TSTP Solution File: ITP004+2 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : ITP004+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n020.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 02:28:59 EDT 2024
% Result : Theorem 4.03s 1.19s
% Output : CNFRefutation 4.03s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( mem(X2,arr(X0,X1))
=> ! [X3] :
( mem(X3,X0)
=> mem(ap(X2,X3),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_tp) ).
fof(f17,axiom,
! [X8] :
( ne(X8)
=> mem(c_2Epred__set_2ECHOICE(X8),arr(arr(X8,bool),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Epred__set_2ECHOICE) ).
fof(f19,axiom,
! [X8] :
( ne(X8)
=> mem(c_2Epred__set_2EREST(X8),arr(arr(X8,bool),arr(X8,bool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Epred__set_2EREST) ).
fof(f24,axiom,
! [X8] :
( ne(X8)
=> ! [X9] :
( mem(X9,arr(X8,bool))
=> ! [X10] :
( mem(X10,arr(X8,bool))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(X8),X9),X10))
<=> ! [X11] :
( mem(X11,X8)
=> ( p(ap(ap(c_2Ebool_2EIN(X8),X11),X9))
=> p(ap(ap(c_2Ebool_2EIN(X8),X11),X10)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Epred__set_2ESUBSET__DEF) ).
fof(f25,axiom,
! [X8] :
( ne(X8)
=> ! [X9] :
( mem(X9,arr(X8,bool))
=> ! [X12] :
( mem(X12,X8)
=> ! [X13] :
( mem(X13,X8)
=> ( p(ap(ap(c_2Ebool_2EIN(X8),X12),ap(ap(c_2Epred__set_2EDELETE(X8),X9),X13)))
<=> ( X12 != X13
& p(ap(ap(c_2Ebool_2EIN(X8),X12),X9)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EIN__DELETE) ).
fof(f26,axiom,
! [X8] :
( ne(X8)
=> ! [X9] :
( mem(X9,arr(X8,bool))
=> ap(c_2Epred__set_2EREST(X8),X9) = ap(ap(c_2Epred__set_2EDELETE(X8),X9),ap(c_2Epred__set_2ECHOICE(X8),X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Epred__set_2EREST__DEF) ).
fof(f27,conjecture,
! [X8] :
( ne(X8)
=> ! [X9] :
( mem(X9,arr(X8,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(X8),ap(c_2Epred__set_2EREST(X8),X9)),X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EREST__SUBSET) ).
fof(f28,negated_conjecture,
~ ! [X8] :
( ne(X8)
=> ! [X9] :
( mem(X9,arr(X8,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(X8),ap(c_2Epred__set_2EREST(X8),X9)),X9)) ) ),
inference(negated_conjecture,[],[f27]) ).
fof(f38,plain,
! [X0] :
( ne(X0)
=> mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0)) ),
inference(rectify,[],[f17]) ).
fof(f40,plain,
! [X0] :
( ne(X0)
=> mem(c_2Epred__set_2EREST(X0),arr(arr(X0,bool),arr(X0,bool))) ),
inference(rectify,[],[f19]) ).
fof(f45,plain,
! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,arr(X0,bool))
=> ! [X2] :
( mem(X2,arr(X0,bool))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
<=> ! [X3] :
( mem(X3,X0)
=> ( p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
=> p(ap(ap(c_2Ebool_2EIN(X0),X3),X2)) ) ) ) ) ) ),
inference(rectify,[],[f24]) ).
fof(f46,plain,
! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,arr(X0,bool))
=> ! [X2] :
( mem(X2,X0)
=> ! [X3] :
( mem(X3,X0)
=> ( p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
<=> ( X2 != X3
& p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) ) ) ) ) ) ),
inference(rectify,[],[f25]) ).
fof(f47,plain,
! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,arr(X0,bool))
=> ap(c_2Epred__set_2EREST(X0),X1) = ap(ap(c_2Epred__set_2EDELETE(X0),X1),ap(c_2Epred__set_2ECHOICE(X0),X1)) ) ),
inference(rectify,[],[f26]) ).
