TSTP Solution File: SET950+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET950+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n012.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 15:10:47 EDT 2023
% Result : Theorem 2.53s 1.18s
% Output : CNFRefutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 11 unt; 0 def)
% Number of atoms : 201 ( 56 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 246 ( 97 ~; 86 |; 53 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 167 ( 0 sgn; 110 !; 29 ?)
% 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(f3,axiom,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f10,conjecture,
! [X0,X1,X2,X3] :
~ ( ! [X4,X5] :
~ ( ordered_pair(X4,X5) = X3
& in(X5,X2)
& in(X4,X1) )
& in(X3,X0)
& subset(X0,cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2,X3] :
~ ( ! [X4,X5] :
~ ( ordered_pair(X4,X5) = X3
& in(X5,X2)
& in(X4,X1) )
& in(X3,X0)
& subset(X0,cartesian_product2(X1,X2)) ),
inference(negated_conjecture,[],[f10]) ).
fof(f13,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f15,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
? [X0,X1,X2,X3] :
( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X2)
| ~ in(X4,X1) )
& in(X3,X0)
& subset(X0,cartesian_product2(X1,X2)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| ~ in(X3,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X1)
& in(X6,X0) )
| in(X3,X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) ) )
& ( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X1)
& in(X11,X0) )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(rectify,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X1)
& in(X6,X0) )
| in(X3,X2) ) )
=> ( ( ! [X5,X4] :
( ordered_pair(X4,X5) != sK0(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ? [X7,X6] :
( ordered_pair(X6,X7) = sK0(X0,X1,X2)
& in(X7,X1)
& in(X6,X0) )
| in(sK0(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( ordered_pair(X6,X7) = sK0(X0,X1,X2)
& in(X7,X1)
& in(X6,X0) )
=> ( sK0(X0,X1,X2) = ordered_pair(sK1(X0,X1,X2),sK2(X0,X1,X2))
& in(sK2(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0,X1,X8] :
( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X1)
& in(X11,X0) )
=> ( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
& in(sK4(X0,X1,X8),X1)
& in(sK3(X0,X1,X8),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ( ( ! [X4,X5] :
( ordered_pair(X4,X5) != sK0(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( sK0(X0,X1,X2) = ordered_pair(sK1(X0,X1,X2),sK2(X0,X1,X2))
& in(sK2(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) ) )
& ( ( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
& in(sK4(X0,X1,X8),X1)
& in(sK3(X0,X1,X8),X0) )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f18,f21,f20,f19]) ).
fof(f27,plain,
( ? [X0,X1,X2,X3] :
( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X2)
| ~ in(X4,X1) )
& in(X3,X0)
& subset(X0,cartesian_product2(X1,X2)) )
=> ( ! [X5,X4] :
( ordered_pair(X4,X5) != sK10
| ~ in(X5,sK9)
| ~ in(X4,sK8) )
& in(sK10,sK7)
& subset(sK7,cartesian_product2(sK8,sK9)) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
( ! [X4,X5] :
( ordered_pair(X4,X5) != sK10
| ~ in(X5,sK9)
| ~ in(X4,sK8) )
& in(sK10,sK7)
& subset(sK7,cartesian_product2(sK8,sK9)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10])],[f16,f27]) ).
fof(f30,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f31,plain,
! [X2,X0,X1,X8] :
( in(sK3(X0,X1,X8),X0)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f32,plain,
! [X2,X0,X1,X8] :
( in(sK4(X0,X1,X8),X1)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f33,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
! [X2,X0,X1] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f40,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f45,plain,
subset(sK7,cartesian_product2(sK8,sK9)),
inference(cnf_transformation,[],[f28]) ).
fof(f46,plain,
in(sK10,sK7),
inference(cnf_transformation,[],[f28]) ).
fof(f47,plain,
! [X4,X5] :
( ordered_pair(X4,X5) != sK10
| ~ in(X5,sK9)
| ~ in(X4,sK8) ),
inference(cnf_transformation,[],[f28]) ).
fof(f51,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(definition_unfolding,[],[f33,f40]) ).
fof(f53,plain,
! [X4,X5] :
( sK10 != unordered_pair(unordered_pair(X4,X5),singleton(X4))
| ~ in(X5,sK9)
| ~ in(X4,sK8) ),
inference(definition_unfolding,[],[f47,f40]) ).
fof(f56,plain,
! [X0,X1,X8] :
( unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f51]) ).
fof(f57,plain,
! [X0,X1,X8] :
( in(sK4(X0,X1,X8),X1)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f32]) ).
fof(f58,plain,
! [X0,X1,X8] :
( in(sK3(X0,X1,X8),X0)
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f31]) ).
cnf(c_50,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f30]) ).
cnf(c_56,plain,
( ~ in(X0,cartesian_product2(X1,X2))
| unordered_pair(unordered_pair(sK3(X1,X2,X0),sK4(X1,X2,X0)),singleton(sK3(X1,X2,X0))) = X0 ),
inference(cnf_transformation,[],[f56]) ).
cnf(c_57,plain,
( ~ in(X0,cartesian_product2(X1,X2))
| in(sK4(X1,X2,X0),X2) ),
inference(cnf_transformation,[],[f57]) ).
cnf(c_58,plain,
( ~ in(X0,cartesian_product2(X1,X2))
| in(sK3(X1,X2,X0),X1) ),
inference(cnf_transformation,[],[f58]) ).
