%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX084_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 : n017.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 01:45:51 PM UTC 2026
% Result : Theorem 2.74s 1.17s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 70 ( 29 ~; 17 |; 12 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 142 ( 41 atm; 0 fun; 41 num; 60 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 : 13 ( 9 usr; 3 prp; 0-4 aty)
% Number of functors : 25 ( 24 usr; 5 con; 0-4 aty)
% Number of variables : 60 ( 34 !; 26 ?; 60 :)
% 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_10,type,
sK0: general > symbol ).
tff(func_def_11,type,
sK1: general > $int ).
tff(func_def_12,type,
sK2: ( general * general * general * general ) > general ).
tff(func_def_13,type,
sK3: ( general * general * general * general ) > general ).
tff(func_def_14,type,
sK4: ( general * general * general * general ) > general ).
tff(func_def_15,type,
sK5: ( general * general * general * general ) > general ).
tff(func_def_16,type,
sK6: ( general * general * general * general ) > general ).
tff(func_def_17,type,
sK7: ( general * general * general * general ) > general ).
tff(func_def_18,type,
sK8: ( general * general * general * general ) > general ).
tff(func_def_19,type,
sK9: ( general * general * general * general ) > general ).
tff(func_def_20,type,
sK10: ( general * general * general * general ) > general ).
tff(func_def_21,type,
sK11: ( general * general * general * general ) > general ).
tff(func_def_22,type,
sK12: ( general * general * general * general ) > $int ).
tff(func_def_23,type,
sK13: ( general * general * general * general ) > $int ).
tff(func_def_24,type,
sK14: ( general * general * general * general ) > $int ).
tff(func_def_25,type,
sK15: ( general * general * general * general ) > $int ).
tff(func_def_26,type,
sK16: $int ).
tff(func_def_27,type,
sK17: $int ).
tff(func_def_28,type,
sK18: ( $int * $int ) > $int ).
tff(func_def_29,type,
sK19: ( $int * $int ) > $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,
div: ( general * general * general * general ) > $o ).
tff(f19,axiom,
! [X1: $int,X0: $int] :
( $greatereq(X1,0)
=> ( $greater(X0,0)
=> ? [X3: $int,X2: $int] : div(f__integer__(X1),f__integer__(X0),f__integer__(X2),f__integer__(X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_3_unnamed_formula) ).
tff(f20,conjecture,
! [X1: $int,X0: $int] :
( ( $greater(X1,0)
& $greatereq(X0,0) )
=> ? [X2: $int,X3: $int] : div(f__integer__(X0),f__integer__(X1),f__integer__(X2),f__integer__(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_4_unnamed_formula) ).
tff(f21,negated_conjecture,
~ ! [X1: $int,X0: $int] :
( ( $greater(X1,0)
& $greatereq(X0,0) )
=> ? [X2: $int,X3: $int] : div(f__integer__(X0),f__integer__(X1),f__integer__(X2),f__integer__(X3)) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
tff(f23,plain,
~ ! [X1: $int,X0: $int] :
( ( $less(0,X1)
& ~ $less(X0,0) )
=> ? [X2: $int,X3: $int] : div(f__integer__(X0),f__integer__(X1),f__integer__(X2),f__integer__(X3)) ),
inference(theory_normalization,[],[f21]) ).
tff(f26,plain,
! [X1: $int,X0: $int] :
( ~ $less(X1,0)
=> ( $less(0,X0)
=> ? [X3: $int,X2: $int] : div(f__integer__(X1),f__integer__(X0),f__integer__(X2),f__integer__(X3)) ) ),
inference(theory_normalization,[],[f19]) ).
tff(f28,plain,
~ ! [X0: $int,X1: $int] :
( ( ~ $less(X1,0)
& $less(0,X0) )
=> ? [X2: $int,X3: $int] : div(f__integer__(X1),f__integer__(X0),f__integer__(X2),f__integer__(X3)) ),
inference(rectify,[],[f23]) ).
tff(f32,plain,
! [X1: $int,X0: $int] :
( ~ $less(X0,0)
=> ( $less(0,X1)
=> ? [X2: $int,X3: $int] : div(f__integer__(X0),f__integer__(X1),f__integer__(X3),f__integer__(X2)) ) ),
inference(rectify,[],[f26]) ).
tff(f40,plain,
? [X0: $int,X1: $int] :
( ! [X3: $int,X2: $int] : ~ div(f__integer__(X1),f__integer__(X0),f__integer__(X2),f__integer__(X3))
& ~ $less(X1,0)
& $less(0,X0) ),
inference(ennf_transformation,[],[f28]) ).
