TSTP Solution File: SET766+4 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET766+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n023.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 15:09:31 EDT 2023
% Result : Theorem 2.69s 1.19s
% Output : CNFRefutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 8 unt; 0 def)
% Number of atoms : 139 ( 2 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 158 ( 52 ~; 41 |; 41 &)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 93 ( 0 sgn; 72 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0,X6] :
( equivalence(X6,X0)
<=> ( ! [X2,X4,X5] :
( ( member(X5,X0)
& member(X4,X0)
& member(X2,X0) )
=> ( ( apply(X6,X4,X5)
& apply(X6,X2,X4) )
=> apply(X6,X2,X5) ) )
& ! [X2,X4] :
( ( member(X4,X0)
& member(X2,X0) )
=> ( apply(X6,X2,X4)
=> apply(X6,X4,X2) ) )
& ! [X2] :
( member(X2,X0)
=> apply(X6,X2,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence) ).
fof(f15,axiom,
! [X6,X3,X0,X2] :
( member(X2,equivalence_class(X0,X3,X6))
<=> ( apply(X6,X0,X2)
& member(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_class) ).
fof(f17,conjecture,
! [X3,X6,X0] :
( ( member(X0,X3)
& equivalence(X6,X3) )
=> member(X0,equivalence_class(X0,X3,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIII02) ).
fof(f18,negated_conjecture,
~ ! [X3,X6,X0] :
( ( member(X0,X3)
& equivalence(X6,X3) )
=> member(X0,equivalence_class(X0,X3,X6)) ),
inference(negated_conjecture,[],[f17]) ).
fof(f29,plain,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X2,X3,X4] :
( ( member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X2,X3) )
=> apply(X1,X2,X4) ) )
& ! [X5,X6] :
( ( member(X6,X0)
& member(X5,X0) )
=> ( apply(X1,X5,X6)
=> apply(X1,X6,X5) ) )
& ! [X7] :
( member(X7,X0)
=> apply(X1,X7,X7) ) ) ),
inference(rectify,[],[f14]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( member(X3,equivalence_class(X2,X1,X0))
<=> ( apply(X0,X2,X3)
& member(X3,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f32,plain,
~ ! [X0,X1,X2] :
( ( member(X2,X0)
& equivalence(X1,X0) )
=> member(X2,equivalence_class(X2,X0,X1)) ),
inference(rectify,[],[f18]) ).
fof(f33,plain,
! [X0,X1] :
( equivalence(X1,X0)
=> ( ! [X2,X3,X4] :
( ( member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X2,X3) )
=> apply(X1,X2,X4) ) )
& ! [X5,X6] :
( ( member(X6,X0)
& member(X5,X0) )
=> ( apply(X1,X5,X6)
=> apply(X1,X6,X5) ) )
& ! [X7] :
( member(X7,X0)
=> apply(X1,X7,X7) ) ) ),
inference(unused_predicate_definition_removal,[],[f29]) ).
fof(f36,plain,
! [X0,X1] :
( ( ! [X2,X3,X4] :
( apply(X1,X2,X4)
| ~ apply(X1,X3,X4)
| ~ apply(X1,X2,X3)
| ~ member(X4,X0)
| ~ member(X3,X0)
| ~ member(X2,X0) )
& ! [X5,X6] :
( apply(X1,X6,X5)
| ~ apply(X1,X5,X6)
| ~ member(X6,X0)
| ~ member(X5,X0) )
& ! [X7] :
( apply(X1,X7,X7)
| ~ member(X7,X0) ) )
| ~ equivalence(X1,X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f37,plain,
! [X0,X1] :
( ( ! [X2,X3,X4] :
( apply(X1,X2,X4)
| ~ apply(X1,X3,X4)
| ~ apply(X1,X2,X3)
| ~ member(X4,X0)
| ~ member(X3,X0)
| ~ member(X2,X0) )
& ! [X5,X6] :
( apply(X1,X6,X5)
| ~ apply(X1,X5,X6)
| ~ member(X6,X0)
| ~ member(X5,X0) )
& ! [X7] :
( apply(X1,X7,X7)
| ~ member(X7,X0) ) )
| ~ equivalence(X1,X0) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
? [X0,X1,X2] :
( ~ member(X2,equivalence_class(X2,X0,X1))
& member(X2,X0)
& equivalence(X1,X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f39,plain,
? [X0,X1,X2] :
( ~ member(X2,equivalence_class(X2,X0,X1))
& member(X2,X0)
& equivalence(X1,X0) ),
inference(flattening,[],[f38]) ).
fof(f62,plain,
! [X0,X1,X2,X3] :
( ( member(X3,equivalence_class(X2,X1,X0))
| ~ apply(X0,X2,X3)
| ~ member(X3,X1) )
& ( ( apply(X0,X2,X3)
& member(X3,X1) )
| ~ member(X3,equivalence_class(X2,X1,X0)) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f63,plain,
! [X0,X1,X2,X3] :
( ( member(X3,equivalence_class(X2,X1,X0))
| ~ apply(X0,X2,X3)
| ~ member(X3,X1) )
& ( ( apply(X0,X2,X3)
& member(X3,X1) )
| ~ member(X3,equivalence_class(X2,X1,X0)) ) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
( ? [X0,X1,X2] :
( ~ member(X2,equivalence_class(X2,X0,X1))
& member(X2,X0)
& equivalence(X1,X0) )
=> ( ~ member(sK5,equivalence_class(sK5,sK3,sK4))
& member(sK5,sK3)
& equivalence(sK4,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
( ~ member(sK5,equivalence_class(sK5,sK3,sK4))
& member(sK5,sK3)
& equivalence(sK4,sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f39,f64]) ).
