TSTP Solution File: NUN066+2 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUN066+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n026.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 12:49:15 EDT 2023
% Result : Theorem 3.50s 1.12s
% Output : CNFRefutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 86 ( 10 unt; 0 def)
% Number of atoms : 243 ( 97 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 256 ( 99 ~; 108 |; 43 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 143 ( 2 sgn; 72 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( X0 = X1
& r1(X1) )
| ( X0 != X1
& ~ r1(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f2,axiom,
! [X2] :
? [X3] :
! [X4] :
( ( X3 = X4
& r2(X2,X4) )
| ( X3 != X4
& ~ r2(X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f7,axiom,
! [X25,X26] :
( X25 = X26
| ! [X27] :
( ~ r2(X26,X27)
| ! [X28] :
( X27 != X28
| ~ r2(X25,X28) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3a) ).
fof(f11,axiom,
! [X40,X41] :
( ~ r2(X40,X41)
| ! [X42] :
( X41 != X42
| ~ r1(X42) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7a) ).
fof(f12,conjecture,
? [X38] :
( ! [X16] :
( X16 != X38
| ~ r1(X16) )
& ! [X21] :
( X21 != X38
| ! [X22] :
( ~ r2(X22,X21)
| ! [X15] :
( ~ r2(X15,X22)
| ~ r1(X15) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonzerononetwoexist) ).
fof(f13,negated_conjecture,
~ ? [X38] :
( ! [X16] :
( X16 != X38
| ~ r1(X16) )
& ! [X21] :
( X21 != X38
| ! [X22] :
( ~ r2(X22,X21)
| ! [X15] :
( ~ r2(X15,X22)
| ~ r1(X15) ) ) ) ),
inference(negated_conjecture,[],[f12]) ).
fof(f14,plain,
! [X0] :
? [X1] :
! [X2] :
( ( X1 = X2
& r2(X0,X2) )
| ( X1 != X2
& ~ r2(X0,X2) ) ),
inference(rectify,[],[f2]) ).
fof(f19,plain,
! [X0,X1] :
( X0 = X1
| ! [X2] :
( ~ r2(X1,X2)
| ! [X3] :
( X2 != X3
| ~ r2(X0,X3) ) ) ),
inference(rectify,[],[f7]) ).
fof(f23,plain,
! [X0,X1] :
( ~ r2(X0,X1)
| ! [X2] :
( X1 != X2
| ~ r1(X2) ) ),
inference(rectify,[],[f11]) ).
fof(f24,plain,
~ ? [X0] :
( ! [X1] :
( X0 != X1
| ~ r1(X1) )
& ! [X2] :
( X0 != X2
| ! [X3] :
( ~ r2(X3,X2)
| ! [X4] :
( ~ r2(X4,X3)
| ~ r1(X4) ) ) ) ),
inference(rectify,[],[f13]) ).
fof(f25,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& r1(X1) )
| ? [X2] :
( X0 = X2
& ? [X3] :
( r2(X3,X2)
& ? [X4] :
( r2(X4,X3)
& r1(X4) ) ) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f26,plain,
( ? [X0] :
! [X1] :
( ( X0 = X1
& r1(X1) )
| ( X0 != X1
& ~ r1(X1) ) )
=> ! [X1] :
( ( sK0 = X1
& r1(X1) )
| ( sK0 != X1
& ~ r1(X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X1] :
( ( sK0 = X1
& r1(X1) )
| ( sK0 != X1
& ~ r1(X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f1,f26]) ).
fof(f28,plain,
! [X0] :
( ? [X1] :
! [X2] :
( ( X1 = X2
& r2(X0,X2) )
| ( X1 != X2
& ~ r2(X0,X2) ) )
=> ! [X2] :
( ( sK1(X0) = X2
& r2(X0,X2) )
| ( sK1(X0) != X2
& ~ r2(X0,X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0,X2] :
( ( sK1(X0) = X2
& r2(X0,X2) )
| ( sK1(X0) != X2
& ~ r2(X0,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f14,f28]) ).
