TSTP Solution File: SET776+4 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET776+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n002.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 15:09:47 EDT 2023
% Result : Theorem 2.97s 1.14s
% Output : CNFRefutation 2.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 54 ( 22 unt; 0 def)
% Number of atoms : 325 ( 2 equ)
% Maximal formula atoms : 34 ( 6 avg)
% Number of connectives : 387 ( 116 ~; 102 |; 138 &)
% ( 7 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 153 ( 0 sgn; 82 !; 50 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X6,X3] :
( pre_order(X6,X3)
<=> ( ! [X2,X4,X5] :
( ( member(X5,X3)
& member(X4,X3)
& member(X2,X3) )
=> ( ( apply(X6,X4,X5)
& apply(X6,X2,X4) )
=> apply(X6,X2,X5) ) )
& ! [X2] :
( member(X2,X3)
=> apply(X6,X2,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pre_order) ).
fof(f17,conjecture,
! [X3,X7,X6] :
( ( ! [X0,X1] :
( ( member(X1,X3)
& member(X0,X3) )
=> ( apply(X6,X0,X1)
<=> ( apply(X7,X1,X0)
& apply(X7,X0,X1) ) ) )
& pre_order(X7,X3) )
=> ! [X8,X9,X10,X11] :
( ( member(X11,X3)
& member(X10,X3)
& member(X9,X3)
& member(X8,X3) )
=> ( ( apply(X7,X8,X9)
& apply(X6,X9,X11)
& apply(X6,X8,X10) )
=> apply(X7,X10,X11) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIII12) ).
fof(f18,negated_conjecture,
~ ! [X3,X7,X6] :
( ( ! [X0,X1] :
( ( member(X1,X3)
& member(X0,X3) )
=> ( apply(X6,X0,X1)
<=> ( apply(X7,X1,X0)
& apply(X7,X0,X1) ) ) )
& pre_order(X7,X3) )
=> ! [X8,X9,X10,X11] :
( ( member(X11,X3)
& member(X10,X3)
& member(X9,X3)
& member(X8,X3) )
=> ( ( apply(X7,X8,X9)
& apply(X6,X9,X11)
& apply(X6,X8,X10) )
=> apply(X7,X10,X11) ) ) ),
inference(negated_conjecture,[],[f17]) ).
fof(f31,plain,
! [X0,X1] :
( pre_order(X0,X1)
<=> ( ! [X2,X3,X4] :
( ( member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X2,X3) )
=> apply(X0,X2,X4) ) )
& ! [X5] :
( member(X5,X1)
=> apply(X0,X5,X5) ) ) ),
inference(rectify,[],[f16]) ).
fof(f32,plain,
~ ! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( member(X4,X0)
& member(X3,X0) )
=> ( apply(X2,X3,X4)
<=> ( apply(X1,X4,X3)
& apply(X1,X3,X4) ) ) )
& pre_order(X1,X0) )
=> ! [X5,X6,X7,X8] :
( ( member(X8,X0)
& member(X7,X0)
& member(X6,X0)
& member(X5,X0) )
=> ( ( apply(X1,X5,X6)
& apply(X2,X6,X8)
& apply(X2,X5,X7) )
=> apply(X1,X7,X8) ) ) ),
inference(rectify,[],[f18]) ).
