TSTP Solution File: SWW678_1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWW678_1 : TPTP v8.1.2. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n006.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 00:40:06 EDT 2023
% Result : Theorem 26.74s 4.15s
% Output : CNFRefutation 26.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 17
% Syntax : Number of formulae : 164 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 1175 ( 312 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 966 ( 332 ~; 397 |; 158 &)
% ( 19 <=>; 57 =>; 0 <=; 3 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 377 ( 377 fml; 0 var)
% Number arithmetic : 159 ( 80 atm; 0 fun; 0 num; 79 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 22 ( 15 usr; 6 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 258 ( 3 sgn; 129 !; 44 ?; 173 :)
% Comments :
%------------------------------------------------------------------------------
tff(f6,axiom,
! [X4: $int,X5: 'Tree'] :
( in(X4,X5)
<=> ( ( ( 'empty:Tree' != X5 )
=> ( in(X4,'right:(Tree)>Tree'(X5))
| in(X4,'left:(Tree)>Tree'(X5))
| ( 'val:(Tree)>Int'(X5) = X4 ) ) )
& ( ( 'empty:Tree' = X5 )
=> $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_005) ).
tff(f7,axiom,
! [X5: 'Tree'] :
( searchtree(X5)
<=> ( ( ( 'empty:Tree' != X5 )
=> ( ! [X4: $int] :
( in(X4,'right:(Tree)>Tree'(X5))
=> $greater(X4,'val:(Tree)>Int'(X5)) )
& ! [X4: $int] :
( in(X4,'left:(Tree)>Tree'(X5))
=> $lesseq(X4,'val:(Tree)>Int'(X5)) )
& searchtree('right:(Tree)>Tree'(X5))
& searchtree('left:(Tree)>Tree'(X5)) ) )
& ( ( 'empty:Tree' = X5 )
=> $true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_006) ).
tff(f8,conjecture,
! [X5: 'Tree',X4: $int] :
( searchtree(X5)
=> ( ( ( ( 'empty:Tree' != X5 )
=> ( ( ( 'val:(Tree)>Int'(X5) != X4 )
=> ( ( ~ $less(X4,'val:(Tree)>Int'(X5))
=> ? [X7: 'Tree'] :
( in(X4,X7)
& ( 'right:(Tree)>Tree'(X5) = X7 ) ) )
& ( $less(X4,'val:(Tree)>Int'(X5))
=> ? [X6: 'Tree'] :
( in(X4,X6)
& ( 'left:(Tree)>Tree'(X5) = X6 ) ) ) ) )
& ( ( 'val:(Tree)>Int'(X5) = X4 )
=> $true ) ) )
& ( ( 'empty:Tree' = X5 )
=> $false ) )
<=> in(X4,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_007) ).
tff(f9,negated_conjecture,
~ ! [X5: 'Tree',X4: $int] :
( searchtree(X5)
=> ( ( ( ( 'empty:Tree' != X5 )
=> ( ( ( 'val:(Tree)>Int'(X5) != X4 )
=> ( ( ~ $less(X4,'val:(Tree)>Int'(X5))
=> ? [X7: 'Tree'] :
( in(X4,X7)
& ( 'right:(Tree)>Tree'(X5) = X7 ) ) )
& ( $less(X4,'val:(Tree)>Int'(X5))
=> ? [X6: 'Tree'] :
( in(X4,X6)
& ( 'left:(Tree)>Tree'(X5) = X6 ) ) ) ) )
& ( ( 'val:(Tree)>Int'(X5) = X4 )
=> $true ) ) )
& ( ( 'empty:Tree' = X5 )
=> $false ) )
<=> in(X4,X5) ) ),
inference(negated_conjecture,[],[f8]) ).
tff(f10,plain,
! [X5: 'Tree'] :
( searchtree(X5)
<=> ( ( ( 'empty:Tree' != X5 )
=> ( ! [X4: $int] :
( in(X4,'right:(Tree)>Tree'(X5))
=> $less('val:(Tree)>Int'(X5),X4) )
& ! [X4: $int] :
( in(X4,'left:(Tree)>Tree'(X5))
=> ~ $less('val:(Tree)>Int'(X5),X4) )
& searchtree('right:(Tree)>Tree'(X5))
& searchtree('left:(Tree)>Tree'(X5)) ) )
& ( ( 'empty:Tree' = X5 )
=> $true ) ) ),
inference(theory_normalization,[],[f7]) ).
tff(f16,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_145,[]) ).
tff(f17,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_146,[]) ).
tff(f18,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_147,[]) ).
tff(f27,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,X1)
<=> ( ( ( 'empty:Tree' != X1 )
=> ( in(X0,'right:(Tree)>Tree'(X1))
| in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 ) ) )
& ( ( 'empty:Tree' = X1 )
=> $false ) ) ),
inference(rectify,[],[f6]) ).
tff(f28,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,X1)
<=> ( ( ( 'empty:Tree' != X1 )
=> ( in(X0,'right:(Tree)>Tree'(X1))
| in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 ) ) )
& ( ~ 'empty:Tree' = X1 ) ) ),
inference(true_and_false_elimination,[],[f27]) ).
tff(f29,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,X1)
<=> ( ( ( 'empty:Tree' != X1 )
=> ( in(X0,'right:(Tree)>Tree'(X1))
| in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 ) ) )
& ( 'empty:Tree' != X1 ) ) ),
inference(flattening,[],[f28]) ).
tff(f30,plain,
! [X0: 'Tree'] :
( searchtree(X0)
<=> ( ( ( 'empty:Tree' != X0 )
=> ( ! [X1: $int] :
( in(X1,'right:(Tree)>Tree'(X0))
=> $less('val:(Tree)>Int'(X0),X1) )
& ! [X2: $int] :
( in(X2,'left:(Tree)>Tree'(X0))
=> ~ $less('val:(Tree)>Int'(X0),X2) )
& searchtree('right:(Tree)>Tree'(X0))
& searchtree('left:(Tree)>Tree'(X0)) ) )
& ( ( 'empty:Tree' = X0 )
=> $true ) ) ),
inference(rectify,[],[f10]) ).
tff(f31,plain,
! [X0: 'Tree'] :
( searchtree(X0)
<=> ( ( 'empty:Tree' != X0 )
=> ( ! [X1: $int] :
( in(X1,'right:(Tree)>Tree'(X0))
=> $less('val:(Tree)>Int'(X0),X1) )
& ! [X2: $int] :
( in(X2,'left:(Tree)>Tree'(X0))
=> ~ $less('val:(Tree)>Int'(X0),X2) )
& searchtree('right:(Tree)>Tree'(X0))
& searchtree('left:(Tree)>Tree'(X0)) ) ) ),
inference(true_and_false_elimination,[],[f30]) ).
tff(f32,plain,
~ ! [X0: 'Tree',X1: $int] :
( searchtree(X0)
=> ( ( ( ( 'empty:Tree' != X0 )
=> ( ( ( 'val:(Tree)>Int'(X0) != X1 )
=> ( ( ~ $less(X1,'val:(Tree)>Int'(X0))
=> ? [X2: 'Tree'] :
( in(X1,X2)
& ( 'right:(Tree)>Tree'(X0) = X2 ) ) )
& ( $less(X1,'val:(Tree)>Int'(X0))
=> ? [X3: 'Tree'] :
( in(X1,X3)
& ( 'left:(Tree)>Tree'(X0) = X3 ) ) ) ) )
& ( ( 'val:(Tree)>Int'(X0) = X1 )
=> $true ) ) )
& ( ( 'empty:Tree' = X0 )
=> $false ) )
<=> in(X1,X0) ) ),
inference(rectify,[],[f9]) ).