fof(f92,plain,
! [X0,X1,X7] :
( apply(X1,X7,X7)
| ~ member(X7,X0)
| ~ equivalence(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f97,plain,
! [X2,X3,X0,X1] :
( member(X3,equivalence_class(X2,X1,X0))
| ~ apply(X0,X2,X3)
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f98,plain,
equivalence(sK4,sK3),
inference(cnf_transformation,[],[f65]) ).
fof(f99,plain,
member(sK5,sK3),
inference(cnf_transformation,[],[f65]) ).
fof(f100,plain,
~ member(sK5,equivalence_class(sK5,sK3,sK4)),
inference(cnf_transformation,[],[f65]) ).
cnf(c_77,plain,
( ~ member(X0,X1)
| ~ equivalence(X2,X1)
| apply(X2,X0,X0) ),
inference(cnf_transformation,[],[f92]) ).
cnf(c_78,plain,
( ~ apply(X0,X1,X2)
| ~ member(X2,X3)
| member(X2,equivalence_class(X1,X3,X0)) ),
inference(cnf_transformation,[],[f97]) ).
cnf(c_81,negated_conjecture,
~ member(sK5,equivalence_class(sK5,sK3,sK4)),
inference(cnf_transformation,[],[f100]) ).
cnf(c_82,negated_conjecture,
member(sK5,sK3),
inference(cnf_transformation,[],[f99]) ).
cnf(c_83,negated_conjecture,
equivalence(sK4,sK3),
inference(cnf_transformation,[],[f98]) ).
cnf(c_574,plain,
( X0 != sK3
| X1 != sK4
| ~ member(X2,X0)
| apply(X1,X2,X2) ),
inference(resolution_lifted,[status(thm)],[c_77,c_83]) ).
cnf(c_575,plain,
( ~ member(X0,sK3)
| apply(sK4,X0,X0) ),
inference(unflattening,[status(thm)],[c_574]) ).
cnf(c_725,plain,
( ~ member(X0,sK3)
| apply(sK4,X0,X0) ),
inference(prop_impl_just,[status(thm)],[c_575]) ).
cnf(c_2009,plain,
( ~ member(sK5,sK3)
| apply(sK4,sK5,sK5) ),
inference(instantiation,[status(thm)],[c_725]) ).
cnf(c_3241,plain,
( ~ apply(sK4,sK5,sK5)
| ~ member(sK5,sK3) ),
inference(superposition,[status(thm)],[c_78,c_81]) ).
cnf(c_3244,plain,
~ apply(sK4,sK5,sK5),
inference(forward_subsumption_resolution,[status(thm)],[c_3241,c_82]) ).
cnf(c_3263,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3244,c_2009,c_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET766+4 : TPTP v8.1.2. Released v2.2.0.
% 0.08/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 11:40:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.69/1.19 % SZS status Started for theBenchmark.p
% 2.69/1.19 % SZS status Theorem for theBenchmark.p
% 2.69/1.19
% 2.69/1.19 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.69/1.19
% 2.69/1.19 ------ iProver source info
% 2.69/1.19
% 2.69/1.19 git: date: 2023-05-31 18:12:56 +0000
% 2.69/1.19 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.69/1.19 git: non_committed_changes: false
% 2.69/1.19 git: last_make_outside_of_git: false
% 2.69/1.19
% 2.69/1.19 ------ Parsing...
% 2.69/1.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.69/1.19
% 2.69/1.19 ------ 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
% 2.69/1.19
% 2.69/1.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.69/1.19
% 2.69/1.19 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.69/1.19 ------ Proving...
% 2.69/1.19 ------ Problem Properties
% 2.69/1.19
% 2.69/1.19
% 2.69/1.19 clauses 34
% 2.69/1.19 conjectures 2
% 2.69/1.19 EPR 6
% 2.69/1.19 Horn 29
% 2.69/1.19 unary 6
% 2.69/1.19 binary 18
% 2.69/1.19 lits 76
% 2.69/1.19 lits eq 3
% 2.69/1.19 fd_pure 0
% 2.69/1.19 fd_pseudo 0
% 2.69/1.19 fd_cond 0
% 2.69/1.19 fd_pseudo_cond 2
% 2.69/1.19 AC symbols 0
% 2.69/1.19
% 2.69/1.19 ------ Schedule dynamic 5 is on
% 2.69/1.19
% 2.69/1.19 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.69/1.19
% 2.69/1.19
% 2.69/1.19 ------
% 2.69/1.19 Current options:
% 2.69/1.19 ------
% 2.69/1.19
% 2.69/1.19
% 2.69/1.19
% 2.69/1.19
% 2.69/1.19 ------ Proving...
% 2.69/1.19
% 2.69/1.19
% 2.69/1.19 % SZS status Theorem for theBenchmark.p
% 2.69/1.19
% 2.69/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.69/1.19
% 2.69/1.19
%------------------------------------------------------------------------------