fof(f48,plain,
~ ! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,arr(X0,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(c_2Epred__set_2EREST(X0),X1)),X1)) ) ),
inference(rectify,[],[f28]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ! [X3] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0) )
| ~ mem(X2,arr(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f62,plain,
! [X0] :
( mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0))
| ~ ne(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f64,plain,
! [X0] :
( mem(c_2Epred__set_2EREST(X0),arr(arr(X0,bool),arr(X0,bool)))
| ~ ne(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
<=> ! [X3] :
( p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
| ~ mem(X3,X0) ) )
| ~ mem(X2,arr(X0,bool)) )
| ~ mem(X1,arr(X0,bool)) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
<=> ! [X3] :
( p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
| ~ mem(X3,X0) ) )
| ~ mem(X2,arr(X0,bool)) )
| ~ mem(X1,arr(X0,bool)) )
| ~ ne(X0) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
<=> ( X2 != X3
& p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) ) )
| ~ mem(X3,X0) )
| ~ mem(X2,X0) )
| ~ mem(X1,arr(X0,bool)) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( ap(c_2Epred__set_2EREST(X0),X1) = ap(ap(c_2Epred__set_2EDELETE(X0),X1),ap(c_2Epred__set_2ECHOICE(X0),X1))
| ~ mem(X1,arr(X0,bool)) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f73,plain,
? [X0] :
( ? [X1] :
( ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(c_2Epred__set_2EREST(X0),X1)),X1))
& mem(X1,arr(X0,bool)) )
& ne(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f87,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ? [X3] :
( ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
& p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
& mem(X3,X0) ) )
& ( ! [X3] :
( p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
| ~ mem(X3,X0) )
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ) )
| ~ mem(X2,arr(X0,bool)) )
| ~ mem(X1,arr(X0,bool)) )
| ~ ne(X0) ),
inference(nnf_transformation,[],[f70]) ).
fof(f88,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ? [X3] :
( ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
& p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
& mem(X3,X0) ) )
& ( ! [X4] :
( p(ap(ap(c_2Ebool_2EIN(X0),X4),X2))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X4),X1))
| ~ mem(X4,X0) )
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ) )
| ~ mem(X2,arr(X0,bool)) )
| ~ mem(X1,arr(X0,bool)) )
| ~ ne(X0) ),
inference(rectify,[],[f87]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
& p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
& mem(X3,X0) )
=> ( ~ p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X2))
& p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X1))
& mem(sK2(X0,X1,X2),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f90,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ( ~ p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X2))
& p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X1))
& mem(sK2(X0,X1,X2),X0) ) )
& ( ! [X4] :
( p(ap(ap(c_2Ebool_2EIN(X0),X4),X2))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X4),X1))
| ~ mem(X4,X0) )
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ) )
| ~ mem(X2,arr(X0,bool)) )
| ~ mem(X1,arr(X0,bool)) )
| ~ ne(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f88,f89]) ).
fof(f91,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
| X2 = X3
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) )
& ( ( X2 != X3
& p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) )
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3))) ) )
| ~ mem(X3,X0) )
| ~ mem(X2,X0) )
| ~ mem(X1,arr(X0,bool)) )
| ~ ne(X0) ),
inference(nnf_transformation,[],[f71]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
| X2 = X3
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) )
& ( ( X2 != X3
& p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) )
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3))) ) )
| ~ mem(X3,X0) )
| ~ mem(X2,X0) )
| ~ mem(X1,arr(X0,bool)) )
| ~ ne(X0) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
( ? [X0] :
( ? [X1] :
( ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(c_2Epred__set_2EREST(X0),X1)),X1))
& mem(X1,arr(X0,bool)) )
& ne(X0) )
=> ( ? [X1] :
( ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),X1)),X1))
& mem(X1,arr(sK3,bool)) )
& ne(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f94,plain,
( ? [X1] :
( ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),X1)),X1))
& mem(X1,arr(sK3,bool)) )
=> ( ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),sK4))
& mem(sK4,arr(sK3,bool)) ) ),
introduced(choice_axiom,[]) ).
fof(f95,plain,
( ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),sK4))
& mem(sK4,arr(sK3,bool))
& ne(sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f73,f94,f93]) ).
