TSTP Solution File: SWC254+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWC254+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n013.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 20:42:03 EDT 2023
% Result : Theorem 3.60s 1.15s
% Output : CNFRefutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 53 ( 11 unt; 0 def)
% Number of atoms : 275 ( 81 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 306 ( 84 ~; 76 |; 124 &)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 128 ( 14 sgn; 56 !; 47 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( singletonP(X0)
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(X5,cons(X4,nil)) != X3
| cons(X4,nil) != X2 ) ) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( singletonP(X0)
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(X5,cons(X4,nil)) != X3
| cons(X4,nil) != X2 ) ) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f100,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ~ singletonP(X0)
& ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X3
& cons(X4,nil) = X2
& ssList(X5) )
& ssItem(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ~ singletonP(X0)
& ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X3
& cons(X4,nil) = X2
& ssList(X5) )
& ssItem(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f232,plain,
! [X0,X3,X2,X1] :
( ( ~ singletonP(X0)
& ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X3
& cons(X4,nil) = X2
& ssList(X5) )
& ssItem(X4) )
& neq(X1,nil) )
| ~ sP6(X0,X3,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f233,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP6(X0,X3,X2,X1) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f222,f232]) ).
fof(f243,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f100]) ).
fof(f244,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f243]) ).
fof(f245,plain,
! [X0] :
( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
=> ( cons(sK11(X0),nil) = X0
& ssItem(sK11(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f246,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ( cons(sK11(X0),nil) = X0
& ssItem(sK11(X0)) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f244,f245]) ).
fof(f345,plain,
! [X0,X3,X2,X1] :
( ( ~ singletonP(X0)
& ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X3
& cons(X4,nil) = X2
& ssList(X5) )
& ssItem(X4) )
& neq(X1,nil) )
| ~ sP6(X0,X3,X2,X1) ),
inference(nnf_transformation,[],[f232]) ).
fof(f346,plain,
! [X0,X1,X2,X3] :
( ( ~ singletonP(X0)
& ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X1
& cons(X4,nil) = X2
& ssList(X5) )
& ssItem(X4) )
& neq(X3,nil) )
| ~ sP6(X0,X1,X2,X3) ),
inference(rectify,[],[f345]) ).
fof(f347,plain,
! [X1,X2] :
( ? [X4] :
( ? [X5] :
( app(X5,cons(X4,nil)) = X1
& cons(X4,nil) = X2
& ssList(X5) )
& ssItem(X4) )
=> ( ? [X5] :
( app(X5,cons(sK54(X1,X2),nil)) = X1
& cons(sK54(X1,X2),nil) = X2
& ssList(X5) )
& ssItem(sK54(X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
! [X1,X2] :
( ? [X5] :
( app(X5,cons(sK54(X1,X2),nil)) = X1
& cons(sK54(X1,X2),nil) = X2
& ssList(X5) )
=> ( app(sK55(X1,X2),cons(sK54(X1,X2),nil)) = X1
& cons(sK54(X1,X2),nil) = X2
& ssList(sK55(X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
! [X0,X1,X2,X3] :
( ( ~ singletonP(X0)
& app(sK55(X1,X2),cons(sK54(X1,X2),nil)) = X1
& cons(sK54(X1,X2),nil) = X2
& ssList(sK55(X1,X2))
& ssItem(sK54(X1,X2))
& neq(X3,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(X0,X3,X2,X1) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP6(sK56,X3,X2,X1) )
& 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(sK56,X3,X2,X1) )
& sK56 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK57,nil) )
| sP6(sK56,X3,X2,sK57) )
& 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(sK56,X3,X2,sK57) )
& sK56 = X2
& sK57 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK57,nil) )
| sP6(sK56,X3,sK58,sK57) )
& sK56 = sK58
& sK57 = X3
& ssList(X3) )
& ssList(sK58) ) ),
introduced(choice_axiom,[]) ).
fof(f353,plain,
( ? [X3] :
( ( ( ~ neq(X3,nil)
& neq(sK57,nil) )
| sP6(sK56,X3,sK58,sK57) )
& sK56 = sK58
& sK57 = X3
& ssList(X3) )
=> ( ( ( ~ neq(sK59,nil)
& neq(sK57,nil) )
| sP6(sK56,sK59,sK58,sK57) )
& sK56 = sK58
& sK57 = sK59
& ssList(sK59) ) ),
introduced(choice_axiom,[]) ).
fof(f354,plain,
( ( ( ~ neq(sK59,nil)
& neq(sK57,nil) )
| sP6(sK56,sK59,sK58,sK57) )
& 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(f366,plain,
! [X0,X1] :
( singletonP(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f246]) ).
fof(f555,plain,
! [X2,X3,X0,X1] :
( ssItem(sK54(X1,X2))
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f349]) ).
fof(f557,plain,
! [X2,X3,X0,X1] :
( cons(sK54(X1,X2),nil) = X2
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f349]) ).
fof(f559,plain,
! [X2,X3,X0,X1] :
( ~ singletonP(X0)
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f349]) ).
fof(f560,plain,
ssList(sK56),
inference(cnf_transformation,[],[f354]) ).
