TSTP Solution File: SWC131+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWC131+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n031.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 20:41:12 EDT 2023
% Result : Theorem 0.47s 1.15s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 20 unt; 0 def)
% Number of atoms : 236 ( 46 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 292 ( 115 ~; 81 |; 68 &)
% ( 7 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn; 46 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( ssList(X0)
=> ( cyclefreeP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ~ ( leq(X2,X1)
& leq(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( cyclefreeP(X1)
| neq(X3,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( cyclefreeP(X1)
| neq(X3,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f104,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f105,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f104]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ cyclefreeP(X1)
& ~ neq(X3,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ cyclefreeP(X1)
& ~ neq(X3,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f223,plain,
! [X0] :
( sP0(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f224,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> sP0(X0) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f225,plain,
! [X0] :
( sP1(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f105,f224,f223]) ).
fof(f258,plain,
! [X0] :
( ( ( cyclefreeP(X0)
| ~ sP0(X0) )
& ( sP0(X0)
| ~ cyclefreeP(X0) ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f224]) ).
fof(f316,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f343,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ cyclefreeP(X1)
& ~ neq(X3,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ cyclefreeP(X1)
& ~ neq(X3,nil)
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f344,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ cyclefreeP(X1)
& ~ neq(X3,nil)
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ~ cyclefreeP(sK54)
& ~ neq(X3,nil)
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
( ? [X2] :
( ? [X3] :
( ~ cyclefreeP(sK54)
& ~ neq(X3,nil)
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ~ cyclefreeP(sK54)
& ~ neq(X3,nil)
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
& ssList(sK55) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
( ? [X3] :
( ~ cyclefreeP(sK54)
& ~ neq(X3,nil)
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
=> ( ~ cyclefreeP(sK54)
& ~ neq(sK56,nil)
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
( ~ cyclefreeP(sK54)
& ~ neq(sK56,nil)
& sK53 = sK55
& sK54 = sK56
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56])],[f222,f346,f345,f344,f343]) ).
fof(f370,plain,
! [X0] :
( sP0(X0)
| ~ cyclefreeP(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f258]) ).
fof(f371,plain,
! [X0] :
( cyclefreeP(X0)
| ~ sP0(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f258]) ).
fof(f381,plain,
! [X0] :
( sP1(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f225]) ).
fof(f438,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f316]) ).
fof(f440,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f497,plain,
cyclefreeP(nil),
inference(cnf_transformation,[],[f60]) ).
fof(f548,plain,
ssList(sK54),
inference(cnf_transformation,[],[f347]) ).
fof(f551,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f347]) ).
fof(f553,plain,
~ neq(sK56,nil),
inference(cnf_transformation,[],[f347]) ).
fof(f554,plain,
~ cyclefreeP(sK54),
inference(cnf_transformation,[],[f347]) ).
fof(f555,plain,
~ cyclefreeP(sK56),
inference(definition_unfolding,[],[f554,f551]) ).
fof(f556,plain,
ssList(sK56),
inference(definition_unfolding,[],[f548,f551]) ).
cnf(c_71,plain,
( ~ sP0(X0)
| ~ sP1(X0)
| cyclefreeP(X0) ),
inference(cnf_transformation,[],[f371]) ).
cnf(c_72,plain,
( ~ cyclefreeP(X0)
| ~ sP1(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f370]) ).
cnf(c_82,plain,
( ~ ssList(X0)
| sP1(X0) ),
inference(cnf_transformation,[],[f381]) ).
cnf(c_138,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f438]) ).
cnf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f440]) ).
cnf(c_198,plain,
cyclefreeP(nil),
inference(cnf_transformation,[],[f497]) ).
cnf(c_246,negated_conjecture,
~ cyclefreeP(sK56),
inference(cnf_transformation,[],[f555]) ).
cnf(c_247,negated_conjecture,
~ neq(sK56,nil),
inference(cnf_transformation,[],[f553]) ).
cnf(c_250,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f556]) ).
cnf(c_264,plain,
( ~ ssList(nil)
| sP1(nil) ),
inference(instantiation,[status(thm)],[c_82]) ).
cnf(c_291,plain,
( ~ cyclefreeP(nil)
| ~ sP1(nil)
| sP0(nil) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_2981,plain,
( X0 != X1
| ~ ssList(X0)
| ~ cyclefreeP(X1)
| sP0(X1) ),
inference(resolution_lifted,[status(thm)],[c_82,c_72]) ).
cnf(c_2982,plain,
( ~ ssList(X0)
| ~ cyclefreeP(X0)
| sP0(X0) ),
inference(unflattening,[status(thm)],[c_2981]) ).
cnf(c_2993,plain,
( X0 != X1
| ~ ssList(X0)
| ~ sP0(X1)
| cyclefreeP(X1) ),
inference(resolution_lifted,[status(thm)],[c_82,c_71]) ).
cnf(c_2994,plain,
( ~ ssList(X0)
| ~ sP0(X0)
| cyclefreeP(X0) ),
inference(unflattening,[status(thm)],[c_2993]) ).
cnf(c_3176,plain,
( X0 != nil
| ~ ssList(X0)
| sP0(X0) ),
inference(resolution_lifted,[status(thm)],[c_2982,c_198]) ).
cnf(c_3177,plain,
( ~ ssList(nil)
| sP0(nil) ),
inference(unflattening,[status(thm)],[c_3176]) ).
cnf(c_3178,plain,
sP0(nil),
inference(global_subsumption_just,[status(thm)],[c_3177,c_198,c_141,c_264,c_291]) ).
cnf(c_3183,plain,
( X0 != sK56
| ~ ssList(X0)
| ~ sP0(X0) ),
inference(resolution_lifted,[status(thm)],[c_2994,c_246]) ).
cnf(c_3184,plain,
( ~ ssList(sK56)
| ~ sP0(sK56) ),
inference(unflattening,[status(thm)],[c_3183]) ).
cnf(c_3185,plain,
~ sP0(sK56),
inference(global_subsumption_just,[status(thm)],[c_3184,c_250,c_3184]) ).
cnf(c_3218,plain,
( X0 != sK56
| X1 != nil
| ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1 ),
inference(resolution_lifted,[status(thm)],[c_138,c_247]) ).
cnf(c_3219,plain,
( ~ ssList(nil)
| ~ ssList(sK56)
| sK56 = nil ),
inference(unflattening,[status(thm)],[c_3218]) ).
cnf(c_3220,plain,
sK56 = nil,
inference(global_subsumption_just,[status(thm)],[c_3219,c_250,c_141,c_3219]) ).
cnf(c_6084,plain,
~ sP0(nil),
inference(demodulation,[status(thm)],[c_3185,c_3220]) ).
cnf(c_6086,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6084,c_3178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWC131+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n031.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 18:43:25 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
% 0.47/1.15 % SZS status Started for theBenchmark.p
% 0.47/1.15 % SZS status Theorem for theBenchmark.p
% 0.47/1.15
% 0.47/1.15 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.47/1.15
% 0.47/1.15 ------ iProver source info
% 0.47/1.15
% 0.47/1.15 git: date: 2023-05-31 18:12:56 +0000
% 0.47/1.15 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.47/1.15 git: non_committed_changes: false
% 0.47/1.15 git: last_make_outside_of_git: false
% 0.47/1.15
% 0.47/1.15 ------ Parsing...
% 0.47/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.47/1.15
% 0.47/1.15 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e
% 0.47/1.15
% 0.47/1.15 % SZS status Theorem for theBenchmark.p
% 0.47/1.15
% 0.47/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.47/1.16
% 0.47/1.16
%------------------------------------------------------------------------------