TSTP Solution File: SWW629_2 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWW629_2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n015.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 Sep 1 00:39:58 EDT 2023
% Result : Theorem 27.09s 4.21s
% Output : CNFRefutation 27.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 1910 ( 194 equ)
% Maximal formula atoms : 50 ( 42 avg)
% Number of connectives : 578 ( 98 ~; 89 |; 334 &)
% ( 5 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 1385 (1385 fml; 0 var)
% Number arithmetic : 68 ( 10 atm; 16 fun; 42 num; 0 var)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 26 ( 23 usr; 17 prp; 0-3 aty)
% Number of functors : 3 ( 0 usr; 2 con; 0-2 aty)
% Number of variables : 211 ( 0 sgn; 75 !; 118 ?; 193 :)
% Comments :
%------------------------------------------------------------------------------
tff(f45,axiom,
! [X0: ty,X14: uni,X13: uni,X15: uni] :
( permut(X0,X14,X13)
=> ( permut(X0,X13,X15)
=> permut(X0,X14,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',permut_trans) ).
tff(f50,axiom,
! [X0: ty,X14: uni,X13: uni,X16: uni,X17: uni] :
( permut(X0,X14,X16)
=> ( permut(X0,X13,X17)
=> permut(X0,infix_plpl(X0,X14,X13),infix_plpl(X0,X16,X17)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',permut_append) ).
tff(f74,conjecture,
! [X18: list_elt] :
( $less(1,length2(elt,t2tb(X18)))
=> ! [X21: list_elt] :
( ( tb2t(nil(elt)) = X21 )
=> ! [X22: list_elt] :
( ( tb2t(nil(elt)) = X22 )
=> ! [X23: list_elt,X24: list_elt,X25: list_elt] :
( ( ( ( ( length2(elt,t2tb(X24)) = $sum(length2(elt,t2tb(X23)),1) )
& ( 0 = length2(elt,t2tb(X25)) ) )
| ( length2(elt,t2tb(X24)) = length2(elt,t2tb(X23)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X24),t2tb(X23)),t2tb(X25)),t2tb(X18)) )
=> ! [X26: bool1] :
( ( ( true1 = X26 )
<=> ( tb2t(nil(elt)) = X25 ) )
=> ( ( true1 = X26 )
=> ( ( tb2t(nil(elt)) = X25 )
=> ( permut(elt,infix_plpl(elt,t2tb(X24),t2tb(X23)),t2tb(X18))
=> ! [X27: list_elt] :
( ( permut(elt,t2tb(X27),t2tb(X24))
& sorted1(X27) )
=> ! [X28: list_elt] :
( ( permut(elt,t2tb(X28),t2tb(X23))
& sorted1(X28) )
=> ( ( sorted1(X28)
& sorted1(X27)
& ( tb2t(nil(elt)) = X25 ) )
=> ! [X29: list_elt] :
( ( permut(elt,t2tb(X29),infix_plpl(elt,t2tb(X27),t2tb(X28)))
& sorted1(X29) )
=> ( permut(elt,t2tb(X29),t2tb(X18))
& sorted1(X29) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wP_parameter_mergesort) ).
tff(f75,negated_conjecture,
~ ! [X18: list_elt] :
( $less(1,length2(elt,t2tb(X18)))
=> ! [X21: list_elt] :
( ( tb2t(nil(elt)) = X21 )
=> ! [X22: list_elt] :
( ( tb2t(nil(elt)) = X22 )
=> ! [X23: list_elt,X24: list_elt,X25: list_elt] :
( ( ( ( ( length2(elt,t2tb(X24)) = $sum(length2(elt,t2tb(X23)),1) )
& ( 0 = length2(elt,t2tb(X25)) ) )
| ( length2(elt,t2tb(X24)) = length2(elt,t2tb(X23)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X24),t2tb(X23)),t2tb(X25)),t2tb(X18)) )
=> ! [X26: bool1] :
( ( ( true1 = X26 )
<=> ( tb2t(nil(elt)) = X25 ) )
=> ( ( true1 = X26 )
=> ( ( tb2t(nil(elt)) = X25 )
=> ( permut(elt,infix_plpl(elt,t2tb(X24),t2tb(X23)),t2tb(X18))
=> ! [X27: list_elt] :
( ( permut(elt,t2tb(X27),t2tb(X24))
& sorted1(X27) )
=> ! [X28: list_elt] :
( ( permut(elt,t2tb(X28),t2tb(X23))
& sorted1(X28) )
=> ( ( sorted1(X28)
& sorted1(X27)
& ( tb2t(nil(elt)) = X25 ) )
=> ! [X29: list_elt] :
( ( permut(elt,t2tb(X29),infix_plpl(elt,t2tb(X27),t2tb(X28)))
& sorted1(X29) )
=> ( permut(elt,t2tb(X29),t2tb(X18))
& sorted1(X29) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f74]) ).
