TSTP Solution File: SWC398+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWC398+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n028.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 20:43:07 EDT 2023
% Result : Theorem 3.85s 1.15s
% Output : CNFRefutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 18 unt; 0 def)
% Number of atoms : 344 ( 108 equ)
% Maximal formula atoms : 38 ( 8 avg)
% Number of connectives : 447 ( 142 ~; 116 |; 160 &)
% ( 2 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 132 ( 0 sgn; 72 !; 55 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| ! [X8] :
( ssItem(X8)
=> ( memberP(X1,X8)
| ~ memberP(X0,X8) ) )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = X2
& ssList(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ equalelemsP(X2)
| app(X2,X4) != X3 ) )
| 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)
=> ( ( nil = X2
& nil != X3 )
| ! [X8] :
( ssItem(X8)
=> ( memberP(X1,X8)
| ~ memberP(X0,X8) ) )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = X2
& ssList(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ equalelemsP(X2)
| app(X2,X4) != X3 ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| ! [X4] :
( ssItem(X4)
=> ( memberP(X1,X4)
| ~ memberP(X0,X4) ) )
| ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( app(X8,cons(X6,nil)) = X2
& ssList(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ~ equalelemsP(X2)
| app(X2,X5) != X3 ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f147,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ~ memberP(X1,X4)
& memberP(X0,X4)
& ssItem(X4) )
& ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(X2)
& app(X2,X5) = X3
& ssList(X5) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f223,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ~ memberP(X1,X4)
& memberP(X0,X4)
& ssItem(X4) )
& ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(X2)
& app(X2,X5) = X3
& ssList(X5) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f323,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f147]) ).
fof(f324,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f323]) ).
fof(f344,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ~ memberP(X1,X4)
& memberP(X0,X4)
& ssItem(X4) )
& ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(X2)
& app(X2,X5) = X3
& ssList(X5) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ~ memberP(X1,X4)
& memberP(sK53,X4)
& ssItem(X4) )
& ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(X2)
& app(X2,X5) = X3
& ssList(X5) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ~ memberP(X1,X4)
& memberP(sK53,X4)
& ssItem(X4) )
& ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(X2)
& app(X2,X5) = X3
& ssList(X5) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ~ memberP(sK54,X4)
& memberP(sK53,X4)
& ssItem(X4) )
& ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(X2)
& app(X2,X5) = X3
& ssList(X5) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ~ memberP(sK54,X4)
& memberP(sK53,X4)
& ssItem(X4) )
& ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(X2)
& app(X2,X5) = X3
& ssList(X5) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( nil != sK55
| nil = X3 )
& ? [X4] :
( ~ memberP(sK54,X4)
& memberP(sK53,X4)
& ssItem(X4) )
& ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK55
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(sK55)
& app(sK55,X5) = X3
& ssList(X5) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
& ssList(sK55) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
( ? [X3] :
( ( nil != sK55
| nil = X3 )
& ? [X4] :
( ~ memberP(sK54,X4)
& memberP(sK53,X4)
& ssItem(X4) )
& ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK55
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(sK55)
& app(sK55,X5) = X3
& ssList(X5) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
=> ( ( nil != sK55
| nil = sK56 )
& ? [X4] :
( ~ memberP(sK54,X4)
& memberP(sK53,X4)
& ssItem(X4) )
& ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK55
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(sK55)
& app(sK55,X5) = sK56
& ssList(X5) )
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
( ? [X4] :
( ~ memberP(sK54,X4)
& memberP(sK53,X4)
& ssItem(X4) )
=> ( ~ memberP(sK54,sK57)
& memberP(sK53,sK57)
& ssItem(sK57) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK55
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(sK55)
& app(sK55,X5) = sK56
& ssList(X5) )
=> ( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK55
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != sK58
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(sK55)
& sK56 = app(sK55,sK58)
& ssList(sK58) ) ),
introduced(choice_axiom,[]) ).
fof(f350,plain,
( ( nil != sK55
| nil = sK56 )
& ~ memberP(sK54,sK57)
& memberP(sK53,sK57)
& ssItem(sK57)
& ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK55
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != sK58
| ~ ssList(X7) )
| ~ ssItem(X6) )
& equalelemsP(sK55)
& sK56 = app(sK55,sK58)
& ssList(sK58)
& sK53 = sK55
& sK54 = sK56
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58])],[f223,f349,f348,f347,f346,f345,f344]) ).
fof(f468,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f324]) ).
fof(f550,plain,
ssList(sK53),
inference(cnf_transformation,[],[f350]) ).
fof(f554,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f350]) ).