tff(f41,plain,
? [X1: $int,X0: $int] :
( $less(0,X0)
& ! [X3: $int,X2: $int] : ~ div(f__integer__(X1),f__integer__(X0),f__integer__(X2),f__integer__(X3))
& ~ $less(X1,0) ),
inference(flattening,[],[f40]) ).
tff(f45,plain,
! [X1: $int,X0: $int] :
( ? [X2: $int,X3: $int] : div(f__integer__(X0),f__integer__(X1),f__integer__(X3),f__integer__(X2))
| ~ $less(0,X1)
| $less(X0,0) ),
inference(ennf_transformation,[],[f32]) ).
tff(f46,plain,
! [X1: $int,X0: $int] :
( ~ $less(0,X1)
| ? [X2: $int,X3: $int] : div(f__integer__(X0),f__integer__(X1),f__integer__(X3),f__integer__(X2))
| $less(X0,0) ),
inference(flattening,[],[f45]) ).
tff(f61,plain,
? [X0: $int,X1: $int] :
( $less(0,X1)
& ! [X2: $int,X3: $int] : ~ div(f__integer__(X0),f__integer__(X1),f__integer__(X3),f__integer__(X2))
& ~ $less(X0,0) ),
inference(rectify,[],[f41]) ).
tff(f62,plain,
( $less(0,sK17)
& ! [X2: $int,X3: $int] : ~ div(f__integer__(sK16),f__integer__(sK17),f__integer__(X3),f__integer__(X2))
& ~ $less(sK16,0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17]),skolemize(X0,sK16),skolemize(X1,sK17)],[f61]) ).
tff(f69,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,X0)
| ? [X2: $int,X3: $int] : div(f__integer__(X1),f__integer__(X0),f__integer__(X3),f__integer__(X2))
| $less(X1,0) ),
inference(rectify,[],[f46]) ).
tff(f70,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,X0)
| div(f__integer__(X1),f__integer__(X0),f__integer__(sK19(X0,X1)),f__integer__(sK18(X0,X1)))
| $less(X1,0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19]),skolemize(X2,sK18(X0,X1)),skolemize(X3,sK19(X0,X1))],[f69]) ).
tff(f101,plain,
~ $less(sK16,0),
inference(cnf_transformation,[],[f62]) ).
tff(f102,plain,
! [X2: $int,X3: $int] : ~ div(f__integer__(sK16),f__integer__(sK17),f__integer__(X3),f__integer__(X2)),
inference(cnf_transformation,[],[f62]) ).
tff(f103,plain,
$less(0,sK17),
inference(cnf_transformation,[],[f62]) ).
tff(f113,plain,
! [X0: $int,X1: $int] :
( div(f__integer__(X1),f__integer__(X0),f__integer__(sK19(X0,X1)),f__integer__(sK18(X0,X1)))
| $less(X1,0)
| ~ $less(0,X0) ),
inference(cnf_transformation,[],[f70]) ).
tff(f137,definition,
( spl20_1
<=> $less(sK16,0) ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
tff(f139,plain,
( ~ $less(sK16,0)
| spl20_1 ),
inference(avatar_component_clause,[],[f137]) ).
tff(f140,plain,
~ spl20_1,
inference(avatar_split_clause,[],[f101,f137]) ).
tff(f142,definition,
( spl20_2
<=> $less(0,sK17) ),
introduced(definition,[new_symbols(definition,[spl20_2])],[avatar_definition]) ).
tff(f144,plain,
( $less(0,sK17)
| ~ spl20_2 ),
inference(avatar_component_clause,[],[f142]) ).
tff(f145,plain,
spl20_2,
inference(avatar_split_clause,[],[f103,f142]) ).
tff(f308,plain,
( ~ $less(0,sK17)
| $less(sK16,0) ),
inference(resolution,[],[f113,f102]) ).
tff(f349,plain,
( $less(sK16,0)
| ~ spl20_2 ),
inference(forward_subsumption_resolution,[],[f308,f144]) ).
tff(f350,plain,
( $false
| spl20_1
| ~ spl20_2 ),
inference(forward_subsumption_resolution,[],[f349,f139]) ).
tff(f351,plain,
( spl20_1
| ~ spl20_2 ),
inference(avatar_contradiction_clause,[],[f350]) ).
tff(f352,plain,
$false,
inference(avatar_smt_refutation,[],[f351,f145,f140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX084_1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n017.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 14:55:51 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 1.29/0.97 % (3612855)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 1.29/0.97 % (3612867)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=4018801456:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 1.29/0.97 % (3612867)First to succeed.
