%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX153_1 : TPTP v9.3.1. Released v9.3.0.
% 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 01:45:59 PM UTC 2026
% Result : Theorem 3.82s 1.37s
% Output : Refutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 104 ( 6 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 102 ( 41 ~; 34 |; 12 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 152 ( 23 atm; 9 fun; 53 num; 67 var)
% Number of types : 2 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 11 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 2 usr; 4 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 59 !; 8 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_4,type,
'$inst0': $int ).
tff(func_def_5,type,
'$inst1': $int ).
tff(pred_def_1,type,
sl1sl2: ( $int * $int ) > $o ).
tff(pred_def_2,type,
w1w2: ( $int * $int ) > $o ).
tff(pred_def_3,type,
cr1cr2: ( $int * $int ) > $o ).
tff(pred_def_4,type,
sl1w2: ( $int * $int ) > $o ).
tff(pred_def_5,type,
w1cr2: ( $int * $int ) > $o ).
tff(pred_def_6,type,
sl1cr2: ( $int * $int ) > $o ).
tff(pred_def_7,type,
w1sl2: ( $int * $int ) > $o ).
tff(pred_def_8,type,
cr1w2: ( $int * $int ) > $o ).
tff(pred_def_9,type,
cr1sl2: ( $int * $int ) > $o ).
tff(f10,axiom,
! [X1: $int,X0: $int] :
( sl1sl2(X0,X1)
=> w1sl2($sum(X1,1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10) ).
tff(f11,axiom,
! [X1: $int,X0: $int] :
( ( w1sl2(X0,X1)
& ( ( X1 = 0 )
| $less(X0,X1) ) )
=> cr1sl2(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax11) ).
tff(f14,axiom,
! [X0: $int,X1: $int] :
( cr1sl2(X0,X1)
=> cr1w2(X0,$sum(X0,1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax14) ).
tff(f19,conjecture,
( ! [X0: $int,X1: $int] :
( ( $greatereq(X0,0)
& $greatereq(X1,0) )
=> sl1sl2(X0,X1) )
=> ? [X3: $int,X2: $int] : cr1w2(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj1) ).
tff(f20,negated_conjecture,
~ ( ! [X0: $int,X1: $int] :
( ( $greatereq(X0,0)
& $greatereq(X1,0) )
=> sl1sl2(X0,X1) )
=> ? [X3: $int,X2: $int] : cr1w2(X2,X3) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
tff(f21,plain,
~ ( ! [X1: $int,X0: $int] :
( ( ~ $less(X1,0)
& ~ $less(X0,0) )
=> sl1sl2(X0,X1) )
=> ? [X3: $int,X2: $int] : cr1w2(X2,X3) ),
inference(theory_normalization,[],[f20]) ).
tff(f34,plain,
~ ( ! [X1: $int,X0: $int] :
( ( ~ $less(X1,0)
& ~ $less(X0,0) )
=> sl1sl2(X0,X1) )
=> ? [X3: $int,X2: $int] : cr1w2(X3,X2) ),
inference(rectify,[],[f21]) ).
tff(f35,plain,
! [X0: $int,X1: $int] :
( sl1sl2(X1,X0)
=> w1sl2($sum(X0,1),X0) ),
inference(rectify,[],[f10]) ).
tff(f39,plain,
! [X1: $int,X0: $int] :
( ( ( $less(X1,X0)
| ( 0 = X0 ) )
& w1sl2(X1,X0) )
=> cr1sl2(X1,X0) ),
inference(rectify,[],[f11]) ).
tff(f46,plain,
! [X1: $int,X0: $int] :
( ~ cr1sl2(X0,X1)
| cr1w2(X0,$sum(X0,1)) ),
inference(ennf_transformation,[],[f14]) ).
tff(f53,plain,
! [X1: $int,X0: $int] :
( cr1sl2(X1,X0)
| ( ~ $less(X1,X0)
& ( 0 != X0 ) )
| ~ w1sl2(X1,X0) ),
inference(ennf_transformation,[],[f39]) ).
tff(f54,plain,
! [X1: $int,X0: $int] :
( ( ~ $less(X1,X0)
& ( 0 != X0 ) )
| cr1sl2(X1,X0)
| ~ w1sl2(X1,X0) ),
inference(flattening,[],[f53]) ).
tff(f59,plain,
! [X0: $int,X1: $int] :
( ~ sl1sl2(X1,X0)
| w1sl2($sum(X0,1),X0) ),
inference(ennf_transformation,[],[f35]) ).
tff(f63,plain,
( ! [X2: $int,X3: $int] : ~ cr1w2(X3,X2)
& ! [X1: $int,X0: $int] :
( sl1sl2(X0,X1)
| $less(X1,0)
| $less(X0,0) ) ),
inference(ennf_transformation,[],[f34]) ).
