TSTP Solution File: SET988+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET988+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n007.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 03:02:11 EDT 2024
% Result : Theorem 3.16s 1.17s
% Output : CNFRefutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 63 ( 9 unt; 0 def)
% Number of atoms : 208 ( 66 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 238 ( 93 ~; 83 |; 45 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-2 aty)
% Number of variables : 176 ( 2 sgn 119 !; 33 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f30,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(f31,conjecture,
! [X0] :
( ( ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> X2 = X3 )
& ! [X1] :
~ ( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
=> ( function(X0)
& relation(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_funct_1) ).
fof(f32,negated_conjecture,
~ ! [X0] :
( ( ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> X2 = X3 )
& ! [X1] :
~ ( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
=> ( function(X0)
& relation(X0) ) ),
inference(negated_conjecture,[],[f31]) ).
fof(f33,axiom,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_1) ).
fof(f34,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f36,plain,
~ ! [X0] :
( ( ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> X2 = X3 )
& ! [X4] :
~ ( ! [X5,X6] : ordered_pair(X5,X6) != X4
& in(X4,X0) ) )
=> ( function(X0)
& relation(X0) ) ),
inference(rectify,[],[f32]) ).
fof(f54,plain,
? [X0] :
( ( ~ function(X0)
| ~ relation(X0) )
& ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) )
& ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X0) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f55,plain,
? [X0] :
( ( ~ function(X0)
| ~ relation(X0) )
& ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) )
& ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X0) ) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f57,plain,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) ) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0] :
( relation(X0)
<=> ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f77,plain,
( ? [X0] :
( ( ~ function(X0)
| ~ relation(X0) )
& ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) )
& ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X0) ) )
=> ( ( ~ function(sK9)
| ~ relation(sK9) )
& ! [X3,X2,X1] :
( X2 = X3
| ~ in(ordered_pair(X1,X3),sK9)
| ~ in(ordered_pair(X1,X2),sK9) )
& ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,sK9) ) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
=> ordered_pair(sK10(X4),sK11(X4)) = X4 ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
( ( ~ function(sK9)
| ~ relation(sK9) )
& ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X3),sK9)
| ~ in(ordered_pair(X1,X2),sK9) )
& ! [X4] :
( ordered_pair(sK10(X4),sK11(X4)) = X4
| ~ in(X4,sK9) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f55,f78,f77]) ).
fof(f80,plain,
! [X0] :
( ( function(X0)
| ? [X1,X2,X3] :
( X2 != X3
& in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) ) )
& ( ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) )
| ~ function(X0) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f81,plain,
! [X0] :
( ( function(X0)
| ? [X1,X2,X3] :
( X2 != X3
& in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) ) )
& ( ! [X4,X5,X6] :
( X5 = X6
| ~ in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X4,X5),X0) )
| ~ function(X0) ) ),
inference(rectify,[],[f80]) ).
fof(f82,plain,
! [X0] :
( ? [X1,X2,X3] :
( X2 != X3
& in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> ( sK13(X0) != sK14(X0)
& in(ordered_pair(sK12(X0),sK14(X0)),X0)
& in(ordered_pair(sK12(X0),sK13(X0)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
! [X0] :
( ( function(X0)
| ( sK13(X0) != sK14(X0)
& in(ordered_pair(sK12(X0),sK14(X0)),X0)
& in(ordered_pair(sK12(X0),sK13(X0)),X0) ) )
& ( ! [X4,X5,X6] :
( X5 = X6
| ~ in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X4,X5),X0) )
| ~ function(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f81,f82]) ).
fof(f84,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
& ( ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) )
| ~ relation(X0) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f85,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
& ( ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X0) )
| ~ relation(X0) ) ),
inference(rectify,[],[f84]) ).
fof(f86,plain,
! [X0] :
( ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) )
=> ( ! [X3,X2] : ordered_pair(X2,X3) != sK15(X0)
& in(sK15(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
=> ordered_pair(sK16(X4),sK17(X4)) = X4 ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
! [X0] :
( ( relation(X0)
| ( ! [X2,X3] : ordered_pair(X2,X3) != sK15(X0)
& in(sK15(X0),X0) ) )
& ( ! [X4] :
( ordered_pair(sK16(X4),sK17(X4)) = X4
| ~ in(X4,X0) )
| ~ relation(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17])],[f85,f87,f86]) ).
fof(f95,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f125,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f30]) ).