tff(f33,plain,
~ ! [X0: 'Tree',X1: $int] :
( searchtree(X0)
=> ( ( ( ( 'empty:Tree' != X0 )
=> ( ( 'val:(Tree)>Int'(X0) != X1 )
=> ( ( ~ $less(X1,'val:(Tree)>Int'(X0))
=> ? [X2: 'Tree'] :
( in(X1,X2)
& ( 'right:(Tree)>Tree'(X0) = X2 ) ) )
& ( $less(X1,'val:(Tree)>Int'(X0))
=> ? [X3: 'Tree'] :
( in(X1,X3)
& ( 'left:(Tree)>Tree'(X0) = X3 ) ) ) ) ) )
& ( ~ 'empty:Tree' = X0 ) )
<=> in(X1,X0) ) ),
inference(true_and_false_elimination,[],[f32]) ).
tff(f34,plain,
~ ! [X0: 'Tree',X1: $int] :
( searchtree(X0)
=> ( ( ( ( 'empty:Tree' != X0 )
=> ( ( 'val:(Tree)>Int'(X0) != X1 )
=> ( ( ~ $less(X1,'val:(Tree)>Int'(X0))
=> ? [X2: 'Tree'] :
( in(X1,X2)
& ( 'right:(Tree)>Tree'(X0) = X2 ) ) )
& ( $less(X1,'val:(Tree)>Int'(X0))
=> ? [X3: 'Tree'] :
( in(X1,X3)
& ( 'left:(Tree)>Tree'(X0) = X3 ) ) ) ) ) )
& ( 'empty:Tree' != X0 ) )
<=> in(X1,X0) ) ),
inference(flattening,[],[f33]) ).
tff(f35,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,X1)
<=> ( ( in(X0,'right:(Tree)>Tree'(X1))
| in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 )
| ( 'empty:Tree' = X1 ) )
& ( 'empty:Tree' != X1 ) ) ),
inference(ennf_transformation,[],[f29]) ).
tff(f36,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,X1)
<=> ( ( in(X0,'right:(Tree)>Tree'(X1))
| in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 )
| ( 'empty:Tree' = X1 ) )
& ( 'empty:Tree' != X1 ) ) ),
inference(flattening,[],[f35]) ).
tff(f37,plain,
! [X0: 'Tree'] :
( searchtree(X0)
<=> ( ( ! [X1: $int] :
( $less('val:(Tree)>Int'(X0),X1)
| ~ in(X1,'right:(Tree)>Tree'(X0)) )
& ! [X2: $int] :
( ~ $less('val:(Tree)>Int'(X0),X2)
| ~ in(X2,'left:(Tree)>Tree'(X0)) )
& searchtree('right:(Tree)>Tree'(X0))
& searchtree('left:(Tree)>Tree'(X0)) )
| ( 'empty:Tree' = X0 ) ) ),
inference(ennf_transformation,[],[f31]) ).
tff(f38,plain,
? [X0: 'Tree',X1: $int] :
( ( ( ( ( ( ? [X2: 'Tree'] :
( in(X1,X2)
& ( 'right:(Tree)>Tree'(X0) = X2 ) )
| $less(X1,'val:(Tree)>Int'(X0)) )
& ( ? [X3: 'Tree'] :
( in(X1,X3)
& ( 'left:(Tree)>Tree'(X0) = X3 ) )
| ~ $less(X1,'val:(Tree)>Int'(X0)) ) )
| ( 'val:(Tree)>Int'(X0) = X1 )
| ( 'empty:Tree' = X0 ) )
& ( 'empty:Tree' != X0 ) )
<~> in(X1,X0) )
& searchtree(X0) ),
inference(ennf_transformation,[],[f34]) ).
tff(f39,plain,
? [X0: 'Tree',X1: $int] :
( ( ( ( ( ( ? [X2: 'Tree'] :
( in(X1,X2)
& ( 'right:(Tree)>Tree'(X0) = X2 ) )
| $less(X1,'val:(Tree)>Int'(X0)) )
& ( ? [X3: 'Tree'] :
( in(X1,X3)
& ( 'left:(Tree)>Tree'(X0) = X3 ) )
| ~ $less(X1,'val:(Tree)>Int'(X0)) ) )
| ( 'val:(Tree)>Int'(X0) = X1 )
| ( 'empty:Tree' = X0 ) )
& ( 'empty:Tree' != X0 ) )
<~> in(X1,X0) )
& searchtree(X0) ),
inference(flattening,[],[f38]) ).
tff(f40,plain,
! [X0: 'Tree'] :
( sP0(X0)
<=> ( ( ! [X1: $int] :
( $less('val:(Tree)>Int'(X0),X1)
| ~ in(X1,'right:(Tree)>Tree'(X0)) )
& ! [X2: $int] :
( ~ $less('val:(Tree)>Int'(X0),X2)
| ~ in(X2,'left:(Tree)>Tree'(X0)) )
& searchtree('right:(Tree)>Tree'(X0))
& searchtree('left:(Tree)>Tree'(X0)) )
| ( 'empty:Tree' = X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f41,plain,
! [X0: 'Tree'] :
( searchtree(X0)
<=> sP0(X0) ),
inference(definition_folding,[],[f37,f40]) ).
tff(f42,plain,
! [X1: $int,X0: 'Tree'] :
( sP1(X1,X0)
<=> ( ( ( ( ? [X2: 'Tree'] :
( in(X1,X2)
& ( 'right:(Tree)>Tree'(X0) = X2 ) )
| $less(X1,'val:(Tree)>Int'(X0)) )
& ( ? [X3: 'Tree'] :
( in(X1,X3)
& ( 'left:(Tree)>Tree'(X0) = X3 ) )
| ~ $less(X1,'val:(Tree)>Int'(X0)) ) )
| ( 'val:(Tree)>Int'(X0) = X1 )
| ( 'empty:Tree' = X0 ) )
& ( 'empty:Tree' != X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f43,plain,
? [X0: 'Tree',X1: $int] :
( ( sP1(X1,X0)
<~> in(X1,X0) )
& searchtree(X0) ),
inference(definition_folding,[],[f39,f42]) ).
tff(f44,plain,
! [X0: $int,X1: 'Tree'] :
( ( in(X0,X1)
| ( ~ in(X0,'right:(Tree)>Tree'(X1))
& ~ in(X0,'left:(Tree)>Tree'(X1))
& ( 'val:(Tree)>Int'(X1) != X0 )
& ( 'empty:Tree' != X1 ) )
| ( 'empty:Tree' = X1 ) )
& ( ( ( in(X0,'right:(Tree)>Tree'(X1))
| in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 )
| ( 'empty:Tree' = X1 ) )
& ( 'empty:Tree' != X1 ) )
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f36]) ).
tff(f45,plain,
! [X0: $int,X1: 'Tree'] :
( ( in(X0,X1)
| ( ~ in(X0,'right:(Tree)>Tree'(X1))
& ~ in(X0,'left:(Tree)>Tree'(X1))
& ( 'val:(Tree)>Int'(X1) != X0 )
& ( 'empty:Tree' != X1 ) )
| ( 'empty:Tree' = X1 ) )
& ( ( ( in(X0,'right:(Tree)>Tree'(X1))
| in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 )
| ( 'empty:Tree' = X1 ) )
& ( 'empty:Tree' != X1 ) )
| ~ in(X0,X1) ) ),
inference(flattening,[],[f44]) ).