fof(f555,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f350]) ).
fof(f556,plain,
ssList(sK58),
inference(cnf_transformation,[],[f350]) ).
fof(f557,plain,
sK56 = app(sK55,sK58),
inference(cnf_transformation,[],[f350]) ).
fof(f560,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f350]) ).
fof(f561,plain,
memberP(sK53,sK57),
inference(cnf_transformation,[],[f350]) ).
fof(f562,plain,
~ memberP(sK54,sK57),
inference(cnf_transformation,[],[f350]) ).
fof(f564,plain,
~ memberP(sK56,sK57),
inference(definition_unfolding,[],[f562,f554]) ).
fof(f565,plain,
memberP(sK55,sK57),
inference(definition_unfolding,[],[f561,f555]) ).
fof(f567,plain,
ssList(sK55),
inference(definition_unfolding,[],[f550,f555]) ).
cnf(c_166,plain,
( ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| memberP(app(X0,X2),X1) ),
inference(cnf_transformation,[],[f468]) ).
cnf(c_247,negated_conjecture,
~ memberP(sK56,sK57),
inference(cnf_transformation,[],[f564]) ).
cnf(c_248,negated_conjecture,
memberP(sK55,sK57),
inference(cnf_transformation,[],[f565]) ).
cnf(c_249,negated_conjecture,
ssItem(sK57),
inference(cnf_transformation,[],[f560]) ).
cnf(c_252,negated_conjecture,
app(sK55,sK58) = sK56,
inference(cnf_transformation,[],[f557]) ).
cnf(c_253,negated_conjecture,
ssList(sK58),
inference(cnf_transformation,[],[f556]) ).
cnf(c_257,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f567]) ).
cnf(c_18505,plain,
( ~ memberP(sK55,X0)
| ~ ssItem(X0)
| ~ ssList(sK55)
| ~ ssList(sK58)
| memberP(sK56,X0) ),
inference(superposition,[status(thm)],[c_252,c_166]) ).
cnf(c_18525,plain,
( ~ memberP(sK55,X0)
| ~ ssItem(X0)
| memberP(sK56,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18505,c_253,c_257]) ).
cnf(c_20082,plain,
( ~ ssItem(sK57)
| memberP(sK56,sK57) ),
inference(superposition,[status(thm)],[c_248,c_18525]) ).
cnf(c_20083,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_20082,c_247,c_249]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWC398+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13 % Command : run_iprover %s %d THM
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 28 15:14:39 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.85/1.15 % SZS status Started for theBenchmark.p
% 3.85/1.15 % SZS status Theorem for theBenchmark.p
% 3.85/1.15
% 3.85/1.15 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.85/1.15
% 3.85/1.15 ------ iProver source info
% 3.85/1.15
% 3.85/1.15 git: date: 2023-05-31 18:12:56 +0000
% 3.85/1.15 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.85/1.15 git: non_committed_changes: false
% 3.85/1.15 git: last_make_outside_of_git: false
% 3.85/1.15
% 3.85/1.15 ------ Parsing...
% 3.85/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.85/1.15
% 3.85/1.15 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e
% 3.85/1.15
% 3.85/1.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.85/1.15
% 3.85/1.15 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.85/1.15 ------ Proving...
% 3.85/1.15 ------ Problem Properties
% 3.85/1.15
% 3.85/1.15
% 3.85/1.15 clauses 190
% 3.85/1.15 conjectures 10
% 3.85/1.15 EPR 57
% 3.85/1.15 Horn 122
% 3.85/1.15 unary 24
% 3.85/1.15 binary 41
% 3.85/1.15 lits 633
% 3.85/1.15 lits eq 83
% 3.85/1.15 fd_pure 0
% 3.85/1.15 fd_pseudo 0
% 3.85/1.15 fd_cond 21
% 3.85/1.15 fd_pseudo_cond 14
% 3.85/1.15 AC symbols 0
% 3.85/1.15
% 3.85/1.15 ------ Schedule dynamic 5 is on
% 3.85/1.15
% 3.85/1.15 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.85/1.15
% 3.85/1.15
% 3.85/1.15 ------
% 3.85/1.15 Current options:
% 3.85/1.15 ------
% 3.85/1.15
% 3.85/1.15
% 3.85/1.15
% 3.85/1.15
% 3.85/1.15 ------ Proving...
% 3.85/1.15
% 3.85/1.15
% 3.85/1.15 % SZS status Theorem for theBenchmark.p
% 3.85/1.15
% 3.85/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.85/1.15
% 3.85/1.16
%------------------------------------------------------------------------------