TSTP Solution File: ANA140_1 by SnakeForV-SAT---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : ANA140_1 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n026.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 : Mon May 22 15:23:11 EDT 2023
% Result : Theorem 1.26s 0.65s
% Output : Refutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 5 unt; 3 typ; 0 def)
% Number of atoms : 134 ( 10 equ)
% Maximal formula atoms : 22 ( 6 avg)
% Number of connectives : 177 ( 65 ~; 40 |; 52 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 430 ( 123 atm; 204 fun; 76 num; 27 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 27 (; 16 !; 11 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $real ).
tff(func_def_6,type,
sK0: $real ).
tff(func_def_7,type,
sK1: $real > $real ).
tff(f42,plain,
$false,
inference(subsumption_resolution,[],[f41,f35]) ).
tff(f35,plain,
$less($sum(sK1(sK0),$uminus(a)),0.0),
inference(subsumption_resolution,[],[f34,f20]) ).
tff(f20,plain,
$less(0.0,sK0),
inference(cnf_transformation,[],[f19]) ).
tff(f19,plain,
( ! [X1: $real] :
( ~ $less(0.0,X1)
| ( ( $less($uminus($sum(sK1(X1),$uminus(a))),X1)
| ~ $less($sum(sK1(X1),$uminus(a)),0.0) )
& ( a != sK1(X1) )
& ( ( ~ $less($uminus($sum(sK1(X1),$uminus(a))),sK0)
& $less($sum(sK1(X1),$uminus(a)),0.0) )
| ( ~ $less($sum(sK1(X1),$uminus(a)),sK0)
& ~ $less($sum(sK1(X1),$uminus(a)),0.0) ) )
& ( $less($sum(sK1(X1),$uminus(a)),X1)
| $less($sum(sK1(X1),$uminus(a)),0.0) ) ) )
& $less(0.0,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f18,f17]) ).
tff(f17,plain,
( ? [X0: $real] :
( ! [X1: $real] :
( ~ $less(0.0,X1)
| ? [X2: $real] :
( ( $less($uminus($sum(X2,$uminus(a))),X1)
| ~ $less($sum(X2,$uminus(a)),0.0) )
& ( a != X2 )
& ( ( ~ $less($uminus($sum(X2,$uminus(a))),X0)
& $less($sum(X2,$uminus(a)),0.0) )
| ( ~ $less($sum(X2,$uminus(a)),X0)
& ~ $less($sum(X2,$uminus(a)),0.0) ) )
& ( $less($sum(X2,$uminus(a)),X1)
| $less($sum(X2,$uminus(a)),0.0) ) ) )
& $less(0.0,X0) )
=> ( ! [X1: $real] :
( ~ $less(0.0,X1)
| ? [X2: $real] :
( ( $less($uminus($sum(X2,$uminus(a))),X1)
| ~ $less($sum(X2,$uminus(a)),0.0) )
& ( a != X2 )
& ( ( ~ $less($uminus($sum(X2,$uminus(a))),sK0)
& $less($sum(X2,$uminus(a)),0.0) )
| ( ~ $less($sum(X2,$uminus(a)),sK0)
& ~ $less($sum(X2,$uminus(a)),0.0) ) )
& ( $less($sum(X2,$uminus(a)),X1)
| $less($sum(X2,$uminus(a)),0.0) ) ) )
& $less(0.0,sK0) ) ),
introduced(choice_axiom,[]) ).
