TSTP Solution File: SET961+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET961+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n014.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 15:10:50 EDT 2023
% Result : Theorem 2.39s 1.17s
% Output : CNFRefutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 76 ( 21 unt; 0 def)
% Number of atoms : 189 ( 68 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 193 ( 80 ~; 76 |; 27 &)
% ( 3 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 137 ( 14 sgn; 76 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f4,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f10,conjecture,
! [X0,X1] :
( cartesian_product2(X0,X1) = cartesian_product2(X1,X0)
=> ( X0 = X1
| empty_set = X1
| empty_set = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t114_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] :
( cartesian_product2(X0,X1) = cartesian_product2(X1,X0)
=> ( X0 = X1
| empty_set = X1
| empty_set = X0 ) ),
inference(negated_conjecture,[],[f10]) ).
fof(f12,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f14,plain,
? [X0,X1] :
( X0 != X1
& empty_set != X1
& empty_set != X0
& cartesian_product2(X0,X1) = cartesian_product2(X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f15,plain,
? [X0,X1] :
( X0 != X1
& empty_set != X1
& empty_set != X0
& cartesian_product2(X0,X1) = cartesian_product2(X1,X0) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f17,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f18,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f17]) ).
fof(f19,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK0(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
! [X0] :
( ( empty_set = X0
| in(sK0(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f18,f19]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f21]) ).
fof(f27,plain,
( ? [X0,X1] :
( X0 != X1
& empty_set != X1
& empty_set != X0
& cartesian_product2(X0,X1) = cartesian_product2(X1,X0) )
=> ( sK3 != sK4
& empty_set != sK4
& empty_set != sK3
& cartesian_product2(sK3,sK4) = cartesian_product2(sK4,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
( sK3 != sK4
& empty_set != sK4
& empty_set != sK3
& cartesian_product2(sK3,sK4) = cartesian_product2(sK4,sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f15,f27]) ).
fof(f29,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK5(X0,X1),X1)
| ~ in(sK5(X0,X1),X0) )
& ( in(sK5(X0,X1),X1)
| in(sK5(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK5(X0,X1),X1)
| ~ in(sK5(X0,X1),X0) )
& ( in(sK5(X0,X1),X1)
| in(sK5(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f29,f30]) ).
fof(f33,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f34,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f20]) ).
fof(f35,plain,
! [X0] :
( empty_set = X0
| in(sK0(X0),X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f44,plain,
cartesian_product2(sK3,sK4) = cartesian_product2(sK4,sK3),
inference(cnf_transformation,[],[f28]) ).
fof(f45,plain,
empty_set != sK3,
inference(cnf_transformation,[],[f28]) ).
fof(f46,plain,
empty_set != sK4,
inference(cnf_transformation,[],[f28]) ).
fof(f47,plain,
sK3 != sK4,
inference(cnf_transformation,[],[f28]) ).
fof(f48,plain,
! [X0,X1] :
( X0 = X1
| in(sK5(X0,X1),X1)
| in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f49,plain,
! [X0,X1] :
( X0 = X1
| ~ in(sK5(X0,X1),X1)
| ~ in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f51,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(definition_unfolding,[],[f41,f36]) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f40,f36]) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f39,f36]) ).
fof(f54,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f34]) ).
cnf(c_50,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f33]) ).
cnf(c_51,plain,
( X0 = empty_set
| in(sK0(X0),X0) ),
inference(cnf_transformation,[],[f35]) ).
cnf(c_52,plain,
~ in(X0,empty_set),
inference(cnf_transformation,[],[f54]) ).
cnf(c_55,plain,
( ~ in(X0,X1)
| ~ in(X2,X3)
| in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),cartesian_product2(X3,X1)) ),
inference(cnf_transformation,[],[f51]) ).
cnf(c_56,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f52]) ).
cnf(c_57,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f53]) ).
cnf(c_60,negated_conjecture,
sK3 != sK4,
inference(cnf_transformation,[],[f47]) ).
cnf(c_61,negated_conjecture,
empty_set != sK4,
inference(cnf_transformation,[],[f46]) ).
cnf(c_62,negated_conjecture,
empty_set != sK3,
inference(cnf_transformation,[],[f45]) ).
cnf(c_63,negated_conjecture,
cartesian_product2(sK3,sK4) = cartesian_product2(sK4,sK3),
inference(cnf_transformation,[],[f44]) ).
cnf(c_64,plain,
( ~ in(sK5(X0,X1),X0)
| ~ in(sK5(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f49]) ).
cnf(c_65,plain,
( X0 = X1
| in(sK5(X0,X1),X0)
| in(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f48]) ).
cnf(c_140,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(demodulation,[status(thm)],[c_57,c_50]) ).
cnf(c_145,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(demodulation,[status(thm)],[c_56,c_50]) ).
cnf(c_156,plain,
( ~ in(X0,X1)
| ~ in(X2,X3)
| in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),cartesian_product2(X3,X1)) ),
inference(demodulation,[status(thm)],[c_55,c_50]) ).
cnf(c_401,plain,
( X0 = empty_set
| in(sK5(X0,empty_set),X0) ),
inference(superposition,[status(thm)],[c_65,c_52]) ).
cnf(c_403,plain,
( X0 = empty_set
| in(sK5(empty_set,X0),X0) ),
inference(superposition,[status(thm)],[c_65,c_52]) ).
