TSTP Solution File: NUM552+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM552+1 : 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 : Thu Aug 31 11:31:23 EDT 2023
% Result : Theorem 3.91s 1.13s
% Output : CNFRefutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 16 unt; 0 def)
% Number of atoms : 241 ( 38 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 308 ( 121 ~; 117 |; 55 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 85 ( 0 sgn; 66 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f57,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aSet0(X0) )
=> ! [X2] :
( slbdtsldtrb0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSel) ).
fof(f61,axiom,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202) ).
fof(f62,axiom,
( sz00 != xk
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(f63,axiom,
( slcrc0 != slbdtsldtrb0(xS,xk)
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2227) ).
fof(f65,axiom,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2270) ).
fof(f68,conjecture,
( aElementOf0(xx,xQ)
=> aElementOf0(xx,xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f69,negated_conjecture,
~ ( aElementOf0(xx,xQ)
=> aElementOf0(xx,xT) ),
inference(negated_conjecture,[],[f68]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f150,plain,
! [X0,X1] :
( ! [X2] :
( slbdtsldtrb0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f151,plain,
! [X0,X1] :
( ! [X2] :
( slbdtsldtrb0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(flattening,[],[f150]) ).
fof(f158,plain,
( ~ aElementOf0(xx,xT)
& aElementOf0(xx,xQ) ),
inference(ennf_transformation,[],[f69]) ).
fof(f170,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f83]) ).
fof(f171,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f170]) ).
fof(f172,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f171]) ).
fof(f173,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK5(X0,X1),X0)
& aElementOf0(sK5(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f174,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ( ~ aElementOf0(sK5(X0,X1),X0)
& aElementOf0(sK5(X0,X1),X1) )
| ~ aSet0(X1) )
& ( ( ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f172,f173]) ).
fof(f214,plain,
! [X0,X1] :
( ! [X2] :
( ( slbdtsldtrb0(X0,X1) = X2
| ? [X3] :
( ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f151]) ).
fof(f215,plain,
! [X0,X1] :
( ! [X2] :
( ( slbdtsldtrb0(X0,X1) = X2
| ? [X3] :
( ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(flattening,[],[f214]) ).
fof(f216,plain,
! [X0,X1] :
( ! [X2] :
( ( slbdtsldtrb0(X0,X1) = X2
| ? [X3] :
( ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| sbrdtbr0(X4) != X1
| ~ aSubsetOf0(X4,X0) )
& ( ( sbrdtbr0(X4) = X1
& aSubsetOf0(X4,X0) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(rectify,[],[f215]) ).
fof(f217,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
=> ( ( sbrdtbr0(sK14(X0,X1,X2)) != X1
| ~ aSubsetOf0(sK14(X0,X1,X2),X0)
| ~ aElementOf0(sK14(X0,X1,X2),X2) )
& ( ( sbrdtbr0(sK14(X0,X1,X2)) = X1
& aSubsetOf0(sK14(X0,X1,X2),X0) )
| aElementOf0(sK14(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f218,plain,
! [X0,X1] :
( ! [X2] :
( ( slbdtsldtrb0(X0,X1) = X2
| ( ( sbrdtbr0(sK14(X0,X1,X2)) != X1
| ~ aSubsetOf0(sK14(X0,X1,X2),X0)
| ~ aElementOf0(sK14(X0,X1,X2),X2) )
& ( ( sbrdtbr0(sK14(X0,X1,X2)) = X1
& aSubsetOf0(sK14(X0,X1,X2),X0) )
| aElementOf0(sK14(X0,X1,X2),X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| sbrdtbr0(X4) != X1
| ~ aSubsetOf0(X4,X0) )
& ( ( sbrdtbr0(X4) = X1
& aSubsetOf0(X4,X0) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f216,f217]) ).
fof(f227,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f174]) ).
fof(f318,plain,
! [X2,X0,X1] :
( aSet0(X2)
| slbdtsldtrb0(X0,X1) != X2
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f218]) ).
fof(f319,plain,
! [X2,X0,X1,X4] :
( aSubsetOf0(X4,X0)
| ~ aElementOf0(X4,X2)
| slbdtsldtrb0(X0,X1) != X2
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f218]) ).
fof(f328,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f61]) ).
fof(f330,plain,
aSet0(xT),
inference(cnf_transformation,[],[f62]) ).
fof(f332,plain,
aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
inference(cnf_transformation,[],[f63]) ).
fof(f335,plain,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f65]) ).
fof(f341,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f158]) ).
fof(f342,plain,
~ aElementOf0(xx,xT),
inference(cnf_transformation,[],[f158]) ).
fof(f363,plain,
! [X0,X1,X4] :
( aSubsetOf0(X4,X0)
| ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f319]) ).
fof(f364,plain,
! [X0,X1] :
( aSet0(slbdtsldtrb0(X0,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f318]) ).
cnf(c_58,plain,
( ~ aElementOf0(X0,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2)
| aElementOf0(X0,X2) ),
inference(cnf_transformation,[],[f227]) ).
cnf(c_153,plain,
( ~ aElementOf0(X0,slbdtsldtrb0(X1,X2))
| ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X1)
| aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f363]) ).
cnf(c_154,plain,
( ~ aElementOf0(X0,szNzAzT0)
| ~ aSet0(X1)
| aSet0(slbdtsldtrb0(X1,X0)) ),
inference(cnf_transformation,[],[f364]) ).
cnf(c_158,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f328]) ).
