TSTP Solution File: NUM561+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM561+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n032.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 11:31:27 EDT 2023
% Result : Theorem 3.23s 1.00s
% Output : CNFRefutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 15 unt; 0 def)
% Number of atoms : 169 ( 41 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 213 ( 85 ~; 81 |; 36 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 88 ( 0 sgn; 61 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] :
( aSet0(X0)
=> aSubsetOf0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
fof(f64,axiom,
! [X0] :
( aFunction0(X0)
=> aSet0(szDzozmdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDomSet) ).
fof(f68,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( aSubsetOf0(X1,szDzozmdt0(X0))
=> ! [X2] :
( sdtlcdtrc0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& aSet0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSImg) ).
fof(f69,axiom,
aFunction0(xF),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2911) ).
fof(f70,axiom,
aElementOf0(xx,szDzozmdt0(xF)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2911_02) ).
fof(f71,conjecture,
aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f72,negated_conjecture,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(negated_conjecture,[],[f71]) ).
fof(f80,plain,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(flattening,[],[f72]) ).
fof(f91,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f167,plain,
! [X0] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f64]) ).
fof(f173,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( sdtlcdtrc0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& aSet0(X2) ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f241,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( sdtlcdtrc0(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) )
& ( ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) ) )
& ( ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| sdtlcdtrc0(X0,X1) != X2 ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(nnf_transformation,[],[f173]) ).
fof(f242,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( sdtlcdtrc0(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) )
& ( ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) ) )
& ( ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| sdtlcdtrc0(X0,X1) != X2 ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(flattening,[],[f241]) ).
fof(f243,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( sdtlcdtrc0(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) )
& ( ? [X5] :
( sdtlpdtrp0(X0,X5) = X3
& aElementOf0(X5,X1) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X6] :
( ( aElementOf0(X6,X2)
| ! [X7] :
( sdtlpdtrp0(X0,X7) != X6
| ~ aElementOf0(X7,X1) ) )
& ( ? [X8] :
( sdtlpdtrp0(X0,X8) = X6
& aElementOf0(X8,X1) )
| ~ aElementOf0(X6,X2) ) )
& aSet0(X2) )
| sdtlcdtrc0(X0,X1) != X2 ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(rectify,[],[f242]) ).
fof(f244,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) )
& ( ? [X5] :
( sdtlpdtrp0(X0,X5) = X3
& aElementOf0(X5,X1) )
| aElementOf0(X3,X2) ) )
=> ( ( ! [X4] :
( sdtlpdtrp0(X0,X4) != sK17(X0,X1,X2)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(sK17(X0,X1,X2),X2) )
& ( ? [X5] :
( sdtlpdtrp0(X0,X5) = sK17(X0,X1,X2)
& aElementOf0(X5,X1) )
| aElementOf0(sK17(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f245,plain,
! [X0,X1,X2] :
( ? [X5] :
( sdtlpdtrp0(X0,X5) = sK17(X0,X1,X2)
& aElementOf0(X5,X1) )
=> ( sK17(X0,X1,X2) = sdtlpdtrp0(X0,sK18(X0,X1,X2))
& aElementOf0(sK18(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f246,plain,
! [X0,X1,X6] :
( ? [X8] :
( sdtlpdtrp0(X0,X8) = X6
& aElementOf0(X8,X1) )
=> ( sdtlpdtrp0(X0,sK19(X0,X1,X6)) = X6
& aElementOf0(sK19(X0,X1,X6),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f247,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( sdtlcdtrc0(X0,X1) = X2
| ( ( ! [X4] :
( sdtlpdtrp0(X0,X4) != sK17(X0,X1,X2)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(sK17(X0,X1,X2),X2) )
& ( ( sK17(X0,X1,X2) = sdtlpdtrp0(X0,sK18(X0,X1,X2))
& aElementOf0(sK18(X0,X1,X2),X1) )
| aElementOf0(sK17(X0,X1,X2),X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X6] :
( ( aElementOf0(X6,X2)
| ! [X7] :
( sdtlpdtrp0(X0,X7) != X6
| ~ aElementOf0(X7,X1) ) )
& ( ( sdtlpdtrp0(X0,sK19(X0,X1,X6)) = X6
& aElementOf0(sK19(X0,X1,X6),X1) )
| ~ aElementOf0(X6,X2) ) )
& aSet0(X2) )
| sdtlcdtrc0(X0,X1) != X2 ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19])],[f243,f246,f245,f244]) ).
fof(f260,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f361,plain,
! [X0] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f374,plain,
! [X2,X0,X1,X6,X7] :
( aElementOf0(X6,X2)
| sdtlpdtrp0(X0,X7) != X6
| ~ aElementOf0(X7,X1)
| sdtlcdtrc0(X0,X1) != X2
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f247]) ).
fof(f378,plain,
aFunction0(xF),
inference(cnf_transformation,[],[f69]) ).
fof(f379,plain,
aElementOf0(xx,szDzozmdt0(xF)),
inference(cnf_transformation,[],[f70]) ).
fof(f380,plain,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(cnf_transformation,[],[f80]) ).
fof(f408,plain,
! [X2,X0,X1,X7] :
( aElementOf0(sdtlpdtrp0(X0,X7),X2)
| ~ aElementOf0(X7,X1)
| sdtlcdtrc0(X0,X1) != X2
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(equality_resolution,[],[f374]) ).