fof(f54,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& r1(X1) )
=> ( sK20(X0) = X0
& r1(sK20(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f55,plain,
! [X0] :
( ? [X2] :
( X0 = X2
& ? [X3] :
( r2(X3,X2)
& ? [X4] :
( r2(X4,X3)
& r1(X4) ) ) )
=> ( sK21(X0) = X0
& ? [X3] :
( r2(X3,sK21(X0))
& ? [X4] :
( r2(X4,X3)
& r1(X4) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
! [X0] :
( ? [X3] :
( r2(X3,sK21(X0))
& ? [X4] :
( r2(X4,X3)
& r1(X4) ) )
=> ( r2(sK22(X0),sK21(X0))
& ? [X4] :
( r2(X4,sK22(X0))
& r1(X4) ) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
! [X0] :
( ? [X4] :
( r2(X4,sK22(X0))
& r1(X4) )
=> ( r2(sK23(X0),sK22(X0))
& r1(sK23(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
! [X0] :
( ( sK20(X0) = X0
& r1(sK20(X0)) )
| ( sK21(X0) = X0
& r2(sK22(X0),sK21(X0))
& r2(sK23(X0),sK22(X0))
& r1(sK23(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23])],[f25,f57,f56,f55,f54]) ).
fof(f60,plain,
! [X1] :
( r1(X1)
| sK0 != X1 ),
inference(cnf_transformation,[],[f27]) ).
fof(f61,plain,
! [X1] :
( sK0 = X1
| ~ r1(X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f64,plain,
! [X2,X0] :
( r2(X0,X2)
| sK1(X0) != X2 ),
inference(cnf_transformation,[],[f29]) ).
fof(f65,plain,
! [X2,X0] :
( sK1(X0) = X2
| ~ r2(X0,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f85,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| ~ r2(X1,X2)
| X2 != X3
| ~ r2(X0,X3) ),
inference(cnf_transformation,[],[f19]) ).
fof(f97,plain,
! [X2,X0,X1] :
( ~ r2(X0,X1)
| X1 != X2
| ~ r1(X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f98,plain,
! [X0] :
( r1(sK20(X0))
| r1(sK23(X0)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f99,plain,
! [X0] :
( r1(sK20(X0))
| r2(sK23(X0),sK22(X0)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f100,plain,
! [X0] :
( r1(sK20(X0))
| r2(sK22(X0),sK21(X0)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f101,plain,
! [X0] :
( r1(sK20(X0))
| sK21(X0) = X0 ),
inference(cnf_transformation,[],[f58]) ).
fof(f102,plain,
! [X0] :
( sK20(X0) = X0
| r1(sK23(X0)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f103,plain,
! [X0] :
( sK20(X0) = X0
| r2(sK23(X0),sK22(X0)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f104,plain,
! [X0] :
( sK20(X0) = X0
| r2(sK22(X0),sK21(X0)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f105,plain,
! [X0] :
( sK20(X0) = X0
| sK21(X0) = X0 ),
inference(cnf_transformation,[],[f58]) ).
fof(f110,plain,
r1(sK0),
inference(equality_resolution,[],[f60]) ).
fof(f112,plain,
! [X0] : r2(X0,sK1(X0)),
inference(equality_resolution,[],[f64]) ).
fof(f117,plain,
! [X3,X0,X1] :
( X0 = X1
| ~ r2(X1,X3)
| ~ r2(X0,X3) ),
inference(equality_resolution,[],[f85]) ).
fof(f118,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| ~ r1(X2) ),
inference(equality_resolution,[],[f97]) ).
cnf(c_49,plain,
( ~ r1(X0)
| X0 = sK0 ),
inference(cnf_transformation,[],[f61]) ).
cnf(c_50,plain,
r1(sK0),
inference(cnf_transformation,[],[f110]) ).
cnf(c_51,plain,
( ~ r2(X0,X1)
| sK1(X0) = X1 ),
inference(cnf_transformation,[],[f65]) ).
cnf(c_52,plain,
r2(X0,sK1(X0)),
inference(cnf_transformation,[],[f112]) ).
cnf(c_65,plain,
( ~ r2(X0,X1)
| ~ r2(X2,X1)
| X0 = X2 ),
inference(cnf_transformation,[],[f117]) ).
cnf(c_76,plain,
( ~ r2(X0,X1)
| ~ r1(X1) ),
inference(cnf_transformation,[],[f118]) ).
cnf(c_77,negated_conjecture,
( sK20(X0) = X0
| sK21(X0) = X0 ),
inference(cnf_transformation,[],[f105]) ).
cnf(c_78,negated_conjecture,
( sK20(X0) = X0
| r2(sK22(X0),sK21(X0)) ),
inference(cnf_transformation,[],[f104]) ).