tff(f64,plain,
( ! [X1: $int,X0: $int] :
( $less(X0,0)
| sl1sl2(X0,X1)
| $less(X1,0) )
& ! [X2: $int,X3: $int] : ~ cr1w2(X3,X2) ),
inference(flattening,[],[f63]) ).
tff(f74,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,0)
| sl1sl2(X1,X0)
| $less(X0,0) )
& ! [X2: $int,X3: $int] : ~ cr1w2(X3,X2) ),
inference(rectify,[],[f64]) ).
tff(f76,plain,
! [X0: $int,X1: $int] :
( ( ~ $less(X0,X1)
& ( 0 != X1 ) )
| cr1sl2(X0,X1)
| ~ w1sl2(X0,X1) ),
inference(rectify,[],[f54]) ).
tff(f78,plain,
! [X0: $int,X1: $int] :
( ~ cr1sl2(X1,X0)
| cr1w2(X1,$sum(X1,1)) ),
inference(rectify,[],[f46]) ).
tff(f82,plain,
! [X0: $int,X1: $int] :
( w1sl2($sum(X0,1),X0)
| ~ sl1sl2(X1,X0) ),
inference(cnf_transformation,[],[f59]) ).
tff(f89,plain,
! [X2: $int,X3: $int] : ~ cr1w2(X3,X2),
inference(cnf_transformation,[],[f74]) ).
tff(f90,plain,
! [X0: $int,X1: $int] :
( sl1sl2(X1,X0)
| $less(X0,0)
| $less(X1,0) ),
inference(cnf_transformation,[],[f74]) ).
tff(f94,plain,
! [X0: $int,X1: $int] :
( ( 0 != X1 )
| cr1sl2(X0,X1)
| ~ w1sl2(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
tff(f101,plain,
! [X0: $int,X1: $int] :
( ~ cr1sl2(X1,X0)
| cr1w2(X1,$sum(X1,1)) ),
inference(cnf_transformation,[],[f78]) ).
tff(f109,plain,
! [X0: $int] :
( ~ w1sl2(X0,0)
| cr1sl2(X0,0) ),
inference(equality_resolution,[],[f94]) ).
tff(f113,plain,
( sl1sl2(0,0)
| $less(0,0)
| $less(0,0) ),
inference(instantiation,[],[f90]) ).
tff(f114,plain,
sl1sl2(0,0),
inference(interpreted_simplification,[],[f113]) ).
tff(f197,plain,
! [X0: $int] :
( ~ sl1sl2(X0,0)
| cr1sl2($sum(0,1),0) ),
inference(resolution,[],[f82,f109]) ).
tff(f201,plain,
! [X0: $int] :
( ~ sl1sl2(X0,0)
| cr1sl2(1,0) ),
inference(evaluation,[],[f197]) ).
tff(f204,definition,
( spl2_1
<=> cr1sl2(1,0) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f206,plain,
( cr1sl2(1,0)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f204]) ).
tff(f208,definition,
( spl2_2
<=> ! [X0: $int] : ~ sl1sl2(X0,0) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f209,plain,
( ! [X0: $int] : ~ sl1sl2(X0,0)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f208]) ).
tff(f210,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f201,f208,f204]) ).
tff(f227,plain,
( $false
| ~ spl2_2 ),
inference(resolution,[],[f209,f114]) ).
tff(f229,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f227]) ).
tff(f234,plain,
! [X0: $int,X1: $int] : ~ cr1sl2(X1,X0),
inference(forward_subsumption_resolution,[],[f101,f89]) ).
tff(f235,plain,
( $false
| ~ spl2_1 ),
inference(resolution,[],[f234,f206]) ).
tff(f236,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f235]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f210]) ).
cnf(s3,plain,
~ spl2_2,
inference(sat_conversion,[],[f229]) ).
cnf(s4,plain,
~ spl2_1,
inference(sat_conversion,[],[f236]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s4]) ).
tff(f237,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX153_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n004.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 15:06:06 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 3.11/1.12 % (443456)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.11/1.12 % (443510)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1101942922:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.11/1.12 % (443510)Refutation not found, incomplete strategy
% 3.11/1.12 % (443510)------------------------------
% 3.11/1.12 % (443510)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.11/1.12 % (443510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/1.12 % (443510)CaDiCaL version: 2.1.3
% 3.11/1.12 % (443510)Termination reason: Refutation not found, incomplete strategy
% 3.11/1.12 % (443510)Time elapsed: 0.018 s
% 3.11/1.12 % (443510)Peak memory usage: 112 MB
% 3.11/1.12 % (443510)Instructions burned: 8 (million)
% 3.11/1.12 % (443516)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2033808524:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.11/1.12 % (443513)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1362085411:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.11/1.12 % (443512)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1393619687:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.11/1.12 % (443511)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=792388396:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.11/1.12 % (443513)Instruction limit reached!
