TSTP Solution File: NUM555+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM555+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n022.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 11:31:25 EDT 2023
% Result : Theorem 3.84s 1.17s
% Output : CNFRefutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 13 unt; 0 def)
% Number of atoms : 189 ( 34 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 242 ( 91 ~; 85 |; 55 &)
% ( 9 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 75 ( 1 sgn; 54 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aSet0(X0) )
=> ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(f66,axiom,
( xk = sbrdtbr0(xQ)
& isFinite0(xQ)
& aSet0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2291) ).
fof(f67,axiom,
( aElementOf0(xy,xQ)
& aElement0(xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2304) ).
fof(f69,axiom,
~ aElementOf0(xx,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2338) ).
fof(f71,conjecture,
~ aElementOf0(xx,sdtmndt0(xQ,xy)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f72,negated_conjecture,
~ ~ aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(negated_conjecture,[],[f71]) ).
fof(f79,plain,
aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(flattening,[],[f72]) ).
fof(f97,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f98,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f97]) ).
fof(f165,plain,
! [X1,X0,X2] :
( sP2(X1,X0,X2)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f166,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> sP2(X1,X0,X2) )
| ~ sP3(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f167,plain,
! [X0,X1] :
( sP3(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f98,f166,f165]) ).
fof(f184,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X0,X1) = X2
| ~ sP2(X1,X0,X2) )
& ( sP2(X1,X0,X2)
| sdtmndt0(X0,X1) != X2 ) )
| ~ sP3(X0,X1) ),
inference(nnf_transformation,[],[f166]) ).
fof(f185,plain,
! [X1,X0,X2] :
( ( sP2(X1,X0,X2)
| ? [X3] :
( ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) )
& ( ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP2(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f165]) ).
fof(f186,plain,
! [X1,X0,X2] :
( ( sP2(X1,X0,X2)
| ? [X3] :
( ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) )
& ( ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP2(X1,X0,X2) ) ),
inference(flattening,[],[f185]) ).
fof(f187,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3] :
( ( X0 = X3
| ~ aElementOf0(X3,X1)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( X0 != X3
& aElementOf0(X3,X1)
& aElement0(X3) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| X0 = X4
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4) )
& ( ( X0 != X4
& aElementOf0(X4,X1)
& aElement0(X4) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f186]) ).
fof(f188,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( X0 = X3
| ~ aElementOf0(X3,X1)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( X0 != X3
& aElementOf0(X3,X1)
& aElement0(X3) )
| aElementOf0(X3,X2) ) )
=> ( ( sK7(X0,X1,X2) = X0
| ~ aElementOf0(sK7(X0,X1,X2),X1)
| ~ aElement0(sK7(X0,X1,X2))
| ~ aElementOf0(sK7(X0,X1,X2),X2) )
& ( ( sK7(X0,X1,X2) != X0
& aElementOf0(sK7(X0,X1,X2),X1)
& aElement0(sK7(X0,X1,X2)) )
| aElementOf0(sK7(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f189,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ( ( sK7(X0,X1,X2) = X0
| ~ aElementOf0(sK7(X0,X1,X2),X1)
| ~ aElement0(sK7(X0,X1,X2))
| ~ aElementOf0(sK7(X0,X1,X2),X2) )
& ( ( sK7(X0,X1,X2) != X0
& aElementOf0(sK7(X0,X1,X2),X1)
& aElement0(sK7(X0,X1,X2)) )
| aElementOf0(sK7(X0,X1,X2),X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| X0 = X4
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4) )
& ( ( X0 != X4
& aElementOf0(X4,X1)
& aElement0(X4) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| ~ sP2(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f187,f188]) ).
fof(f249,plain,
! [X2,X0,X1] :
( sP2(X1,X0,X2)
| sdtmndt0(X0,X1) != X2
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f184]) ).
fof(f253,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X1)
| ~ aElementOf0(X4,X2)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f189]) ).
fof(f260,plain,
! [X0,X1] :
( sP3(X0,X1)
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f339,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f66]) ).
fof(f342,plain,
aElement0(xy),
inference(cnf_transformation,[],[f67]) ).
fof(f345,plain,
~ aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f69]) ).
fof(f347,plain,
aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(cnf_transformation,[],[f79]) ).