tff(f18,plain,
! [X1: $real] :
( ? [X2: $real] :
( ( $less($uminus($sum(X2,$uminus(a))),X1)
| ~ $less($sum(X2,$uminus(a)),0.0) )
& ( a != X2 )
& ( ( ~ $less($uminus($sum(X2,$uminus(a))),sK0)
& $less($sum(X2,$uminus(a)),0.0) )
| ( ~ $less($sum(X2,$uminus(a)),sK0)
& ~ $less($sum(X2,$uminus(a)),0.0) ) )
& ( $less($sum(X2,$uminus(a)),X1)
| $less($sum(X2,$uminus(a)),0.0) ) )
=> ( ( $less($uminus($sum(sK1(X1),$uminus(a))),X1)
| ~ $less($sum(sK1(X1),$uminus(a)),0.0) )
& ( a != sK1(X1) )
& ( ( ~ $less($uminus($sum(sK1(X1),$uminus(a))),sK0)
& $less($sum(sK1(X1),$uminus(a)),0.0) )
| ( ~ $less($sum(sK1(X1),$uminus(a)),sK0)
& ~ $less($sum(sK1(X1),$uminus(a)),0.0) ) )
& ( $less($sum(sK1(X1),$uminus(a)),X1)
| $less($sum(sK1(X1),$uminus(a)),0.0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f16,plain,
? [X0: $real] :
( ! [X1: $real] :
( ~ $less(0.0,X1)
| ? [X2: $real] :
( ( $less($uminus($sum(X2,$uminus(a))),X1)
| ~ $less($sum(X2,$uminus(a)),0.0) )
& ( a != X2 )
& ( ( ~ $less($uminus($sum(X2,$uminus(a))),X0)
& $less($sum(X2,$uminus(a)),0.0) )
| ( ~ $less($sum(X2,$uminus(a)),X0)
& ~ $less($sum(X2,$uminus(a)),0.0) ) )
& ( $less($sum(X2,$uminus(a)),X1)
| $less($sum(X2,$uminus(a)),0.0) ) ) )
& $less(0.0,X0) ),
inference(flattening,[],[f15]) ).
tff(f15,plain,
? [X0: $real] :
( ! [X1: $real] :
( ? [X2: $real] :
( ( ( ~ $less($uminus($sum(X2,$uminus(a))),X0)
& $less($sum(X2,$uminus(a)),0.0) )
| ( ~ $less($sum(X2,$uminus(a)),X0)
& ~ $less($sum(X2,$uminus(a)),0.0) ) )
& ( a != X2 )
& ( $less($sum(X2,$uminus(a)),X1)
| $less($sum(X2,$uminus(a)),0.0) )
& ( $less($uminus($sum(X2,$uminus(a))),X1)
| ~ $less($sum(X2,$uminus(a)),0.0) ) )
| ~ $less(0.0,X1) )
& $less(0.0,X0) ),
inference(ennf_transformation,[],[f3]) ).
tff(f3,plain,
~ ! [X0: $real] :
( $less(0.0,X0)
=> ? [X1: $real] :
( ! [X2: $real] :
( ( ( a != X2 )
& ( ~ $less($sum(X2,$uminus(a)),0.0)
=> $less($sum(X2,$uminus(a)),X1) )
& ( $less($sum(X2,$uminus(a)),0.0)
=> $less($uminus($sum(X2,$uminus(a))),X1) ) )
=> ( ( ~ $less($sum(X2,$uminus(a)),0.0)
=> $less($sum(X2,$uminus(a)),X0) )
& ( $less($sum(X2,$uminus(a)),0.0)
=> $less($uminus($sum(X2,$uminus(a))),X0) ) ) )
& $less(0.0,X1) ) ),
inference(theory_normalization,[],[f2]) ).
tff(f2,negated_conjecture,
~ ! [X0: $real] :
( $less(0.0,X0)
=> ? [X1: $real] :
( ! [X2: $real] :
( ( ( a != X2 )
& ( $greatereq($difference(X2,a),0.0)
=> $less($difference(X2,a),X1) )
& ( ~ $greatereq($difference(X2,a),0.0)
=> $less($uminus($difference(X2,a)),X1) ) )
=> ( ( ~ $greatereq($difference(X2,a),0.0)
=> $less($uminus($difference(X2,a)),X0) )
& ( $greatereq($difference(X2,a),0.0)
=> $less($difference(X2,a),X0) ) ) )
& $less(0.0,X1) ) ),
inference(negated_conjecture,[],[f1]) ).