tff(f127,plain,
! [X0: ty,X1: uni,X2: uni,X3: uni] :
( permut(X0,X1,X2)
=> ( permut(X0,X2,X3)
=> permut(X0,X1,X3) ) ),
inference(rectify,[],[f45]) ).
tff(f132,plain,
! [X0: ty,X1: uni,X2: uni,X3: uni,X4: uni] :
( permut(X0,X1,X3)
=> ( permut(X0,X2,X4)
=> permut(X0,infix_plpl(X0,X1,X2),infix_plpl(X0,X3,X4)) ) ),
inference(rectify,[],[f50]) ).
tff(f153,plain,
~ ! [X0: list_elt] :
( $less(1,length2(elt,t2tb(X0)))
=> ! [X1: list_elt] :
( ( tb2t(nil(elt)) = X1 )
=> ! [X2: list_elt] :
( ( tb2t(nil(elt)) = X2 )
=> ! [X3: list_elt,X4: list_elt,X5: list_elt] :
( ( ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(X0)) )
=> ! [X6: bool1] :
( ( ( true1 = X6 )
<=> ( tb2t(nil(elt)) = X5 ) )
=> ( ( true1 = X6 )
=> ( ( tb2t(nil(elt)) = X5 )
=> ( permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X0))
=> ! [X7: list_elt] :
( ( permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
=> ! [X8: list_elt] :
( ( permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
=> ( ( sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 ) )
=> ! [X9: list_elt] :
( ( permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
=> ( permut(elt,t2tb(X9),t2tb(X0))
& sorted1(X9) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f75]) ).
tff(f166,plain,
! [X0: ty,X1: uni,X2: uni,X3: uni] :
( permut(X0,X1,X3)
| ~ permut(X0,X2,X3)
| ~ permut(X0,X1,X2) ),
inference(ennf_transformation,[],[f127]) ).
tff(f167,plain,
! [X0: ty,X1: uni,X2: uni,X3: uni] :
( permut(X0,X1,X3)
| ~ permut(X0,X2,X3)
| ~ permut(X0,X1,X2) ),
inference(flattening,[],[f166]) ).
tff(f169,plain,
! [X0: ty,X1: uni,X2: uni,X3: uni,X4: uni] :
( permut(X0,infix_plpl(X0,X1,X2),infix_plpl(X0,X3,X4))
| ~ permut(X0,X2,X4)
| ~ permut(X0,X1,X3) ),
inference(ennf_transformation,[],[f132]) ).
tff(f170,plain,
! [X0: ty,X1: uni,X2: uni,X3: uni,X4: uni] :
( permut(X0,infix_plpl(X0,X1,X2),infix_plpl(X0,X3,X4))
| ~ permut(X0,X2,X4)
| ~ permut(X0,X1,X3) ),
inference(flattening,[],[f169]) ).
tff(f184,plain,
? [X0: list_elt] :
( ? [X1: list_elt] :
( ? [X2: list_elt] :
( ? [X3: list_elt,X4: list_elt,X5: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(X0))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X0))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
<=> ( tb2t(nil(elt)) = X5 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(X0)) )
& ( tb2t(nil(elt)) = X2 ) )
& ( tb2t(nil(elt)) = X1 ) )
& $less(1,length2(elt,t2tb(X0))) ),
inference(ennf_transformation,[],[f153]) ).