fof(f126,plain,
! [X4] :
( ordered_pair(sK10(X4),sK11(X4)) = X4
| ~ in(X4,sK9) ),
inference(cnf_transformation,[],[f79]) ).
fof(f127,plain,
! [X2,X3,X1] :
( X2 = X3
| ~ in(ordered_pair(X1,X3),sK9)
| ~ in(ordered_pair(X1,X2),sK9) ),
inference(cnf_transformation,[],[f79]) ).
fof(f128,plain,
( ~ function(sK9)
| ~ relation(sK9) ),
inference(cnf_transformation,[],[f79]) ).
fof(f130,plain,
! [X0] :
( function(X0)
| in(ordered_pair(sK12(X0),sK13(X0)),X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f131,plain,
! [X0] :
( function(X0)
| in(ordered_pair(sK12(X0),sK14(X0)),X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f132,plain,
! [X0] :
( function(X0)
| sK13(X0) != sK14(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f134,plain,
! [X0] :
( relation(X0)
| in(sK15(X0),X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f135,plain,
! [X2,X3,X0] :
( relation(X0)
| ordered_pair(X2,X3) != sK15(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f137,plain,
! [X2,X3,X1] :
( X2 = X3
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),sK9)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),sK9) ),
inference(definition_unfolding,[],[f127,f125,f125]) ).
fof(f138,plain,
! [X4] :
( unordered_pair(unordered_pair(sK10(X4),sK11(X4)),singleton(sK10(X4))) = X4
| ~ in(X4,sK9) ),
inference(definition_unfolding,[],[f126,f125]) ).
fof(f139,plain,
! [X0] :
( function(X0)
| in(unordered_pair(unordered_pair(sK12(X0),sK14(X0)),singleton(sK12(X0))),X0) ),
inference(definition_unfolding,[],[f131,f125]) ).
fof(f140,plain,
! [X0] :
( function(X0)
| in(unordered_pair(unordered_pair(sK12(X0),sK13(X0)),singleton(sK12(X0))),X0) ),
inference(definition_unfolding,[],[f130,f125]) ).
fof(f142,plain,
! [X2,X3,X0] :
( relation(X0)
| sK15(X0) != unordered_pair(unordered_pair(X2,X3),singleton(X2)) ),
inference(definition_unfolding,[],[f135,f125]) ).
cnf(c_55,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f95]) ).
cnf(c_85,negated_conjecture,
( ~ relation(sK9)
| ~ function(sK9) ),
inference(cnf_transformation,[],[f128]) ).
cnf(c_86,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK9)
| ~ in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),sK9)
| X1 = X2 ),
inference(cnf_transformation,[],[f137]) ).
cnf(c_87,negated_conjecture,
( ~ in(X0,sK9)
| unordered_pair(unordered_pair(sK10(X0),sK11(X0)),singleton(sK10(X0))) = X0 ),
inference(cnf_transformation,[],[f138]) ).
cnf(c_88,plain,
( sK13(X0) != sK14(X0)
| function(X0) ),
inference(cnf_transformation,[],[f132]) ).
cnf(c_89,plain,
( in(unordered_pair(unordered_pair(sK12(X0),sK14(X0)),singleton(sK12(X0))),X0)
| function(X0) ),
inference(cnf_transformation,[],[f139]) ).
cnf(c_90,plain,
( in(unordered_pair(unordered_pair(sK12(X0),sK13(X0)),singleton(sK12(X0))),X0)
| function(X0) ),
inference(cnf_transformation,[],[f140]) ).
cnf(c_92,plain,
( unordered_pair(unordered_pair(X0,X1),singleton(X0)) != sK15(X2)
| relation(X2) ),
inference(cnf_transformation,[],[f142]) ).
cnf(c_93,plain,
( in(sK15(X0),X0)
| relation(X0) ),
inference(cnf_transformation,[],[f134]) ).
cnf(c_332,plain,
( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK15(X2)
| relation(X2) ),
inference(demodulation,[status(thm)],[c_92,c_55]) ).
cnf(c_337,plain,
( in(unordered_pair(singleton(sK12(X0)),unordered_pair(sK12(X0),sK13(X0))),X0)
| function(X0) ),
inference(demodulation,[status(thm)],[c_90,c_55]) ).
cnf(c_342,plain,
( in(unordered_pair(singleton(sK12(X0)),unordered_pair(sK12(X0),sK14(X0))),X0)
| function(X0) ),
inference(demodulation,[status(thm)],[c_89,c_55]) ).
