TSTP Solution File: SWC096+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWC096+1 : TPTP v8.1.2. Released v2.4.0.
% 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 : Fri May 3 03:11:12 EDT 2024
% Result : Theorem 0.45s 1.14s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 53 ( 11 unt; 0 def)
% Number of atoms : 290 ( 107 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 357 ( 120 ~; 107 |; 112 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 165 ( 20 sgn 79 !; 42 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( app(X7,cons(X6,nil)) != X3
| cons(X6,nil) != X2
| ~ ssList(X7) ) )
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X1
& cons(X4,nil) = X0
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( app(X7,cons(X6,nil)) != X3
| cons(X6,nil) != X2
| ~ ssList(X7) ) )
| ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X1
& cons(X4,nil) = X0
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( app(X5,cons(X4,nil)) != X3
| cons(X4,nil) != X2
| ~ ssList(X5) ) )
| ? [X6] :
( ? [X7] :
( app(X7,cons(X6,nil)) = X1
& cons(X6,nil) = X0
& ssList(X7) )
& ssItem(X6) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X3
& cons(X4,nil) = X2
& ssList(X5) )
& ssItem(X4) )
& ! [X6] :
( ! [X7] :
( app(X7,cons(X6,nil)) != X1
| cons(X6,nil) != X0
| ~ ssList(X7) )
| ~ ssItem(X6) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f232,plain,
! [X3,X2,X1,X0] :
( ( ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X3
& cons(X4,nil) = X2
& ssList(X5) )
& ssItem(X4) )
& ! [X6] :
( ! [X7] :
( app(X7,cons(X6,nil)) != X1
| cons(X6,nil) != X0
| ~ ssList(X7) )
| ~ ssItem(X6) )
& neq(X1,nil) )
| ~ sP6(X3,X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f233,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP6(X3,X2,X1,X0) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f222,f232]) ).
fof(f345,plain,
! [X3,X2,X1,X0] :
( ( ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X3
& cons(X4,nil) = X2
& ssList(X5) )
& ssItem(X4) )
& ! [X6] :
( ! [X7] :
( app(X7,cons(X6,nil)) != X1
| cons(X6,nil) != X0
| ~ ssList(X7) )
| ~ ssItem(X6) )
& neq(X1,nil) )
| ~ sP6(X3,X2,X1,X0) ),
inference(nnf_transformation,[],[f232]) ).
fof(f346,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X0
& cons(X4,nil) = X1
& ssList(X5) )
& ssItem(X4) )
& ! [X6] :
( ! [X7] :
( app(X7,cons(X6,nil)) != X2
| cons(X6,nil) != X3
| ~ ssList(X7) )
| ~ ssItem(X6) )
& neq(X2,nil) )
| ~ sP6(X0,X1,X2,X3) ),
inference(rectify,[],[f345]) ).
fof(f347,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X0
& cons(X4,nil) = X1
& ssList(X5) )
& ssItem(X4) )
=> ( ? [X5] :
( app(X5,cons(sK54(X0,X1),nil)) = X0
& cons(sK54(X0,X1),nil) = X1
& ssList(X5) )
& ssItem(sK54(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
! [X0,X1] :
( ? [X5] :
( app(X5,cons(sK54(X0,X1),nil)) = X0
& cons(sK54(X0,X1),nil) = X1
& ssList(X5) )
=> ( app(sK55(X0,X1),cons(sK54(X0,X1),nil)) = X0
& cons(sK54(X0,X1),nil) = X1
& ssList(sK55(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
! [X0,X1,X2,X3] :
( ( app(sK55(X0,X1),cons(sK54(X0,X1),nil)) = X0
& cons(sK54(X0,X1),nil) = X1
& ssList(sK55(X0,X1))
& ssItem(sK54(X0,X1))
& ! [X6] :
( ! [X7] :
( app(X7,cons(X6,nil)) != X2
| cons(X6,nil) != X3
| ~ ssList(X7) )
| ~ ssItem(X6) )
& neq(X2,nil) )
| ~ sP6(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54,sK55])],[f346,f348,f347]) ).
fof(f350,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP6(X3,X2,X1,X0) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP6(X3,X2,X1,sK56) )
& sK56 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f351,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP6(X3,X2,X1,sK56) )
& sK56 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK57,nil) )
| sP6(X3,X2,sK57,sK56) )
& sK56 = X2
& sK57 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK57) ) ),
introduced(choice_axiom,[]) ).
fof(f352,plain,
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK57,nil) )
| sP6(X3,X2,sK57,sK56) )
& sK56 = X2
& sK57 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK57,nil) )
| sP6(X3,sK58,sK57,sK56) )
& sK56 = sK58
& sK57 = X3
& ssList(X3) )
& ssList(sK58) ) ),
introduced(choice_axiom,[]) ).