tff(f185,plain,
? [X0: list_elt] :
( ? [X1: list_elt] :
( ? [X2: list_elt] :
( ? [X3: list_elt,X4: list_elt,X5: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(X0))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X0))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
<=> ( tb2t(nil(elt)) = X5 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(X0)) )
& ( tb2t(nil(elt)) = X2 ) )
& ( tb2t(nil(elt)) = X1 ) )
& $less(1,length2(elt,t2tb(X0))) ),
inference(flattening,[],[f184]) ).
tff(f210,plain,
? [X0: list_elt] :
( ? [X1: list_elt] :
( ? [X2: list_elt] :
( ? [X3: list_elt,X4: list_elt,X5: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(X0))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X0))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != X5 ) )
& ( ( tb2t(nil(elt)) = X5 )
| ( true1 != X6 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(X0)) )
& ( tb2t(nil(elt)) = X2 ) )
& ( tb2t(nil(elt)) = X1 ) )
& $less(1,length2(elt,t2tb(X0))) ),
inference(nnf_transformation,[],[f185]) ).
tff(f211,plain,
? [X0: list_elt] :
( ? [X1: list_elt] :
( ? [X2: list_elt] :
( ? [X3: list_elt,X4: list_elt,X5: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(X0))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X0))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != X5 ) )
& ( ( tb2t(nil(elt)) = X5 )
| ( true1 != X6 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(X0)) )
& ( tb2t(nil(elt)) = X2 ) )
& ( tb2t(nil(elt)) = X1 ) )
& $less(1,length2(elt,t2tb(X0))) ),
inference(flattening,[],[f210]) ).
tff(f212,plain,
( ? [X0: list_elt] :
( ? [X1: list_elt] :
( ? [X2: list_elt] :
( ? [X3: list_elt,X4: list_elt,X5: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(X0))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X0))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != X5 ) )
& ( ( tb2t(nil(elt)) = X5 )
| ( true1 != X6 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(X0)) )
& ( tb2t(nil(elt)) = X2 ) )
& ( tb2t(nil(elt)) = X1 ) )
& $less(1,length2(elt,t2tb(X0))) )
=> ( ? [X1: list_elt] :
( ? [X2: list_elt] :
( ? [X5: list_elt,X4: list_elt,X3: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(sK10))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != X5 ) )
& ( ( tb2t(nil(elt)) = X5 )
| ( true1 != X6 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(sK10)) )
& ( tb2t(nil(elt)) = X2 ) )
& ( tb2t(nil(elt)) = X1 ) )
& $less(1,length2(elt,t2tb(sK10))) ) ),
introduced(choice_axiom,[]) ).
tff(f213,plain,
( ? [X1: list_elt] :
( ? [X2: list_elt] :
( ? [X5: list_elt,X4: list_elt,X3: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(sK10))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != X5 ) )
& ( ( tb2t(nil(elt)) = X5 )
| ( true1 != X6 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(sK10)) )
& ( tb2t(nil(elt)) = X2 ) )
& ( tb2t(nil(elt)) = X1 ) )
=> ( ? [X2: list_elt] :
( ? [X5: list_elt,X4: list_elt,X3: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(sK10))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != X5 ) )
& ( ( tb2t(nil(elt)) = X5 )
| ( true1 != X6 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(sK10)) )
& ( tb2t(nil(elt)) = X2 ) )
& ( tb2t(nil(elt)) = sK11 ) ) ),
introduced(choice_axiom,[]) ).
tff(f214,plain,
( ? [X2: list_elt] :
( ? [X5: list_elt,X4: list_elt,X3: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(sK10))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != X5 ) )
& ( ( tb2t(nil(elt)) = X5 )
| ( true1 != X6 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(sK10)) )
& ( tb2t(nil(elt)) = X2 ) )
=> ( ? [X5: list_elt,X4: list_elt,X3: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(sK10))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != X5 ) )
& ( ( tb2t(nil(elt)) = X5 )
| ( true1 != X6 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(sK10)) )
& ( tb2t(nil(elt)) = sK12 ) ) ),
introduced(choice_axiom,[]) ).
