%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI574_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 09:33:23 AM UTC 2026
% Result : Theorem 0.30s 1.40s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 42 ( 10 unt; 0 typ; 11 def)
% Number of atoms : 127 ( 47 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 132 ( 47 ~; 45 |; 28 &)
% ( 11 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 228 ( 53 atm; 53 fun; 108 num; 14 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 : 12 ( 8 usr; 9 prp; 0-2 aty)
% Number of functors : 12 ( 5 usr; 10 con; 0-2 aty)
% Number of variables : 14 ( 6 !; 8 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_7,type,
sK0: $int ).
tff(func_def_8,type,
sK1: $int ).
tff(func_def_9,type,
sF2: $int ).
tff(func_def_10,type,
sF3: $int ).
tff(func_def_11,type,
sF4: $int ).
tff(f1,conjecture,
! [X0: $int,X1: $int] :
( ( ( X1 = 4 )
& ( X0 = 3 ) )
<=> ( $lesseq(7,$sum(X0,X1))
& $lesseq($sum(X0,5),$product(2,X1))
& $lesseq(X1,4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ineq_sys_has_1_sol) ).
tff(f2,negated_conjecture,
~ ! [X0: $int,X1: $int] :
( ( ( X1 = 4 )
& ( X0 = 3 ) )
<=> ( $lesseq(7,$sum(X0,X1))
& $lesseq($sum(X0,5),$product(2,X1))
& $lesseq(X1,4) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ! [X1: $int,X0: $int] :
( ( ~ $less($product(2,X1),$sum(X0,5))
& ~ $less(4,X1)
& ~ $less($sum(X0,X1),7) )
<=> ( ( X1 = 4 )
& ( X0 = 3 ) ) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
? [X1: $int,X0: $int] :
( ( ~ $less($product(2,X1),$sum(X0,5))
& ~ $less(4,X1)
& ~ $less($sum(X0,X1),7) )
<~> ( ( X1 = 4 )
& ( X0 = 3 ) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f5,plain,
? [X1: $int,X0: $int] :
( ( ( 4 != X1 )
| ( 3 != X0 )
| $less($product(2,X1),$sum(X0,5))
| $less(4,X1)
| $less($sum(X0,X1),7) )
& ( ( ( X1 = 4 )
& ( X0 = 3 ) )
| ( ~ $less($product(2,X1),$sum(X0,5))
& ~ $less(4,X1)
& ~ $less($sum(X0,X1),7) ) ) ),
inference(nnf_transformation,[],[f4]) ).
tff(f6,plain,
? [X1: $int,X0: $int] :
( ( ( 4 != X1 )
| ( 3 != X0 )
| $less($product(2,X1),$sum(X0,5))
| $less(4,X1)
| $less($sum(X0,X1),7) )
& ( ( ( X1 = 4 )
& ( X0 = 3 ) )
| ( ~ $less($product(2,X1),$sum(X0,5))
& ~ $less(4,X1)
& ~ $less($sum(X0,X1),7) ) ) ),
inference(flattening,[],[f5]) ).
tff(f7,plain,
? [X0: $int,X1: $int] :
( ( ( 4 != X0 )
| ( 3 != X1 )
| $less($product(2,X0),$sum(X1,5))
| $less(4,X0)
| $less($sum(X1,X0),7) )
& ( ( ( 4 = X0 )
& ( 3 = X1 ) )
| ( ~ $less($product(2,X0),$sum(X1,5))
& ~ $less(4,X0)
& ~ $less($sum(X1,X0),7) ) ) ),
inference(rectify,[],[f6]) ).
tff(f8,plain,
( ( ( 4 != sK0 )
| ( 3 != sK1 )
| $less($product(2,sK0),$sum(sK1,5))
| $less(4,sK0)
| $less($sum(sK1,sK0),7) )
& ( ( ( 4 = sK0 )
& ( 3 = sK1 ) )
| ( ~ $less($product(2,sK0),$sum(sK1,5))
& ~ $less(4,sK0)
& ~ $less($sum(sK1,sK0),7) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f7]) ).