tff(f46,plain,
! [X0: 'Tree'] :
( ( sP0(X0)
| ( ( ? [X1: $int] :
( ~ $less('val:(Tree)>Int'(X0),X1)
& in(X1,'right:(Tree)>Tree'(X0)) )
| ? [X2: $int] :
( $less('val:(Tree)>Int'(X0),X2)
& in(X2,'left:(Tree)>Tree'(X0)) )
| ~ searchtree('right:(Tree)>Tree'(X0))
| ~ searchtree('left:(Tree)>Tree'(X0)) )
& ( 'empty:Tree' != X0 ) ) )
& ( ( ! [X1: $int] :
( $less('val:(Tree)>Int'(X0),X1)
| ~ in(X1,'right:(Tree)>Tree'(X0)) )
& ! [X2: $int] :
( ~ $less('val:(Tree)>Int'(X0),X2)
| ~ in(X2,'left:(Tree)>Tree'(X0)) )
& searchtree('right:(Tree)>Tree'(X0))
& searchtree('left:(Tree)>Tree'(X0)) )
| ( 'empty:Tree' = X0 )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f40]) ).
tff(f47,plain,
! [X0: 'Tree'] :
( ( sP0(X0)
| ( ( ? [X1: $int] :
( ~ $less('val:(Tree)>Int'(X0),X1)
& in(X1,'right:(Tree)>Tree'(X0)) )
| ? [X2: $int] :
( $less('val:(Tree)>Int'(X0),X2)
& in(X2,'left:(Tree)>Tree'(X0)) )
| ~ searchtree('right:(Tree)>Tree'(X0))
| ~ searchtree('left:(Tree)>Tree'(X0)) )
& ( 'empty:Tree' != X0 ) ) )
& ( ( ! [X1: $int] :
( $less('val:(Tree)>Int'(X0),X1)
| ~ in(X1,'right:(Tree)>Tree'(X0)) )
& ! [X2: $int] :
( ~ $less('val:(Tree)>Int'(X0),X2)
| ~ in(X2,'left:(Tree)>Tree'(X0)) )
& searchtree('right:(Tree)>Tree'(X0))
& searchtree('left:(Tree)>Tree'(X0)) )
| ( 'empty:Tree' = X0 )
| ~ sP0(X0) ) ),
inference(flattening,[],[f46]) ).
tff(f48,plain,
! [X0: 'Tree'] :
( ( sP0(X0)
| ( ( ? [X1: $int] :
( ~ $less('val:(Tree)>Int'(X0),X1)
& in(X1,'right:(Tree)>Tree'(X0)) )
| ? [X2: $int] :
( $less('val:(Tree)>Int'(X0),X2)
& in(X2,'left:(Tree)>Tree'(X0)) )
| ~ searchtree('right:(Tree)>Tree'(X0))
| ~ searchtree('left:(Tree)>Tree'(X0)) )
& ( 'empty:Tree' != X0 ) ) )
& ( ( ! [X3: $int] :
( $less('val:(Tree)>Int'(X0),X3)
| ~ in(X3,'right:(Tree)>Tree'(X0)) )
& ! [X4: $int] :
( ~ $less('val:(Tree)>Int'(X0),X4)
| ~ in(X4,'left:(Tree)>Tree'(X0)) )
& searchtree('right:(Tree)>Tree'(X0))
& searchtree('left:(Tree)>Tree'(X0)) )
| ( 'empty:Tree' = X0 )
| ~ sP0(X0) ) ),
inference(rectify,[],[f47]) ).
tff(f49,plain,
! [X0: 'Tree'] :
( ? [X1: $int] :
( ~ $less('val:(Tree)>Int'(X0),X1)
& in(X1,'right:(Tree)>Tree'(X0)) )
=> ( ~ $less('val:(Tree)>Int'(X0),sK2(X0))
& in(sK2(X0),'right:(Tree)>Tree'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f50,plain,
! [X0: 'Tree'] :
( ? [X2: $int] :
( $less('val:(Tree)>Int'(X0),X2)
& in(X2,'left:(Tree)>Tree'(X0)) )
=> ( $less('val:(Tree)>Int'(X0),sK3(X0))
& in(sK3(X0),'left:(Tree)>Tree'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f51,plain,
! [X0: 'Tree'] :
( ( sP0(X0)
| ( ( ( ~ $less('val:(Tree)>Int'(X0),sK2(X0))
& in(sK2(X0),'right:(Tree)>Tree'(X0)) )
| ( $less('val:(Tree)>Int'(X0),sK3(X0))
& in(sK3(X0),'left:(Tree)>Tree'(X0)) )
| ~ searchtree('right:(Tree)>Tree'(X0))
| ~ searchtree('left:(Tree)>Tree'(X0)) )
& ( 'empty:Tree' != X0 ) ) )
& ( ( ! [X3: $int] :
( $less('val:(Tree)>Int'(X0),X3)
| ~ in(X3,'right:(Tree)>Tree'(X0)) )
& ! [X4: $int] :
( ~ $less('val:(Tree)>Int'(X0),X4)
| ~ in(X4,'left:(Tree)>Tree'(X0)) )
& searchtree('right:(Tree)>Tree'(X0))
& searchtree('left:(Tree)>Tree'(X0)) )
| ( 'empty:Tree' = X0 )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f48,f50,f49]) ).
tff(f52,plain,
! [X0: 'Tree'] :
( ( searchtree(X0)
| ~ sP0(X0) )
& ( sP0(X0)
| ~ searchtree(X0) ) ),
inference(nnf_transformation,[],[f41]) ).
tff(f53,plain,
! [X1: $int,X0: 'Tree'] :
( ( sP1(X1,X0)
| ( ( ( ! [X2: 'Tree'] :
( ~ in(X1,X2)
| ( 'right:(Tree)>Tree'(X0) != X2 ) )
& ~ $less(X1,'val:(Tree)>Int'(X0)) )
| ( ! [X3: 'Tree'] :
( ~ in(X1,X3)
| ( 'left:(Tree)>Tree'(X0) != X3 ) )
& $less(X1,'val:(Tree)>Int'(X0)) ) )
& ( 'val:(Tree)>Int'(X0) != X1 )
& ( 'empty:Tree' != X0 ) )
| ( 'empty:Tree' = X0 ) )
& ( ( ( ( ( ? [X2: 'Tree'] :
( in(X1,X2)
& ( 'right:(Tree)>Tree'(X0) = X2 ) )
| $less(X1,'val:(Tree)>Int'(X0)) )
& ( ? [X3: 'Tree'] :
( in(X1,X3)
& ( 'left:(Tree)>Tree'(X0) = X3 ) )
| ~ $less(X1,'val:(Tree)>Int'(X0)) ) )
| ( 'val:(Tree)>Int'(X0) = X1 )
| ( 'empty:Tree' = X0 ) )
& ( 'empty:Tree' != X0 ) )
| ~ sP1(X1,X0) ) ),
inference(nnf_transformation,[],[f42]) ).
tff(f54,plain,
! [X1: $int,X0: 'Tree'] :
( ( sP1(X1,X0)
| ( ( ( ! [X2: 'Tree'] :
( ~ in(X1,X2)
| ( 'right:(Tree)>Tree'(X0) != X2 ) )
& ~ $less(X1,'val:(Tree)>Int'(X0)) )
| ( ! [X3: 'Tree'] :
( ~ in(X1,X3)
| ( 'left:(Tree)>Tree'(X0) != X3 ) )
& $less(X1,'val:(Tree)>Int'(X0)) ) )
& ( 'val:(Tree)>Int'(X0) != X1 )
& ( 'empty:Tree' != X0 ) )
| ( 'empty:Tree' = X0 ) )
& ( ( ( ( ( ? [X2: 'Tree'] :
( in(X1,X2)
& ( 'right:(Tree)>Tree'(X0) = X2 ) )
| $less(X1,'val:(Tree)>Int'(X0)) )
& ( ? [X3: 'Tree'] :
( in(X1,X3)
& ( 'left:(Tree)>Tree'(X0) = X3 ) )
| ~ $less(X1,'val:(Tree)>Int'(X0)) ) )
| ( 'val:(Tree)>Int'(X0) = X1 )
| ( 'empty:Tree' = X0 ) )
& ( 'empty:Tree' != X0 ) )
| ~ sP1(X1,X0) ) ),
inference(flattening,[],[f53]) ).
