%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI734_1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 09:33:45 AM UTC 2026
% Result : Theorem 4.24s 1.67s
% Output : Refutation 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 44 ( 18 unt; 0 typ; 14 def)
% Number of atoms : 112 ( 85 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 120 ( 52 ~; 32 |; 18 &)
% ( 9 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 224 ( 7 atm; 82 fun; 104 num; 31 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 : 13 ( 9 usr; 10 prp; 0-2 aty)
% Number of functors : 14 ( 6 usr; 10 con; 0-2 aty)
% Number of variables : 31 ( 21 !; 10 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_7,type,
sK0: $int ).
tff(func_def_8,type,
sF1: $int ).
tff(func_def_9,type,
sF2: $int ).
tff(func_def_10,type,
sF3: $int ).
tff(func_def_11,type,
sF4: $int ).
tff(func_def_12,type,
sF5: $int ).
tff(f1,conjecture,
! [X0: $int] :
( $greatereq(X0,0)
=> ? [X1: $int] :
( ( X1 = $product(2,X0) )
& ? [X2: $int] :
( ( ( X0 != 0 )
=> ( X1 = $sum(X2,2) ) )
& ( ( X0 = 0 )
=> ( X1 = 0 ) )
& ? [X3: $int] :
( ( X3 = $difference(X0,1) )
& ( X2 = $product(2,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula) ).
tff(f2,negated_conjecture,
~ ! [X0: $int] :
( $greatereq(X0,0)
=> ? [X1: $int] :
( ( X1 = $product(2,X0) )
& ? [X2: $int] :
( ( ( X0 != 0 )
=> ( X1 = $sum(X2,2) ) )
& ( ( X0 = 0 )
=> ( X1 = 0 ) )
& ? [X3: $int] :
( ( X3 = $difference(X0,1) )
& ( X2 = $product(2,X3) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ! [X0: $int] :
( ~ $less(X0,0)
=> ? [X1: $int] :
( ? [X2: $int] :
( ? [X3: $int] :
( ( X2 = $product(2,X3) )
& ( $sum(X0,$uminus(1)) = X3 ) )
& ( ( X0 = 0 )
=> ( X1 = 0 ) )
& ( ( X0 != 0 )
=> ( X1 = $sum(X2,2) ) ) )
& ( X1 = $product(2,X0) ) ) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
? [X0: $int] :
( ~ $less(X0,0)
& ! [X1: $int] :
( ! [X2: $int] :
( ( ( $sum(X2,2) != X1 )
& ( X0 != 0 ) )
| ( ( 0 != X1 )
& ( X0 = 0 ) )
| ! [X3: $int] :
( ( $sum(X0,$uminus(1)) != X3 )
| ( $product(2,X3) != X2 ) ) )
| ( $product(2,X0) != X1 ) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f5,plain,
( ~ $less(sK0,0)
& ! [X1: $int] :
( ! [X2: $int] :
( ( ( $sum(X2,2) != X1 )
& ( 0 != sK0 ) )
| ( ( 0 != X1 )
& ( 0 = sK0 ) )
| ! [X3: $int] :
( ( $sum(sK0,$uminus(1)) != X3 )
| ( $product(2,X3) != X2 ) ) )
| ( $product(2,sK0) != X1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f4]) ).
tff(f8,plain,
! [X2: $int,X3: $int,X1: $int] :
( ( $sum(X2,2) != X1 )
| ( 0 = sK0 )
| ( $sum(sK0,$uminus(1)) != X3 )
| ( $product(2,X3) != X2 )
| ( $product(2,sK0) != X1 ) ),
inference(cnf_transformation,[],[f5]) ).
tff(f9,plain,
! [X2: $int,X3: $int,X1: $int] :
( ( $sum(X2,2) != X1 )
| ( 0 != X1 )
| ( $sum(sK0,$uminus(1)) != X3 )
| ( $product(2,X3) != X2 )
| ( $product(2,sK0) != X1 ) ),
inference(cnf_transformation,[],[f5]) ).