tff(f9,plain,
( ( 3 = sK1 )
| ~ $less($sum(sK1,sK0),7) ),
inference(cnf_transformation,[],[f8]) ).
tff(f10,plain,
( ~ $less(4,sK0)
| ( 3 = sK1 ) ),
inference(cnf_transformation,[],[f8]) ).
tff(f11,plain,
( ( 3 = sK1 )
| ~ $less($product(2,sK0),$sum(sK1,5)) ),
inference(cnf_transformation,[],[f8]) ).
tff(f13,plain,
( ~ $less(4,sK0)
| ( 4 = sK0 ) ),
inference(cnf_transformation,[],[f8]) ).
tff(f14,plain,
( ( 4 = sK0 )
| ~ $less($product(2,sK0),$sum(sK1,5)) ),
inference(cnf_transformation,[],[f8]) ).
tff(f15,plain,
( ( 4 != sK0 )
| ( 3 != sK1 )
| $less($product(2,sK0),$sum(sK1,5))
| $less(4,sK0)
| $less($sum(sK1,sK0),7) ),
inference(cnf_transformation,[],[f8]) ).
tff(f16,definition,
sF2 = $product(2,sK0),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f17,plain,
$product(2,sK0) = sF2,
inference(reorient_equations,[],[f16]) ).
tff(f18,definition,
sF3 = $sum(sK1,5),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f19,plain,
$sum(sK1,5) = sF3,
inference(reorient_equations,[],[f18]) ).
tff(f20,definition,
sF4 = $sum(sK1,sK0),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f21,plain,
$sum(sK1,sK0) = sF4,
inference(reorient_equations,[],[f20]) ).
tff(f22,plain,
( ( 4 != sK0 )
| $less(4,sK0)
| $less(sF2,sF3)
| ( 3 != sK1 )
| $less(sF4,7) ),
inference(definition_folding,[],[f15,f21,f19,f17]) ).
tff(f23,plain,
( ~ $less(sF2,sF3)
| ( 4 = sK0 ) ),
inference(definition_folding,[],[f14,f19,f17]) ).
tff(f25,plain,
( ( 3 = sK1 )
| ~ $less(sF2,sF3) ),
inference(definition_folding,[],[f11,f19,f17]) ).
tff(f26,plain,
( ~ $less(sF4,7)
| ( 3 = sK1 ) ),
inference(definition_folding,[],[f9,f21]) ).
tff(f28,definition,
( spl5_1
<=> $less(sF2,sF3) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
tff(f32,definition,
( spl5_2
<=> ( 3 = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
tff(f35,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f25,f32,f28]) ).
tff(f37,definition,
( spl5_3
<=> $less(sF4,7) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
tff(f41,definition,
( spl5_4
<=> $less(4,sK0) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
tff(f45,definition,
( spl5_5
<=> ( 4 = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
tff(f48,plain,
( ~ spl5_2
| spl5_3
| spl5_4
| spl5_1
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f22,f45,f28,f41,f37,f32]) ).
tff(f49,plain,
( spl5_5
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f23,f28,f45]) ).
tff(f52,definition,
( spl5_6
<=> ( $sum(sK1,sK0) = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
tff(f55,plain,
spl5_6,
inference(avatar_split_clause,[],[f21,f52]) ).
tff(f56,plain,
( ~ spl5_4
| spl5_5 ),
inference(avatar_split_clause,[],[f13,f45,f41]) ).
tff(f58,definition,
( spl5_7
<=> ( $sum(sK1,5) = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
tff(f61,plain,
spl5_7,
inference(avatar_split_clause,[],[f19,f58]) ).
tff(f62,plain,
( spl5_2
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f26,f37,f32]) ).
tff(f64,definition,
( spl5_8
<=> ( $product(2,sK0) = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
tff(f67,plain,
spl5_8,
inference(avatar_split_clause,[],[f17,f64]) ).
tff(f68,plain,
( spl5_2
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f10,f41,f32]) ).