tff(f215,plain,
( ? [X5: list_elt,X4: list_elt,X3: list_elt] :
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = X5 )
& permut(elt,t2tb(X8),t2tb(X3))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(X4))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(sK10))
& ( tb2t(nil(elt)) = X5 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != X5 ) )
& ( ( tb2t(nil(elt)) = X5 )
| ( true1 != X6 ) ) )
& ( ( ( length2(elt,t2tb(X4)) = $sum(length2(elt,t2tb(X3)),1) )
& ( 0 = length2(elt,t2tb(X5)) ) )
| ( length2(elt,t2tb(X4)) = length2(elt,t2tb(X3)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(X4),t2tb(X3)),t2tb(X5)),t2tb(sK10)) )
=> ( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = sK15 )
& permut(elt,t2tb(X8),t2tb(sK13))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(sK14))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK10))
& ( tb2t(nil(elt)) = sK15 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != sK15 ) )
& ( ( tb2t(nil(elt)) = sK15 )
| ( true1 != X6 ) ) )
& ( ( ( length2(elt,t2tb(sK14)) = $sum(length2(elt,t2tb(sK13)),1) )
& ( 0 = length2(elt,t2tb(sK15)) ) )
| ( length2(elt,t2tb(sK14)) = length2(elt,t2tb(sK13)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK15)),t2tb(sK10)) ) ),
introduced(choice_axiom,[]) ).
tff(f216,plain,
( ? [X6: bool1] :
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = sK15 )
& permut(elt,t2tb(X8),t2tb(sK13))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(sK14))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK10))
& ( tb2t(nil(elt)) = sK15 )
& ( true1 = X6 )
& ( ( true1 = X6 )
| ( tb2t(nil(elt)) != sK15 ) )
& ( ( tb2t(nil(elt)) = sK15 )
| ( true1 != X6 ) ) )
=> ( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = sK15 )
& permut(elt,t2tb(X8),t2tb(sK13))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(sK14))
& sorted1(X7) )
& permut(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK10))
& ( tb2t(nil(elt)) = sK15 )
& ( true1 = sK16 )
& ( ( true1 = sK16 )
| ( tb2t(nil(elt)) != sK15 ) )
& ( ( tb2t(nil(elt)) = sK15 )
| ( true1 != sK16 ) ) ) ),
introduced(choice_axiom,[]) ).
tff(f217,plain,
( ? [X7: list_elt] :
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(X7),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(X7)
& ( tb2t(nil(elt)) = sK15 )
& permut(elt,t2tb(X8),t2tb(sK13))
& sorted1(X8) )
& permut(elt,t2tb(X7),t2tb(sK14))
& sorted1(X7) )
=> ( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(sK17),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(sK17)
& ( tb2t(nil(elt)) = sK15 )
& permut(elt,t2tb(X8),t2tb(sK13))
& sorted1(X8) )
& permut(elt,t2tb(sK17),t2tb(sK14))
& sorted1(sK17) ) ),
introduced(choice_axiom,[]) ).
tff(f218,plain,
( ? [X8: list_elt] :
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(sK17),t2tb(X8)))
& sorted1(X9) )
& sorted1(X8)
& sorted1(sK17)
& ( tb2t(nil(elt)) = sK15 )
& permut(elt,t2tb(X8),t2tb(sK13))
& sorted1(X8) )
=> ( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(sK17),t2tb(sK18)))
& sorted1(X9) )
& sorted1(sK18)
& sorted1(sK17)
& ( tb2t(nil(elt)) = sK15 )
& permut(elt,t2tb(sK18),t2tb(sK13))
& sorted1(sK18) ) ),
introduced(choice_axiom,[]) ).
tff(f219,plain,
( ? [X9: list_elt] :
( ( ~ permut(elt,t2tb(X9),t2tb(sK10))
| ~ sorted1(X9) )
& permut(elt,t2tb(X9),infix_plpl(elt,t2tb(sK17),t2tb(sK18)))
& sorted1(X9) )
=> ( ( ~ permut(elt,t2tb(sK19),t2tb(sK10))
| ~ sorted1(sK19) )
& permut(elt,t2tb(sK19),infix_plpl(elt,t2tb(sK17),t2tb(sK18)))
& sorted1(sK19) ) ),
introduced(choice_axiom,[]) ).