tff(f55,plain,
! [X0: $int,X1: 'Tree'] :
( ( sP1(X0,X1)
| ( ( ( ! [X2: 'Tree'] :
( ~ in(X0,X2)
| ( 'right:(Tree)>Tree'(X1) != X2 ) )
& ~ $less(X0,'val:(Tree)>Int'(X1)) )
| ( ! [X3: 'Tree'] :
( ~ in(X0,X3)
| ( 'left:(Tree)>Tree'(X1) != X3 ) )
& $less(X0,'val:(Tree)>Int'(X1)) ) )
& ( 'val:(Tree)>Int'(X1) != X0 )
& ( 'empty:Tree' != X1 ) )
| ( 'empty:Tree' = X1 ) )
& ( ( ( ( ( ? [X4: 'Tree'] :
( in(X0,X4)
& ( 'right:(Tree)>Tree'(X1) = X4 ) )
| $less(X0,'val:(Tree)>Int'(X1)) )
& ( ? [X5: 'Tree'] :
( in(X0,X5)
& ( 'left:(Tree)>Tree'(X1) = X5 ) )
| ~ $less(X0,'val:(Tree)>Int'(X1)) ) )
| ( 'val:(Tree)>Int'(X1) = X0 )
| ( 'empty:Tree' = X1 ) )
& ( 'empty:Tree' != X1 ) )
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f54]) ).
tff(f56,plain,
! [X0: $int,X1: 'Tree'] :
( ? [X4: 'Tree'] :
( in(X0,X4)
& ( 'right:(Tree)>Tree'(X1) = X4 ) )
=> ( in(X0,sK4(X0,X1))
& ( 'right:(Tree)>Tree'(X1) = sK4(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f57,plain,
! [X0: $int,X1: 'Tree'] :
( ? [X5: 'Tree'] :
( in(X0,X5)
& ( 'left:(Tree)>Tree'(X1) = X5 ) )
=> ( in(X0,sK5(X0,X1))
& ( 'left:(Tree)>Tree'(X1) = sK5(X0,X1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f58,plain,
! [X0: $int,X1: 'Tree'] :
( ( sP1(X0,X1)
| ( ( ( ! [X2: 'Tree'] :
( ~ in(X0,X2)
| ( 'right:(Tree)>Tree'(X1) != X2 ) )
& ~ $less(X0,'val:(Tree)>Int'(X1)) )
| ( ! [X3: 'Tree'] :
( ~ in(X0,X3)
| ( 'left:(Tree)>Tree'(X1) != X3 ) )
& $less(X0,'val:(Tree)>Int'(X1)) ) )
& ( 'val:(Tree)>Int'(X1) != X0 )
& ( 'empty:Tree' != X1 ) )
| ( 'empty:Tree' = X1 ) )
& ( ( ( ( ( ( in(X0,sK4(X0,X1))
& ( 'right:(Tree)>Tree'(X1) = sK4(X0,X1) ) )
| $less(X0,'val:(Tree)>Int'(X1)) )
& ( ( in(X0,sK5(X0,X1))
& ( 'left:(Tree)>Tree'(X1) = sK5(X0,X1) ) )
| ~ $less(X0,'val:(Tree)>Int'(X1)) ) )
| ( 'val:(Tree)>Int'(X1) = X0 )
| ( 'empty:Tree' = X1 ) )
& ( 'empty:Tree' != X1 ) )
| ~ sP1(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f55,f57,f56]) ).
tff(f59,plain,
? [X0: 'Tree',X1: $int] :
( ( ~ in(X1,X0)
| ~ sP1(X1,X0) )
& ( in(X1,X0)
| sP1(X1,X0) )
& searchtree(X0) ),
inference(nnf_transformation,[],[f43]) ).
tff(f60,plain,
? [X0: 'Tree',X1: $int] :
( ( ~ in(X1,X0)
| ~ sP1(X1,X0) )
& ( in(X1,X0)
| sP1(X1,X0) )
& searchtree(X0) ),
inference(flattening,[],[f59]) ).
tff(f61,plain,
( ? [X0: 'Tree',X1: $int] :
( ( ~ in(X1,X0)
| ~ sP1(X1,X0) )
& ( in(X1,X0)
| sP1(X1,X0) )
& searchtree(X0) )
=> ( ( ~ in(sK7,sK6)
| ~ sP1(sK7,sK6) )
& ( in(sK7,sK6)
| sP1(sK7,sK6) )
& searchtree(sK6) ) ),
introduced(choice_axiom,[]) ).
tff(f62,plain,
( ( ~ in(sK7,sK6)
| ~ sP1(sK7,sK6) )
& ( in(sK7,sK6)
| sP1(sK7,sK6) )
& searchtree(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f60,f61]) ).
tff(f68,plain,
! [X0: $int,X1: 'Tree'] :
( ( 'empty:Tree' != X1 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tff(f69,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,'right:(Tree)>Tree'(X1))
| in(X0,'left:(Tree)>Tree'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 )
| ( 'empty:Tree' = X1 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tff(f71,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,X1)
| ( 'val:(Tree)>Int'(X1) != X0 )
| ( 'empty:Tree' = X1 ) ),
inference(cnf_transformation,[],[f45]) ).
tff(f72,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,X1)
| ~ in(X0,'left:(Tree)>Tree'(X1))
| ( 'empty:Tree' = X1 ) ),
inference(cnf_transformation,[],[f45]) ).
tff(f73,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,X1)
| ~ in(X0,'right:(Tree)>Tree'(X1))
| ( 'empty:Tree' = X1 ) ),
inference(cnf_transformation,[],[f45]) ).
tff(f76,plain,
! [X0: 'Tree',X4: $int] :
( ~ $less('val:(Tree)>Int'(X0),X4)
| ~ in(X4,'left:(Tree)>Tree'(X0))
| ( 'empty:Tree' = X0 )
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f51]) ).
tff(f77,plain,
! [X3: $int,X0: 'Tree'] :
( $less('val:(Tree)>Int'(X0),X3)
| ~ in(X3,'right:(Tree)>Tree'(X0))
| ( 'empty:Tree' = X0 )
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f51]) ).
tff(f83,plain,
! [X0: 'Tree'] :
( sP0(X0)
| ~ searchtree(X0) ),
inference(cnf_transformation,[],[f52]) ).
tff(f85,plain,
! [X0: $int,X1: 'Tree'] :
( ( 'empty:Tree' != X1 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
tff(f86,plain,
! [X0: $int,X1: 'Tree'] :
( ( 'left:(Tree)>Tree'(X1) = sK5(X0,X1) )
| ~ $less(X0,'val:(Tree)>Int'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 )
| ( 'empty:Tree' = X1 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
tff(f87,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,sK5(X0,X1))
| ~ $less(X0,'val:(Tree)>Int'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 )
| ( 'empty:Tree' = X1 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
tff(f88,plain,
! [X0: $int,X1: 'Tree'] :
( ( 'right:(Tree)>Tree'(X1) = sK4(X0,X1) )
| $less(X0,'val:(Tree)>Int'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 )
| ( 'empty:Tree' = X1 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
tff(f89,plain,
! [X0: $int,X1: 'Tree'] :
( in(X0,sK4(X0,X1))
| $less(X0,'val:(Tree)>Int'(X1))
| ( 'val:(Tree)>Int'(X1) = X0 )
| ( 'empty:Tree' = X1 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
tff(f91,plain,
! [X0: $int,X1: 'Tree'] :
( sP1(X0,X1)
| ( 'val:(Tree)>Int'(X1) != X0 )
| ( 'empty:Tree' = X1 ) ),
inference(cnf_transformation,[],[f58]) ).