fof(f99,plain,
! [X2,X3,X0,X1] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0)
| ~ mem(X2,arr(X0,X1)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f119,plain,
! [X0] :
( mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f121,plain,
! [X0] :
( mem(c_2Epred__set_2EREST(X0),arr(arr(X0,bool),arr(X0,bool)))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f130,plain,
! [X2,X0,X1] :
( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| mem(sK2(X0,X1,X2),X0)
| ~ mem(X2,arr(X0,bool))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f131,plain,
! [X2,X0,X1] :
( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X1))
| ~ mem(X2,arr(X0,bool))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f132,plain,
! [X2,X0,X1] :
( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X2))
| ~ mem(X2,arr(X0,bool))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f133,plain,
! [X2,X3,X0,X1] :
( p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
| ~ mem(X3,X0)
| ~ mem(X2,X0)
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f136,plain,
! [X0,X1] :
( ap(c_2Epred__set_2EREST(X0),X1) = ap(ap(c_2Epred__set_2EDELETE(X0),X1),ap(c_2Epred__set_2ECHOICE(X0),X1))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f137,plain,
ne(sK3),
inference(cnf_transformation,[],[f95]) ).
fof(f138,plain,
mem(sK4,arr(sK3,bool)),
inference(cnf_transformation,[],[f95]) ).
fof(f139,plain,
~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),sK4)),
inference(cnf_transformation,[],[f95]) ).
cnf(c_52,plain,
( ~ mem(X0,arr(X1,X2))
| ~ mem(X3,X1)
| mem(ap(X0,X3),X2) ),
inference(cnf_transformation,[],[f99]) ).
cnf(c_72,plain,
( ~ ne(X0)
| mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0)) ),
inference(cnf_transformation,[],[f119]) ).
cnf(c_74,plain,
( ~ ne(X0)
| mem(c_2Epred__set_2EREST(X0),arr(arr(X0,bool),arr(X0,bool))) ),
inference(cnf_transformation,[],[f121]) ).
cnf(c_82,plain,
( ~ p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X2))
| ~ mem(X1,arr(X0,bool))
| ~ mem(X2,arr(X0,bool))
| ~ ne(X0)
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ),
inference(cnf_transformation,[],[f132]) ).
cnf(c_83,plain,
( ~ mem(X0,arr(X1,bool))
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1)
| p(ap(ap(c_2Ebool_2EIN(X1),sK2(X1,X0,X2)),X0))
| p(ap(ap(c_2Epred__set_2ESUBSET(X1),X0),X2)) ),
inference(cnf_transformation,[],[f131]) ).
cnf(c_84,plain,
( ~ mem(X0,arr(X1,bool))
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1)
| p(ap(ap(c_2Epred__set_2ESUBSET(X1),X0),X2))
| mem(sK2(X1,X0,X2),X1) ),
inference(cnf_transformation,[],[f130]) ).
cnf(c_88,plain,
( ~ p(ap(ap(c_2Ebool_2EIN(X0),X1),ap(ap(c_2Epred__set_2EDELETE(X0),X2),X3)))
| ~ mem(X2,arr(X0,bool))
| ~ mem(X1,X0)
| ~ mem(X3,X0)
| ~ ne(X0)
| p(ap(ap(c_2Ebool_2EIN(X0),X1),X2)) ),
inference(cnf_transformation,[],[f133]) ).
cnf(c_89,plain,
( ~ mem(X0,arr(X1,bool))
| ~ ne(X1)
| ap(ap(c_2Epred__set_2EDELETE(X1),X0),ap(c_2Epred__set_2ECHOICE(X1),X0)) = ap(c_2Epred__set_2EREST(X1),X0) ),
inference(cnf_transformation,[],[f136]) ).
cnf(c_90,negated_conjecture,
~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),sK4)),
inference(cnf_transformation,[],[f139]) ).
cnf(c_91,negated_conjecture,
mem(sK4,arr(sK3,bool)),
inference(cnf_transformation,[],[f138]) ).
cnf(c_92,negated_conjecture,
ne(sK3),
inference(cnf_transformation,[],[f137]) ).
