%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI619_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 09:33:29 AM UTC 2026
% Result : Theorem 3.65s 1.26s
% Output : Refutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 3 unt; 0 typ; 2 def)
% Number of atoms : 87 ( 30 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 101 ( 32 ~; 31 |; 29 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 108 ( 12 atm; 16 fun; 60 num; 20 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 : 7 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 1 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 13 !; 7 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_4,type,
sK0: $int > $int ).
tff(pred_def_1,type,
pow2: $int > $o ).
tff(f1,conjecture,
( ! [X0: $int] :
( ( ( X0 = 1 )
| ( $lesseq(2,X0)
& ? [X1: $int] :
( pow2(X1)
& ( $product(2,X1) = X0 ) ) ) )
<=> pow2(X0) )
=> ~ pow2(5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_pow_of_2_5) ).
tff(f2,negated_conjecture,
~ ( ! [X0: $int] :
( ( ( X0 = 1 )
| ( $lesseq(2,X0)
& ? [X1: $int] :
( pow2(X1)
& ( $product(2,X1) = X0 ) ) ) )
<=> pow2(X0) )
=> ~ pow2(5) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ! [X0: $int] :
( pow2(X0)
<=> ( ( X0 = 1 )
| ( ? [X1: $int] :
( pow2(X1)
& ( $product(2,X1) = X0 ) )
& ~ $less(X0,2) ) ) )
=> ~ pow2(5) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
( pow2(5)
& ! [X0: $int] :
( pow2(X0)
<=> ( ( X0 = 1 )
| ( ? [X1: $int] :
( pow2(X1)
& ( $product(2,X1) = X0 ) )
& ~ $less(X0,2) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f5,plain,
( pow2(5)
& ! [X0: $int] :
( ( pow2(X0)
| ( ( 1 != X0 )
& ( ! [X1: $int] :
( ~ pow2(X1)
| ( $product(2,X1) != X0 ) )
| $less(X0,2) ) ) )
& ( ( X0 = 1 )
| ( ? [X1: $int] :
( pow2(X1)
& ( $product(2,X1) = X0 ) )
& ~ $less(X0,2) )
| ~ pow2(X0) ) ) ),
inference(nnf_transformation,[],[f4]) ).
tff(f6,plain,
( pow2(5)
& ! [X0: $int] :
( ( pow2(X0)
| ( ( 1 != X0 )
& ( ! [X1: $int] :
( ~ pow2(X1)
| ( $product(2,X1) != X0 ) )
| $less(X0,2) ) ) )
& ( ( X0 = 1 )
| ( ? [X1: $int] :
( pow2(X1)
& ( $product(2,X1) = X0 ) )
& ~ $less(X0,2) )
| ~ pow2(X0) ) ) ),
inference(flattening,[],[f5]) ).
tff(f7,plain,
( pow2(5)
& ! [X0: $int] :
( ( pow2(X0)
| ( ( 1 != X0 )
& ( ! [X1: $int] :
( ~ pow2(X1)
| ( $product(2,X1) != X0 ) )
| $less(X0,2) ) ) )
& ( ( X0 = 1 )
| ( ? [X2: $int] :
( pow2(X2)
& ( $product(2,X2) = X0 ) )
& ~ $less(X0,2) )
| ~ pow2(X0) ) ) ),
inference(rectify,[],[f6]) ).
tff(f8,plain,
( pow2(5)
& ! [X0: $int] :
( ( pow2(X0)
| ( ( 1 != X0 )
& ( ! [X1: $int] :
( ~ pow2(X1)
| ( $product(2,X1) != X0 ) )
| $less(X0,2) ) ) )
& ( ( X0 = 1 )
| ( pow2(sK0(X0))
& ( $product(2,sK0(X0)) = X0 )
& ~ $less(X0,2) )
| ~ pow2(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0))],[f7]) ).
tff(f10,plain,
! [X0: $int] :
( ~ pow2(X0)
| ( 1 = X0 )
| ( $product(2,sK0(X0)) = X0 ) ),
inference(cnf_transformation,[],[f8]) ).
tff(f14,plain,
pow2(5),
inference(cnf_transformation,[],[f8]) ).