fof(f409,plain,
! [X0,X1,X7] :
( aElementOf0(sdtlpdtrp0(X0,X7),sdtlcdtrc0(X0,X1))
| ~ aElementOf0(X7,X1)
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(equality_resolution,[],[f408]) ).
cnf(c_61,plain,
( ~ aSet0(X0)
| aSubsetOf0(X0,X0) ),
inference(cnf_transformation,[],[f260]) ).
cnf(c_162,plain,
( ~ aFunction0(X0)
| aSet0(szDzozmdt0(X0)) ),
inference(cnf_transformation,[],[f361]) ).
cnf(c_175,plain,
( ~ aSubsetOf0(X0,szDzozmdt0(X1))
| ~ aElementOf0(X2,X0)
| ~ aFunction0(X1)
| aElementOf0(sdtlpdtrp0(X1,X2),sdtlcdtrc0(X1,X0)) ),
inference(cnf_transformation,[],[f409]) ).
cnf(c_179,plain,
aFunction0(xF),
inference(cnf_transformation,[],[f378]) ).
cnf(c_180,plain,
aElementOf0(xx,szDzozmdt0(xF)),
inference(cnf_transformation,[],[f379]) ).
cnf(c_181,negated_conjecture,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(cnf_transformation,[],[f380]) ).
cnf(c_2325,plain,
( X0 != xF
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aElementOf0(X2,X1)
| aElementOf0(sdtlpdtrp0(X0,X2),sdtlcdtrc0(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_175,c_179]) ).
cnf(c_2326,plain,
( ~ aSubsetOf0(X0,szDzozmdt0(xF))
| ~ aElementOf0(X1,X0)
| aElementOf0(sdtlpdtrp0(xF,X1),sdtlcdtrc0(xF,X0)) ),
inference(unflattening,[status(thm)],[c_2325]) ).
cnf(c_2466,plain,
( X0 != xF
| aSet0(szDzozmdt0(X0)) ),
inference(resolution_lifted,[status(thm)],[c_162,c_179]) ).
cnf(c_2467,plain,
aSet0(szDzozmdt0(xF)),
inference(unflattening,[status(thm)],[c_2466]) ).
cnf(c_14363,plain,
( ~ aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF))
| ~ aElementOf0(xx,szDzozmdt0(xF)) ),
inference(superposition,[status(thm)],[c_2326,c_181]) ).
cnf(c_14485,plain,
( ~ aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF))
| ~ aElementOf0(xx,szDzozmdt0(xF)) ),
inference(superposition,[status(thm)],[c_2326,c_181]) ).
cnf(c_14509,plain,
~ aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF)),
inference(global_subsumption_just,[status(thm)],[c_14485,c_180,c_14363]) ).
cnf(c_14511,plain,
~ aSet0(szDzozmdt0(xF)),
inference(superposition,[status(thm)],[c_61,c_14509]) ).
cnf(c_14512,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_2467,c_14511]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : NUM561+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.09 % Command : run_iprover %s %d THM
% 0.09/0.27 % Computer : n032.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Fri Aug 25 10:09:13 EDT 2023
% 0.09/0.28 % CPUTime :
% 0.12/0.37 Running first-order theorem proving
% 0.12/0.37 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.23/1.00 % SZS status Started for theBenchmark.p
% 3.23/1.00 % SZS status Theorem for theBenchmark.p
% 3.23/1.00
% 3.23/1.00 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.23/1.00
% 3.23/1.00 ------ iProver source info
% 3.23/1.00
% 3.23/1.00 git: date: 2023-05-31 18:12:56 +0000
% 3.23/1.00 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.23/1.00 git: non_committed_changes: false
% 3.23/1.00 git: last_make_outside_of_git: false
% 3.23/1.00
% 3.23/1.00 ------ Parsing...
% 3.23/1.00 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.23/1.00
% 3.23/1.00 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 3.23/1.00
% 3.23/1.00 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.23/1.00
% 3.23/1.00 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.23/1.00 ------ Proving...
% 3.23/1.00 ------ Problem Properties
% 3.23/1.00
% 3.23/1.00
% 3.23/1.00 clauses 130
% 3.23/1.00 conjectures 1
% 3.23/1.00 EPR 29
% 3.23/1.00 Horn 95
% 3.23/1.00 unary 12
% 3.23/1.00 binary 21
% 3.23/1.00 lits 459
% 3.23/1.00 lits eq 69
% 3.23/1.00 fd_pure 0
% 3.23/1.00 fd_pseudo 0
% 3.23/1.00 fd_cond 10
% 3.23/1.00 fd_pseudo_cond 24
% 3.23/1.00 AC symbols 0
% 3.23/1.00
% 3.23/1.00 ------ Input Options Time Limit: Unbounded
% 3.23/1.00
% 3.23/1.00
% 3.23/1.00 ------
% 3.23/1.00 Current options:
% 3.23/1.00 ------
% 3.23/1.00
% 3.23/1.00
% 3.23/1.00
% 3.23/1.00
% 3.23/1.00 ------ Proving...
% 3.23/1.00
% 3.23/1.00
% 3.23/1.00 ------ Proving...
% 3.23/1.00
% 3.23/1.00
% 3.23/1.00 ------ Proving...
% 3.23/1.00
% 3.23/1.00
% 3.23/1.00 % SZS status Theorem for theBenchmark.p
% 3.23/1.00
% 3.23/1.00 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.23/1.00
% 3.23/1.01
%------------------------------------------------------------------------------