cnf(c_452,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(sK3,sK4))
| in(X0,sK4) ),
inference(superposition,[status(thm)],[c_63,c_140]) ).
cnf(c_478,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(sK3,sK4))
| in(X1,sK3) ),
inference(superposition,[status(thm)],[c_63,c_145]) ).
cnf(c_510,plain,
( ~ in(X0,sK4)
| ~ in(X1,sK3)
| in(X0,sK3) ),
inference(superposition,[status(thm)],[c_156,c_478]) ).
cnf(c_511,plain,
( ~ in(X0,sK4)
| ~ in(X1,sK3)
| in(X1,sK4) ),
inference(superposition,[status(thm)],[c_156,c_452]) ).
cnf(c_546,plain,
( ~ in(X0,sK3)
| empty_set = sK4
| in(sK0(sK4),sK3) ),
inference(superposition,[status(thm)],[c_51,c_510]) ).
cnf(c_551,plain,
( ~ in(X0,sK3)
| in(sK0(sK4),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_546,c_61]) ).
cnf(c_584,plain,
( empty_set = sK3
| in(sK0(sK4),sK3) ),
inference(superposition,[status(thm)],[c_401,c_551]) ).
cnf(c_586,plain,
in(sK0(sK4),sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_584,c_62]) ).
cnf(c_596,plain,
( ~ in(X0,sK3)
| empty_set = sK4
| in(X0,sK4) ),
inference(superposition,[status(thm)],[c_401,c_511]) ).
cnf(c_598,plain,
( ~ in(X0,sK3)
| in(X0,sK4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_596,c_61]) ).
cnf(c_610,plain,
( X0 = sK3
| in(sK5(X0,sK3),X0)
| in(sK5(X0,sK3),sK4) ),
inference(superposition,[status(thm)],[c_65,c_598]) ).
cnf(c_613,plain,
( empty_set = sK3
| in(sK5(empty_set,sK3),sK4) ),
inference(superposition,[status(thm)],[c_403,c_598]) ).
cnf(c_616,plain,
in(sK5(empty_set,sK3),sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_613,c_62]) ).
cnf(c_638,plain,
( ~ in(X0,sK3)
| in(sK5(empty_set,sK3),sK3) ),
inference(superposition,[status(thm)],[c_616,c_510]) ).
cnf(c_740,plain,
in(sK5(empty_set,sK3),sK3),
inference(superposition,[status(thm)],[c_586,c_638]) ).
cnf(c_776,plain,
( sK3 = sK4
| in(sK5(sK4,sK3),sK4) ),
inference(equality_factoring,[status(thm)],[c_610]) ).
cnf(c_778,plain,
in(sK5(sK4,sK3),sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_776,c_60]) ).
cnf(c_790,plain,
( ~ in(X0,sK3)
| in(sK5(sK4,sK3),sK3) ),
inference(superposition,[status(thm)],[c_778,c_510]) ).
cnf(c_831,plain,
in(sK5(sK4,sK3),sK3),
inference(superposition,[status(thm)],[c_740,c_790]) ).
cnf(c_835,plain,
( ~ in(sK5(sK4,sK3),sK4)
| sK3 = sK4 ),
inference(superposition,[status(thm)],[c_831,c_64]) ).
cnf(c_837,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_835,c_60,c_778]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET961+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.13/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 14:12:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.39/1.17 % SZS status Started for theBenchmark.p
% 2.39/1.17 % SZS status Theorem for theBenchmark.p
% 2.39/1.17
% 2.39/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.39/1.17
% 2.39/1.17 ------ iProver source info
% 2.39/1.17
% 2.39/1.17 git: date: 2023-05-31 18:12:56 +0000
% 2.39/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.39/1.17 git: non_committed_changes: false
% 2.39/1.17 git: last_make_outside_of_git: false
% 2.39/1.17
% 2.39/1.17 ------ Parsing...
% 2.39/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.39/1.17
% 2.39/1.17 ------ Preprocessing... sup_sim: 4 sf_s rm: 1 0s sf_e pe_s pe_e
% 2.39/1.17
% 2.39/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.39/1.17
% 2.39/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.39/1.17 ------ Proving...
% 2.39/1.17 ------ Problem Properties
% 2.39/1.17
% 2.39/1.17
% 2.39/1.17 clauses 17
% 2.39/1.17 conjectures 4
% 2.39/1.17 EPR 8
% 2.39/1.17 Horn 15
% 2.39/1.17 unary 10
% 2.39/1.17 binary 4
% 2.39/1.17 lits 27
% 2.39/1.17 lits eq 8
% 2.39/1.17 fd_pure 0
% 2.39/1.17 fd_pseudo 0
% 2.39/1.17 fd_cond 1
% 2.39/1.17 fd_pseudo_cond 2
% 2.39/1.17 AC symbols 0
% 2.39/1.17
% 2.39/1.17 ------ Schedule dynamic 5 is on
% 2.39/1.17
% 2.39/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.39/1.17
% 2.39/1.17
% 2.39/1.17 ------
% 2.39/1.17 Current options:
% 2.39/1.17 ------
% 2.39/1.17
% 2.39/1.17
% 2.39/1.17
% 2.39/1.17
% 2.39/1.17 ------ Proving...
% 2.39/1.17
% 2.39/1.17
% 2.39/1.17 % SZS status Theorem for theBenchmark.p
% 2.39/1.17
% 2.39/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.39/1.17
% 2.39/1.18
%------------------------------------------------------------------------------