fof(f33,plain,
! [X0,X1] :
( pre_order(X0,X1)
=> ( ! [X2,X3,X4] :
( ( member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X2,X3) )
=> apply(X0,X2,X4) ) )
& ! [X5] :
( member(X5,X1)
=> apply(X0,X5,X5) ) ) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f36,plain,
! [X0,X1] :
( ( ! [X2,X3,X4] :
( apply(X0,X2,X4)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X2,X3)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ member(X2,X1) )
& ! [X5] :
( apply(X0,X5,X5)
| ~ member(X5,X1) ) )
| ~ pre_order(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f37,plain,
! [X0,X1] :
( ( ! [X2,X3,X4] :
( apply(X0,X2,X4)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X2,X3)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ member(X2,X1) )
& ! [X5] :
( apply(X0,X5,X5)
| ~ member(X5,X1) ) )
| ~ pre_order(X0,X1) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
? [X0,X1,X2] :
( ? [X5,X6,X7,X8] :
( ~ apply(X1,X7,X8)
& apply(X1,X5,X6)
& apply(X2,X6,X8)
& apply(X2,X5,X7)
& member(X8,X0)
& member(X7,X0)
& member(X6,X0)
& member(X5,X0) )
& ! [X3,X4] :
( ( apply(X2,X3,X4)
<=> ( apply(X1,X4,X3)
& apply(X1,X3,X4) ) )
| ~ member(X4,X0)
| ~ member(X3,X0) )
& pre_order(X1,X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f39,plain,
? [X0,X1,X2] :
( ? [X5,X6,X7,X8] :
( ~ apply(X1,X7,X8)
& apply(X1,X5,X6)
& apply(X2,X6,X8)
& apply(X2,X5,X7)
& member(X8,X0)
& member(X7,X0)
& member(X6,X0)
& member(X5,X0) )
& ! [X3,X4] :
( ( apply(X2,X3,X4)
<=> ( apply(X1,X4,X3)
& apply(X1,X3,X4) ) )
| ~ member(X4,X0)
| ~ member(X3,X0) )
& pre_order(X1,X0) ),
inference(flattening,[],[f38]) ).
fof(f64,plain,
? [X0,X1,X2] :
( ? [X5,X6,X7,X8] :
( ~ apply(X1,X7,X8)
& apply(X1,X5,X6)
& apply(X2,X6,X8)
& apply(X2,X5,X7)
& member(X8,X0)
& member(X7,X0)
& member(X6,X0)
& member(X5,X0) )
& ! [X3,X4] :
( ( ( apply(X2,X3,X4)
| ~ apply(X1,X4,X3)
| ~ apply(X1,X3,X4) )
& ( ( apply(X1,X4,X3)
& apply(X1,X3,X4) )
| ~ apply(X2,X3,X4) ) )
| ~ member(X4,X0)
| ~ member(X3,X0) )
& pre_order(X1,X0) ),
inference(nnf_transformation,[],[f39]) ).
fof(f65,plain,
? [X0,X1,X2] :
( ? [X5,X6,X7,X8] :
( ~ apply(X1,X7,X8)
& apply(X1,X5,X6)
& apply(X2,X6,X8)
& apply(X2,X5,X7)
& member(X8,X0)
& member(X7,X0)
& member(X6,X0)
& member(X5,X0) )
& ! [X3,X4] :
( ( ( apply(X2,X3,X4)
| ~ apply(X1,X4,X3)
| ~ apply(X1,X3,X4) )
& ( ( apply(X1,X4,X3)
& apply(X1,X3,X4) )
| ~ apply(X2,X3,X4) ) )
| ~ member(X4,X0)
| ~ member(X3,X0) )
& pre_order(X1,X0) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
? [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( ~ apply(X1,X5,X6)
& apply(X1,X3,X4)
& apply(X2,X4,X6)
& apply(X2,X3,X5)
& member(X6,X0)
& member(X5,X0)
& member(X4,X0)
& member(X3,X0) )
& ! [X7,X8] :
( ( ( apply(X2,X7,X8)
| ~ apply(X1,X8,X7)
| ~ apply(X1,X7,X8) )
& ( ( apply(X1,X8,X7)
& apply(X1,X7,X8) )
| ~ apply(X2,X7,X8) ) )
| ~ member(X8,X0)
| ~ member(X7,X0) )
& pre_order(X1,X0) ),
inference(rectify,[],[f65]) ).