tff(f10,plain,
~ $less(sK0,0),
inference(cnf_transformation,[],[f5]) ).
tff(f11,plain,
! [X2: $int,X3: $int] :
( ( 0 != $sum(X2,2) )
| ( $sum(sK0,$uminus(1)) != X3 )
| ( $product(2,X3) != X2 )
| ( $sum(X2,2) != $product(2,sK0) ) ),
inference(equality_resolution,[],[f9]) ).
tff(f12,plain,
! [X2: $int] :
( ( 0 != $sum(X2,2) )
| ( $product(2,$sum(sK0,$uminus(1))) != X2 )
| ( $sum(X2,2) != $product(2,sK0) ) ),
inference(equality_resolution,[],[f11]) ).
tff(f13,plain,
( ( 0 != $sum($product(2,$sum(sK0,$uminus(1))),2) )
| ( $sum($product(2,$sum(sK0,$uminus(1))),2) != $product(2,sK0) ) ),
inference(equality_resolution,[],[f12]) ).
tff(f14,plain,
! [X2: $int,X3: $int] :
( ( 0 = sK0 )
| ( $sum(sK0,$uminus(1)) != X3 )
| ( $product(2,X3) != X2 )
| ( $sum(X2,2) != $product(2,sK0) ) ),
inference(equality_resolution,[],[f8]) ).
tff(f15,plain,
! [X2: $int] :
( ( 0 = sK0 )
| ( $product(2,$sum(sK0,$uminus(1))) != X2 )
| ( $sum(X2,2) != $product(2,sK0) ) ),
inference(equality_resolution,[],[f14]) ).
tff(f16,plain,
( ( 0 = sK0 )
| ( $sum($product(2,$sum(sK0,$uminus(1))),2) != $product(2,sK0) ) ),
inference(equality_resolution,[],[f15]) ).
tff(f23,definition,
sF1 = $uminus(1),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f24,plain,
$uminus(1) = sF1,
inference(reorient_equations,[],[f23]) ).
tff(f25,definition,
sF2 = $sum(sK0,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f26,definition,
sF3 = $product(2,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f27,plain,
$product(2,sF2) = sF3,
inference(reorient_equations,[],[f26]) ).
tff(f28,definition,
sF4 = $sum(sF3,2),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f29,plain,
$sum(sF3,2) = sF4,
inference(reorient_equations,[],[f28]) ).
tff(f30,definition,
sF5 = $product(2,sK0),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
tff(f31,plain,
$product(2,sK0) = sF5,
inference(reorient_equations,[],[f30]) ).
tff(f32,plain,
( ( 0 != sF4 )
| ( sF5 != sF4 ) ),
inference(definition_folding,[],[f13,f31,f29,f27,f25,f24,f29,f27,f25,f24]) ).
tff(f33,plain,
( ( sF5 != sF4 )
| ( 0 = sK0 ) ),
inference(definition_folding,[],[f16,f31,f29,f27,f25,f24]) ).
tff(f35,plain,
-1 = sF1,
inference(evaluation,[],[f24]) ).
tff(f37,definition,
( spl6_1
<=> ( 0 = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
tff(f41,definition,
( spl6_2
<=> ( sF5 = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
tff(f44,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f32,f41,f37]) ).
tff(f46,definition,
( spl6_3
<=> ( 0 = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
tff(f55,definition,
( spl6_5
<=> ( sF2 = $sum(sK0,sF1) ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
tff(f58,plain,
spl6_5,
inference(avatar_split_clause,[],[f25,f55]) ).
tff(f59,plain,
( ~ spl6_2
| spl6_3 ),
inference(avatar_split_clause,[],[f33,f46,f41]) ).
tff(f61,definition,
( spl6_6
<=> ( $product(2,sF2) = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
tff(f64,plain,
spl6_6,
inference(avatar_split_clause,[],[f27,f61]) ).
tff(f66,definition,
( spl6_7
<=> ( $sum(sF3,2) = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
tff(f69,plain,
spl6_7,
inference(avatar_split_clause,[],[f29,f66]) ).
