sK2,sK5)
| ~ subset(sK4,sK2)
| ~ subset(sK3,sK2) ),
inference(cnf_transformation,[],[f56]) ).
cnf(c_65,negated_conjecture,
( union(sK3,sK4) != sK2
| ~ subset(sK4,sK2)
| ~ subset(sK3,sK2)
| subset(sK4,sK5) ),
inference(cnf_transformation,[],[f55]) ).
cnf(c_66,negated_conjecture,
( union(sK3,sK4) != sK2
| ~ subset(sK4,sK2)
| ~ subset(sK3,sK2)
| subset(sK3,sK5) ),
inference(cnf_transformation,[],[f54]) ).
cnf(c_67,negated_conjecture,
( ~ subset(sK4,X0)
| ~ subset(sK3,X0)
| union(sK3,sK4) = sK2
| subset(sK2,X0) ),
inference(cnf_transformation,[],[f53]) ).
cnf(c_68,negated_conjecture,
( union(sK3,sK4) = sK2
| subset(sK4,sK2) ),
inference(cnf_transformation,[],[f52]) ).
cnf(c_69,negated_conjecture,
( union(sK3,sK4) = sK2
| subset(sK3,sK2) ),
inference(cnf_transformation,[],[f51]) ).
cnf(c_179,plain,
( union(sK4,sK3) = sK2
| subset(sK3,sK2) ),
inference(demodulation,[status(thm)],[c_69,c_60]) ).
cnf(c_184,plain,
( union(sK4,sK3) = sK2
| subset(sK4,sK2) ),
inference(demodulation,[status(thm)],[c_68,c_60]) ).
cnf(c_237,plain,
( ~ subset(sK4,X0)
| ~ subset(sK3,X0)
| union(sK4,sK3) = sK2
| subset(sK2,X0) ),
inference(demodulation,[status(thm)],[c_67,c_60]) ).
cnf(c_246,plain,
( union(sK4,sK3) != sK2
| ~ subset(sK4,sK2)
| ~ subset(sK3,sK2)
| subset(sK3,sK5) ),
inference(demodulation,[status(thm)],[c_66,c_60]) ).
cnf(c_255,plain,
( union(sK4,sK3) != sK2
| ~ subset(sK4,sK2)
| ~ subset(sK3,sK2)
| subset(sK4,sK5) ),
inference(demodulation,[status(thm)],[c_65,c_60]) ).
cnf(c_264,plain,
( union(sK4,sK3) != sK2
| ~ subset(sK2,sK5)
| ~ subset(sK4,sK2)
| ~ subset(sK3,sK2) ),
inference(demodulation,[status(thm)],[c_64,c_60]) ).
cnf(c_802,plain,
subset(X0,union(X1,X0)),
inference(superposition,[status(thm)],[c_60,c_49]) ).
cnf(c_812,plain,
( ~ subset(sK4,union(X0,sK3))
| union(sK4,sK3) = sK2
| subset(sK2,union(X0,sK3)) ),
inference(superposition,[status(thm)],[c_802,c_237]) ).
cnf(c_894,plain,
( union(sK4,sK3) = sK2
| subset(sK2,union(sK4,sK3)) ),
inference(superposition,[status(thm)],[c_49,c_812]) ).
cnf(c_963,plain,
( ~ subset(union(X0,X1),X1)
| union(X0,X1) = X1 ),
inference(superposition,[status(thm)],[c_802,c_57]) ).
cnf(c_964,plain,
( ~ subset(union(sK4,sK3),sK2)
| union(sK4,sK3) = sK2 ),
inference(superposition,[status(thm)],[c_894,c_57]) ).
cnf(c_986,plain,
( ~ subset(X0,X1)
| ~ subset(X2,X1)
| subset(union(X2,X0),X1) ),
inference(superposition,[status(thm)],[c_60,c_50]) ).
cnf(c_1207,plain,
( ~ subset(X0,X0)
| ~ subset(X1,X0)
| union(X1,X0) = X0 ),
inference(superposition,[status(thm)],[c_986,c_963]) ).
cnf(c_1208,plain,
( ~ subset(sK4,sK2)
| ~ subset(sK3,sK2)
| union(sK4,sK3) = sK2 ),
inference(superposition,[status(thm)],[c_986,c_964]) ).
cnf(c_1212,plain,
( ~ subset(X0,X1)
| union(X0,X1) = X1 ),
inference(forward_subsumption_resolution,[status(thm)],[c_1207,c_61]) ).
cnf(c_1332,plain,
( union(sK4,sK2) = sK2
| union(sK4,sK3) = sK2 ),
inference(superposition,[status(thm)],[c_184,c_1212]) ).