fof(f353,plain,
! [X0,X1] :
( sP2(X1,X0,sdtmndt0(X0,X1))
| ~ sP3(X0,X1) ),
inference(equality_resolution,[],[f249]) ).
cnf(c_77,plain,
( ~ sP3(X0,X1)
| sP2(X1,X0,sdtmndt0(X0,X1)) ),
inference(cnf_transformation,[],[f353]) ).
cnf(c_84,plain,
( ~ sP2(X0,X1,X2)
| ~ aElementOf0(X3,X2)
| aElementOf0(X3,X1) ),
inference(cnf_transformation,[],[f253]) ).
cnf(c_87,plain,
( ~ aElement0(X0)
| ~ aSet0(X1)
| sP3(X1,X0) ),
inference(cnf_transformation,[],[f260]) ).
cnf(c_168,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f339]) ).
cnf(c_170,plain,
aElement0(xy),
inference(cnf_transformation,[],[f342]) ).
cnf(c_172,plain,
~ aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f345]) ).
cnf(c_174,negated_conjecture,
aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(cnf_transformation,[],[f347]) ).
cnf(c_1868,plain,
( X0 != X1
| X2 != X3
| ~ aElement0(X0)
| ~ aSet0(X2)
| sP2(X1,X3,sdtmndt0(X3,X1)) ),
inference(resolution_lifted,[status(thm)],[c_87,c_77]) ).
cnf(c_1869,plain,
( ~ aElement0(X0)
| ~ aSet0(X1)
| sP2(X0,X1,sdtmndt0(X1,X0)) ),
inference(unflattening,[status(thm)],[c_1868]) ).
cnf(c_11194,plain,
( ~ aElementOf0(X0,sdtmndt0(X1,X2))
| ~ aElement0(X2)
| ~ aSet0(X1)
| aElementOf0(X0,X1) ),
inference(superposition,[status(thm)],[c_1869,c_84]) ).
cnf(c_11407,plain,
( ~ aElement0(xy)
| ~ aSet0(xQ)
| aElementOf0(xx,xQ) ),
inference(superposition,[status(thm)],[c_174,c_11194]) ).
cnf(c_11408,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11407,c_172,c_168,c_170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM555+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.16/0.35 % Computer : n022.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Fri Aug 25 11:01:40 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.84/1.17 % SZS status Started for theBenchmark.p
% 3.84/1.17 % SZS status Theorem for theBenchmark.p
% 3.84/1.17
% 3.84/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.84/1.17
% 3.84/1.17 ------ iProver source info
% 3.84/1.17
% 3.84/1.17 git: date: 2023-05-31 18:12:56 +0000
% 3.84/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.84/1.17 git: non_committed_changes: false
% 3.84/1.17 git: last_make_outside_of_git: false
% 3.84/1.17
% 3.84/1.17 ------ Parsing...
% 3.84/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.84/1.17
% 3.84/1.17 ------ 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
% 3.84/1.17
% 3.84/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.84/1.17
% 3.84/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.84/1.17 ------ Proving...
% 3.84/1.17 ------ Problem Properties
% 3.84/1.17
% 3.84/1.17
% 3.84/1.17 clauses 123
% 3.84/1.17 conjectures 1
% 3.84/1.17 EPR 39
% 3.84/1.17 Horn 93
% 3.84/1.17 unary 25
% 3.84/1.17 binary 16
% 3.84/1.17 lits 393
% 3.84/1.17 lits eq 59
% 3.84/1.17 fd_pure 0
% 3.84/1.17 fd_pseudo 0
% 3.84/1.17 fd_cond 9
% 3.84/1.17 fd_pseudo_cond 18
% 3.84/1.17 AC symbols 0
% 3.84/1.17
% 3.84/1.17 ------ Input Options Time Limit: Unbounded
% 3.84/1.17
% 3.84/1.17
% 3.84/1.17 ------
% 3.84/1.17 Current options:
% 3.84/1.17 ------
% 3.84/1.17
% 3.84/1.17
% 3.84/1.17
% 3.84/1.17
% 3.84/1.17 ------ Proving...
% 3.84/1.17
% 3.84/1.17
% 3.84/1.17 ------ Proving...
% 3.84/1.17
% 3.84/1.17
% 3.84/1.17 % SZS status Theorem for theBenchmark.p
% 3.84/1.17
% 3.84/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.84/1.18
% 3.84/1.18
%------------------------------------------------------------------------------