cnf(c_160,plain,
aSet0(xT),
inference(cnf_transformation,[],[f330]) ).
cnf(c_163,plain,
aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
inference(cnf_transformation,[],[f332]) ).
cnf(c_165,plain,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f335]) ).
cnf(c_171,negated_conjecture,
~ aElementOf0(xx,xT),
inference(cnf_transformation,[],[f342]) ).
cnf(c_172,negated_conjecture,
aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f341]) ).
cnf(c_11479,plain,
( ~ aSubsetOf0(slbdtsldtrb0(xS,xk),X0)
| ~ aSet0(X0)
| aElementOf0(xQ,X0) ),
inference(superposition,[status(thm)],[c_165,c_58]) ).
cnf(c_11789,plain,
( ~ aSet0(slbdtsldtrb0(xT,xk))
| aElementOf0(xQ,slbdtsldtrb0(xT,xk)) ),
inference(superposition,[status(thm)],[c_163,c_11479]) ).
cnf(c_11925,plain,
( ~ aSubsetOf0(slbdtsldtrb0(xS,xk),X0)
| ~ aSet0(X0)
| aElementOf0(xQ,X0) ),
inference(superposition,[status(thm)],[c_165,c_58]) ).
cnf(c_11926,plain,
( ~ aSubsetOf0(xQ,X0)
| ~ aSet0(X0)
| aElementOf0(xx,X0) ),
inference(superposition,[status(thm)],[c_172,c_58]) ).
cnf(c_12607,plain,
( ~ aSet0(slbdtsldtrb0(xT,xk))
| aElementOf0(xQ,slbdtsldtrb0(xT,xk)) ),
inference(superposition,[status(thm)],[c_163,c_11925]) ).
cnf(c_12694,plain,
( ~ aSet0(slbdtsldtrb0(xT,xk))
| ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(xT)
| aSubsetOf0(xQ,xT) ),
inference(superposition,[status(thm)],[c_11789,c_153]) ).
cnf(c_14395,plain,
( ~ aSet0(slbdtsldtrb0(xT,xk))
| aSubsetOf0(xQ,xT) ),
inference(global_subsumption_just,[status(thm)],[c_12694,c_160,c_158,c_12694]) ).
cnf(c_14401,plain,
( ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(xT)
| aSubsetOf0(xQ,xT) ),
inference(superposition,[status(thm)],[c_154,c_14395]) ).
cnf(c_14508,plain,
( ~ aSet0(slbdtsldtrb0(xT,xk))
| ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(xT)
| aSubsetOf0(xQ,xT) ),
inference(superposition,[status(thm)],[c_12607,c_153]) ).
cnf(c_16955,plain,
aSubsetOf0(xQ,xT),
inference(global_subsumption_just,[status(thm)],[c_14508,c_160,c_158,c_14401]) ).
cnf(c_16965,plain,
( ~ aSet0(xT)
| aElementOf0(xx,xT) ),
inference(superposition,[status(thm)],[c_16955,c_11926]) ).
cnf(c_16966,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_16965,c_171,c_160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM552+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n004.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 : Fri Aug 25 15:51:23 EDT 2023
% 0.12/0.34 % 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
% 3.91/1.13 % SZS status Started for theBenchmark.p
% 3.91/1.13 % SZS status Theorem for theBenchmark.p
% 3.91/1.13
% 3.91/1.13 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.91/1.13
% 3.91/1.13 ------ iProver source info
% 3.91/1.13
% 3.91/1.13 git: date: 2023-05-31 18:12:56 +0000
% 3.91/1.13 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.91/1.13 git: non_committed_changes: false
% 3.91/1.13 git: last_make_outside_of_git: false
% 3.91/1.13
% 3.91/1.13 ------ Parsing...
% 3.91/1.13 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.91/1.13
% 3.91/1.13 ------ 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: 1 0s sf_e pe_s pe_e
% 3.91/1.13
% 3.91/1.13 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.91/1.13
% 3.91/1.13 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.91/1.13 ------ Proving...
% 3.91/1.13 ------ Problem Properties
% 3.91/1.13
% 3.91/1.13
% 3.91/1.13 clauses 122
% 3.91/1.13 conjectures 2
% 3.91/1.13 EPR 40
% 3.91/1.13 Horn 92
% 3.91/1.13 unary 24
% 3.91/1.13 binary 16
% 3.91/1.13 lits 392
% 3.91/1.13 lits eq 58
% 3.91/1.13 fd_pure 0
% 3.91/1.13 fd_pseudo 0
% 3.91/1.13 fd_cond 9
% 3.91/1.13 fd_pseudo_cond 18
% 3.91/1.13 AC symbols 0
% 3.91/1.13
% 3.91/1.13 ------ Input Options Time Limit: Unbounded
% 3.91/1.13
% 3.91/1.13
% 3.91/1.13 ------
% 3.91/1.13 Current options:
% 3.91/1.13 ------
% 3.91/1.13
% 3.91/1.13
% 3.91/1.13
% 3.91/1.13
% 3.91/1.13 ------ Proving...
% 3.91/1.13
% 3.91/1.13
% 3.91/1.13 ------ Proving...
% 3.91/1.13
% 3.91/1.13
% 3.91/1.13 ------ Proving...
% 3.91/1.13
% 3.91/1.13
% 3.91/1.13 % SZS status Theorem for theBenchmark.p
% 3.91/1.13
% 3.91/1.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.91/1.13
% 3.91/1.13
%------------------------------------------------------------------------------