fof(f353,plain,
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK57,nil) )
| sP6(X3,sK58,sK57,sK56) )
& sK56 = sK58
& sK57 = X3
& ssList(X3) )
=> ( ( ( ~ neq(sK59,nil)
& neq(sK57,nil) )
| sP6(sK59,sK58,sK57,sK56) )
& sK56 = sK58
& sK57 = sK59
& ssList(sK59) ) ),
introduced(choice_axiom,[]) ).
fof(f354,plain,
( ( ( ~ neq(sK59,nil)
& neq(sK57,nil) )
| sP6(sK59,sK58,sK57,sK56) )
& sK56 = sK58
& sK57 = sK59
& ssList(sK59)
& ssList(sK58)
& ssList(sK57)
& ssList(sK56) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56,sK57,sK58,sK59])],[f233,f353,f352,f351,f350]) ).
fof(f555,plain,
! [X2,X3,X0,X1,X6,X7] :
( app(X7,cons(X6,nil)) != X2
| cons(X6,nil) != X3
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f349]) ).
fof(f556,plain,
! [X2,X3,X0,X1] :
( ssItem(sK54(X0,X1))
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f349]) ).
fof(f557,plain,
! [X2,X3,X0,X1] :
( ssList(sK55(X0,X1))
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f349]) ).
fof(f558,plain,
! [X2,X3,X0,X1] :
( cons(sK54(X0,X1),nil) = X1
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f349]) ).
fof(f559,plain,
! [X2,X3,X0,X1] :
( app(sK55(X0,X1),cons(sK54(X0,X1),nil)) = X0
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f349]) ).
fof(f564,plain,
sK57 = sK59,
inference(cnf_transformation,[],[f354]) ).
fof(f565,plain,
sK56 = sK58,
inference(cnf_transformation,[],[f354]) ).
fof(f566,plain,
( neq(sK57,nil)
| sP6(sK59,sK58,sK57,sK56) ),
inference(cnf_transformation,[],[f354]) ).
fof(f567,plain,
( ~ neq(sK59,nil)
| sP6(sK59,sK58,sK57,sK56) ),
inference(cnf_transformation,[],[f354]) ).
fof(f568,plain,
( ~ neq(sK59,nil)
| sP6(sK59,sK58,sK59,sK58) ),
inference(definition_unfolding,[],[f567,f564,f565]) ).
fof(f569,plain,
( neq(sK59,nil)
| sP6(sK59,sK58,sK59,sK58) ),
inference(definition_unfolding,[],[f566,f564,f564,f565]) ).
fof(f599,plain,
! [X3,X0,X1,X6,X7] :
( cons(X6,nil) != X3
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ sP6(X0,X1,app(X7,cons(X6,nil)),X3) ),
inference(equality_resolution,[],[f555]) ).
fof(f600,plain,
! [X0,X1,X6,X7] :
( ~ ssList(X7)
| ~ ssItem(X6)
| ~ sP6(X0,X1,app(X7,cons(X6,nil)),cons(X6,nil)) ),
inference(equality_resolution,[],[f599]) ).
cnf(c_246,plain,
( ~ sP6(X0,X1,X2,X3)
| app(sK55(X0,X1),cons(sK54(X0,X1),nil)) = X0 ),
inference(cnf_transformation,[],[f559]) ).
cnf(c_247,plain,
( ~ sP6(X0,X1,X2,X3)
| cons(sK54(X0,X1),nil) = X1 ),
inference(cnf_transformation,[],[f558]) ).
cnf(c_248,plain,
( ~ sP6(X0,X1,X2,X3)
| ssList(sK55(X0,X1)) ),
inference(cnf_transformation,[],[f557]) ).
cnf(c_249,plain,
( ~ sP6(X0,X1,X2,X3)
| ssItem(sK54(X0,X1)) ),
inference(cnf_transformation,[],[f556]) ).
cnf(c_250,plain,
( ~ sP6(X0,X1,app(X2,cons(X3,nil)),cons(X3,nil))
| ~ ssItem(X3)
| ~ ssList(X2) ),
inference(cnf_transformation,[],[f600]) ).
cnf(c_252,negated_conjecture,
( ~ neq(sK59,nil)
| sP6(sK59,sK58,sK59,sK58) ),
inference(cnf_transformation,[],[f568]) ).
cnf(c_253,negated_conjecture,
( sP6(sK59,sK58,sK59,sK58)
| neq(sK59,nil) ),
inference(cnf_transformation,[],[f569]) ).
cnf(c_376,negated_conjecture,
sP6(sK59,sK58,sK59,sK58),
inference(global_subsumption_just,[status(thm)],[c_253,c_253,c_252]) ).
cnf(c_378,negated_conjecture,
sP6(sK59,sK58,sK59,sK58),
inference(global_subsumption_just,[status(thm)],[c_252,c_376]) ).