cnf(c_696,plain,
arr(sK3,bool) = sP0_iProver_def,
definition ).
cnf(c_697,plain,
c_2Epred__set_2ESUBSET(sK3) = sP1_iProver_def,
definition ).
cnf(c_698,plain,
c_2Epred__set_2EREST(sK3) = sP2_iProver_def,
definition ).
cnf(c_699,plain,
ap(sP2_iProver_def,sK4) = sP3_iProver_def,
definition ).
cnf(c_700,plain,
ap(sP1_iProver_def,sP3_iProver_def) = sP4_iProver_def,
definition ).
cnf(c_701,plain,
ap(sP4_iProver_def,sK4) = sP5_iProver_def,
definition ).
cnf(c_702,negated_conjecture,
ne(sK3),
inference(demodulation,[status(thm)],[c_92]) ).
cnf(c_703,negated_conjecture,
mem(sK4,sP0_iProver_def),
inference(demodulation,[status(thm)],[c_91,c_696]) ).
cnf(c_704,negated_conjecture,
~ p(sP5_iProver_def),
inference(demodulation,[status(thm)],[c_90,c_698,c_699,c_697,c_700,c_701]) ).
cnf(c_1446,plain,
( ~ ne(sK3)
| mem(c_2Epred__set_2ECHOICE(sK3),arr(sP0_iProver_def,sK3)) ),
inference(superposition,[status(thm)],[c_696,c_72]) ).
cnf(c_1448,plain,
mem(c_2Epred__set_2ECHOICE(sK3),arr(sP0_iProver_def,sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_1446,c_702]) ).
cnf(c_1534,plain,
( ~ ne(sK3)
| mem(c_2Epred__set_2EREST(sK3),arr(sP0_iProver_def,sP0_iProver_def)) ),
inference(superposition,[status(thm)],[c_696,c_74]) ).
cnf(c_1538,plain,
( ~ ne(sK3)
| mem(sP2_iProver_def,arr(sP0_iProver_def,sP0_iProver_def)) ),
inference(light_normalisation,[status(thm)],[c_1534,c_698]) ).
cnf(c_1539,plain,
mem(sP2_iProver_def,arr(sP0_iProver_def,sP0_iProver_def)),
inference(forward_subsumption_resolution,[status(thm)],[c_1538,c_702]) ).
cnf(c_1568,plain,
( ~ mem(X0,sP0_iProver_def)
| mem(ap(c_2Epred__set_2ECHOICE(sK3),X0),sK3) ),
inference(superposition,[status(thm)],[c_1448,c_52]) ).
cnf(c_1642,plain,
( ~ mem(X0,sP0_iProver_def)
| mem(ap(sP2_iProver_def,X0),sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_1539,c_52]) ).
cnf(c_1688,plain,
( ~ mem(sK4,sP0_iProver_def)
| mem(sP3_iProver_def,sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_699,c_1642]) ).
cnf(c_1691,plain,
mem(sP3_iProver_def,sP0_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_1688,c_703]) ).
cnf(c_3155,plain,
( ~ mem(X0,sP0_iProver_def)
| ~ ne(sK3)
| ap(ap(c_2Epred__set_2EDELETE(sK3),X0),ap(c_2Epred__set_2ECHOICE(sK3),X0)) = ap(c_2Epred__set_2EREST(sK3),X0) ),
inference(superposition,[status(thm)],[c_696,c_89]) ).
cnf(c_3159,plain,
( ~ mem(X0,sP0_iProver_def)
| ~ ne(sK3)
| ap(ap(c_2Epred__set_2EDELETE(sK3),X0),ap(c_2Epred__set_2ECHOICE(sK3),X0)) = ap(sP2_iProver_def,X0) ),
inference(light_normalisation,[status(thm)],[c_3155,c_698]) ).
cnf(c_3160,plain,
( ~ mem(X0,sP0_iProver_def)
| ap(ap(c_2Epred__set_2EDELETE(sK3),X0),ap(c_2Epred__set_2ECHOICE(sK3),X0)) = ap(sP2_iProver_def,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3159,c_702]) ).
