%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI621_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 : n008.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 09:33:30 AM UTC 2026
% Result : Theorem 2.88s 1.11s
% Output : Refutation 2.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 3 unt; 0 typ; 7 def)
% Number of atoms : 136 ( 47 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 145 ( 45 ~; 57 |; 29 &)
% ( 11 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 156 ( 12 atm; 22 fun; 100 num; 22 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 : 12 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 1 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 15 !; 7 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_7,type,
sK0: $int > $int ).
tff(pred_def_1,type,
pow2: $int > $o ).
tff(f1,conjecture,
( ! [X0: $int] :
( ( ( ? [X1: $int] :
( pow2(X1)
& ( $product(2,X1) = X0 ) )
& $lesseq(2,X0) )
| ( X0 = 1 ) )
<=> pow2(X0) )
=> ~ pow2(12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_pow_of_2_10) ).
tff(f2,negated_conjecture,
~ ( ! [X0: $int] :
( ( ( ? [X1: $int] :
( pow2(X1)
& ( $product(2,X1) = X0 ) )
& $lesseq(2,X0) )
| ( X0 = 1 ) )
<=> pow2(X0) )
=> ~ pow2(12) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ! [X0: $int] :
( ( ( ? [X1: $int] :
( pow2(X1)
& ( $product(2,X1) = X0 ) )
& ~ $less(X0,2) )
| ( X0 = 1 ) )
<=> pow2(X0) )
=> ~ pow2(12) ),
inference(theory_normalization,[],[f2]) ).
tff(f22,plain,
( pow2(12)
& ! [X0: $int] :
( ( ( ? [X1: $int] :
( pow2(X1)
& ( $product(2,X1) = X0 ) )
& ~ $less(X0,2) )
| ( X0 = 1 ) )
<=> pow2(X0) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f23,plain,
( pow2(12)
& ! [X0: $int] :
( ( ( ? [X1: $int] :
( pow2(X1)
& ( $product(2,X1) = X0 ) )
& ~ $less(X0,2) )
| ( X0 = 1 )
| ~ pow2(X0) )
& ( pow2(X0)
| ( ( ! [X1: $int] :
( ~ pow2(X1)
| ( $product(2,X1) != X0 ) )
| $less(X0,2) )
& ( 1 != X0 ) ) ) ) ),
inference(nnf_transformation,[],[f22]) ).
tff(f24,plain,
( pow2(12)
& ! [X0: $int] :
( ( ( ? [X1: $int] :
( pow2(X1)
& ( $product(2,X1) = X0 ) )
& ~ $less(X0,2) )
| ( X0 = 1 )
| ~ pow2(X0) )
& ( pow2(X0)
| ( ( ! [X1: $int] :
( ~ pow2(X1)
| ( $product(2,X1) != X0 ) )
| $less(X0,2) )
& ( 1 != X0 ) ) ) ) ),
inference(flattening,[],[f23]) ).
tff(f25,plain,
( pow2(12)
& ! [X0: $int] :
( ( ( ? [X1: $int] :
( pow2(X1)
& ( $product(2,X1) = X0 ) )
& ~ $less(X0,2) )
| ( X0 = 1 )
| ~ pow2(X0) )
& ( pow2(X0)
| ( ( ! [X2: $int] :
( ~ pow2(X2)
| ( $product(2,X2) != X0 ) )
| $less(X0,2) )
& ( 1 != X0 ) ) ) ) ),
inference(rectify,[],[f24]) ).
tff(f26,plain,
( pow2(12)
& ! [X0: $int] :
( ( ( pow2(sK0(X0))
& ( $product(2,sK0(X0)) = X0 )
& ~ $less(X0,2) )
| ( X0 = 1 )
| ~ pow2(X0) )
& ( pow2(X0)
| ( ( ! [X2: $int] :
( ~ pow2(X2)
| ( $product(2,X2) != X0 ) )
| $less(X0,2) )
& ( 1 != X0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f25]) ).
tff(f30,plain,
! [X0: $int] :
( ~ pow2(X0)
| ( $product(2,sK0(X0)) = X0 )
| ( 1 = X0 ) ),
inference(cnf_transformation,[],[f26]) ).
tff(f31,plain,
! [X0: $int] :
( pow2(sK0(X0))
| ( 1 = X0 )
| ~ pow2(X0) ),
inference(cnf_transformation,[],[f26]) ).
tff(f32,plain,
pow2(12),
inference(cnf_transformation,[],[f26]) ).
tff(f37,definition,
( spl1_1
<=> pow2(12) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f39,plain,
( pow2(12)
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f37]) ).
tff(f40,plain,
spl1_1,
inference(avatar_split_clause,[],[f32,f37]) ).
tff(f46,plain,
( ( 12 = $product(2,sK0(12)) )
| ( 1 = 12 )
| ~ spl1_1 ),
inference(resolution,[],[f30,f39]) ).
tff(f48,plain,
! [X0: $int] :
( ~ pow2(X0)
| ( sK0(X0) = $product(2,sK0(sK0(X0))) )
| ( 1 = sK0(X0) )
| ( 1 = X0 ) ),
inference(resolution,[],[f30,f31]) ).
tff(f49,plain,
( ( 12 = $product(2,sK0(12)) )
| ~ spl1_1 ),
inference(evaluation,[],[f46]) ).
tff(f51,definition,
( spl1_3
<=> ( 12 = $product(2,sK0(12)) ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
tff(f54,plain,
( spl1_3
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f49,f37,f51]) ).
