%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX096_1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 01:45:52 PM UTC 2026
% Result : Theorem 4.86s 1.59s
% Output : Refutation 4.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 10 unt; 0 typ; 3 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 42 ( 18 ~; 0 |; 17 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 110 ( 37 atm; 34 fun; 27 num; 12 var)
% Number of types : 4 ( 2 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 14 usr; 4 prp; 0-2 aty)
% Number of functors : 13 ( 7 usr; 8 con; 0-2 aty)
% Number of variables : 12 ( 8 !; 4 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
general: $tType ).
tff(type_def_6,type,
symbol: $tType ).
tff(func_def_0,type,
f__integer__: $int > general ).
tff(func_def_1,type,
f__symbolic__: symbol > general ).
tff(func_def_2,type,
c__infimum__: general ).
tff(func_def_3,type,
c__supremum__: general ).
tff(func_def_4,type,
n_i: $int ).
tff(func_def_10,type,
sK0: $int ).
tff(func_def_11,type,
sK1: $int ).
tff(pred_def_1,type,
p__is_integer__: general > $o ).
tff(pred_def_2,type,
p__is_symbolic__: general > $o ).
tff(pred_def_3,type,
p__less_equal__: ( general * general ) > $o ).
tff(pred_def_4,type,
p__less__: ( general * general ) > $o ).
tff(pred_def_5,type,
p__greater_equal__: ( general * general ) > $o ).
tff(pred_def_6,type,
p__greater__: ( general * general ) > $o ).
tff(pred_def_8,type,
three: general > $o ).
tff(pred_def_9,type,
sqrt: general > $o ).
tff(pred_def_10,type,
three_p: general > $o ).
tff(pred_def_11,type,
more_than_three: general > $o ).
tff(pred_def_12,type,
sqrt: ( general * general ) > $o ).
tff(f25,conjecture,
! [X1: $int,X0: $int] :
( ( $greatereq(X0,1)
& $greatereq(X1,1)
& $less(X0,X1) )
=> $less($product(X0,X0),$product(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_9_unnamed_formula) ).
tff(f26,negated_conjecture,
~ ! [X1: $int,X0: $int] :
( ( $greatereq(X0,1)
& $greatereq(X1,1)
& $less(X0,X1) )
=> $less($product(X0,X0),$product(X1,X1)) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
tff(f36,plain,
~ ! [X1: $int,X0: $int] :
( ( ~ $less(X0,1)
& ~ $less(X1,1)
& $less(X0,X1) )
=> $less($product(X0,X0),$product(X1,X1)) ),
inference(theory_normalization,[],[f26]) ).
tff(f55,plain,
~ ! [X0: $int,X1: $int] :
( ( $less(X1,X0)
& ~ $less(X0,1)
& ~ $less(X1,1) )
=> $less($product(X1,X1),$product(X0,X0)) ),
inference(rectify,[],[f36]) ).
tff(f57,plain,
? [X0: $int,X1: $int] :
( ~ $less($product(X1,X1),$product(X0,X0))
& $less(X1,X0)
& ~ $less(X0,1)
& ~ $less(X1,1) ),
inference(ennf_transformation,[],[f55]) ).
tff(f58,plain,
? [X0: $int,X1: $int] :
( ~ $less($product(X1,X1),$product(X0,X0))
& ~ $less(X1,1)
& $less(X1,X0)
& ~ $less(X0,1) ),
inference(flattening,[],[f57]) ).
tff(f60,plain,
( ~ $less($product(sK1,sK1),$product(sK0,sK0))
& ~ $less(sK1,1)
& $less(sK1,sK0)
& ~ $less(sK0,1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f58]) ).
tff(f64,plain,
$less(sK1,sK0),
inference(cnf_transformation,[],[f60]) ).
tff(f65,plain,
~ $less(sK1,1),
inference(cnf_transformation,[],[f60]) ).
tff(f66,plain,
~ $less($product(sK1,sK1),$product(sK0,sK0)),
inference(cnf_transformation,[],[f60]) ).
tff(f69,plain,
$less(0,$sum($sum($product(sK1,sK1),1),$uminus($product(sK0,sK0)))),
inference(evaluation,[],[f66]) ).
tff(f70,plain,
$less(0,$sum(sK0,$uminus(sK1))),
inference(evaluation,[],[f64]) ).
tff(f71,plain,
$less(0,$sum($sum(sK1,1),-1)),
inference(evaluation,[],[f65]) ).
tff(f78,definition,
( spl2_2
<=> $less(0,$sum($sum($product(sK1,sK1),1),$uminus($product(sK0,sK0)))) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f81,plain,
spl2_2,
inference(avatar_split_clause,[],[f69,f78]) ).
tff(f83,definition,
( spl2_3
<=> $less(0,$sum(sK0,$uminus(sK1))) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f86,plain,
spl2_3,
inference(avatar_split_clause,[],[f70,f83]) ).