% 1.29/0.97 % (3612867)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3612855"
% 1.29/0.97 % (3612866)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2449636706:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 1.29/0.97 % (3612864)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3647647543:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 1.29/0.97 % (3612862)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1855079588:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 1.29/0.97 % (3612863)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2591360942:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 1.29/0.97 % (3612865)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2142082490:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 1.29/0.97 % (3612866)Instruction limit reached!
% 1.29/0.97 % (3612866)------------------------------
% 1.29/0.97 % (3612866)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.29/0.97 % (3612866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.97 % (3612866)CaDiCaL version: 2.1.3
% 1.29/0.97 % (3612866)Termination reason: Instruction limit
% 1.29/0.97 % (3612866)Termination phase: Saturation
% 1.29/0.97 % (3612866)Time elapsed: 0.004 s
% 1.29/0.97 % (3612866)Peak memory usage: 89 MB
% 1.29/0.97 % (3612866)Instructions burned: 4 (million)
% 1.29/0.97 % (3612865)Instruction limit reached!
% 1.29/0.97 % (3612865)------------------------------
% 1.29/0.97 % (3612865)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.29/0.97 % (3612865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.97 % (3612865)CaDiCaL version: 2.1.3
% 1.29/0.97 % (3612865)Termination reason: Instruction limit
% 1.29/0.97 % (3612865)Termination phase: Saturation
% 1.29/0.97 % (3612865)Time elapsed: 0.005 s
% 1.29/0.97 % (3612865)Peak memory usage: 88 MB
% 1.29/0.97 % (3612865)Instructions burned: 8 (million)
% 1.29/0.97 % (3612868)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3417899381:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 1.29/0.97 % (3612862)Instruction limit reached!
% 1.29/0.97 % (3612862)------------------------------
% 1.29/0.97 % (3612862)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.29/0.97 % (3612862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.97 % (3612862)CaDiCaL version: 2.1.3
% 1.29/0.97 % (3612862)Termination reason: Instruction limit
% 1.29/0.97 % (3612862)Termination phase: Saturation
% 1.29/0.97 % (3612862)Time elapsed: 0.030 s
% 1.29/0.97 % (3612862)Peak memory usage: 115 MB
% 1.29/0.97 % (3612862)Instructions burned: 12 (million)
% 1.29/0.97 % (3612864)Also succeeded, but the first one will report.
% 1.29/0.97 % (3612863)Also succeeded, but the first one will report.
% 1.29/0.97 % (3612868)Instruction limit reached!
% 1.29/0.97 % (3612868)------------------------------
% 1.29/0.97 % (3612868)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.29/0.97 % (3612868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.97 % (3612868)CaDiCaL version: 2.1.3
% 1.29/0.97 % (3612868)Termination reason: Instruction limit
% 1.29/0.97 % (3612868)Termination phase: Saturation
% 1.29/0.97 % (3612868)Time elapsed: 0.046 s
% 1.29/0.97 % (3612868)Peak memory usage: 116 MB
% 1.29/0.97 % (3612868)Instructions burned: 33 (million)
% 1.29/0.97 % (3612875)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=951170772:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.29/0.97 % (3612875)Instruction limit reached!
% 1.29/0.97 % (3612875)------------------------------
% 1.29/0.97 % (3612875)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.29/0.97 % (3612875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.97 % (3612875)CaDiCaL version: 2.1.3
% 1.29/0.97 % (3612875)Termination reason: Instruction limit
% 1.29/0.97 % (3612875)Termination phase: Saturation
% 2.74/1.17 % (3612875)Time elapsed: 0.011 s
% 2.74/1.17 % (3612875)Peak memory usage: 88 MB
% 2.74/1.17 % (3612875)Instructions burned: 14 (million)
% 2.74/1.17 % (3612876)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=3776924647:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 2.74/1.17 % (3612867)Refutation found. Thanks to Tanya!
% 2.74/1.17 % SZS status Theorem for theBenchmark
% 2.74/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.74/1.17 % (3612867)------------------------------
% 2.74/1.17 % (3612867)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.17 % (3612867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.17 % (3612867)CaDiCaL version: 2.1.3
% 2.74/1.17 % (3612867)Termination reason: Refutation
% 2.74/1.17 % (3612867)Time elapsed: 0.025 s
% 2.74/1.17 % (3612867)Peak memory usage: 116 MB
% 2.74/1.17 % (3612867)Instructions burned: 21 (million)
% 2.74/1.17 % (3612867)------------------------------
% 2.74/1.17 % (3612867)------------------------------
% 2.74/1.17 % (3612855)Success in time 0.297 s
% 2.74/1.17 % Vampire exiting
%------------------------------------------------------------------------------