cnf(c_1360,plain,
union(sK4,sK3) = sK2,
inference(global_subsumption_just,[status(thm)],[c_179,c_179,c_184,c_1208]) ).
cnf(c_1439,plain,
subset(sK4,sK2),
inference(superposition,[status(thm)],[c_1360,c_49]) ).
cnf(c_1492,plain,
union(sK4,sK3) = sK2,
inference(global_subsumption_just,[status(thm)],[c_1332,c_1360]) ).
cnf(c_1505,plain,
( sK2 != sK2
| ~ subset(sK4,sK2)
| ~ subset(sK3,sK2)
| subset(sK4,sK5) ),
inference(demodulation,[status(thm)],[c_255,c_1492]) ).
cnf(c_1506,plain,
( sK2 != sK2
| ~ subset(sK4,sK2)
| ~ subset(sK3,sK2)
| subset(sK3,sK5) ),
inference(demodulation,[status(thm)],[c_246,c_1492]) ).
cnf(c_1508,plain,
( ~ subset(sK4,sK2)
| ~ subset(sK3,sK2)
| subset(sK3,sK5) ),
inference(equality_resolution_simp,[status(thm)],[c_1506]) ).
cnf(c_1512,plain,
( ~ subset(sK4,sK2)
| ~ subset(sK3,sK2)
| subset(sK4,sK5) ),
inference(equality_resolution_simp,[status(thm)],[c_1505]) ).
cnf(c_1531,plain,
subset(sK3,sK2),
inference(superposition,[status(thm)],[c_1492,c_802]) ).
cnf(c_1532,plain,
( ~ subset(sK4,X0)
| ~ subset(sK3,X0)
| subset(sK2,X0) ),
inference(superposition,[status(thm)],[c_1492,c_986]) ).
cnf(c_1788,plain,
subset(sK3,sK5),
inference(global_subsumption_just,[status(thm)],[c_1508,c_179,c_184,c_246,c_1208,c_1439,c_1531]) ).
cnf(c_2023,plain,
subset(sK4,sK5),
inference(global_subsumption_just,[status(thm)],[c_1512,c_255,c_1360,c_1439,c_1531]) ).
cnf(c_2049,plain,
( ~ subset(sK3,sK5)
| subset(sK2,sK5) ),
inference(superposition,[status(thm)],[c_2023,c_1532]) ).
cnf(c_2053,plain,
subset(sK2,sK5),
inference(forward_subsumption_resolution,[status(thm)],[c_2049,c_1788]) ).
cnf(c_2060,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2053,c_1531,c_1439,c_1360,c_264]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET597+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 13:06:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.50/1.17 % SZS status Started for theBenchmark.p
% 0.50/1.17 % SZS status Theorem for theBenchmark.p
% 0.50/1.17
% 0.50/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.50/1.17
% 0.50/1.17 ------ iProver source info
% 0.50/1.17
% 0.50/1.17 git: date: 2023-05-31 18:12:56 +0000
% 0.50/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.50/1.17 git: non_committed_changes: false
% 0.50/1.17 git: last_make_outside_of_git: false
% 0.50/1.17
% 0.50/1.17 ------ Parsing...
% 0.50/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.50/1.17
% 0.50/1.17 ------ Preprocessing... sup_sim: 6 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
% 0.50/1.17
% 0.50/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.50/1.17
% 0.50/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.50/1.17 ------ Proving...
% 0.50/1.17 ------ Problem Properties
% 0.50/1.17
% 0.50/1.17
% 0.50/1.17 clauses 19
% 0.50/1.17 conjectures 0
% 0.50/1.17 EPR 3
% 0.50/1.17 Horn 13
% 0.50/1.17 unary 3
% 0.50/1.17 binary 6
% 0.50/1.17 lits 49
% 0.50/1.17 lits eq 10
% 0.50/1.17 fd_pure 0
% 0.50/1.17 fd_pseudo 0
% 0.50/1.17 fd_cond 0
% 0.50/1.17 fd_pseudo_cond 3
% 0.50/1.17 AC symbols 0
% 0.50/1.17
% 0.50/1.17 ------ Schedule dynamic 5 is on
% 0.50/1.17
% 0.50/1.17 ------ no conjectures: strip conj schedule
% 0.50/1.17
% 0.50/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.50/1.17
% 0.50/1.17
% 0.50/1.17 ------
% 0.50/1.17 Current options:
% 0.50/1.17 ------
% 0.50/1.17
% 0.50/1.17
% 0.50/1.17
% 0.50/1.17
% 0.50/1.17 ------ Proving...
% 0.50/1.17
% 0.50/1.17
% 0.50/1.17 % SZS status Theorem for theBenchmark.p
% 0.50/1.17
% 0.50/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.50/1.17
% 0.50/1.18
%------------------------------------------------------------------------------