tff(f23,definition,
( spl1_2
<=> pow2(5) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
tff(f25,plain,
( pow2(5)
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f23]) ).
tff(f26,plain,
spl1_2,
inference(avatar_split_clause,[],[f14,f23]) ).
tff(f28,plain,
( ( 1 = 5 )
| ( 5 = $product(2,sK0(5)) )
| ~ spl1_2 ),
inference(resolution,[],[f10,f25]) ).
tff(f30,plain,
( ( 5 = $product(2,sK0(5)) )
| ~ spl1_2 ),
inference(evaluation,[],[f28]) ).
tff(f32,definition,
( spl1_3
<=> ( 5 = $product(2,sK0(5)) ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
tff(f35,plain,
( spl1_3
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f30,f23,f32]) ).
tff(f36,plain,
$false,
inference(avatar_smt_refutation,[],[f35,f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI619_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.18 % Computer : n026.cluster.edu
% 0.12/0.18 % Model : x86_64 x86_64
% 0.12/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.18 % Memory : 8046.5625MB
% 0.12/0.18 % OS : Linux 6.8.0-71-generic
% 0.12/0.18 % CPULimit : 300
% 0.12/0.18 % WCLimit : 300
% 0.12/0.18 % DateTime : Mon Sep 28 20:56:42 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.22 Running first-order theorem proving
% 0.12/0.22 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
% 3.65/1.26 % (61547)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.65/1.26 % (61671)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=750203667:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.65/1.26 % (61671)Instruction limit reached!
% 3.65/1.26 % (61671)------------------------------
% 3.65/1.26 % (61671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.26 % (61671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.26 % (61671)CaDiCaL version: 2.1.3
% 3.65/1.26 % (61671)Termination reason: Instruction limit
% 3.65/1.26 % (61671)Termination phase: Saturation
% 3.65/1.26 % (61671)Time elapsed: 0.004 s
% 3.65/1.26 % (61671)Peak memory usage: 88 MB
% 3.65/1.26 % (61671)Instructions burned: 9 (million)
% 3.65/1.26 % (61672)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2817093741:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.65/1.26 % (61668)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=4033345074:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.65/1.26 % (61673)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=377683185:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.65/1.26 % (61674)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3886579835:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.65/1.26 % (61669)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1954533935:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.65/1.26 % (61670)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1146685853:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.65/1.26 % (61672)Instruction limit reached!
% 3.65/1.26 % (61672)------------------------------
% 3.65/1.26 % (61672)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.26 % (61672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.26 % (61672)CaDiCaL version: 2.1.3
% 3.65/1.26 % (61672)Termination reason: Instruction limit
% 3.65/1.26 % (61672)Termination phase: Saturation
% 3.65/1.26 % (61672)Time elapsed: 0.004 s
% 3.65/1.26 % (61672)Peak memory usage: 89 MB
% 3.65/1.26 % (61672)Instructions burned: 4 (million)
% 3.65/1.26 % (61669)Refutation not found, incomplete strategy
% 3.65/1.26 % (61669)------------------------------
% 3.65/1.26 % (61669)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.26 % (61669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.26 % (61669)CaDiCaL version: 2.1.3
% 3.65/1.26 % (61669)Termination reason: Refutation not found, incomplete strategy
% 3.65/1.26 % (61669)Time elapsed: 0.028 s
% 3.65/1.26 % (61669)Peak memory usage: 115 MB
% 3.65/1.26 % (61669)Instructions burned: 6 (million)
% 3.65/1.26 % (61668)Instruction limit reached!
% 3.65/1.26 % (61668)------------------------------
% 3.65/1.26 % (61668)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.26 % (61668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.26 % (61668)CaDiCaL version: 2.1.3
% 3.65/1.26 % (61668)Termination reason: Instruction limit
% 3.65/1.26 % (61668)Termination phase: Saturation
% 3.65/1.26 % (61668)Time elapsed: 0.031 s
% 3.65/1.26 % (61668)Peak memory usage: 115 MB
% 3.65/1.26 % (61668)Instructions burned: 13 (million)
% 3.65/1.26 % (61673)First to succeed.
% 3.65/1.26 % (61674)Also succeeded, but the first one will report.