cnf(c_3140,plain,
( X0 != sK59
| X1 != sK58
| X2 != sK59
| X3 != sK58
| ssItem(sK54(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_249,c_378]) ).
cnf(c_3141,plain,
ssItem(sK54(sK59,sK58)),
inference(unflattening,[status(thm)],[c_3140]) ).
cnf(c_3145,plain,
( X0 != sK59
| X1 != sK58
| X2 != sK59
| X3 != sK58
| ssList(sK55(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_248,c_378]) ).
cnf(c_3146,plain,
ssList(sK55(sK59,sK58)),
inference(unflattening,[status(thm)],[c_3145]) ).
cnf(c_3150,plain,
( X0 != sK59
| X1 != sK58
| X2 != sK59
| X3 != sK58
| cons(sK54(X0,X1),nil) = X1 ),
inference(resolution_lifted,[status(thm)],[c_247,c_378]) ).
cnf(c_3151,plain,
cons(sK54(sK59,sK58),nil) = sK58,
inference(unflattening,[status(thm)],[c_3150]) ).
cnf(c_3155,plain,
( X0 != sK59
| X1 != sK58
| X2 != sK59
| X3 != sK58
| app(sK55(X0,X1),cons(sK54(X0,X1),nil)) = X0 ),
inference(resolution_lifted,[status(thm)],[c_246,c_378]) ).
cnf(c_3156,plain,
app(sK55(sK59,sK58),cons(sK54(sK59,sK58),nil)) = sK59,
inference(unflattening,[status(thm)],[c_3155]) ).
cnf(c_3160,plain,
( app(X0,cons(X1,nil)) != sK59
| cons(X1,nil) != sK58
| X2 != sK59
| X3 != sK58
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(resolution_lifted,[status(thm)],[c_250,c_378]) ).
cnf(c_3161,plain,
( app(X0,cons(X1,nil)) != sK59
| cons(X1,nil) != sK58
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(unflattening,[status(thm)],[c_3160]) ).
cnf(c_6518,plain,
app(sK55(sK59,sK58),sK58) = sK59,
inference(light_normalisation,[status(thm)],[c_3156,c_3151]) ).
cnf(c_11774,plain,
( cons(sK54(sK59,sK58),nil) != sK58
| app(X0,sK58) != sK59
| ~ ssItem(sK54(sK59,sK58))
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_3151,c_3161]) ).
cnf(c_11775,plain,
( app(X0,sK58) != sK59
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11774,c_3141,c_3151]) ).
cnf(c_11783,plain,
~ ssList(sK55(sK59,sK58)),
inference(superposition,[status(thm)],[c_6518,c_11775]) ).
cnf(c_11784,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11783,c_3146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC096+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.12 % Command : run_iprover %s %d THM
% 0.12/0.32 % Computer : n004.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu May 2 23:18:18 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.18/0.44 Running first-order theorem proving
% 0.18/0.44 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
% 0.45/1.14 % SZS status Started for theBenchmark.p
% 0.45/1.14 % SZS status Theorem for theBenchmark.p
% 0.45/1.14
% 0.45/1.14 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.45/1.14
% 0.45/1.14 ------ iProver source info
% 0.45/1.14
% 0.45/1.14 git: date: 2024-05-02 19:28:25 +0000
% 0.45/1.14 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.45/1.14 git: non_committed_changes: false
% 0.45/1.14
% 0.45/1.14 ------ Parsing...
% 0.45/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.45/1.14
% 0.45/1.14 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 1 sf_s rm: 6 0s sf_e pe_s pe_e
% 0.45/1.14
% 0.45/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.45/1.14
% 0.45/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.45/1.14 ------ Proving...
% 0.45/1.14 ------ Problem Properties
% 0.45/1.14
% 0.45/1.14
% 0.45/1.14 clauses 188
% 0.45/1.14 conjectures 2
% 0.45/1.14 EPR 52
% 0.45/1.14 Horn 120
% 0.45/1.14 unary 23
% 0.45/1.14 binary 40
% 0.45/1.14 lits 629
% 0.45/1.14 lits eq 83
% 0.45/1.14 fd_pure 0
% 0.45/1.14 fd_pseudo 0
% 0.45/1.14 fd_cond 21
% 0.45/1.14 fd_pseudo_cond 14
% 0.45/1.14 AC symbols 0
% 0.45/1.14
% 0.45/1.14 ------ Schedule dynamic 5 is on
% 0.45/1.14
% 0.45/1.14 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.45/1.14
% 0.45/1.14
% 0.45/1.14 ------
% 0.45/1.14 Current options:
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% 0.45/1.14 ------ Proving...
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% 0.45/1.14 % SZS status Theorem for theBenchmark.p
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% 0.45/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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