%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA139_1 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:31:12 AM UTC 2026
% Result : Theorem 3.36s 1.22s
% Output : Refutation 3.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 81 ( 7 equ)
% Maximal formula atoms : 11 ( 5 avg)
% Number of connectives : 105 ( 39 ~; 18 |; 30 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 246 ( 73 atm; 102 fun; 49 num; 22 var)
% Number of types : 1 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 22 ( 15 !; 7 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $real ).
tff(func_def_1,type,
c: $real ).
tff(func_def_7,type,
sK0: $real ).
tff(func_def_8,type,
sK1: $real > $real ).
tff(f1,conjecture,
! [X0: $real] :
( $less(0/1,X0)
=> ? [X1: $real] :
( ! [X2: $real] :
( ( ( X2 != a )
& ( $greatereq($difference(X2,a),0/1)
=> $less($difference(X2,a),X1) )
& ( ~ $greatereq($difference(X2,a),0/1)
=> $less($uminus($difference(X2,a)),X1) ) )
=> ( ( ~ $greatereq($difference(c,c),0/1)
=> $less($uminus($difference(c,c)),X0) )
& ( $greatereq($difference(c,c),0/1)
=> $less($difference(c,c),X0) ) ) )
& $less(0/1,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_1) ).
tff(f2,negated_conjecture,
~ ! [X0: $real] :
( $less(0/1,X0)
=> ? [X1: $real] :
( ! [X2: $real] :
( ( ( X2 != a )
& ( $greatereq($difference(X2,a),0/1)
=> $less($difference(X2,a),X1) )
& ( ~ $greatereq($difference(X2,a),0/1)
=> $less($uminus($difference(X2,a)),X1) ) )
=> ( ( ~ $greatereq($difference(c,c),0/1)
=> $less($uminus($difference(c,c)),X0) )
& ( $greatereq($difference(c,c),0/1)
=> $less($difference(c,c),X0) ) ) )
& $less(0/1,X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ! [X0: $real] :
( $less(0/1,X0)
=> ? [X1: $real] :
( $less(0/1,X1)
& ! [X2: $real] :
( ( ( X2 != a )
& ( $less($sum(X2,$uminus(a)),0/1)
=> $less($uminus($sum(X2,$uminus(a))),X1) )
& ( ~ $less($sum(X2,$uminus(a)),0/1)
=> $less($sum(X2,$uminus(a)),X1) ) )
=> ( ( ~ $less($sum(c,$uminus(c)),0/1)
=> $less($sum(c,$uminus(c)),X0) )
& ( $less($sum(c,$uminus(c)),0/1)
=> $less($uminus($sum(c,$uminus(c))),X0) ) ) ) ) ),
inference(theory_normalization,[],[f2]) ).
tff(f8,plain,
! [X0: $real] : ( 0/1 = $sum(X0,$uminus(X0)) ),
introduced(definition,[],[tha_inverse_op_unit]) ).
tff(f15,plain,
? [X0: $real] :
( ! [X1: $real] :
( ~ $less(0/1,X1)
| ? [X2: $real] :
( ( ( ~ $less($sum(c,$uminus(c)),X0)
& ~ $less($sum(c,$uminus(c)),0/1) )
| ( ~ $less($uminus($sum(c,$uminus(c))),X0)
& $less($sum(c,$uminus(c)),0/1) ) )
& ( X2 != a )
& ( ~ $less($sum(X2,$uminus(a)),0/1)
| $less($uminus($sum(X2,$uminus(a))),X1) )
& ( $less($sum(X2,$uminus(a)),X1)
| $less($sum(X2,$uminus(a)),0/1) ) ) )
& $less(0/1,X0) ),
inference(ennf_transformation,[],[f3]) ).
tff(f16,plain,
? [X0: $real] :
( ! [X1: $real] :
( ~ $less(0/1,X1)
| ? [X2: $real] :
( ( ~ $less($sum(X2,$uminus(a)),0/1)
| $less($uminus($sum(X2,$uminus(a))),X1) )
& ( $less($sum(X2,$uminus(a)),X1)
| $less($sum(X2,$uminus(a)),0/1) )
& ( X2 != a )
& ( ( ~ $less($sum(c,$uminus(c)),X0)
& ~ $less($sum(c,$uminus(c)),0/1) )
| ( ~ $less($uminus($sum(c,$uminus(c))),X0)
& $less($sum(c,$uminus(c)),0/1) ) ) ) )
& $less(0/1,X0) ),
inference(flattening,[],[f15]) ).