cnf(c_3340,plain,
ap(ap(c_2Epred__set_2EDELETE(sK3),sK4),ap(c_2Epred__set_2ECHOICE(sK3),sK4)) = ap(sP2_iProver_def,sK4),
inference(superposition,[status(thm)],[c_703,c_3160]) ).
cnf(c_3349,plain,
ap(ap(c_2Epred__set_2EDELETE(sK3),sK4),ap(c_2Epred__set_2ECHOICE(sK3),sK4)) = sP3_iProver_def,
inference(light_normalisation,[status(thm)],[c_3340,c_699]) ).
cnf(c_3508,plain,
( ~ mem(X0,arr(sK3,bool))
| ~ mem(X1,arr(sK3,bool))
| ~ ne(sK3)
| mem(sK2(sK3,X0,X1),sK3)
| p(ap(ap(sP1_iProver_def,X0),X1)) ),
inference(superposition,[status(thm)],[c_697,c_84]) ).
cnf(c_3523,plain,
( ~ mem(X0,sP0_iProver_def)
| ~ mem(X1,sP0_iProver_def)
| ~ ne(sK3)
| mem(sK2(sK3,X0,X1),sK3)
| p(ap(ap(sP1_iProver_def,X0),X1)) ),
inference(light_normalisation,[status(thm)],[c_3508,c_696]) ).
cnf(c_3524,plain,
( ~ mem(X0,sP0_iProver_def)
| ~ mem(X1,sP0_iProver_def)
| mem(sK2(sK3,X0,X1),sK3)
| p(ap(ap(sP1_iProver_def,X0),X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3523,c_702]) ).
cnf(c_3788,plain,
( ~ mem(X0,sP0_iProver_def)
| ~ mem(sP3_iProver_def,sP0_iProver_def)
| mem(sK2(sK3,sP3_iProver_def,X0),sK3)
| p(ap(sP4_iProver_def,X0)) ),
inference(superposition,[status(thm)],[c_700,c_3524]) ).
cnf(c_3790,plain,
( ~ mem(X0,sP0_iProver_def)
| mem(sK2(sK3,sP3_iProver_def,X0),sK3)
| p(ap(sP4_iProver_def,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3788,c_1691]) ).
cnf(c_4357,plain,
( ~ p(ap(ap(c_2Ebool_2EIN(sK3),X0),sP3_iProver_def))
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
| ~ mem(sK4,arr(sK3,bool))
| ~ mem(X0,sK3)
| ~ ne(sK3)
| p(ap(ap(c_2Ebool_2EIN(sK3),X0),sK4)) ),
inference(superposition,[status(thm)],[c_3349,c_88]) ).
cnf(c_4359,plain,
( ~ p(ap(ap(c_2Ebool_2EIN(sK3),X0),sP3_iProver_def))
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
| ~ mem(X0,sK3)
| ~ mem(sK4,sP0_iProver_def)
| ~ ne(sK3)
| p(ap(ap(c_2Ebool_2EIN(sK3),X0),sK4)) ),
inference(light_normalisation,[status(thm)],[c_4357,c_696]) ).
cnf(c_4360,plain,
( ~ p(ap(ap(c_2Ebool_2EIN(sK3),X0),sP3_iProver_def))
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
| ~ mem(X0,sK3)
| p(ap(ap(c_2Ebool_2EIN(sK3),X0),sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4359,c_702,c_703]) ).
cnf(c_4715,plain,
( ~ mem(sK2(sK3,sP3_iProver_def,X0),sK3)
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
| ~ mem(X0,arr(sK3,bool))
| ~ mem(sP3_iProver_def,arr(sK3,bool))
| ~ ne(sK3)
| p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,sP3_iProver_def,X0)),sK4))
| p(ap(ap(c_2Epred__set_2ESUBSET(sK3),sP3_iProver_def),X0)) ),
inference(superposition,[status(thm)],[c_83,c_4360]) ).