% 3.65/1.26 % (61673)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-61547"
% 3.65/1.26 % (61676)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3216963538:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.65/1.26 % (61676)Instruction limit reached!
% 3.65/1.26 % (61676)------------------------------
% 3.65/1.26 % (61676)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.26 % (61676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.26 % (61676)CaDiCaL version: 2.1.3
% 3.65/1.26 % (61676)Termination reason: Instruction limit
% 3.65/1.26 % (61676)Termination phase: Saturation
% 3.65/1.26 % (61676)Time elapsed: 0.006 s
% 3.65/1.26 % (61676)Peak memory usage: 88 MB
% 3.65/1.26 % (61676)Instructions burned: 16 (million)
% 3.65/1.26 % (61683)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=1648584142:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.65/1.26 % (61683)Instruction limit reached!
% 3.65/1.26 % (61683)------------------------------
% 3.65/1.26 % (61683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.26 % (61683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.26 % (61683)CaDiCaL version: 2.1.3
% 3.65/1.26 % (61683)Termination reason: Instruction limit
% 3.65/1.26 % (61683)Termination phase: Saturation
% 3.65/1.26 % (61683)Time elapsed: 0.018 s
% 3.65/1.26 % (61683)Peak memory usage: 88 MB
% 3.65/1.26 % (61683)Instructions burned: 30 (million)
% 3.65/1.26 % (61684)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1230960899:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 3.65/1.26 % (61670)Instruction limit reached!
% 3.65/1.26 % (61670)------------------------------
% 3.65/1.26 % (61670)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.26 % (61670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.26 % (61670)CaDiCaL version: 2.1.3
% 3.65/1.26 % (61670)Termination reason: Instruction limit
% 3.65/1.26 % (61670)Termination phase: Saturation
% 3.65/1.26 % (61670)Time elapsed: 0.175 s
% 3.65/1.26 % (61670)Peak memory usage: 117 MB
% 3.65/1.26 % (61670)Instructions burned: 201 (million)
% 3.65/1.26 % (61686)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=2149683243:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 3.65/1.26 % (61684)Refutation not found, incomplete strategy
% 3.65/1.26 % (61684)------------------------------
% 3.65/1.26 % (61684)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.26 % (61684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.26 % (61684)CaDiCaL version: 2.1.3
% 3.65/1.26 % (61684)Termination reason: Refutation not found, incomplete strategy
% 3.65/1.26 % (61684)Time elapsed: 0.006 s
% 3.65/1.26 % (61684)Peak memory usage: 90 MB
% 3.65/1.26 % (61684)Instructions burned: 8 (million)
% 3.65/1.26 % (61686)Instruction limit reached!
% 3.65/1.26 % (61686)------------------------------
% 3.65/1.26 % (61686)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.26 % (61686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.26 % (61686)CaDiCaL version: 2.1.3
% 3.65/1.26 % (61686)Termination reason: Instruction limit
% 3.65/1.26 % (61686)Termination phase: Saturation
% 3.65/1.26 % (61686)Time elapsed: 0.010 s
% 3.65/1.26 % (61686)Peak memory usage: 89 MB
% 3.65/1.26 % (61686)Instructions burned: 25 (million)
% 3.65/1.26 % (61669)------------------------------
% 3.65/1.26 % (61669)------------------------------
% 3.65/1.26 % (61673)Refutation found. Thanks to Tanya!
% 3.65/1.26 % SZS status Theorem for theBenchmark
% 3.65/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.65/1.26 % (61673)------------------------------
% 3.65/1.26 % (61673)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.26 % (61673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.26 % (61673)CaDiCaL version: 2.1.3
% 3.65/1.26 % (61673)Termination reason: Refutation
% 3.65/1.26 % (61673)Time elapsed: 0.032 s
% 3.65/1.26 % (61673)Peak memory usage: 116 MB
% 3.65/1.26 % (61673)Instructions burned: 9 (million)
% 3.65/1.26 % (61673)------------------------------
% 3.65/1.26 % (61673)------------------------------
% 3.65/1.26 % (61547)Success in time 0.434 s
% 3.65/1.26 % Vampire exiting
%------------------------------------------------------------------------------