cnf(c_79,negated_conjecture,
( sK20(X0) = X0
| r2(sK23(X0),sK22(X0)) ),
inference(cnf_transformation,[],[f103]) ).
cnf(c_80,negated_conjecture,
( sK20(X0) = X0
| r1(sK23(X0)) ),
inference(cnf_transformation,[],[f102]) ).
cnf(c_81,negated_conjecture,
( sK21(X0) = X0
| r1(sK20(X0)) ),
inference(cnf_transformation,[],[f101]) ).
cnf(c_82,negated_conjecture,
( r2(sK22(X0),sK21(X0))
| r1(sK20(X0)) ),
inference(cnf_transformation,[],[f100]) ).
cnf(c_83,negated_conjecture,
( r2(sK23(X0),sK22(X0))
| r1(sK20(X0)) ),
inference(cnf_transformation,[],[f99]) ).
cnf(c_84,negated_conjecture,
( r1(sK20(X0))
| r1(sK23(X0)) ),
inference(cnf_transformation,[],[f98]) ).
cnf(c_88,plain,
r2(sK0,sK1(sK0)),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_99,plain,
( ~ r2(sK0,sK0)
| ~ r1(sK0) ),
inference(instantiation,[status(thm)],[c_76]) ).
cnf(c_101,plain,
( ~ r1(sK0)
| sK0 = sK0 ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_540,plain,
( X0 != X1
| ~ r1(X1)
| r1(X0) ),
theory(equality) ).
cnf(c_541,plain,
( X0 != X1
| X2 != X3
| ~ r2(X1,X3)
| r2(X0,X2) ),
theory(equality) ).
cnf(c_841,plain,
( sK20(X0) = X0
| r2(sK22(X0),X0) ),
inference(superposition,[status(thm)],[c_77,c_78]) ).
cnf(c_861,plain,
( sK20(X0) = X0
| sK23(X0) = sK0 ),
inference(superposition,[status(thm)],[c_80,c_49]) ).
cnf(c_862,plain,
( sK23(X0) = sK0
| r1(sK20(X0)) ),
inference(superposition,[status(thm)],[c_84,c_49]) ).
cnf(c_882,plain,
( sK20(X0) = sK0
| sK23(X0) = sK0 ),
inference(superposition,[status(thm)],[c_862,c_49]) ).
cnf(c_889,plain,
( sK20(X0) = X0
| r2(sK0,sK22(X0)) ),
inference(superposition,[status(thm)],[c_861,c_79]) ).
cnf(c_923,plain,
( sK20(X0) = sK0
| r2(sK0,sK22(X0))
| r1(sK20(X0)) ),
inference(superposition,[status(thm)],[c_882,c_83]) ).
cnf(c_936,plain,
~ r1(sK1(X0)),
inference(superposition,[status(thm)],[c_52,c_76]) ).
cnf(c_945,plain,
( ~ r1(sK22(X0))
| sK20(X0) = X0 ),
inference(superposition,[status(thm)],[c_889,c_76]) ).
cnf(c_958,plain,
~ r1(sK1(sK0)),
inference(instantiation,[status(thm)],[c_936]) ).
cnf(c_1056,plain,
( sK20(X0) = sK0
| r2(sK0,sK22(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_923,c_49]) ).
cnf(c_1059,plain,
( sK20(X0) = sK0
| sK22(X0) = sK1(sK0) ),
inference(superposition,[status(thm)],[c_1056,c_51]) ).
cnf(c_1115,plain,
( ~ r2(X0,sK1(X1))
| X0 = X1 ),
inference(superposition,[status(thm)],[c_52,c_65]) ).
cnf(c_1190,plain,
( X0 != X1
| X2 != sK1(X1)
| ~ r2(X1,sK1(X1))
| r2(X0,X2) ),
inference(instantiation,[status(thm)],[c_541]) ).
cnf(c_1191,plain,
( sK0 != sK1(sK0)
| sK0 != sK0
| ~ r2(sK0,sK1(sK0))
| r2(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_1190]) ).
cnf(c_1275,plain,
( sK1(X0) != X1
| ~ r1(X1)
| r1(sK1(X0)) ),
inference(instantiation,[status(thm)],[c_540]) ).
cnf(c_1276,plain,
( sK1(sK0) != sK0
| ~ r1(sK0)
| r1(sK1(sK0)) ),
inference(instantiation,[status(thm)],[c_1275]) ).
