TSTP Solution File: NUM504+3 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM504+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n004.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 02:49:37 EDT 2024
% Result : Theorem 3.75s 1.14s
% Output : CNFRefutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 59 ( 24 unt; 0 def)
% Number of atoms : 217 ( 76 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 228 ( 70 ~; 56 |; 91 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 12 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 32 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(f45,axiom,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(f48,axiom,
( isPrime0(xr)
& ! [X0] :
( ( ( doDivides0(X0,xr)
| ? [X1] :
( sdtasdt0(X0,X1) = xr
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( xr = X0
| sz10 = X0 ) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(f49,axiom,
( doDivides0(xr,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& ? [X0] :
( xk = sdtpldt0(xr,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).
fof(f51,axiom,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& ? [X0] :
( sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),X0)
& aNaturalNumber0(X0) )
& sdtasdt0(xp,xk) != sdtasdt0(xp,xm)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& ? [X0] :
( sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),X0)
& aNaturalNumber0(X0) )
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2414) ).
fof(f59,plain,
( isPrime0(xr)
& ! [X0] :
( ( ( doDivides0(X0,xr)
| ? [X1] :
( sdtasdt0(X0,X1) = xr
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( xr = X0
| sz10 = X0 ) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& ? [X2] :
( xk = sdtasdt0(xr,X2)
& aNaturalNumber0(X2) )
& aNaturalNumber0(xr) ),
inference(rectify,[],[f48]) ).
fof(f60,plain,
( doDivides0(xr,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& ? [X1] :
( xk = sdtpldt0(xr,X1)
& aNaturalNumber0(X1) ) ),
inference(rectify,[],[f49]) ).
fof(f61,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& ? [X0] :
( sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),X0)
& aNaturalNumber0(X0) )
& sdtasdt0(xp,xk) != sdtasdt0(xp,xm)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& ? [X1] :
( sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),X1)
& aNaturalNumber0(X1) )
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
inference(rectify,[],[f51]) ).
fof(f63,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f64,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f66,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f65]) ).
fof(f93,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f94,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f93]) ).
fof(f134,plain,
( isPrime0(xr)
& ! [X0] :
( xr = X0
| sz10 = X0
| ( ~ doDivides0(X0,xr)
& ! [X1] :
( sdtasdt0(X0,X1) != xr
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& ? [X2] :
( xk = sdtasdt0(xr,X2)
& aNaturalNumber0(X2) )
& aNaturalNumber0(xr) ),
inference(ennf_transformation,[],[f59]) ).
fof(f135,plain,
( isPrime0(xr)
& ! [X0] :
( xr = X0
| sz10 = X0
| ( ~ doDivides0(X0,xr)
& ! [X1] :
( sdtasdt0(X0,X1) != xr
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& ? [X2] :
( xk = sdtasdt0(xr,X2)
& aNaturalNumber0(X2) )
& aNaturalNumber0(xr) ),
inference(flattening,[],[f134]) ).
fof(f175,plain,
( ? [X2] :
( xk = sdtasdt0(xr,X2)
& aNaturalNumber0(X2) )
=> ( xk = sdtasdt0(xr,sK13)
& aNaturalNumber0(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f176,plain,
( isPrime0(xr)
& ! [X0] :
( xr = X0
| sz10 = X0
| ( ~ doDivides0(X0,xr)
& ! [X1] :
( sdtasdt0(X0,X1) != xr
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0) )
& sz10 != xr
& sz00 != xr
& doDivides0(xr,xk)
& xk = sdtasdt0(xr,sK13)
& aNaturalNumber0(sK13)
& aNaturalNumber0(xr) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f135,f175]) ).
fof(f177,plain,
( ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(xn,xm) = sdtasdt0(xr,sK14)
& aNaturalNumber0(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f178,plain,
( ? [X1] :
( xk = sdtpldt0(xr,X1)
& aNaturalNumber0(X1) )
=> ( xk = sdtpldt0(xr,sK15)
& aNaturalNumber0(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f179,plain,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xr,sK14)
& aNaturalNumber0(sK14)
& xk = sdtpldt0(xr,sK15)
& aNaturalNumber0(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f60,f178,f177]) ).
fof(f182,plain,
( ? [X0] :
( sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),X0)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),sK17)
& aNaturalNumber0(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f183,plain,
( ? [X1] :
( sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),X1)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),sK18)
& aNaturalNumber0(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f184,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),sK17)
& aNaturalNumber0(sK17)
& sdtasdt0(xp,xk) != sdtasdt0(xp,xm)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),sK18)
& aNaturalNumber0(sK18)
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18])],[f61,f183,f182]) ).
fof(f188,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f189,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f216,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f293,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f45]) ).
fof(f299,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f176]) ).
fof(f310,plain,
aNaturalNumber0(sK14),
inference(cnf_transformation,[],[f179]) ).
fof(f311,plain,
sdtasdt0(xn,xm) = sdtasdt0(xr,sK14),
inference(cnf_transformation,[],[f179]) ).
fof(f317,plain,
aNaturalNumber0(sK18),
inference(cnf_transformation,[],[f184]) ).