tff(f1,conjecture,
! [X0: $real] :
( $less(0.0,X0)
=> ? [X1: $real] :
( ! [X2: $real] :
( ( ( a != X2 )
& ( $greatereq($difference(X2,a),0.0)
=> $less($difference(X2,a),X1) )
& ( ~ $greatereq($difference(X2,a),0.0)
=> $less($uminus($difference(X2,a)),X1) ) )
=> ( ( ~ $greatereq($difference(X2,a),0.0)
=> $less($uminus($difference(X2,a)),X0) )
& ( $greatereq($difference(X2,a),0.0)
=> $less($difference(X2,a),X0) ) ) )
& $less(0.0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_1) ).
tff(f34,plain,
( ~ $less(0.0,sK0)
| $less($sum(sK1(sK0),$uminus(a)),0.0) ),
inference(duplicate_literal_removal,[],[f33]) ).
tff(f33,plain,
( ~ $less(0.0,sK0)
| $less($sum(sK1(sK0),$uminus(a)),0.0)
| $less($sum(sK1(sK0),$uminus(a)),0.0) ),
inference(resolution,[],[f29,f23]) ).
tff(f23,plain,
! [X1: $real] :
( ~ $less($sum(sK1(X1),$uminus(a)),sK0)
| ~ $less(0.0,X1)
| $less($sum(sK1(X1),$uminus(a)),0.0) ),
inference(cnf_transformation,[],[f19]) ).
tff(f29,plain,
( $less($sum(sK1(sK0),$uminus(a)),sK0)
| $less($sum(sK1(sK0),$uminus(a)),0.0) ),
inference(resolution,[],[f21,f20]) ).
tff(f21,plain,
! [X1: $real] :
( ~ $less(0.0,X1)
| $less($sum(sK1(X1),$uminus(a)),0.0)
| $less($sum(sK1(X1),$uminus(a)),X1) ),
inference(cnf_transformation,[],[f19]) ).
tff(f41,plain,
~ $less($sum(sK1(sK0),$uminus(a)),0.0),
inference(subsumption_resolution,[],[f39,f20]) ).
tff(f39,plain,
( ~ $less(0.0,sK0)
| ~ $less($sum(sK1(sK0),$uminus(a)),0.0) ),
inference(resolution,[],[f37,f24]) ).
tff(f24,plain,
! [X1: $real] :
( ~ $less($uminus($sum(sK1(X1),$uminus(a))),sK0)
| ~ $less(0.0,X1)
| ~ $less($sum(sK1(X1),$uminus(a)),0.0) ),
inference(cnf_transformation,[],[f19]) ).
tff(f37,plain,
$less($uminus($sum(sK1(sK0),$uminus(a))),sK0),
inference(subsumption_resolution,[],[f36,f20]) ).
tff(f36,plain,
( $less($uminus($sum(sK1(sK0),$uminus(a))),sK0)
| ~ $less(0.0,sK0) ),
inference(resolution,[],[f35,f27]) ).
tff(f27,plain,
! [X1: $real] :
( ~ $less($sum(sK1(X1),$uminus(a)),0.0)
| ~ $less(0.0,X1)
| $less($uminus($sum(sK1(X1),$uminus(a))),X1) ),
inference(cnf_transformation,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ANA140_1 : TPTP v8.2.0. Released v8.2.0.
% 0.06/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon May 22 11:13:38 EDT 2023
% 0.12/0.34 % CPUTime :
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% 1.08/0.63 % (16879)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2998ds/37Mi)
% 1.26/0.65 % (16879)First to succeed.
% 1.26/0.65 % (16879)Refutation found. Thanks to Tanya!
% 1.26/0.65 % SZS status Theorem for theBenchmark
% 1.26/0.65 % SZS output start Proof for theBenchmark
% See solution above
% 1.26/0.65 % (16879)------------------------------
% 1.26/0.65 % (16879)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.26/0.65 % (16879)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.26/0.65 % (16879)Termination reason: Refutation
% 1.26/0.65
% 1.26/0.65 % (16879)Memory used [KB]: 895
% 1.26/0.65 % (16879)Time elapsed: 0.102 s
% 1.26/0.65 % (16879)Instructions burned: 2 (million)
% 1.26/0.65 % (16879)------------------------------
% 1.26/0.65 % (16879)------------------------------
% 1.26/0.65 % (16742)Success in time 0.3 s
%------------------------------------------------------------------------------