tff(f93,plain,
! [X3: 'Tree',X0: $int,X1: 'Tree'] :
( sP1(X0,X1)
| ~ $less(X0,'val:(Tree)>Int'(X1))
| ~ in(X0,X3)
| ( 'left:(Tree)>Tree'(X1) != X3 )
| ( 'empty:Tree' = X1 ) ),
inference(cnf_transformation,[],[f58]) ).
tff(f94,plain,
! [X2: 'Tree',X0: $int,X1: 'Tree'] :
( sP1(X0,X1)
| ~ in(X0,X2)
| ( 'right:(Tree)>Tree'(X1) != X2 )
| $less(X0,'val:(Tree)>Int'(X1))
| ( 'empty:Tree' = X1 ) ),
inference(cnf_transformation,[],[f58]) ).
tff(f96,plain,
searchtree(sK6),
inference(cnf_transformation,[],[f62]) ).
tff(f97,plain,
( in(sK7,sK6)
| sP1(sK7,sK6) ),
inference(cnf_transformation,[],[f62]) ).
tff(f98,plain,
( ~ in(sK7,sK6)
| ~ sP1(sK7,sK6) ),
inference(cnf_transformation,[],[f62]) ).
tff(f99,plain,
! [X1: 'Tree'] :
( in('val:(Tree)>Int'(X1),X1)
| ( 'empty:Tree' = X1 ) ),
inference(equality_resolution,[],[f71]) ).
tff(f101,plain,
! [X0: $int] : ~ in(X0,'empty:Tree'),
inference(equality_resolution,[],[f68]) ).
tff(f105,plain,
! [X0: $int,X1: 'Tree'] :
( sP1(X0,X1)
| ~ in(X0,'right:(Tree)>Tree'(X1))
| $less(X0,'val:(Tree)>Int'(X1))
| ( 'empty:Tree' = X1 ) ),
inference(equality_resolution,[],[f94]) ).
tff(f106,plain,
! [X0: $int,X1: 'Tree'] :
( sP1(X0,X1)
| ~ $less(X0,'val:(Tree)>Int'(X1))
| ~ in(X0,'left:(Tree)>Tree'(X1))
| ( 'empty:Tree' = X1 ) ),
inference(equality_resolution,[],[f93]) ).
tff(f107,plain,
! [X1: 'Tree'] :
( sP1('val:(Tree)>Int'(X1),X1)
| ( 'empty:Tree' = X1 ) ),
inference(equality_resolution,[],[f91]) ).
tff(f109,plain,
! [X0: $int] : ~ sP1(X0,'empty:Tree'),
inference(equality_resolution,[],[f85]) ).
cnf(c_53,plain,
( X0_3 = X1_3
| $less_int(X0_3,X1_3)
| $less_int(X1_3,X0_3) ),
inference(cnf_transformation,[],[f18]) ).
cnf(c_54,plain,
( ~ $less_int(X0_3,X1_3)
| ~ $less_int(X1_3,X2_3)
| $less_int(X0_3,X2_3) ),
inference(cnf_transformation,[],[f17]) ).
cnf(c_55,plain,
~ $less_int(X0_3,X0_3),
inference(cnf_transformation,[],[f16]) ).
cnf(c_66,plain,
( ~ in(X0_3,'right:(Tree)>Tree'(X0_13))
| X0_13 = 'empty:Tree'
| in(X0_3,X0_13) ),
inference(cnf_transformation,[],[f73]) ).
cnf(c_67,plain,
( ~ in(X0_3,'left:(Tree)>Tree'(X0_13))
| X0_13 = 'empty:Tree'
| in(X0_3,X0_13) ),
inference(cnf_transformation,[],[f72]) ).
cnf(c_68,plain,
( X0_13 = 'empty:Tree'
| in('val:(Tree)>Int'(X0_13),X0_13) ),
inference(cnf_transformation,[],[f99]) ).
cnf(c_69,plain,
( ~ in(X0_3,X0_13)
| 'val:(Tree)>Int'(X0_13) = X0_3
| X0_13 = 'empty:Tree'
| in(X0_3,'left:(Tree)>Tree'(X0_13))
| in(X0_3,'right:(Tree)>Tree'(X0_13)) ),
inference(cnf_transformation,[],[f69]) ).
cnf(c_70,plain,
~ in(X0_3,'empty:Tree'),
inference(cnf_transformation,[],[f101]) ).
cnf(c_76,plain,
( ~ in(X0_3,'right:(Tree)>Tree'(X0_13))
| ~ sP0(X0_13)
| X0_13 = 'empty:Tree'
| $less_int('val:(Tree)>Int'(X0_13),X0_3) ),
inference(cnf_transformation,[],[f77]) ).
cnf(c_77,plain,
( ~ $less_int('val:(Tree)>Int'(X0_13),X0_3)
| ~ in(X0_3,'left:(Tree)>Tree'(X0_13))
| ~ sP0(X0_13)
| X0_13 = 'empty:Tree' ),
inference(cnf_transformation,[],[f76]) ).
cnf(c_81,plain,
( ~ searchtree(X0_13)
| sP0(X0_13) ),
inference(cnf_transformation,[],[f83]) ).
cnf(c_83,plain,
( ~ in(X0_3,'right:(Tree)>Tree'(X0_13))
| X0_13 = 'empty:Tree'
| $less_int(X0_3,'val:(Tree)>Int'(X0_13))
| sP1(X0_3,X0_13) ),
inference(cnf_transformation,[],[f105]) ).
cnf(c_84,plain,
( ~ $less_int(X0_3,'val:(Tree)>Int'(X0_13))
| ~ in(X0_3,'left:(Tree)>Tree'(X0_13))
| X0_13 = 'empty:Tree'
| sP1(X0_3,X0_13) ),
inference(cnf_transformation,[],[f106]) ).
cnf(c_85,plain,
( X0_13 = 'empty:Tree'
| sP1('val:(Tree)>Int'(X0_13),X0_13) ),
inference(cnf_transformation,[],[f107]) ).
cnf(c_86,plain,
( ~ sP1(X0_3,X0_13)
| 'val:(Tree)>Int'(X0_13) = X0_3
| X0_13 = 'empty:Tree'
| in(X0_3,sK4(X0_3,X0_13))
| $less_int(X0_3,'val:(Tree)>Int'(X0_13)) ),
inference(cnf_transformation,[],[f89]) ).
cnf(c_87,plain,
( ~ sP1(X0_3,X0_13)
| sK4(X0_3,X0_13) = 'right:(Tree)>Tree'(X0_13)
| 'val:(Tree)>Int'(X0_13) = X0_3
| X0_13 = 'empty:Tree'
| $less_int(X0_3,'val:(Tree)>Int'(X0_13)) ),
inference(cnf_transformation,[],[f88]) ).
cnf(c_88,plain,
( ~ $less_int(X0_3,'val:(Tree)>Int'(X0_13))
| ~ sP1(X0_3,X0_13)
| 'val:(Tree)>Int'(X0_13) = X0_3
| X0_13 = 'empty:Tree'
| in(X0_3,sK5(X0_3,X0_13)) ),
inference(cnf_transformation,[],[f87]) ).