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(sK56,sK59,sK58,sK57) ),
inference(cnf_transformation,[],[f354]) ).
fof(f567,plain,
( ~ neq(sK59,nil)
| sP6(sK56,sK59,sK58,sK57) ),
inference(cnf_transformation,[],[f354]) ).
fof(f568,plain,
( ~ neq(sK59,nil)
| sP6(sK58,sK59,sK58,sK59) ),
inference(definition_unfolding,[],[f567,f565,f564]) ).
fof(f569,plain,
( neq(sK59,nil)
| sP6(sK58,sK59,sK58,sK59) ),
inference(definition_unfolding,[],[f566,f564,f565,f564]) ).
fof(f571,plain,
ssList(sK58),
inference(definition_unfolding,[],[f560,f565]) ).
fof(f574,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f366]) ).
cnf(c_58,plain,
( ~ ssList(cons(X0,nil))
| ~ ssItem(X0)
| singletonP(cons(X0,nil)) ),
inference(cnf_transformation,[],[f574]) ).
cnf(c_246,plain,
( ~ sP6(X0,X1,X2,X3)
| ~ singletonP(X0) ),
inference(cnf_transformation,[],[f559]) ).
cnf(c_248,plain,
( ~ sP6(X0,X1,X2,X3)
| cons(sK54(X1,X2),nil) = X2 ),
inference(cnf_transformation,[],[f557]) ).
cnf(c_250,plain,
( ~ sP6(X0,X1,X2,X3)
| ssItem(sK54(X1,X2)) ),
inference(cnf_transformation,[],[f555]) ).
cnf(c_252,negated_conjecture,
( ~ neq(sK59,nil)
| sP6(sK58,sK59,sK58,sK59) ),
inference(cnf_transformation,[],[f568]) ).
cnf(c_253,negated_conjecture,
( sP6(sK58,sK59,sK58,sK59)
| neq(sK59,nil) ),
inference(cnf_transformation,[],[f569]) ).
cnf(c_257,negated_conjecture,
ssList(sK58),
inference(cnf_transformation,[],[f571]) ).
cnf(c_375,negated_conjecture,
sP6(sK58,sK59,sK58,sK59),
inference(global_subsumption_just,[status(thm)],[c_253,c_253,c_252]) ).
cnf(c_377,negated_conjecture,
sP6(sK58,sK59,sK58,sK59),
inference(global_subsumption_just,[status(thm)],[c_252,c_375]) ).
cnf(c_3135,plain,
( X0 != sK58
| X1 != sK59
| X2 != sK58
| X3 != sK59
| ssItem(sK54(X1,X2)) ),
inference(resolution_lifted,[status(thm)],[c_250,c_377]) ).
cnf(c_3136,plain,
ssItem(sK54(sK59,sK58)),
inference(unflattening,[status(thm)],[c_3135]) ).
cnf(c_3145,plain,
( X0 != sK58
| X1 != sK59
| X2 != sK58
| X3 != sK59
| cons(sK54(X1,X2),nil) = X2 ),
inference(resolution_lifted,[status(thm)],[c_248,c_377]) ).
cnf(c_3146,plain,
cons(sK54(sK59,sK58),nil) = sK58,
inference(unflattening,[status(thm)],[c_3145]) ).
cnf(c_3155,plain,
( X0 != sK58
| X1 != sK59
| X2 != sK58
| X3 != sK59
| ~ singletonP(X0) ),
inference(resolution_lifted,[status(thm)],[c_246,c_377]) ).
cnf(c_3156,plain,
~ singletonP(sK58),
inference(unflattening,[status(thm)],[c_3155]) ).
cnf(c_11759,plain,
( ~ ssItem(sK54(sK59,sK58))
| ~ ssList(sK58)
| singletonP(cons(sK54(sK59,sK58),nil)) ),
inference(superposition,[status(thm)],[c_3146,c_58]) ).
cnf(c_11760,plain,
( ~ ssItem(sK54(sK59,sK58))
| ~ ssList(sK58)
| singletonP(sK58) ),
inference(light_normalisation,[status(thm)],[c_11759,c_3146]) ).
cnf(c_11761,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11760,c_3156,c_257,c_3136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWC254+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n013.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 : Mon Aug 28 16:07:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.60/1.15 % SZS status Started for theBenchmark.p
% 3.60/1.15 % SZS status Theorem for theBenchmark.p
% 3.60/1.15
% 3.60/1.15 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.60/1.15
% 3.60/1.15 ------ iProver source info
% 3.60/1.15
% 3.60/1.15 git: date: 2023-05-31 18:12:56 +0000
% 3.60/1.15 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.60/1.15 git: non_committed_changes: false
% 3.60/1.15 git: last_make_outside_of_git: false
% 3.60/1.15
% 3.60/1.15 ------ Parsing...
% 3.60/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.60/1.15
% 3.60/1.15 ------ 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
% 3.60/1.15
% 3.60/1.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.60/1.15
% 3.60/1.15 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.60/1.15 ------ Proving...
% 3.60/1.15 ------ Problem Properties
% 3.60/1.15
% 3.60/1.15
% 3.60/1.15 clauses 188
% 3.60/1.15 conjectures 2
% 3.60/1.15 EPR 53
% 3.60/1.15 Horn 120
% 3.60/1.15 unary 24
% 3.60/1.15 binary 40
% 3.60/1.15 lits 626
% 3.60/1.15 lits eq 81
% 3.60/1.15 fd_pure 0
% 3.60/1.15 fd_pseudo 0
% 3.60/1.15 fd_cond 21
% 3.60/1.15 fd_pseudo_cond 14
% 3.60/1.15 AC symbols 0
% 3.60/1.15
% 3.60/1.15 ------ Schedule dynamic 5 is on
% 3.60/1.15
% 3.60/1.15 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.60/1.15
% 3.60/1.15
% 3.60/1.15 ------
% 3.60/1.15 Current options:
% 3.60/1.15 ------
% 3.60/1.15
% 3.60/1.15
% 3.60/1.15
% 3.60/1.15
% 3.60/1.15 ------ Proving...
% 3.60/1.15
% 3.60/1.15
% 3.60/1.15 % SZS status Theorem for theBenchmark.p
% 3.60/1.15
% 3.60/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.60/1.15
% 3.60/1.15
%------------------------------------------------------------------------------