fof(f67,plain,
( ? [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( ~ apply(X1,X5,X6)
& apply(X1,X3,X4)
& apply(X2,X4,X6)
& apply(X2,X3,X5)
& member(X6,X0)
& member(X5,X0)
& member(X4,X0)
& member(X3,X0) )
& ! [X7,X8] :
( ( ( apply(X2,X7,X8)
| ~ apply(X1,X8,X7)
| ~ apply(X1,X7,X8) )
& ( ( apply(X1,X8,X7)
& apply(X1,X7,X8) )
| ~ apply(X2,X7,X8) ) )
| ~ member(X8,X0)
| ~ member(X7,X0) )
& pre_order(X1,X0) )
=> ( ? [X6,X5,X4,X3] :
( ~ apply(sK4,X5,X6)
& apply(sK4,X3,X4)
& apply(sK5,X4,X6)
& apply(sK5,X3,X5)
& member(X6,sK3)
& member(X5,sK3)
& member(X4,sK3)
& member(X3,sK3) )
& ! [X8,X7] :
( ( ( apply(sK5,X7,X8)
| ~ apply(sK4,X8,X7)
| ~ apply(sK4,X7,X8) )
& ( ( apply(sK4,X8,X7)
& apply(sK4,X7,X8) )
| ~ apply(sK5,X7,X8) ) )
| ~ member(X8,sK3)
| ~ member(X7,sK3) )
& pre_order(sK4,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
( ? [X6,X5,X4,X3] :
( ~ apply(sK4,X5,X6)
& apply(sK4,X3,X4)
& apply(sK5,X4,X6)
& apply(sK5,X3,X5)
& member(X6,sK3)
& member(X5,sK3)
& member(X4,sK3)
& member(X3,sK3) )
=> ( ~ apply(sK4,sK8,sK9)
& apply(sK4,sK6,sK7)
& apply(sK5,sK7,sK9)
& apply(sK5,sK6,sK8)
& member(sK9,sK3)
& member(sK8,sK3)
& member(sK7,sK3)
& member(sK6,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
( ~ apply(sK4,sK8,sK9)
& apply(sK4,sK6,sK7)
& apply(sK5,sK7,sK9)
& apply(sK5,sK6,sK8)
& member(sK9,sK3)
& member(sK8,sK3)
& member(sK7,sK3)
& member(sK6,sK3)
& ! [X7,X8] :
( ( ( apply(sK5,X7,X8)
| ~ apply(sK4,X8,X7)
| ~ apply(sK4,X7,X8) )
& ( ( apply(sK4,X8,X7)
& apply(sK4,X7,X8) )
| ~ apply(sK5,X7,X8) ) )
| ~ member(X8,sK3)
| ~ member(X7,sK3) )
& pre_order(sK4,sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7,sK8,sK9])],[f66,f68,f67]) ).
fof(f100,plain,
! [X2,X3,X0,X1,X4] :
( apply(X0,X2,X4)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X2,X3)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ member(X2,X1)
| ~ pre_order(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f101,plain,
pre_order(sK4,sK3),
inference(cnf_transformation,[],[f69]) ).
fof(f102,plain,
! [X8,X7] :
( apply(sK4,X7,X8)
| ~ apply(sK5,X7,X8)
| ~ member(X8,sK3)
| ~ member(X7,sK3) ),
inference(cnf_transformation,[],[f69]) ).
fof(f103,plain,
! [X8,X7] :
( apply(sK4,X8,X7)
| ~ apply(sK5,X7,X8)
| ~ member(X8,sK3)
| ~ member(X7,sK3) ),
inference(cnf_transformation,[],[f69]) ).
fof(f105,plain,
member(sK6,sK3),
inference(cnf_transformation,[],[f69]) ).
fof(f106,plain,
member(sK7,sK3),
inference(cnf_transformation,[],[f69]) ).
fof(f107,plain,
member(sK8,sK3),
inference(cnf_transformation,[],[f69]) ).