tff(f69,plain,
$false,
inference(avatar_smt_refutation,[],[f68,f67,f62,f61,f56,f55,f49,f48,f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ARI574_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.27 % Computer : n015.cluster.edu
% 0.25/0.27 % Model : x86_64 x86_64
% 0.25/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.27 % Memory : 8046.5625MB
% 0.25/0.27 % OS : Linux 6.8.0-71-generic
% 0.25/0.27 % CPULimit : 300
% 0.25/0.27 % WCLimit : 300
% 0.25/0.27 % DateTime : Mon Sep 28 20:55:47 UTC 2026
% 0.25/0.28 % CPUTime :
% 0.25/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.33 Running first-order theorem proving
% 0.25/0.33 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
% 0.30/1.40 % (3005582)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 0.30/1.40 % (3005588)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2455824623:i=307:kws=precedence:nm=0:rtra=on_3000 on theBenchmark for (3000ds/307Mi)
% 0.30/1.40 % (3005593)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2266885468:i=33:rtra=on_3000 on theBenchmark for (3000ds/33Mi)
% 0.30/1.40 % (3005588)First to succeed.
% 0.30/1.40 % (3005588)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3005582"
% 0.30/1.40 % (3005593)Also succeeded, but the first one will report.
% 0.30/1.40 % (3005592)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1253991077:i=46:rtra=on_3000 on theBenchmark for (3000ds/46Mi)
% 0.30/1.40 % (3005591)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3174835226:i=4:rtra=on_3000 on theBenchmark for (3000ds/4Mi)
% 0.30/1.40 % (3005587)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2590633594:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_3000 on theBenchmark for (3000ds/12Mi)
% 0.30/1.40 % (3005590)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2061433726:s2a=on:i=7:rtra=on:inst=on_3000 on theBenchmark for (3000ds/7Mi)
% 0.30/1.40 % (3005589)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3020615818:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_3000 on theBenchmark for (3000ds/201Mi)
% 0.30/1.40 % (3005591)Instruction limit reached!
% 0.30/1.40 % (3005591)------------------------------
% 0.30/1.40 % (3005591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/1.40 % (3005591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/1.40 % (3005591)CaDiCaL version: 2.1.3
% 0.30/1.40 % (3005591)Termination reason: Instruction limit
% 0.30/1.40 % (3005591)Termination phase: Saturation
% 0.30/1.40 % (3005591)Time elapsed: 0.006 s
% 0.30/1.40 % (3005591)Peak memory usage: 89 MB
% 0.30/1.40 % (3005591)Instructions burned: 4 (million)
% 0.30/1.40 % (3005590)Instruction limit reached!
% 0.30/1.40 % (3005590)------------------------------
% 0.30/1.40 % (3005590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/1.40 % (3005590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/1.40 % (3005590)CaDiCaL version: 2.1.3
% 0.30/1.40 % (3005590)Termination reason: Instruction limit
% 0.30/1.40 % (3005590)Termination phase: Saturation
% 0.30/1.40 % (3005590)Time elapsed: 0.009 s
% 0.30/1.40 % (3005590)Peak memory usage: 88 MB
% 0.30/1.40 % (3005590)Instructions burned: 7 (million)
% 0.30/1.40 % (3005592)Also succeeded, but the first one will report.
% 0.30/1.40 % (3005587)Also succeeded, but the first one will report.
% 0.30/1.40 % (3005588)Refutation found. Thanks to Tanya!
% 0.30/1.40 % SZS status Theorem for theBenchmark
% 0.30/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.30/1.40 % (3005588)------------------------------
% 0.30/1.40 % (3005588)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/1.40 % (3005588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/1.40 % (3005588)CaDiCaL version: 2.1.3
% 0.30/1.40 % (3005588)Termination reason: Refutation
% 0.30/1.40 % (3005588)Time elapsed: 0.029 s
% 0.30/1.40 % (3005588)Peak memory usage: 115 MB
% 0.30/1.40 % (3005588)Instructions burned: 12 (million)
% 0.30/1.40 % (3005588)------------------------------
% 0.30/1.40 % (3005588)------------------------------
% 0.30/1.40 % (3005582)Success in time 0.439 s
% 0.30/1.40 % Vampire exiting
%------------------------------------------------------------------------------