%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI178_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 09:32:38 AM UTC 2026
% Result : Theorem 3.82s 1.32s
% Output : Refutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 10 unt; 0 typ; 2 def)
% Number of atoms : 35 ( 30 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 5 ~; 0 |; 11 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 134 ( 0 atm; 62 fun; 54 num; 18 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 : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 3 usr; 6 con; 0-2 aty)
% Number of variables : 18 ( 9 !; 9 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_7,type,
sK0: $int ).
tff(func_def_8,type,
sK1: $int ).
tff(func_def_9,type,
sK2: $int ).
tff(f1,conjecture,
! [X1: $int,X2: $int,X0: $int] :
( ( ( $sum($sum(X0,$product(2,X1)),X2) = 10 )
& ( $sum($sum($product(2,X0),X1),X2) = 10 ) )
=> ( X2 != 0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f2,negated_conjecture,
~ ! [X1: $int,X2: $int,X0: $int] :
( ( ( $sum($sum(X0,$product(2,X1)),X2) = 10 )
& ( $sum($sum($product(2,X0),X1),X2) = 10 ) )
=> ( X2 != 0 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f21,plain,
~ ! [X2: $int,X1: $int,X0: $int] :
( ( ( 10 = $sum($sum($product(2,X2),X0),X1) )
& ( 10 = $sum($sum(X2,$product(2,X0)),X1) ) )
=> ( 0 != X1 ) ),
inference(rectify,[],[f2]) ).
tff(f22,plain,
? [X2: $int,X1: $int,X0: $int] :
( ( 0 = X1 )
& ( 10 = $sum($sum($product(2,X2),X0),X1) )
& ( 10 = $sum($sum(X2,$product(2,X0)),X1) ) ),
inference(ennf_transformation,[],[f21]) ).
tff(f23,plain,
? [X1: $int,X0: $int,X2: $int] :
( ( 10 = $sum($sum(X2,$product(2,X0)),X1) )
& ( 10 = $sum($sum($product(2,X2),X0),X1) )
& ( 0 = X1 ) ),
inference(flattening,[],[f22]) ).
tff(f24,plain,
? [X0: $int,X1: $int,X2: $int] :
( ( 10 = $sum($sum(X2,$product(2,X1)),X0) )
& ( 10 = $sum($sum($product(2,X2),X1),X0) )
& ( 0 = X0 ) ),
inference(rectify,[],[f23]) ).
tff(f25,plain,
( ( 10 = $sum($sum(sK2,$product(2,sK1)),sK0) )
& ( 10 = $sum($sum($product(2,sK2),sK1),sK0) )
& ( 0 = sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f24]) ).
tff(f26,plain,
0 = sK0,
inference(cnf_transformation,[],[f25]) ).
tff(f27,plain,
10 = $sum($sum($product(2,sK2),sK1),sK0),
inference(cnf_transformation,[],[f25]) ).
tff(f28,plain,
10 = $sum($sum(sK2,$product(2,sK1)),sK0),
inference(cnf_transformation,[],[f25]) ).
tff(f29,plain,
10 = $sum($sum(sK2,$product(2,sK1)),0),
inference(definition_unfolding,[],[f28,f26]) ).
tff(f30,plain,
10 = $sum($sum($product(2,sK2),sK1),0),
inference(definition_unfolding,[],[f27,f26]) ).
tff(f32,plain,
10 = $sum(sK2,$product(2,sK1)),
inference(evaluation,[],[f29]) ).
tff(f33,plain,
10 = $sum($product(2,sK2),sK1),
inference(evaluation,[],[f30]) ).
tff(f35,definition,
( spl3_1
<=> ( 10 = $sum(sK2,$product(2,sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f38,plain,
spl3_1,
inference(avatar_split_clause,[],[f32,f35]) ).
tff(f40,definition,
( spl3_2
<=> ( 10 = $sum($product(2,sK2),sK1) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f43,plain,
spl3_2,
inference(avatar_split_clause,[],[f33,f40]) ).
tff(f44,plain,
$false,
inference(avatar_smt_refutation,[],[f43,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI178_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.19 % Computer : n007.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Mon Sep 28 20:42:10 UTC 2026
% 0.12/0.20 % CPUTime :
% 0.12/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.23 Running first-order theorem proving
% 0.12/0.23 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.82/1.32 % (2787082)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.82/1.32 % (2787229)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=380929040:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.82/1.32 % (2787229)Instruction limit reached!