fof(f318,plain,
sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),sK18),
inference(cnf_transformation,[],[f184]) ).
fof(f319,plain,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f184]) ).
fof(f320,plain,
sdtasdt0(xp,xk) != sdtasdt0(xp,xm),
inference(cnf_transformation,[],[f184]) ).
fof(f323,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
inference(cnf_transformation,[],[f184]) ).
cnf(c_52,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f188]) ).
cnf(c_53,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f189]) ).
cnf(c_80,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f216]) ).
cnf(c_156,plain,
sdtasdt0(xp,xk) = sdtasdt0(xn,xm),
inference(cnf_transformation,[],[f293]) ).
cnf(c_170,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f299]) ).
cnf(c_172,plain,
sdtasdt0(xn,xm) = sdtasdt0(xr,sK14),
inference(cnf_transformation,[],[f311]) ).
cnf(c_173,plain,
aNaturalNumber0(sK14),
inference(cnf_transformation,[],[f310]) ).
cnf(c_179,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
inference(cnf_transformation,[],[f323]) ).
cnf(c_182,plain,
sdtasdt0(xp,xm) != sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f320]) ).
cnf(c_183,plain,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f319]) ).
cnf(c_184,plain,
sdtpldt0(sdtasdt0(xn,xm),sK18) = sdtasdt0(xp,xm),
inference(cnf_transformation,[],[f318]) ).
cnf(c_185,plain,
aNaturalNumber0(sK18),
inference(cnf_transformation,[],[f317]) ).
cnf(c_1091,plain,
sdtasdt0(xp,xk) = sdtasdt0(xr,sK14),
inference(demodulation,[status(thm)],[c_172,c_156]) ).
cnf(c_1092,plain,
sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm)),
inference(demodulation,[status(thm)],[c_183,c_156]) ).
cnf(c_1126,plain,
sdtpldt0(sdtasdt0(xp,xk),sK18) = sdtasdt0(xp,xm),
inference(light_normalisation,[status(thm)],[c_184,c_156]) ).
cnf(c_11071,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sK14)
| aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(superposition,[status(thm)],[c_1091,c_53]) ).
cnf(c_11078,plain,
aNaturalNumber0(sdtasdt0(xp,xk)),
inference(forward_subsumption_resolution,[status(thm)],[c_11071,c_173,c_170]) ).
cnf(c_11130,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sK18)
| aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(superposition,[status(thm)],[c_1126,c_52]) ).
cnf(c_11131,plain,
aNaturalNumber0(sdtasdt0(xp,xm)),
inference(forward_subsumption_resolution,[status(thm)],[c_11130,c_185,c_11078]) ).
cnf(c_11500,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
inference(instantiation,[status(thm)],[c_80]) ).
cnf(c_11501,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11500,c_11131,c_11078,c_1092,c_182,c_179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM504+3 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu May 2 19:15:03 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.18/0.45 Running first-order theorem proving
% 0.18/0.45 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
% 3.75/1.14 % SZS status Started for theBenchmark.p
% 3.75/1.14 % SZS status Theorem for theBenchmark.p
% 3.75/1.14
% 3.75/1.14 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.75/1.14
% 3.75/1.14 ------ iProver source info
% 3.75/1.14
% 3.75/1.14 git: date: 2024-05-02 19:28:25 +0000
% 3.75/1.14 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.75/1.14 git: non_committed_changes: false
% 3.75/1.14
% 3.75/1.14 ------ Parsing...
% 3.75/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.75/1.14
% 3.75/1.14 ------ Preprocessing... sup_sim: 9 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
% 3.75/1.14
% 3.75/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.75/1.14
% 3.75/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.75/1.14 ------ Proving...
% 3.75/1.14 ------ Problem Properties
% 3.75/1.14
% 3.75/1.14
% 3.75/1.14 clauses 130
% 3.75/1.14 conjectures 0
% 3.75/1.14 EPR 48
% 3.75/1.14 Horn 90
% 3.75/1.14 unary 51
% 3.75/1.14 binary 13
% 3.75/1.14 lits 401
% 3.75/1.14 lits eq 124
% 3.75/1.14 fd_pure 0
% 3.75/1.14 fd_pseudo 0
% 3.75/1.14 fd_cond 24
% 3.75/1.14 fd_pseudo_cond 11
% 3.75/1.14 AC symbols 0
% 3.75/1.14
% 3.75/1.14 ------ Schedule dynamic 5 is on
% 3.75/1.14
% 3.75/1.14 ------ no conjectures: strip conj schedule
% 3.75/1.14
% 3.75/1.14 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.75/1.14
% 3.75/1.14
% 3.75/1.14 ------
% 3.75/1.14 Current options:
% 3.75/1.14 ------
% 3.75/1.14
% 3.75/1.14
% 3.75/1.14
% 3.75/1.14
% 3.75/1.14 ------ Proving...
% 3.75/1.14
% 3.75/1.14
% 3.75/1.14 % SZS status Theorem for theBenchmark.p
% 3.75/1.14
% 3.75/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.75/1.14
% 3.75/1.15
%------------------------------------------------------------------------------