cnf(c_1337,plain,
( ~ r2(sK1(X0),X1)
| ~ r2(X2,X1)
| X2 = sK1(X0) ),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_1778,plain,
( sK20(sK1(X0)) = sK1(X0)
| sK22(sK1(X0)) = X0 ),
inference(superposition,[status(thm)],[c_841,c_1115]) ).
cnf(c_2021,plain,
( sK20(X0) = sK0
| r2(sK1(sK0),sK21(X0))
| r1(sK20(X0)) ),
inference(superposition,[status(thm)],[c_1059,c_82]) ).
cnf(c_2304,plain,
( sK20(X0) = sK0
| r2(sK1(sK0),sK21(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2021,c_49]) ).
cnf(c_3226,plain,
( ~ r2(sK1(X0),sK1(X1))
| ~ r2(X1,sK1(X1))
| X1 = sK1(X0) ),
inference(instantiation,[status(thm)],[c_1337]) ).
cnf(c_3227,plain,
( ~ r2(sK1(sK0),sK1(sK0))
| ~ r2(sK0,sK1(sK0))
| sK0 = sK1(sK0) ),
inference(instantiation,[status(thm)],[c_3226]) ).
cnf(c_3744,plain,
( ~ r1(X0)
| sK20(sK1(X0)) = sK1(X0) ),
inference(superposition,[status(thm)],[c_1778,c_945]) ).
cnf(c_4715,plain,
sK20(sK1(sK0)) = sK1(sK0),
inference(superposition,[status(thm)],[c_50,c_3744]) ).
cnf(c_5245,plain,
( sK21(sK1(sK0)) = sK1(sK0)
| r1(sK1(sK0)) ),
inference(superposition,[status(thm)],[c_4715,c_81]) ).
cnf(c_5247,plain,
sK21(sK1(sK0)) = sK1(sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_5245,c_936]) ).
cnf(c_5321,plain,
( sK20(sK1(sK0)) = sK0
| r2(sK1(sK0),sK1(sK0)) ),
inference(superposition,[status(thm)],[c_5247,c_2304]) ).
cnf(c_5332,plain,
( sK1(sK0) = sK0
| r2(sK1(sK0),sK1(sK0)) ),
inference(light_normalisation,[status(thm)],[c_5321,c_4715]) ).
cnf(c_5344,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5332,c_3227,c_1276,c_1191,c_958,c_101,c_99,c_88,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN066+2 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.12 % Command : run_iprover %s %d THM
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Aug 27 10:17:19 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.50/1.12 % SZS status Started for theBenchmark.p
% 3.50/1.12 % SZS status Theorem for theBenchmark.p
% 3.50/1.12
% 3.50/1.12 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.50/1.12
% 3.50/1.12 ------ iProver source info
% 3.50/1.12
% 3.50/1.12 git: date: 2023-05-31 18:12:56 +0000
% 3.50/1.12 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.50/1.12 git: non_committed_changes: false
% 3.50/1.12 git: last_make_outside_of_git: false
% 3.50/1.12
% 3.50/1.12 ------ Parsing...
% 3.50/1.12 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.50/1.12
% 3.50/1.12 ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 2 sf_s rm: 3 0s sf_e pe_s pe_e
% 3.50/1.12
% 3.50/1.12 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.50/1.12
% 3.50/1.12 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.50/1.12 ------ Proving...
% 3.50/1.12 ------ Problem Properties
% 3.50/1.12
% 3.50/1.12
% 3.50/1.12 clauses 32
% 3.50/1.12 conjectures 8
% 3.50/1.12 EPR 4
% 3.50/1.12 Horn 20
% 3.50/1.12 unary 16
% 3.50/1.12 binary 15
% 3.50/1.12 lits 49
% 3.50/1.12 lits eq 21
% 3.50/1.12 fd_pure 0
% 3.50/1.12 fd_pseudo 0
% 3.50/1.12 fd_cond 1
% 3.50/1.12 fd_pseudo_cond 2
% 3.50/1.12 AC symbols 0
% 3.50/1.12
% 3.50/1.12 ------ Schedule dynamic 5 is on
% 3.50/1.12
% 3.50/1.12 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
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% 3.50/1.12 ------
% 3.50/1.12 Current options:
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% 3.50/1.12 ------ Proving...
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% 3.50/1.12 % SZS status Theorem for theBenchmark.p
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% 3.50/1.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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