cnf(c_89,plain,
( ~ $less_int(X0_3,'val:(Tree)>Int'(X0_13))
| ~ sP1(X0_3,X0_13)
| sK5(X0_3,X0_13) = 'left:(Tree)>Tree'(X0_13)
| 'val:(Tree)>Int'(X0_13) = X0_3
| X0_13 = 'empty:Tree' ),
inference(cnf_transformation,[],[f86]) ).
cnf(c_90,plain,
~ sP1(X0_3,'empty:Tree'),
inference(cnf_transformation,[],[f109]) ).
cnf(c_91,negated_conjecture,
( ~ in(sK7,sK6)
| ~ sP1(sK7,sK6) ),
inference(cnf_transformation,[],[f98]) ).
cnf(c_92,negated_conjecture,
( in(sK7,sK6)
| sP1(sK7,sK6) ),
inference(cnf_transformation,[],[f97]) ).
cnf(c_93,negated_conjecture,
searchtree(sK6),
inference(cnf_transformation,[],[f96]) ).
cnf(c_96,plain,
~ in(sK7,'empty:Tree'),
inference(instantiation,[status(thm)],[c_70]) ).
cnf(c_97,plain,
~ $less_int(sK7,sK7),
inference(instantiation,[status(thm)],[c_55]) ).
cnf(c_112,plain,
( sK7 = sK7
| $less_int(sK7,sK7) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_131,plain,
( ~ sP1(sK7,sK6)
| ~ in(sK7,sK6) ),
inference(prop_impl_just,[status(thm)],[c_91]) ).
cnf(c_132,plain,
( ~ in(sK7,sK6)
| ~ sP1(sK7,sK6) ),
inference(renaming,[status(thm)],[c_131]) ).
cnf(c_133,plain,
( sP1(sK7,sK6)
| in(sK7,sK6) ),
inference(prop_impl_just,[status(thm)],[c_92]) ).
cnf(c_134,plain,
( in(sK7,sK6)
| sP1(sK7,sK6) ),
inference(renaming,[status(thm)],[c_133]) ).
cnf(c_141,plain,
( X0_13 = 'empty:Tree'
| sP1('val:(Tree)>Int'(X0_13),X0_13) ),
inference(prop_impl_just,[status(thm)],[c_85]) ).
cnf(c_1224,plain,
( X0_3 != sK7
| X0_13 != sK6
| ~ $less_int(X0_3,'val:(Tree)>Int'(X0_13))
| ~ in(X0_3,'left:(Tree)>Tree'(X0_13))
| ~ in(sK7,sK6)
| X0_13 = 'empty:Tree' ),
inference(resolution_lifted,[status(thm)],[c_84,c_132]) ).
cnf(c_1225,plain,
( ~ $less_int(sK7,'val:(Tree)>Int'(sK6))
| ~ in(sK7,'left:(Tree)>Tree'(sK6))
| ~ in(sK7,sK6)
| sK6 = 'empty:Tree' ),
inference(unflattening,[status(thm)],[c_1224]) ).
cnf(c_1234,plain,
( ~ $less_int(sK7,'val:(Tree)>Int'(sK6))
| ~ in(sK7,'left:(Tree)>Tree'(sK6))
| sK6 = 'empty:Tree' ),
inference(forward_subsumption_resolution,[status(thm)],[c_1225,c_67]) ).
cnf(c_1238,plain,
( X0_3 != sK7
| X0_13 != sK6
| ~ in(X0_3,'right:(Tree)>Tree'(X0_13))
| ~ in(sK7,sK6)
| X0_13 = 'empty:Tree'
| $less_int(X0_3,'val:(Tree)>Int'(X0_13)) ),
inference(resolution_lifted,[status(thm)],[c_83,c_132]) ).
cnf(c_1239,plain,
( ~ in(sK7,'right:(Tree)>Tree'(sK6))
| ~ in(sK7,sK6)
| sK6 = 'empty:Tree'
| $less_int(sK7,'val:(Tree)>Int'(sK6)) ),
inference(unflattening,[status(thm)],[c_1238]) ).
cnf(c_1248,plain,
( ~ in(sK7,'right:(Tree)>Tree'(sK6))
| sK6 = 'empty:Tree'
| $less_int(sK7,'val:(Tree)>Int'(sK6)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1239,c_66]) ).
cnf(c_1265,plain,
( X0_3 != sK7
| X0_13 != sK6
| ~ $less_int(X0_3,'val:(Tree)>Int'(X0_13))
| sK5(X0_3,X0_13) = 'left:(Tree)>Tree'(X0_13)
| 'val:(Tree)>Int'(X0_13) = X0_3
| X0_13 = 'empty:Tree'
| in(sK7,sK6) ),
inference(resolution_lifted,[status(thm)],[c_89,c_134]) ).
cnf(c_1266,plain,
( ~ $less_int(sK7,'val:(Tree)>Int'(sK6))
| sK5(sK7,sK6) = 'left:(Tree)>Tree'(sK6)
| 'val:(Tree)>Int'(sK6) = sK7
| sK6 = 'empty:Tree'
| in(sK7,sK6) ),
inference(unflattening,[status(thm)],[c_1265]) ).
cnf(c_1282,plain,
( X0_3 != sK7
| X0_13 != sK6
| ~ $less_int(X0_3,'val:(Tree)>Int'(X0_13))
| 'val:(Tree)>Int'(X0_13) = X0_3
| X0_13 = 'empty:Tree'
| in(X0_3,sK5(X0_3,X0_13))
| in(sK7,sK6) ),
inference(resolution_lifted,[status(thm)],[c_88,c_134]) ).
cnf(c_1283,plain,
( ~ $less_int(sK7,'val:(Tree)>Int'(sK6))
| 'val:(Tree)>Int'(sK6) = sK7
| sK6 = 'empty:Tree'
| in(sK7,sK5(sK7,sK6))
| in(sK7,sK6) ),
inference(unflattening,[status(thm)],[c_1282]) ).
cnf(c_1299,plain,
( X0_3 != sK7
| X0_13 != sK6
| sK4(X0_3,X0_13) = 'right:(Tree)>Tree'(X0_13)
| 'val:(Tree)>Int'(X0_13) = X0_3
| X0_13 = 'empty:Tree'
| $less_int(X0_3,'val:(Tree)>Int'(X0_13))
| in(sK7,sK6) ),
inference(resolution_lifted,[status(thm)],[c_87,c_134]) ).
cnf(c_1300,plain,
( sK4(sK7,sK6) = 'right:(Tree)>Tree'(sK6)
| 'val:(Tree)>Int'(sK6) = sK7
| sK6 = 'empty:Tree'
| $less_int(sK7,'val:(Tree)>Int'(sK6))
| in(sK7,sK6) ),
inference(unflattening,[status(thm)],[c_1299]) ).
cnf(c_1316,plain,
( X0_3 != sK7
| X0_13 != sK6
| 'val:(Tree)>Int'(X0_13) = X0_3
| X0_13 = 'empty:Tree'
| in(X0_3,sK4(X0_3,X0_13))
| $less_int(X0_3,'val:(Tree)>Int'(X0_13))
| in(sK7,sK6) ),
inference(resolution_lifted,[status(thm)],[c_86,c_134]) ).
cnf(c_1317,plain,
( 'val:(Tree)>Int'(sK6) = sK7
| sK6 = 'empty:Tree'
| in(sK7,sK4(sK7,sK6))
| $less_int(sK7,'val:(Tree)>Int'(sK6))
| in(sK7,sK6) ),
inference(unflattening,[status(thm)],[c_1316]) ).