tff(f220,plain,
( ( ~ permut(elt,t2tb(sK19),t2tb(sK10))
| ~ sorted1(sK19) )
& permut(elt,t2tb(sK19),infix_plpl(elt,t2tb(sK17),t2tb(sK18)))
& sorted1(sK19)
& sorted1(sK18)
& sorted1(sK17)
& ( tb2t(nil(elt)) = sK15 )
& permut(elt,t2tb(sK18),t2tb(sK13))
& sorted1(sK18)
& permut(elt,t2tb(sK17),t2tb(sK14))
& sorted1(sK17)
& permut(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK10))
& ( tb2t(nil(elt)) = sK15 )
& ( true1 = sK16 )
& ( ( true1 = sK16 )
| ( tb2t(nil(elt)) != sK15 ) )
& ( ( tb2t(nil(elt)) = sK15 )
| ( true1 != sK16 ) )
& ( ( ( length2(elt,t2tb(sK14)) = $sum(length2(elt,t2tb(sK13)),1) )
& ( 0 = length2(elt,t2tb(sK15)) ) )
| ( length2(elt,t2tb(sK14)) = length2(elt,t2tb(sK13)) ) )
& permut(elt,infix_plpl(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK15)),t2tb(sK10))
& ( tb2t(nil(elt)) = sK12 )
& ( tb2t(nil(elt)) = sK11 )
& $less(1,length2(elt,t2tb(sK10))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13,sK14,sK15,sK16,sK17,sK18,sK19])],[f211,f219,f218,f217,f216,f215,f214,f213,f212]) ).
tff(f282,plain,
! [X2: uni,X3: uni,X0: ty,X1: uni] :
( permut(X0,X1,X3)
| ~ permut(X0,X2,X3)
| ~ permut(X0,X1,X2) ),
inference(cnf_transformation,[],[f167]) ).
tff(f287,plain,
! [X2: uni,X3: uni,X0: ty,X1: uni,X4: uni] :
( permut(X0,infix_plpl(X0,X1,X2),infix_plpl(X0,X3,X4))
| ~ permut(X0,X2,X4)
| ~ permut(X0,X1,X3) ),
inference(cnf_transformation,[],[f170]) ).
tff(f331,plain,
permut(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK10)),
inference(cnf_transformation,[],[f220]) ).
tff(f333,plain,
permut(elt,t2tb(sK17),t2tb(sK14)),
inference(cnf_transformation,[],[f220]) ).
tff(f335,plain,
permut(elt,t2tb(sK18),t2tb(sK13)),
inference(cnf_transformation,[],[f220]) ).
tff(f339,plain,
sorted1(sK19),
inference(cnf_transformation,[],[f220]) ).
tff(f340,plain,
permut(elt,t2tb(sK19),infix_plpl(elt,t2tb(sK17),t2tb(sK18))),
inference(cnf_transformation,[],[f220]) ).
tff(f341,plain,
( ~ permut(elt,t2tb(sK19),t2tb(sK10))
| ~ sorted1(sK19) ),
inference(cnf_transformation,[],[f220]) ).
cnf(c_128,plain,
( ~ permut(X0_14,X0_13,X1_13)
| ~ permut(X0_14,X2_13,X0_13)
| permut(X0_14,X2_13,X1_13) ),
inference(cnf_transformation,[],[f282]) ).
cnf(c_133,plain,
( ~ permut(X0_14,X0_13,X1_13)
| ~ permut(X0_14,X2_13,X3_13)
| permut(X0_14,infix_plpl(X0_14,X2_13,X0_13),infix_plpl(X0_14,X3_13,X1_13)) ),
inference(cnf_transformation,[],[f287]) ).
cnf(c_166,negated_conjecture,
( ~ permut(elt,t2tb(sK19),t2tb(sK10))
| ~ sorted1(sK19) ),
inference(cnf_transformation,[],[f341]) ).
cnf(c_167,negated_conjecture,
permut(elt,t2tb(sK19),infix_plpl(elt,t2tb(sK17),t2tb(sK18))),
inference(cnf_transformation,[],[f340]) ).
cnf(c_168,negated_conjecture,
sorted1(sK19),
inference(cnf_transformation,[],[f339]) ).
cnf(c_172,negated_conjecture,
permut(elt,t2tb(sK18),t2tb(sK13)),
inference(cnf_transformation,[],[f335]) ).