fof(f108,plain,
member(sK9,sK3),
inference(cnf_transformation,[],[f69]) ).
fof(f109,plain,
apply(sK5,sK6,sK8),
inference(cnf_transformation,[],[f69]) ).
fof(f110,plain,
apply(sK5,sK7,sK9),
inference(cnf_transformation,[],[f69]) ).
fof(f111,plain,
apply(sK4,sK6,sK7),
inference(cnf_transformation,[],[f69]) ).
fof(f112,plain,
~ apply(sK4,sK8,sK9),
inference(cnf_transformation,[],[f69]) ).
cnf(c_78,plain,
( ~ apply(X0,X1,X2)
| ~ apply(X0,X3,X1)
| ~ member(X1,X4)
| ~ member(X2,X4)
| ~ member(X3,X4)
| ~ pre_order(X0,X4)
| apply(X0,X3,X2) ),
inference(cnf_transformation,[],[f100]) ).
cnf(c_80,negated_conjecture,
~ apply(sK4,sK8,sK9),
inference(cnf_transformation,[],[f112]) ).
cnf(c_81,negated_conjecture,
apply(sK4,sK6,sK7),
inference(cnf_transformation,[],[f111]) ).
cnf(c_82,negated_conjecture,
apply(sK5,sK7,sK9),
inference(cnf_transformation,[],[f110]) ).
cnf(c_83,negated_conjecture,
apply(sK5,sK6,sK8),
inference(cnf_transformation,[],[f109]) ).
cnf(c_84,negated_conjecture,
member(sK9,sK3),
inference(cnf_transformation,[],[f108]) ).
cnf(c_85,negated_conjecture,
member(sK8,sK3),
inference(cnf_transformation,[],[f107]) ).
cnf(c_86,negated_conjecture,
member(sK7,sK3),
inference(cnf_transformation,[],[f106]) ).
cnf(c_87,negated_conjecture,
member(sK6,sK3),
inference(cnf_transformation,[],[f105]) ).
cnf(c_89,negated_conjecture,
( ~ apply(sK5,X0,X1)
| ~ member(X0,sK3)
| ~ member(X1,sK3)
| apply(sK4,X1,X0) ),
inference(cnf_transformation,[],[f103]) ).
cnf(c_90,negated_conjecture,
( ~ apply(sK5,X0,X1)
| ~ member(X0,sK3)
| ~ member(X1,sK3)
| apply(sK4,X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
cnf(c_91,negated_conjecture,
pre_order(sK4,sK3),
inference(cnf_transformation,[],[f101]) ).
cnf(c_605,plain,
( X0 != sK4
| X1 != sK3
| ~ apply(X0,X2,X3)
| ~ apply(X0,X4,X2)
| ~ member(X2,X1)
| ~ member(X3,X1)
| ~ member(X4,X1)
| apply(X0,X4,X3) ),
inference(resolution_lifted,[status(thm)],[c_78,c_91]) ).
cnf(c_606,plain,
( ~ apply(sK4,X0,X1)
| ~ apply(sK4,X2,X0)
| ~ member(X0,sK3)
| ~ member(X1,sK3)
| ~ member(X2,sK3)
| apply(sK4,X2,X1) ),
inference(unflattening,[status(thm)],[c_605]) ).
cnf(c_1961,plain,
( ~ apply(sK4,X0,sK6)
| ~ member(X0,sK3)
| ~ member(sK6,sK3)
| ~ member(sK7,sK3)
| apply(sK4,X0,sK7) ),
inference(superposition,[status(thm)],[c_81,c_606]) ).
cnf(c_1962,plain,
( ~ apply(sK4,X0,sK6)
| ~ member(X0,sK3)
| apply(sK4,X0,sK7) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1961,c_86,c_87]) ).
cnf(c_1995,plain,
( ~ member(sK8,sK3)
| ~ member(sK6,sK3)
| apply(sK4,sK8,sK6) ),
inference(superposition,[status(thm)],[c_83,c_89]) ).