cnf(c_4723,plain,
( ~ mem(sK2(sK3,sP3_iProver_def,X0),sK3)
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
| ~ mem(X0,sP0_iProver_def)
| ~ mem(sP3_iProver_def,sP0_iProver_def)
| ~ ne(sK3)
| p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,sP3_iProver_def,X0)),sK4))
| p(ap(sP4_iProver_def,X0)) ),
inference(light_normalisation,[status(thm)],[c_4715,c_696,c_697,c_700]) ).
cnf(c_4724,plain,
( ~ mem(sK2(sK3,sP3_iProver_def,X0),sK3)
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
| ~ mem(X0,sP0_iProver_def)
| p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,sP3_iProver_def,X0)),sK4))
| p(ap(sP4_iProver_def,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4723,c_702,c_1691]) ).
cnf(c_4758,plain,
( ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
| ~ mem(X0,sP0_iProver_def)
| p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,sP3_iProver_def,X0)),sK4))
| p(ap(sP4_iProver_def,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_4724,c_3790,c_4724]) ).
cnf(c_4769,plain,
( ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
| ~ mem(sK4,arr(sK3,bool))
| ~ mem(sP3_iProver_def,arr(sK3,bool))
| ~ mem(sK4,sP0_iProver_def)
| ~ ne(sK3)
| p(ap(ap(c_2Epred__set_2ESUBSET(sK3),sP3_iProver_def),sK4))
| p(ap(sP4_iProver_def,sK4)) ),
inference(superposition,[status(thm)],[c_4758,c_82]) ).
cnf(c_4770,plain,
( ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
| ~ mem(sK4,sP0_iProver_def)
| ~ mem(sP3_iProver_def,sP0_iProver_def)
| ~ ne(sK3)
| p(sP5_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_4769,c_696,c_697,c_700,c_701]) ).
cnf(c_4771,plain,
~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_4770,c_704,c_702,c_1691,c_703]) ).
cnf(c_4773,plain,
~ mem(sK4,sP0_iProver_def),
inference(superposition,[status(thm)],[c_1568,c_4771]) ).
cnf(c_4774,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4773,c_703]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP004+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.11/0.13 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu May 2 21:50:01 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 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
% 4.03/1.19 % SZS status Started for theBenchmark.p
% 4.03/1.19 % SZS status Theorem for theBenchmark.p
% 4.03/1.19
% 4.03/1.19 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.03/1.19
% 4.03/1.19 ------ iProver source info
% 4.03/1.19
% 4.03/1.19 git: date: 2024-05-02 19:28:25 +0000
% 4.03/1.19 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.03/1.19 git: non_committed_changes: false
% 4.03/1.19
% 4.03/1.19 ------ Parsing...
% 4.03/1.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.03/1.19
% 4.03/1.19 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 4.03/1.19
% 4.03/1.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.03/1.19
% 4.03/1.19 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.03/1.19 ------ Proving...
% 4.03/1.19 ------ Problem Properties
% 4.03/1.19
% 4.03/1.19
% 4.03/1.19 clauses 50
% 4.03/1.19 conjectures 3
% 4.03/1.19 EPR 7
% 4.03/1.19 Horn 42
% 4.03/1.19 unary 14
% 4.03/1.19 binary 9
% 4.03/1.19 lits 151
% 4.03/1.19 lits eq 16
% 4.03/1.19 fd_pure 0
% 4.03/1.19 fd_pseudo 0
% 4.03/1.19 fd_cond 0
% 4.03/1.19 fd_pseudo_cond 6
% 4.03/1.19 AC symbols 0
% 4.03/1.19
% 4.03/1.19 ------ Schedule dynamic 5 is on
% 4.03/1.19
% 4.03/1.19 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.03/1.19
% 4.03/1.19
% 4.03/1.19 ------
% 4.03/1.19 Current options:
% 4.03/1.19 ------
% 4.03/1.19
% 4.03/1.19
% 4.03/1.19
% 4.03/1.19
% 4.03/1.19 ------ Proving...
% 4.03/1.19
% 4.03/1.19
% 4.03/1.19 % SZS status Theorem for theBenchmark.p
% 4.03/1.19
% 4.03/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.03/1.20
% 4.03/1.20
%------------------------------------------------------------------------------