cnf(c_1335,plain,
( 'val:(Tree)>Int'(X0_13) != sK7
| X0_13 != sK6
| ~ in(sK7,sK6)
| X0_13 = 'empty:Tree' ),
inference(resolution_lifted,[status(thm)],[c_141,c_132]) ).
cnf(c_1336,plain,
( 'val:(Tree)>Int'(sK6) != sK7
| ~ in(sK7,sK6)
| sK6 = 'empty:Tree' ),
inference(unflattening,[status(thm)],[c_1335]) ).
cnf(c_1346,plain,
( X0_3 != sK7
| 'empty:Tree' != sK6
| in(sK7,sK6) ),
inference(resolution_lifted,[status(thm)],[c_90,c_134]) ).
cnf(c_1347,plain,
( 'empty:Tree' != sK6
| in(sK7,sK6) ),
inference(unflattening,[status(thm)],[c_1346]) ).
cnf(c_1410,plain,
X0_13 = X0_13,
theory(equality) ).
cnf(c_1411,plain,
( X0_3 != X1_3
| X2_3 != X1_3
| X2_3 = X0_3 ),
theory(equality) ).
cnf(c_1412,plain,
( X0_13 != X1_13
| X2_13 != X1_13
| X2_13 = X0_13 ),
theory(equality) ).
cnf(c_1423,plain,
( X0_3 != X1_3
| X0_13 != X1_13
| ~ in(X1_3,X1_13)
| in(X0_3,X0_13) ),
theory(equality) ).
cnf(c_1434,plain,
'empty:Tree' = 'empty:Tree',
inference(instantiation,[status(thm)],[c_1410]) ).
cnf(c_2409,plain,
sP0(sK6),
inference(superposition,[status(thm)],[c_93,c_81]) ).
cnf(c_2830,plain,
( X0_3 != sK7
| X0_13 != sK6
| ~ in(sK7,sK6)
| in(X0_3,X0_13) ),
inference(instantiation,[status(thm)],[c_1423]) ).
cnf(c_2831,plain,
( 'empty:Tree' != sK6
| sK7 != sK7
| ~ in(sK7,sK6)
| in(sK7,'empty:Tree') ),
inference(instantiation,[status(thm)],[c_2830]) ).
cnf(c_3037,plain,
( 'val:(Tree)>Int'(sK6) = sK7
| $less_int('val:(Tree)>Int'(sK6),sK7)
| $less_int(sK7,'val:(Tree)>Int'(sK6)) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_3184,plain,
( ~ $less_int(X0_3,'val:(Tree)>Int'(sK6))
| ~ $less_int('val:(Tree)>Int'(sK6),sK7)
| $less_int(X0_3,sK7) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_3185,plain,
( ~ $less_int('val:(Tree)>Int'(sK6),sK7)
| ~ $less_int(sK7,'val:(Tree)>Int'(sK6))
| $less_int(sK7,sK7) ),
inference(instantiation,[status(thm)],[c_3184]) ).
cnf(c_3274,plain,
sK6 = sK6,
inference(instantiation,[status(thm)],[c_1410]) ).
cnf(c_3275,plain,
( X0_13 != X1_13
| sK6 != X1_13
| X0_13 = sK6 ),
inference(instantiation,[status(thm)],[c_1412]) ).
cnf(c_3276,plain,
( 'empty:Tree' != 'empty:Tree'
| sK6 != 'empty:Tree'
| 'empty:Tree' = sK6 ),
inference(instantiation,[status(thm)],[c_3275]) ).
cnf(c_4227,plain,
( ~ in(X0_3,sK6)
| 'val:(Tree)>Int'(sK6) = X0_3
| sK6 = 'empty:Tree'
| in(X0_3,'left:(Tree)>Tree'(sK6))
| in(X0_3,'right:(Tree)>Tree'(sK6)) ),
inference(instantiation,[status(thm)],[c_69]) ).
cnf(c_4228,plain,
( ~ $less_int('val:(Tree)>Int'(sK6),X0_3)
| ~ in(X0_3,'left:(Tree)>Tree'(sK6))
| ~ sP0(sK6)
| sK6 = 'empty:Tree' ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_4229,plain,
( ~ in(X0_3,'right:(Tree)>Tree'(sK6))
| ~ sP0(sK6)
| sK6 = 'empty:Tree'
| $less_int('val:(Tree)>Int'(sK6),X0_3) ),
inference(instantiation,[status(thm)],[c_76]) ).
cnf(c_4230,plain,
( ~ in(X0_3,'left:(Tree)>Tree'(sK6))
| sK6 = 'empty:Tree'
| in(X0_3,sK6) ),
inference(instantiation,[status(thm)],[c_67]) ).
cnf(c_4234,plain,
( sK6 = 'empty:Tree'
| in('val:(Tree)>Int'(sK6),sK6) ),
inference(instantiation,[status(thm)],[c_68]) ).
cnf(c_4236,plain,
( ~ in(sK7,'left:(Tree)>Tree'(sK6))
| sK6 = 'empty:Tree'
| in(sK7,sK6) ),
inference(instantiation,[status(thm)],[c_4230]) ).
cnf(c_4237,plain,
( ~ in(sK7,'right:(Tree)>Tree'(sK6))
| ~ sP0(sK6)
| sK6 = 'empty:Tree'
| $less_int('val:(Tree)>Int'(sK6),sK7) ),
inference(instantiation,[status(thm)],[c_4229]) ).
cnf(c_4238,plain,
( ~ $less_int('val:(Tree)>Int'(sK6),sK7)
| ~ in(sK7,'left:(Tree)>Tree'(sK6))
| ~ sP0(sK6)
| sK6 = 'empty:Tree' ),
inference(instantiation,[status(thm)],[c_4228]) ).
cnf(c_4239,plain,
( ~ in(sK7,sK6)
| 'val:(Tree)>Int'(sK6) = sK7
| sK6 = 'empty:Tree'
| in(sK7,'left:(Tree)>Tree'(sK6))
| in(sK7,'right:(Tree)>Tree'(sK6)) ),
inference(instantiation,[status(thm)],[c_4227]) ).
cnf(c_4445,plain,
'empty:Tree' != sK6,
inference(global_subsumption_just,[status(thm)],[c_1347,c_96,c_97,c_112,c_1347,c_2831]) ).
cnf(c_7595,plain,
( X0_3 != 'val:(Tree)>Int'(sK6)
| X0_13 != sK6
| ~ in('val:(Tree)>Int'(sK6),sK6)
| in(X0_3,X0_13) ),
inference(instantiation,[status(thm)],[c_1423]) ).
cnf(c_8894,plain,
~ in(sK7,'right:(Tree)>Tree'(sK6)),
inference(global_subsumption_just,[status(thm)],[c_1248,c_96,c_97,c_112,c_1248,c_1347,c_1434,c_2409,c_2831,c_3185,c_3276,c_4237]) ).
cnf(c_8900,plain,
~ in(sK7,'left:(Tree)>Tree'(sK6)),
inference(global_subsumption_just,[status(thm)],[c_1234,c_96,c_97,c_112,c_1234,c_1336,c_1347,c_1434,c_2409,c_2831,c_3037,c_3276,c_4236,c_4238]) ).
cnf(c_8906,plain,
~ in(sK7,sK6),
inference(global_subsumption_just,[status(thm)],[c_1336,c_1336,c_1434,c_3276,c_4239,c_4445,c_8894,c_8900]) ).