% 3.82/1.32 % (2787229)------------------------------
% 3.82/1.32 % (2787229)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.82/1.32 % (2787229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/1.32 % (2787229)CaDiCaL version: 2.1.3
% 3.82/1.32 % (2787229)Termination reason: Instruction limit
% 3.82/1.32 % (2787229)Termination phase: Saturation
% 3.82/1.32 % (2787229)Time elapsed: 0.003 s
% 3.82/1.32 % (2787229)Peak memory usage: 89 MB
% 3.82/1.32 % (2787229)Instructions burned: 7 (million)
% 3.82/1.32 % (2787228)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1747444952:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.82/1.32 % (2787227)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=281556466:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.82/1.32 % (2787226)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1617376744:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.82/1.32 % (2787225)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2648365052:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.82/1.32 % (2787228)Instruction limit reached!
% 3.82/1.32 % (2787228)------------------------------
% 3.82/1.32 % (2787228)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.82/1.32 % (2787228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/1.32 % (2787228)CaDiCaL version: 2.1.3
% 3.82/1.32 % (2787228)Termination reason: Instruction limit
% 3.82/1.32 % (2787228)Termination phase: Saturation
% 3.82/1.32 % (2787228)Time elapsed: 0.005 s
% 3.82/1.32 % (2787228)Peak memory usage: 88 MB
% 3.82/1.32 % (2787228)Instructions burned: 7 (million)
% 3.82/1.32 % (2787230)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=751001200:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.82/1.32 % (2787231)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2023744686:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.82/1.32 % (2787225)First to succeed.
% 3.82/1.32 % (2787225)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2787082"
% 3.82/1.32 % (2787226)Also succeeded, but the first one will report.
% 3.82/1.32 % (2787230)Also succeeded, but the first one will report.
% 3.82/1.32 % (2787231)Also succeeded, but the first one will report.
% 3.82/1.32 % (2787233)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3695056809:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.82/1.32 % (2787233)Refutation not found, incomplete strategy
% 3.82/1.32 % (2787233)------------------------------
% 3.82/1.32 % (2787233)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.82/1.32 % (2787233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/1.32 % (2787233)CaDiCaL version: 2.1.3
% 3.82/1.32 % (2787233)Termination reason: Refutation not found, incomplete strategy
% 3.82/1.32 % (2787233)Time elapsed: 0.001 s
% 3.82/1.32 % (2787233)Peak memory usage: 89 MB
% 3.82/1.32 % (2787238)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=3682947133:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.82/1.32 % (2787227)Instruction limit reached!
% 3.82/1.32 % (2787227)------------------------------
% 3.82/1.32 % (2787227)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.82/1.32 % (2787227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/1.32 % (2787227)CaDiCaL version: 2.1.3
% 3.82/1.32 % (2787227)Termination reason: Instruction limit
% 3.82/1.32 % (2787227)Termination phase: Saturation
% 3.82/1.32 % (2787227)Time elapsed: 0.175 s
% 3.82/1.32 % (2787227)Peak memory usage: 117 MB
% 3.82/1.32 % (2787227)Instructions burned: 202 (million)
% 3.82/1.32 % (2787238)Instruction limit reached!
% 3.82/1.32 % (2787238)------------------------------
% 3.82/1.32 % (2787238)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.82/1.32 % (2787238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/1.32 % (2787238)CaDiCaL version: 2.1.3
% 3.82/1.32 % (2787238)Termination reason: Instruction limit
% 3.82/1.32 % (2787238)Termination phase: Saturation
% 3.82/1.32 % (2787238)Time elapsed: 0.015 s
% 3.82/1.32 % (2787238)Peak memory usage: 88 MB
% 3.82/1.32 % (2787238)Instructions burned: 31 (million)
% 3.82/1.32 % (2787233)------------------------------
% 3.82/1.32 % (2787233)------------------------------
% 3.82/1.32 % (2787225)Refutation found. Thanks to Tanya!
% 3.82/1.32 % SZS status Theorem for theBenchmark
% 3.82/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.82/1.32 % (2787225)------------------------------
% 3.82/1.32 % (2787225)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.82/1.32 % (2787225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/1.32 % (2787225)CaDiCaL version: 2.1.3
% 3.82/1.32 % (2787225)Termination reason: Refutation
% 3.82/1.32 % (2787225)Time elapsed: 0.032 s
% 3.82/1.32 % (2787225)Peak memory usage: 115 MB
% 3.82/1.32 % (2787225)Instructions burned: 9 (million)
% 3.82/1.32 % (2787225)------------------------------
% 3.82/1.32 % (2787225)------------------------------
% 3.82/1.32 % (2787082)Success in time 0.444 s
% 3.82/1.32 % Vampire exiting
%------------------------------------------------------------------------------