tff(f88,definition,
( spl2_4
<=> $less(0,$sum($sum(sK1,1),-1)) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
tff(f91,plain,
spl2_4,
inference(avatar_split_clause,[],[f71,f88]) ).
tff(f92,plain,
$false,
inference(avatar_smt_refutation,[],[f91,f86,f81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX096_1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.26 % Computer : n002.cluster.edu
% 0.11/0.26 % Model : x86_64 x86_64
% 0.11/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.26 % Memory : 8046.5625MB
% 0.11/0.26 % OS : Linux 6.8.0-71-generic
% 0.11/0.26 % CPULimit : 300
% 0.11/0.26 % WCLimit : 300
% 0.11/0.26 % DateTime : Mon Sep 28 15:03:37 UTC 2026
% 0.11/0.27 % CPUTime :
% 0.11/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.32 Running first-order theorem proving
% 0.25/0.32 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
% 4.86/1.59 % (420458)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.86/1.59 % (420463)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=880137845:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.86/1.59 % (420463)First to succeed.
% 4.86/1.59 % (420463)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-420458"
% 4.86/1.59 % (420468)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3130037399:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.86/1.59 % (420467)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3752942361:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.86/1.59 % (420464)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=757119946:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.86/1.59 % (420466)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2628123977:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.86/1.59 % (420465)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2341708560:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.86/1.59 % (420467)Instruction limit reached!
% 4.86/1.59 % (420467)------------------------------
% 4.86/1.59 % (420467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.59 % (420467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.59 % (420467)CaDiCaL version: 2.1.3
% 4.86/1.59 % (420467)Termination reason: Instruction limit
% 4.86/1.59 % (420467)Termination phase: Saturation
% 4.86/1.59 % (420467)Time elapsed: 0.005 s
% 4.86/1.59 % (420467)Peak memory usage: 88 MB
% 4.86/1.59 % (420467)Instructions burned: 4 (million)
% 4.86/1.59 % (420466)Instruction limit reached!
% 4.86/1.59 % (420466)------------------------------
% 4.86/1.59 % (420466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.59 % (420466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.59 % (420466)CaDiCaL version: 2.1.3
% 4.86/1.59 % (420466)Termination reason: Instruction limit
% 4.86/1.59 % (420466)Termination phase: Saturation
% 4.86/1.59 % (420466)Time elapsed: 0.008 s
% 4.86/1.59 % (420466)Peak memory usage: 88 MB
% 4.86/1.59 % (420466)Instructions burned: 7 (million)
% 4.86/1.59 % (420469)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=399705310:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.86/1.59 % (420468)Also succeeded, but the first one will report.
% 4.86/1.59 % (420464)Also succeeded, but the first one will report.
% 4.86/1.59 % (420469)Also succeeded, but the first one will report.
% 4.86/1.59 % (420476)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1898255082:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 4.86/1.59 % (420465)Instruction limit reached!
% 4.86/1.59 % (420465)------------------------------
% 4.86/1.59 % (420465)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.59 % (420465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.59 % (420465)CaDiCaL version: 2.1.3
% 4.86/1.59 % (420465)Termination reason: Instruction limit
% 4.86/1.59 % (420465)Termination phase: Saturation
% 4.86/1.59 % (420465)Time elapsed: 0.252 s
% 4.86/1.59 % (420465)Peak memory usage: 119 MB
% 4.86/1.59 % (420465)Instructions burned: 201 (million)
% 4.86/1.59 % (420476)Instruction limit reached!
% 4.86/1.59 % (420476)------------------------------
% 4.86/1.59 % (420476)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.59 % (420476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.59 % (420476)CaDiCaL version: 2.1.3
% 4.86/1.59 % (420476)Termination reason: Instruction limit
% 4.86/1.59 % (420476)Termination phase: Saturation
% 4.86/1.59 % (420476)Time elapsed: 0.011 s
% 4.86/1.59 % (420476)Peak memory usage: 89 MB
% 4.86/1.59 % (420476)Instructions burned: 15 (million)
% 4.86/1.59 % (420463)Refutation found. Thanks to Tanya!
% 4.86/1.59 % SZS status Theorem for theBenchmark
% 4.86/1.59 % SZS output start Proof for theBenchmark
% See solution above
% 4.86/1.59 % (420463)------------------------------
% 4.86/1.59 % (420463)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.86/1.59 % (420463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.86/1.59 % (420463)CaDiCaL version: 2.1.3
% 4.86/1.59 % (420463)Termination reason: Refutation
% 4.86/1.59 % (420463)Time elapsed: 0.030 s
% 4.86/1.59 % (420463)Peak memory usage: 117 MB
% 4.86/1.59 % (420463)Instructions burned: 12 (million)
% 4.86/1.59 % (420463)------------------------------
% 4.86/1.59 % (420463)------------------------------
% 4.86/1.59 % (420458)Success in time 0.589 s
% 4.86/1.59 % Vampire exiting
%------------------------------------------------------------------------------