TSTP Solution File: SWC331+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWC331+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n027.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 20:42:36 EDT 2023
% Result : Theorem 3.99s 1.15s
% Output : CNFRefutation 3.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 16 unt; 0 def)
% Number of atoms : 328 ( 106 equ)
% Maximal formula atoms : 36 ( 6 avg)
% Number of connectives : 437 ( 157 ~; 131 |; 127 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 125 ( 0 sgn; 71 !; 41 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
fof(f56,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( segmentP(X0,X1)
=> segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax56) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( equalelemsP(X0)
& segmentP(X1,X0) )
| ( nil = X2
& nil != X3 )
| ! [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)
=> ( ( equalelemsP(X0)
& segmentP(X1,X0) )
| ( nil = X2
& nil != X3 )
| ! [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(f134,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f172,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f173,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f174,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f173]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ equalelemsP(X0)
| ~ segmentP(X1,X0) )
& ( nil != X2
| nil = X3 )
& ? [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
& ssList(X4) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ equalelemsP(X0)
| ~ segmentP(X1,X0) )
& ( nil != X2
| nil = X3 )
& ? [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
& ssList(X4) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f343,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ equalelemsP(X0)
| ~ segmentP(X1,X0) )
& ( nil != X2
| nil = X3 )
& ? [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
& ssList(X4) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ equalelemsP(sK53)
| ~ segmentP(X1,sK53) )
& ( nil != X2
| nil = X3 )
& ? [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
& ssList(X4) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f344,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ equalelemsP(sK53)
| ~ segmentP(X1,sK53) )
& ( nil != X2
| nil = X3 )
& ? [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
& ssList(X4) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ~ equalelemsP(sK53)
| ~ segmentP(sK54,sK53) )
& ( nil != X2
| nil = X3 )
& ? [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
& ssList(X4) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
( ? [X2] :
( ? [X3] :
( ( ~ equalelemsP(sK53)
| ~ segmentP(sK54,sK53) )
& ( nil != X2
| nil = X3 )
& ? [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
& ssList(X4) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ~ equalelemsP(sK53)
| ~ segmentP(sK54,sK53) )
& ( nil != sK55
| nil = X3 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK55
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK55)
& app(sK55,X4) = X3
& ssList(X4) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
& ssList(sK55) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
( ? [X3] :
( ( ~ equalelemsP(sK53)
| ~ segmentP(sK54,sK53) )
& ( nil != sK55
| nil = X3 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK55
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK55)
& app(sK55,X4) = X3
& ssList(X4) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
=> ( ( ~ equalelemsP(sK53)
| ~ segmentP(sK54,sK53) )
& ( nil != sK55
| nil = sK56 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK55
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK55)
& app(sK55,X4) = sK56
& ssList(X4) )
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
( ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK55
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK55)
& app(sK55,X4) = sK56
& ssList(X4) )
=> ( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK55
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != sK57
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK55)
& sK56 = app(sK55,sK57)
& ssList(sK57) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
( ( ~ equalelemsP(sK53)
| ~ segmentP(sK54,sK53) )
& ( nil != sK55
| nil = sK56 )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK55
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != sK57
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK55)
& sK56 = app(sK55,sK57)
& ssList(sK57)
& sK53 = sK55
& sK54 = sK56
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57])],[f222,f347,f346,f345,f344,f343]) ).
fof(f441,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f455,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f492,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f493,plain,
! [X2,X3,X0,X1] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f174]) ).
fof(f548,plain,
ssList(sK53),
inference(cnf_transformation,[],[f348]) ).
fof(f552,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f348]) ).
fof(f553,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f348]) ).
fof(f554,plain,
ssList(sK57),
inference(cnf_transformation,[],[f348]) ).
fof(f555,plain,
sK56 = app(sK55,sK57),
inference(cnf_transformation,[],[f348]) ).
fof(f556,plain,
equalelemsP(sK55),
inference(cnf_transformation,[],[f348]) ).
fof(f559,plain,
( ~ equalelemsP(sK53)
| ~ segmentP(sK54,sK53) ),
inference(cnf_transformation,[],[f348]) ).
fof(f560,plain,
( ~ equalelemsP(sK55)
| ~ segmentP(sK56,sK55) ),
inference(definition_unfolding,[],[f559,f553,f552,f553]) ).
fof(f562,plain,
ssList(sK55),
inference(definition_unfolding,[],[f548,f553]) ).
cnf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f441]) ).
cnf(c_155,plain,
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f455]) ).
cnf(c_192,plain,
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f492]) ).