tff(f71,definition,
( spl6_8
<=> ( -1 = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
tff(f74,plain,
spl6_8,
inference(avatar_split_clause,[],[f35,f71]) ).
tff(f76,definition,
( spl6_9
<=> ( $product(2,sK0) = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition]) ).
tff(f79,plain,
spl6_9,
inference(avatar_split_clause,[],[f31,f76]) ).
tff(f81,definition,
( spl6_10
<=> $less(sK0,0) ),
introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition]) ).
tff(f84,plain,
~ spl6_10,
inference(avatar_split_clause,[],[f10,f81]) ).
tff(f85,plain,
$false,
inference(avatar_smt_refutation,[],[f84,f79,f74,f69,f64,f59,f58,f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ARI734_1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.26 % Computer : n003.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 21:03:27 UTC 2026
% 0.26/0.27 % CPUTime :
% 0.26/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.32 Running first-order theorem proving
% 0.26/0.32 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
% 4.24/1.67 % (2012173)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.24/1.67 % (2012179)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1968775215:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.24/1.67 % (2012179)First to succeed.
% 4.24/1.67 % (2012179)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2012173"
% 4.24/1.67 % (2012182)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=129816524:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.24/1.67 % (2012178)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=4011870830:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.24/1.67 % (2012182)Instruction limit reached!
% 4.24/1.67 % (2012182)------------------------------
% 4.24/1.67 % (2012182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.24/1.67 % (2012182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.24/1.67 % (2012182)CaDiCaL version: 2.1.3
% 4.24/1.67 % (2012182)Termination reason: Instruction limit
% 4.24/1.67 % (2012182)Termination phase: Saturation
% 4.24/1.67 % (2012182)Time elapsed: 0.006 s
% 4.24/1.67 % (2012182)Peak memory usage: 88 MB
% 4.24/1.67 % (2012182)Instructions burned: 5 (million)
% 4.24/1.67 % (2012181)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2618039745:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.24/1.67 % (2012184)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2442242683:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.24/1.67 % (2012183)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3383364599:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.24/1.67 % (2012180)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1336478341:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.24/1.67 % (2012181)Instruction limit reached!
% 4.24/1.67 % (2012181)------------------------------
% 4.24/1.67 % (2012181)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.24/1.67 % (2012181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.24/1.67 % (2012181)CaDiCaL version: 2.1.3
% 4.24/1.67 % (2012181)Termination reason: Instruction limit
% 4.24/1.67 % (2012181)Termination phase: Saturation
% 4.24/1.67 % (2012181)Time elapsed: 0.008 s
% 4.24/1.67 % (2012181)Peak memory usage: 88 MB
% 4.24/1.67 % (2012181)Instructions burned: 7 (million)
% 4.24/1.67 % (2012178)Also succeeded, but the first one will report.
% 4.24/1.67 % (2012183)Also succeeded, but the first one will report.
% 4.24/1.67 % (2012184)Also succeeded, but the first one will report.
% 4.24/1.67 % (2012179)Refutation found. Thanks to Tanya!
% 4.24/1.67 % SZS status Theorem for theBenchmark
% 4.24/1.67 % SZS output start Proof for theBenchmark
% See solution above
% 4.24/1.67 % (2012179)------------------------------
% 4.24/1.67 % (2012179)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.24/1.67 % (2012179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.24/1.67 % (2012179)CaDiCaL version: 2.1.3
% 4.24/1.67 % (2012179)Termination reason: Refutation
% 4.24/1.67 % (2012179)Time elapsed: 0.029 s
% 4.24/1.67 % (2012179)Peak memory usage: 116 MB
% 4.24/1.67 % (2012179)Instructions burned: 12 (million)
% 4.24/1.67 % (2012179)------------------------------
% 4.24/1.67 % (2012179)------------------------------
% 4.24/1.67 % (2012173)Success in time 0.469 s
% 4.24/1.67 % Vampire exiting
%------------------------------------------------------------------------------