cnf(c_1996,plain,
apply(sK4,sK8,sK6),
inference(forward_subsumption_resolution,[status(thm)],[c_1995,c_87,c_85]) ).
cnf(c_2006,plain,
( ~ member(sK9,sK3)
| ~ member(sK7,sK3)
| apply(sK4,sK7,sK9) ),
inference(superposition,[status(thm)],[c_82,c_90]) ).
cnf(c_2009,plain,
apply(sK4,sK7,sK9),
inference(forward_subsumption_resolution,[status(thm)],[c_2006,c_86,c_84]) ).
cnf(c_2052,plain,
( ~ apply(sK4,X0,sK7)
| ~ member(X0,sK3)
| ~ member(sK9,sK3)
| ~ member(sK7,sK3)
| apply(sK4,X0,sK9) ),
inference(superposition,[status(thm)],[c_2009,c_606]) ).
cnf(c_2053,plain,
( ~ apply(sK4,X0,sK7)
| ~ member(X0,sK3)
| apply(sK4,X0,sK9) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2052,c_86,c_84]) ).
cnf(c_2143,plain,
( ~ member(sK8,sK3)
| apply(sK4,sK8,sK7) ),
inference(superposition,[status(thm)],[c_1996,c_1962]) ).
cnf(c_2144,plain,
apply(sK4,sK8,sK7),
inference(forward_subsumption_resolution,[status(thm)],[c_2143,c_85]) ).
cnf(c_2312,plain,
( ~ member(sK8,sK3)
| apply(sK4,sK8,sK9) ),
inference(superposition,[status(thm)],[c_2144,c_2053]) ).
cnf(c_2314,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2312,c_80,c_85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET776+4 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 16:27:03 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.97/1.14 % SZS status Started for theBenchmark.p
% 2.97/1.14 % SZS status Theorem for theBenchmark.p
% 2.97/1.14
% 2.97/1.14 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.97/1.14
% 2.97/1.14 ------ iProver source info
% 2.97/1.14
% 2.97/1.14 git: date: 2023-05-31 18:12:56 +0000
% 2.97/1.14 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.97/1.14 git: non_committed_changes: false
% 2.97/1.14 git: last_make_outside_of_git: false
% 2.97/1.14
% 2.97/1.14 ------ Parsing...
% 2.97/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.97/1.14
% 2.97/1.14 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 2.97/1.14
% 2.97/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.97/1.14
% 2.97/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.97/1.14 ------ Proving...
% 2.97/1.14 ------ Problem Properties
% 2.97/1.14
% 2.97/1.14
% 2.97/1.14 clauses 42
% 2.97/1.14 conjectures 11
% 2.97/1.14 EPR 15
% 2.97/1.14 Horn 37
% 2.97/1.14 unary 12
% 2.97/1.14 binary 18
% 2.97/1.14 lits 91
% 2.97/1.14 lits eq 3
% 2.97/1.14 fd_pure 0
% 2.97/1.14 fd_pseudo 0
% 2.97/1.14 fd_cond 0
% 2.97/1.14 fd_pseudo_cond 2
% 2.97/1.14 AC symbols 0
% 2.97/1.14
% 2.97/1.14 ------ Schedule dynamic 5 is on
% 2.97/1.14
% 2.97/1.14 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.97/1.14
% 2.97/1.14
% 2.97/1.14 ------
% 2.97/1.14 Current options:
% 2.97/1.14 ------
% 2.97/1.14
% 2.97/1.14
% 2.97/1.14
% 2.97/1.14
% 2.97/1.14 ------ Proving...
% 2.97/1.14
% 2.97/1.14
% 2.97/1.14 % SZS status Theorem for theBenchmark.p
% 2.97/1.14
% 2.97/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.97/1.14
% 2.97/1.14
%------------------------------------------------------------------------------