% 3.11/1.12 % (443513)------------------------------
% 3.11/1.12 % (443513)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.11/1.12 % (443513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/1.12 % (443513)CaDiCaL version: 2.1.3
% 3.11/1.12 % (443513)Termination reason: Instruction limit
% 3.11/1.12 % (443513)Termination phase: Saturation
% 3.11/1.12 % (443513)Time elapsed: 0.006 s
% 3.11/1.12 % (443513)Peak memory usage: 88 MB
% 3.11/1.12 % (443513)Instructions burned: 8 (million)
% 3.11/1.12 % (443515)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1942597990:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.11/1.12 % (443514)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=123027639:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.11/1.12 % (443514)Instruction limit reached!
% 3.11/1.12 % (443514)------------------------------
% 3.11/1.12 % (443514)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.11/1.12 % (443514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/1.12 % (443514)CaDiCaL version: 2.1.3
% 3.11/1.12 % (443514)Termination reason: Instruction limit
% 3.11/1.12 % (443514)Termination phase: Saturation
% 3.11/1.12 % (443514)Time elapsed: 0.004 s
% 3.11/1.12 % (443514)Peak memory usage: 89 MB
% 3.11/1.12 % (443514)Instructions burned: 5 (million)
% 3.11/1.12 % (443511)Refutation not found, incomplete strategy
% 3.11/1.12 % (443511)------------------------------
% 3.11/1.12 % (443511)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.11/1.12 % (443511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/1.12 % (443511)CaDiCaL version: 2.1.3
% 3.11/1.12 % (443511)Termination reason: Refutation not found, incomplete strategy
% 3.11/1.12 % (443511)Time elapsed: 0.032 s
% 3.11/1.12 % (443511)Peak memory usage: 115 MB
% 3.11/1.12 % (443511)Instructions burned: 10 (million)
% 3.11/1.12 % (443512)First to succeed.
% 3.11/1.12 % (443512)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-443456"
% 3.11/1.12 % (443515)Refutation not found, incomplete strategy
% 3.11/1.12 % (443515)------------------------------
% 3.11/1.12 % (443515)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.11/1.12 % (443515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/1.12 % (443515)CaDiCaL version: 2.1.3
% 3.11/1.12 % (443515)Termination reason: Refutation not found, incomplete strategy
% 3.11/1.12 % (443515)Time elapsed: 0.030 s
% 3.11/1.12 % (443515)Peak memory usage: 115 MB
% 3.11/1.12 % (443515)Instructions burned: 8 (million)
% 3.11/1.12 % (443516)Also succeeded, but the first one will report.
% 3.11/1.12 % (443510)------------------------------
% 3.11/1.12 % (443510)------------------------------
% 3.11/1.12 % (443562)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=1571509632:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.82/1.37 % (443559)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3252853077:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.82/1.37 % (443559)Refutation not found, incomplete strategy
% 3.82/1.37 % (443559)------------------------------
% 3.82/1.37 % (443559)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.82/1.37 % (443559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/1.37 % (443559)CaDiCaL version: 2.1.3
% 3.82/1.37 % (443559)Termination reason: Refutation not found, incomplete strategy
% 3.82/1.37 % (443559)Time elapsed: 0.002 s
% 3.82/1.37 % (443559)Peak memory usage: 89 MB
% 3.82/1.37 % (443559)Instructions burned: 2 (million)
% 3.82/1.37 % (443562)Also succeeded, but the first one will report.
% 3.82/1.37 % (443606)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=2538114865:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 3.82/1.37 % (443606)Instruction limit reached!
% 3.82/1.37 % (443606)------------------------------
% 3.82/1.37 % (443606)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.82/1.37 % (443606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/1.37 % (443606)CaDiCaL version: 2.1.3
% 3.82/1.37 % (443606)Termination reason: Instruction limit
% 3.82/1.37 % (443606)Termination phase: Saturation
% 3.82/1.37 % (443606)Time elapsed: 0.005 s
% 3.82/1.37 % (443606)Peak memory usage: 90 MB
% 3.82/1.37 % (443606)Instructions burned: 17 (million)
% 3.82/1.37 % (443515)------------------------------
% 3.82/1.37 % (443515)------------------------------
% 3.82/1.37 % (443512)Refutation found. Thanks to Tanya!
% 3.82/1.37 % SZS status Theorem for theBenchmark
% 3.82/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.82/1.37 % (443512)------------------------------
% 3.82/1.37 % (443512)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.82/1.37 % (443512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/1.37 % (443512)CaDiCaL version: 2.1.3
% 3.82/1.37 % (443512)Termination reason: Refutation
% 3.82/1.37 % (443512)Time elapsed: 0.036 s
% 3.82/1.37 % (443512)Peak memory usage: 117 MB
% 3.82/1.37 % (443512)Instructions burned: 16 (million)
% 3.82/1.37 % (443512)------------------------------
% 3.82/1.37 % (443512)------------------------------
% 3.82/1.37 % (443456)Success in time 0.446 s
% 3.82/1.37 % Vampire exiting
%------------------------------------------------------------------------------