cnf(c_347,plain,
( ~ in(X0,sK9)
| unordered_pair(singleton(sK10(X0)),unordered_pair(sK10(X0),sK11(X0))) = X0 ),
inference(demodulation,[status(thm)],[c_87,c_55]) ).
cnf(c_359,plain,
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK9)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X2)),sK9)
| X1 = X2 ),
inference(demodulation,[status(thm)],[c_86,c_55]) ).
cnf(c_1201,negated_conjecture,
( ~ relation(sK9)
| ~ function(sK9) ),
inference(demodulation,[status(thm)],[c_85]) ).
cnf(c_1635,plain,
( ~ in(unordered_pair(singleton(sK12(sK9)),unordered_pair(sK12(sK9),X0)),sK9)
| sK13(sK9) = X0
| function(sK9) ),
inference(superposition,[status(thm)],[c_337,c_359]) ).
cnf(c_1659,plain,
( unordered_pair(singleton(sK10(sK15(sK9))),unordered_pair(sK10(sK15(sK9)),sK11(sK15(sK9)))) = sK15(sK9)
| relation(sK9) ),
inference(superposition,[status(thm)],[c_93,c_347]) ).
cnf(c_1690,plain,
relation(sK9),
inference(forward_subsumption_resolution,[status(thm)],[c_1659,c_332]) ).
cnf(c_1691,plain,
~ function(sK9),
inference(backward_subsumption_resolution,[status(thm)],[c_1201,c_1690]) ).
cnf(c_1692,plain,
( ~ in(unordered_pair(singleton(sK12(sK9)),unordered_pair(sK12(sK9),X0)),sK9)
| sK13(sK9) = X0 ),
inference(backward_subsumption_resolution,[status(thm)],[c_1635,c_1691]) ).
cnf(c_2037,plain,
( sK13(sK9) != sK14(sK9)
| function(sK9) ),
inference(instantiation,[status(thm)],[c_88]) ).
cnf(c_2078,plain,
( sK13(sK9) = sK14(sK9)
| function(sK9) ),
inference(superposition,[status(thm)],[c_342,c_1692]) ).
cnf(c_2079,plain,
sK13(sK9) = sK14(sK9),
inference(forward_subsumption_resolution,[status(thm)],[c_2078,c_1691]) ).
cnf(c_2091,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2079,c_2037,c_1691]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET988+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n007.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 20:20:35 EDT 2024
% 0.12/0.34 % 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 --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.16/1.17 % SZS status Started for theBenchmark.p
% 3.16/1.17 % SZS status Theorem for theBenchmark.p
% 3.16/1.17
% 3.16/1.17 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.16/1.17
% 3.16/1.17 ------ iProver source info
% 3.16/1.17
% 3.16/1.17 git: date: 2024-05-02 19:28:25 +0000
% 3.16/1.17 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.16/1.17 git: non_committed_changes: false
% 3.16/1.17
% 3.16/1.17 ------ Parsing...
% 3.16/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.16/1.17
% 3.16/1.17 ------ Preprocessing... sup_sim: 7 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
% 3.16/1.17
% 3.16/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.16/1.17
% 3.16/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.16/1.17 ------ Proving...
% 3.16/1.17 ------ Problem Properties
% 3.16/1.17
% 3.16/1.17
% 3.16/1.17 clauses 41
% 3.16/1.17 conjectures 1
% 3.16/1.17 EPR 20
% 3.16/1.17 Horn 36
% 3.16/1.17 unary 19
% 3.16/1.17 binary 15
% 3.16/1.17 lits 71
% 3.16/1.17 lits eq 9
% 3.16/1.17 fd_pure 0
% 3.16/1.17 fd_pseudo 0
% 3.16/1.17 fd_cond 1
% 3.16/1.17 fd_pseudo_cond 3
% 3.16/1.17 AC symbols 0
% 3.16/1.17
% 3.16/1.17 ------ Schedule dynamic 5 is on
% 3.16/1.17
% 3.16/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.16/1.17
% 3.16/1.17
% 3.16/1.17 ------
% 3.16/1.17 Current options:
% 3.16/1.17 ------
% 3.16/1.17
% 3.16/1.17
% 3.16/1.17
% 3.16/1.17
% 3.16/1.17 ------ Proving...
% 3.16/1.17
% 3.16/1.17
% 3.16/1.17 % SZS status Theorem for theBenchmark.p
% 3.16/1.17
% 3.16/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.16/1.17
% 3.16/1.17
%------------------------------------------------------------------------------