cnf(c_22885,plain,
( X0_3 != 'val:(Tree)>Int'(sK6)
| sK6 != sK6
| ~ in('val:(Tree)>Int'(sK6),sK6)
| in(X0_3,sK6) ),
inference(instantiation,[status(thm)],[c_7595]) ).
cnf(c_22886,plain,
( sK6 != sK6
| sK7 != 'val:(Tree)>Int'(sK6)
| ~ in('val:(Tree)>Int'(sK6),sK6)
| in(sK7,sK6) ),
inference(instantiation,[status(thm)],[c_22885]) ).
cnf(c_23309,plain,
( 'val:(Tree)>Int'(sK6) != X0_3
| X1_3 != X0_3
| X1_3 = 'val:(Tree)>Int'(sK6) ),
inference(instantiation,[status(thm)],[c_1411]) ).
cnf(c_23310,plain,
( 'val:(Tree)>Int'(sK6) != sK7
| sK7 != sK7
| sK7 = 'val:(Tree)>Int'(sK6) ),
inference(instantiation,[status(thm)],[c_23309]) ).
cnf(c_41550,plain,
( X0_3 != sK7
| X0_13 != sK5(sK7,sK6)
| ~ in(sK7,sK5(sK7,sK6))
| in(X0_3,X0_13) ),
inference(instantiation,[status(thm)],[c_1423]) ).
cnf(c_67506,plain,
( sK5(sK7,sK6) != X0_13
| X1_13 != X0_13
| X1_13 = sK5(sK7,sK6) ),
inference(instantiation,[status(thm)],[c_1412]) ).
cnf(c_100042,plain,
( sK5(sK7,sK6) != 'left:(Tree)>Tree'(sK6)
| X0_13 != 'left:(Tree)>Tree'(sK6)
| X0_13 = sK5(sK7,sK6) ),
inference(instantiation,[status(thm)],[c_67506]) ).
cnf(c_121296,plain,
'right:(Tree)>Tree'(sK6) = 'right:(Tree)>Tree'(sK6),
inference(instantiation,[status(thm)],[c_1410]) ).
cnf(c_134397,plain,
( sK5(sK7,sK6) != 'left:(Tree)>Tree'(sK6)
| 'left:(Tree)>Tree'(sK6) != 'left:(Tree)>Tree'(sK6)
| 'left:(Tree)>Tree'(sK6) = sK5(sK7,sK6) ),
inference(instantiation,[status(thm)],[c_100042]) ).
cnf(c_134398,plain,
'left:(Tree)>Tree'(sK6) = 'left:(Tree)>Tree'(sK6),
inference(instantiation,[status(thm)],[c_1410]) ).
cnf(c_179081,plain,
( 'left:(Tree)>Tree'(sK6) != sK5(sK7,sK6)
| X0_3 != sK7
| ~ in(sK7,sK5(sK7,sK6))
| in(X0_3,'left:(Tree)>Tree'(sK6)) ),
inference(instantiation,[status(thm)],[c_41550]) ).
cnf(c_179082,plain,
( 'left:(Tree)>Tree'(sK6) != sK5(sK7,sK6)
| sK7 != sK7
| ~ in(sK7,sK5(sK7,sK6))
| in(sK7,'left:(Tree)>Tree'(sK6)) ),
inference(instantiation,[status(thm)],[c_179081]) ).
cnf(c_206539,plain,
( X0_3 != sK7
| X0_13 != sK4(sK7,sK6)
| ~ in(sK7,sK4(sK7,sK6))
| in(X0_3,X0_13) ),
inference(instantiation,[status(thm)],[c_1423]) ).
cnf(c_206628,plain,
( sK4(sK7,sK6) != X0_13
| X1_13 != X0_13
| X1_13 = sK4(sK7,sK6) ),
inference(instantiation,[status(thm)],[c_1412]) ).
cnf(c_206916,plain,
( sK4(sK7,sK6) != 'right:(Tree)>Tree'(sK6)
| X0_13 != 'right:(Tree)>Tree'(sK6)
| X0_13 = sK4(sK7,sK6) ),
inference(instantiation,[status(thm)],[c_206628]) ).
cnf(c_207403,plain,
( sK4(sK7,sK6) != 'right:(Tree)>Tree'(sK6)
| 'right:(Tree)>Tree'(sK6) != 'right:(Tree)>Tree'(sK6)
| 'right:(Tree)>Tree'(sK6) = sK4(sK7,sK6) ),
inference(instantiation,[status(thm)],[c_206916]) ).
cnf(c_209142,plain,
( 'right:(Tree)>Tree'(sK6) != sK4(sK7,sK6)
| X0_3 != sK7
| ~ in(sK7,sK4(sK7,sK6))
| in(X0_3,'right:(Tree)>Tree'(sK6)) ),
inference(instantiation,[status(thm)],[c_206539]) ).
cnf(c_209143,plain,
( 'right:(Tree)>Tree'(sK6) != sK4(sK7,sK6)
| sK7 != sK7
| ~ in(sK7,sK4(sK7,sK6))
| in(sK7,'right:(Tree)>Tree'(sK6)) ),
inference(instantiation,[status(thm)],[c_209142]) ).
cnf(c_209144,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_209143,c_207403,c_179082,c_134398,c_134397,c_121296,c_23310,c_22886,c_8906,c_8900,c_8894,c_4445,c_4234,c_3276,c_3274,c_1434,c_1317,c_1300,c_1283,c_1266,c_112,c_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW678_1 : TPTP v8.1.2. Released v6.4.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n006.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 : Sun Aug 27 18:53:52 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Running TFA theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --no_cores 8 --schedule casc_29_tfa /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 26.74/4.15 % SZS status Started for theBenchmark.p
% 26.74/4.15 % SZS status Theorem for theBenchmark.p
% 26.74/4.15
% 26.74/4.15 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 26.74/4.15
% 26.74/4.15 ------ iProver source info
% 26.74/4.15
% 26.74/4.15 git: date: 2023-05-31 18:12:56 +0000
% 26.74/4.15 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 26.74/4.15 git: non_committed_changes: false
% 26.74/4.15 git: last_make_outside_of_git: false
% 26.74/4.15
% 26.74/4.15 ------ Parsing...
% 26.74/4.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 26.74/4.15
% 26.74/4.15 ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e
% 26.74/4.15
% 26.74/4.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 26.74/4.15
% 26.74/4.15 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 26.74/4.15 ------ Proving...
% 26.74/4.15 ------ Problem Properties
% 26.74/4.15
% 26.74/4.15
% 26.74/4.15 clauses 47
% 26.74/4.15 conjectures 1
% 26.74/4.15 EPR 10
% 26.74/4.15 Horn 24
% 26.74/4.15 unary 15
% 26.74/4.15 binary 7
% 26.74/4.15 lits 132
% 26.74/4.15 lits eq 48
% 26.74/4.15 fd_pure 0
% 26.74/4.15 fd_pseudo 0
% 26.74/4.15 fd_cond 7
% 26.74/4.15 fd_pseudo_cond 6
% 26.74/4.15 AC symbols 1
% 26.74/4.15
% 26.74/4.15 ------ Input Options Time Limit: Unbounded
% 26.74/4.15
% 26.74/4.15
% 26.74/4.15 ------
% 26.74/4.15 Current options:
% 26.74/4.15 ------
% 26.74/4.15
% 26.74/4.15
% 26.74/4.15
% 26.74/4.15
% 26.74/4.15 ------ Proving...
% 26.74/4.15
% 26.74/4.15
% 26.74/4.15 % SZS status Theorem for theBenchmark.p
% 26.74/4.15
% 26.74/4.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 26.74/4.15
% 26.74/4.16
%------------------------------------------------------------------------------