cnf(c_59,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_64,negated_conjecture,
( unordered_pair(unordered_pair(X0,X1),singleton(X0)) != sK10
| ~ in(X0,sK8)
| ~ in(X1,sK9) ),
inference(cnf_transformation,[],[f53]) ).
cnf(c_65,negated_conjecture,
in(sK10,sK7),
inference(cnf_transformation,[],[f46]) ).
cnf(c_66,negated_conjecture,
subset(sK7,cartesian_product2(sK8,sK9)),
inference(cnf_transformation,[],[f45]) ).
cnf(c_171,plain,
( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK10
| ~ in(X0,sK8)
| ~ in(X1,sK9) ),
inference(demodulation,[status(thm)],[c_64,c_50]) ).
cnf(c_197,plain,
( ~ in(X0,cartesian_product2(X1,X2))
| unordered_pair(singleton(sK3(X1,X2,X0)),unordered_pair(sK3(X1,X2,X0),sK4(X1,X2,X0))) = X0 ),
inference(demodulation,[status(thm)],[c_56,c_50]) ).
cnf(c_246,plain,
( cartesian_product2(sK8,sK9) != X1
| X0 != sK7
| ~ in(X2,X0)
| in(X2,X1) ),
inference(resolution_lifted,[status(thm)],[c_59,c_66]) ).
cnf(c_247,plain,
( ~ in(X0,sK7)
| in(X0,cartesian_product2(sK8,sK9)) ),
inference(unflattening,[status(thm)],[c_246]) ).
cnf(c_248,plain,
( ~ in(sK10,sK7)
| in(sK10,cartesian_product2(sK8,sK9)) ),
inference(instantiation,[status(thm)],[c_247]) ).
cnf(c_789,plain,
( ~ in(X0,sK7)
| unordered_pair(singleton(sK3(sK8,sK9,X0)),unordered_pair(sK3(sK8,sK9,X0),sK4(sK8,sK9,X0))) = X0 ),
inference(superposition,[status(thm)],[c_247,c_197]) ).
cnf(c_878,plain,
( ~ in(X0,cartesian_product2(sK8,sK9))
| in(sK4(sK8,sK9,X0),sK9) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_879,plain,
( ~ in(sK10,cartesian_product2(sK8,sK9))
| in(sK4(sK8,sK9,sK10),sK9) ),
inference(instantiation,[status(thm)],[c_878]) ).
cnf(c_891,plain,
unordered_pair(singleton(sK3(sK8,sK9,sK10)),unordered_pair(sK3(sK8,sK9,sK10),sK4(sK8,sK9,sK10))) = sK10,
inference(superposition,[status(thm)],[c_65,c_789]) ).
cnf(c_918,plain,
( ~ in(X0,cartesian_product2(sK8,sK9))
| in(sK3(sK8,sK9,X0),sK8) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_919,plain,
( ~ in(sK10,cartesian_product2(sK8,sK9))
| in(sK3(sK8,sK9,sK10),sK8) ),
inference(instantiation,[status(thm)],[c_918]) ).
cnf(c_934,plain,
( ~ in(sK3(sK8,sK9,sK10),sK8)
| ~ in(sK4(sK8,sK9,sK10),sK9) ),
inference(superposition,[status(thm)],[c_891,c_171]) ).
cnf(c_976,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_934,c_919,c_879,c_248,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET950+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n012.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 10:20:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.53/1.18 % SZS status Started for theBenchmark.p
% 2.53/1.18 % SZS status Theorem for theBenchmark.p
% 2.53/1.18
% 2.53/1.18 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.53/1.18
% 2.53/1.18 ------ iProver source info
% 2.53/1.18
% 2.53/1.18 git: date: 2023-05-31 18:12:56 +0000
% 2.53/1.18 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.53/1.18 git: non_committed_changes: false
% 2.53/1.18 git: last_make_outside_of_git: false
% 2.53/1.18
% 2.53/1.18 ------ Parsing...
% 2.53/1.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.53/1.18
% 2.53/1.18 ------ Preprocessing... sup_sim: 6 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 2.53/1.18
% 2.53/1.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.53/1.18
% 2.53/1.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.53/1.18 ------ Proving...
% 2.53/1.18 ------ Problem Properties
% 2.53/1.18
% 2.53/1.18
% 2.53/1.18 clauses 16
% 2.53/1.18 conjectures 1
% 2.53/1.18 EPR 4
% 2.53/1.18 Horn 13
% 2.53/1.18 unary 5
% 2.53/1.18 binary 5
% 2.53/1.18 lits 35
% 2.53/1.18 lits eq 9
% 2.53/1.18 fd_pure 0
% 2.53/1.18 fd_pseudo 0
% 2.53/1.18 fd_cond 0
% 2.53/1.18 fd_pseudo_cond 4
% 2.53/1.18 AC symbols 0
% 2.53/1.18
% 2.53/1.18 ------ Schedule dynamic 5 is on
% 2.53/1.18
% 2.53/1.18 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.53/1.18
% 2.53/1.18
% 2.53/1.18 ------
% 2.53/1.18 Current options:
% 2.53/1.18 ------
% 2.53/1.18
% 2.53/1.18
% 2.53/1.18
% 2.53/1.18
% 2.53/1.18 ------ Proving...
% 2.53/1.18
% 2.53/1.18
% 2.53/1.18 % SZS status Theorem for theBenchmark.p
% 2.53/1.18
% 2.53/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.53/1.18
% 2.53/1.18
%------------------------------------------------------------------------------