cnf(c_193,plain,
( ~ segmentP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| segmentP(app(app(X2,X0),X3),X1) ),
inference(cnf_transformation,[],[f493]) ).
cnf(c_246,negated_conjecture,
( ~ segmentP(sK56,sK55)
| ~ equalelemsP(sK55) ),
inference(cnf_transformation,[],[f560]) ).
cnf(c_249,negated_conjecture,
equalelemsP(sK55),
inference(cnf_transformation,[],[f556]) ).
cnf(c_250,negated_conjecture,
app(sK55,sK57) = sK56,
inference(cnf_transformation,[],[f555]) ).
cnf(c_251,negated_conjecture,
ssList(sK57),
inference(cnf_transformation,[],[f554]) ).
cnf(c_255,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f562]) ).
cnf(c_11769,plain,
app(nil,sK55) = sK55,
inference(superposition,[status(thm)],[c_255,c_155]) ).
cnf(c_12085,plain,
( ~ segmentP(sK55,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(sK55)
| segmentP(app(sK55,X1),X0) ),
inference(superposition,[status(thm)],[c_11769,c_193]) ).
cnf(c_13119,plain,
( ~ segmentP(sK55,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| segmentP(app(sK55,X1),X0) ),
inference(global_subsumption_just,[status(thm)],[c_12085,c_255,c_141,c_12085]) ).
cnf(c_13130,plain,
( ~ segmentP(sK55,X0)
| ~ ssList(X0)
| ~ ssList(sK57)
| segmentP(sK56,X0) ),
inference(superposition,[status(thm)],[c_250,c_13119]) ).
cnf(c_17062,plain,
( ~ ssList(X0)
| ~ segmentP(sK55,X0)
| segmentP(sK56,X0) ),
inference(global_subsumption_just,[status(thm)],[c_13130,c_251,c_13130]) ).
cnf(c_17063,plain,
( ~ segmentP(sK55,X0)
| ~ ssList(X0)
| segmentP(sK56,X0) ),
inference(renaming,[status(thm)],[c_17062]) ).
cnf(c_17070,plain,
( ~ ssList(sK55)
| segmentP(sK56,sK55) ),
inference(superposition,[status(thm)],[c_192,c_17063]) ).
cnf(c_17073,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_17070,c_246,c_249,c_255]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC331+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.15/0.34 % Computer : n027.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon Aug 28 16:18:07 EDT 2023
% 0.15/0.34 % 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
% 3.99/1.15 % SZS status Started for theBenchmark.p
% 3.99/1.15 % SZS status Theorem for theBenchmark.p
% 3.99/1.15
% 3.99/1.15 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.99/1.15
% 3.99/1.15 ------ iProver source info
% 3.99/1.15
% 3.99/1.15 git: date: 2023-05-31 18:12:56 +0000
% 3.99/1.15 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.99/1.15 git: non_committed_changes: false
% 3.99/1.15 git: last_make_outside_of_git: false
% 3.99/1.15
% 3.99/1.15 ------ Parsing...
% 3.99/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.99/1.15
% 3.99/1.15 ------ 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
% 3.99/1.15
% 3.99/1.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.99/1.15
% 3.99/1.15 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.99/1.15 ------ Proving...
% 3.99/1.15 ------ Problem Properties
% 3.99/1.15
% 3.99/1.15
% 3.99/1.15 clauses 188
% 3.99/1.15 conjectures 8
% 3.99/1.15 EPR 55
% 3.99/1.15 Horn 120
% 3.99/1.15 unary 22
% 3.99/1.15 binary 41
% 3.99/1.15 lits 631
% 3.99/1.15 lits eq 83
% 3.99/1.15 fd_pure 0
% 3.99/1.15 fd_pseudo 0
% 3.99/1.15 fd_cond 21
% 3.99/1.15 fd_pseudo_cond 14
% 3.99/1.15 AC symbols 0
% 3.99/1.15
% 3.99/1.15 ------ Input Options Time Limit: Unbounded
% 3.99/1.15
% 3.99/1.15
% 3.99/1.15 ------
% 3.99/1.15 Current options:
% 3.99/1.15 ------
% 3.99/1.15
% 3.99/1.15
% 3.99/1.15
% 3.99/1.15
% 3.99/1.15 ------ Proving...
% 3.99/1.15
% 3.99/1.15
% 3.99/1.15 % SZS status Theorem for theBenchmark.p
% 3.99/1.15
% 3.99/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.99/1.15
% 3.99/1.15
%------------------------------------------------------------------------------