cnf(c_174,negated_conjecture,
permut(elt,t2tb(sK17),t2tb(sK14)),
inference(cnf_transformation,[],[f333]) ).
cnf(c_176,negated_conjecture,
permut(elt,infix_plpl(elt,t2tb(sK14),t2tb(sK13)),t2tb(sK10)),
inference(cnf_transformation,[],[f331]) ).
cnf(c_7021,plain,
( ~ permut(elt,infix_plpl(elt,t2tb(sK17),t2tb(sK18)),X0_13)
| permut(elt,t2tb(sK19),X0_13) ),
inference(resolution,[status(thm)],[c_128,c_167]) ).
cnf(c_8535,plain,
( ~ permut(X0_14,infix_plpl(X0_14,X0_13,X1_13),X2_13)
| ~ permut(X0_14,X3_13,X1_13)
| ~ permut(X0_14,X4_13,X0_13)
| permut(X0_14,infix_plpl(X0_14,X4_13,X3_13),X2_13) ),
inference(resolution,[status(thm)],[c_133,c_128]) ).
cnf(c_44408,plain,
( ~ permut(elt,X0_13,t2tb(sK14))
| ~ permut(elt,X1_13,t2tb(sK13))
| permut(elt,infix_plpl(elt,X0_13,X1_13),t2tb(sK10)) ),
inference(resolution,[status(thm)],[c_8535,c_176]) ).
cnf(c_45400,plain,
( ~ permut(elt,t2tb(sK17),t2tb(sK14))
| ~ permut(elt,t2tb(sK18),t2tb(sK13))
| permut(elt,t2tb(sK19),t2tb(sK10)) ),
inference(resolution,[status(thm)],[c_44408,c_7021]) ).
cnf(c_45401,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_45400,c_166,c_172,c_174,c_168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW629_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.36 % Computer : n015.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sun Aug 27 22:00:24 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.21/0.48 Running TFA theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --no_cores 8 --schedule casc_29_tfa /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 27.09/4.21 % SZS status Started for theBenchmark.p
% 27.09/4.21 % SZS status Theorem for theBenchmark.p
% 27.09/4.21
% 27.09/4.21 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 27.09/4.21
% 27.09/4.21 ------ iProver source info
% 27.09/4.21
% 27.09/4.21 git: date: 2023-05-31 18:12:56 +0000
% 27.09/4.21 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 27.09/4.21 git: non_committed_changes: false
% 27.09/4.21 git: last_make_outside_of_git: false
% 27.09/4.21
% 27.09/4.21 ------ Parsing...
% 27.09/4.21 ------ Clausification by vclausify_rel & Parsing by iProver...
% 27.09/4.21
% 27.09/4.21 ------ Preprocessing... sup_sim: 8 sf_s rm: 4 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e
% 27.09/4.21
% 27.09/4.21 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 27.09/4.21
% 27.09/4.21 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 27.09/4.21 ------ Proving...
% 27.09/4.21 ------ Problem Properties
% 27.09/4.21
% 27.09/4.21
% 27.09/4.21 clauses 125
% 27.09/4.21 conjectures 20
% 27.09/4.21 EPR 16
% 27.09/4.21 Horn 107
% 27.09/4.21 unary 67
% 27.09/4.21 binary 35
% 27.09/4.21 lits 217
% 27.09/4.21 lits eq 69
% 27.09/4.21 fd_pure 1
% 27.09/4.21 fd_pseudo 0
% 27.09/4.21 fd_cond 0
% 27.09/4.21 fd_pseudo_cond 5
% 27.09/4.21 AC symbols 2
% 27.09/4.21
% 27.09/4.21 ------ Input Options Time Limit: Unbounded
% 27.09/4.21
% 27.09/4.21
% 27.09/4.21 ------
% 27.09/4.21 Current options:
% 27.09/4.21 ------
% 27.09/4.21
% 27.09/4.21
% 27.09/4.21
% 27.09/4.21
% 27.09/4.21 ------ Proving...
% 27.09/4.21
% 27.09/4.21
% 27.09/4.21 % SZS status Theorem for theBenchmark.p
% 27.09/4.21
% 27.09/4.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 27.09/4.22
% 27.09/4.22
%------------------------------------------------------------------------------