tff(f17,plain,
( ! [X1: $real] :
( ~ $less(0/1,X1)
| ( ( ~ $less($sum(sK1(X1),$uminus(a)),0/1)
| $less($uminus($sum(sK1(X1),$uminus(a))),X1) )
& ( $less($sum(sK1(X1),$uminus(a)),X1)
| $less($sum(sK1(X1),$uminus(a)),0/1) )
& ( a != sK1(X1) )
& ( ( ~ $less($sum(c,$uminus(c)),sK0)
& ~ $less($sum(c,$uminus(c)),0/1) )
| ( ~ $less($uminus($sum(c,$uminus(c))),sK0)
& $less($sum(c,$uminus(c)),0/1) ) ) ) )
& $less(0/1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X2,sK1(X1))],[f16]) ).
tff(f18,plain,
$less(0/1,sK0),
inference(cnf_transformation,[],[f17]) ).
tff(f21,plain,
! [X1: $real] :
( $less($sum(c,$uminus(c)),0/1)
| ~ $less($sum(c,$uminus(c)),sK0)
| ~ $less(0/1,X1) ),
inference(cnf_transformation,[],[f17]) ).
tff(f26,plain,
! [X1: $real] :
( $less(0/1,0/1)
| ~ $less(0/1,X1)
| ~ $less($sum(c,$uminus(c)),sK0) ),
inference(forward_demodulation,[],[f21,f8]) ).
tff(f27,plain,
! [X1: $real] :
( ~ $less($sum(c,$uminus(c)),sK0)
| ~ $less(0/1,X1) ),
inference(evaluation,[],[f26]) ).
tff(f32,plain,
! [X1: $real] :
( ~ $less(0/1,X1)
| ~ $less(0/1,sK0) ),
inference(forward_demodulation,[],[f27,f8]) ).
tff(f35,plain,
! [X1: $real] : ~ $less(0/1,X1),
inference(forward_subsumption_resolution,[],[f32,f18]) ).
tff(f46,plain,
~ $less(0/1,1/1),
inference(instantiation,[],[f35]) ).
tff(f49,plain,
$false,
inference(evaluation,[],[f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA139_1 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n004.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 20:40:07 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.36/1.22 % (730813)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.36/1.22 % (730841)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1313938882:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.36/1.22 % (730841)First to succeed.
% 3.36/1.22 % (730841)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-730813"
% 3.36/1.22 % (730838)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1565450853:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.36/1.22 % (730842)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=327709227:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.36/1.22 % (730842)Instruction limit reached!
% 3.36/1.22 % (730842)------------------------------
% 3.36/1.22 % (730842)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.36/1.22 % (730842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/1.22 % (730842)CaDiCaL version: 2.1.3
% 3.36/1.22 % (730842)Termination reason: Instruction limit
% 3.36/1.22 % (730842)Termination phase: Saturation
% 3.36/1.22 % (730842)Time elapsed: 0.005 s
% 3.36/1.22 % (730842)Peak memory usage: 89 MB
% 3.36/1.22 % (730842)Instructions burned: 5 (million)
% 3.36/1.22 % (730839)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2815323375:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.36/1.22 % (730844)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3436892234:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.36/1.22 % (730838)Also succeeded, but the first one will report.
% 3.36/1.22 % (730840)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2131694503:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.36/1.22 % (730843)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1703979178:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.36/1.22 % (730839)Also succeeded, but the first one will report.
% 3.36/1.22 % (730844)Also succeeded, but the first one will report.
% 3.36/1.22 % (730840)Also succeeded, but the first one will report.
% 3.36/1.22 % (730843)Also succeeded, but the first one will report.
% 3.36/1.22 % (730841)Refutation found. Thanks to Tanya!
% 3.36/1.22 % SZS status Theorem for theBenchmark
% 3.36/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 3.36/1.22 % (730841)------------------------------
% 3.36/1.22 % (730841)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.36/1.22 % (730841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/1.22 % (730841)CaDiCaL version: 2.1.3
% 3.36/1.22 % (730841)Termination reason: Refutation
% 3.36/1.22 % (730841)Time elapsed: 0.002 s
% 3.36/1.22 % (730841)Peak memory usage: 89 MB
% 3.36/1.22 % (730841)Instructions burned: 2 (million)
% 3.36/1.22 % (730841)------------------------------
% 3.36/1.22 % (730841)------------------------------
% 3.36/1.22 % (730813)Success in time 0.38 s
% 3.36/1.22 % Vampire exiting
%------------------------------------------------------------------------------