tff(f60,plain,
( ( $product(2,sK0(sK0(12))) = sK0(12) )
| ( 1 = sK0(12) )
| ( 1 = 12 )
| ~ spl1_1 ),
inference(resolution,[],[f48,f39]) ).
tff(f62,plain,
( ( 1 = sK0(12) )
| ( $product(2,sK0(sK0(12))) = sK0(12) )
| ~ spl1_1 ),
inference(evaluation,[],[f60]) ).
tff(f64,definition,
( spl1_4
<=> ( 1 = sK0(12) ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
tff(f68,definition,
( spl1_5
<=> ( $product(2,sK0(sK0(12))) = sK0(12) ) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
tff(f71,plain,
( spl1_4
| spl1_5
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f62,f37,f68,f64]) ).
tff(f78,definition,
( spl1_7
<=> pow2(sK0(12)) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
tff(f79,plain,
( ~ pow2(sK0(12))
| spl1_7 ),
inference(avatar_component_clause,[],[f78]) ).
tff(f80,plain,
( pow2(sK0(12))
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f78]) ).
tff(f115,plain,
( ( 1 = 12 )
| ~ pow2(12)
| spl1_7 ),
inference(resolution,[],[f79,f31]) ).
tff(f116,plain,
( ~ pow2(12)
| spl1_7 ),
inference(evaluation,[],[f115]) ).
tff(f117,plain,
( $false
| ~ spl1_1
| spl1_7 ),
inference(forward_subsumption_resolution,[],[f116,f39]) ).
tff(f118,plain,
( ~ spl1_1
| spl1_7 ),
inference(avatar_contradiction_clause,[],[f117]) ).
tff(f121,plain,
( ( 1 = sK0(sK0(12)) )
| ( 1 = sK0(12) )
| ( $product(2,sK0(sK0(sK0(12)))) = sK0(sK0(12)) )
| ~ spl1_7 ),
inference(resolution,[],[f80,f48]) ).
tff(f124,definition,
( spl1_13
<=> ( $product(2,sK0(sK0(sK0(12)))) = sK0(sK0(12)) ) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
tff(f128,definition,
( spl1_14
<=> ( 1 = sK0(sK0(12)) ) ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
tff(f131,plain,
( spl1_13
| spl1_4
| spl1_14
| ~ spl1_7 ),
inference(avatar_split_clause,[],[f121,f78,f128,f64,f124]) ).
tff(f132,plain,
$false,
inference(avatar_smt_refutation,[],[f131,f118,f71,f54,f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI621_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n008.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 20:54:39 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 2.88/1.11 % (2635070)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.88/1.11 % (2635081)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2304183467:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.88/1.11 % (2635081)First to succeed.
% 2.88/1.11 % (2635081)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2635070"
% 2.88/1.11 % (2635078)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=387711899:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.88/1.11 % (2635077)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=907763881:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.88/1.11 % (2635075)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=4011276562:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.88/1.11 % (2635076)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1593273958:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.88/1.11 % (2635079)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1342543780:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.88/1.11 % (2635080)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1091610971:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.88/1.11 % (2635079)Instruction limit reached!
% 2.88/1.11 % (2635079)------------------------------
% 2.88/1.11 % (2635079)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.88/1.11 % (2635079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/1.11 % (2635079)CaDiCaL version: 2.1.3
% 2.88/1.11 % (2635079)Termination reason: Instruction limit
% 2.88/1.11 % (2635079)Termination phase: Saturation
% 2.88/1.11 % (2635079)Time elapsed: 0.004 s
% 2.88/1.11 % (2635079)Peak memory usage: 89 MB
% 2.88/1.11 % (2635079)Instructions burned: 4 (million)
% 2.88/1.11 % (2635078)Instruction limit reached!
% 2.88/1.11 % (2635078)------------------------------
% 2.88/1.11 % (2635078)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.88/1.11 % (2635078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/1.11 % (2635078)CaDiCaL version: 2.1.3
% 2.88/1.11 % (2635078)Termination reason: Instruction limit
% 2.88/1.11 % (2635078)Termination phase: Saturation
% 2.88/1.11 % (2635078)Time elapsed: 0.006 s
% 2.88/1.11 % (2635078)Peak memory usage: 88 MB
% 2.88/1.11 % (2635078)Instructions burned: 7 (million)
% 2.88/1.11 % (2635076)Refutation not found, incomplete strategy
% 2.88/1.11 % (2635076)------------------------------
% 2.88/1.11 % (2635076)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.88/1.11 % (2635076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/1.11 % (2635076)CaDiCaL version: 2.1.3
% 2.88/1.11 % (2635076)Termination reason: Refutation not found, incomplete strategy
% 2.88/1.11 % (2635076)Time elapsed: 0.029 s
% 2.88/1.11 % (2635076)Peak memory usage: 114 MB
% 2.88/1.11 % (2635076)Instructions burned: 6 (million)
% 2.88/1.11 % (2635075)Instruction limit reached!
% 2.88/1.11 % (2635075)------------------------------
% 2.88/1.11 % (2635075)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.88/1.11 % (2635075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/1.11 % (2635075)CaDiCaL version: 2.1.3
% 2.88/1.11 % (2635075)Termination reason: Instruction limit
% 2.88/1.11 % (2635075)Termination phase: Saturation
% 2.88/1.11 % (2635075)Time elapsed: 0.030 s
% 2.88/1.11 % (2635075)Peak memory usage: 115 MB
% 2.88/1.11 % (2635075)Instructions burned: 12 (million)
% 2.88/1.11 % (2635080)Also succeeded, but the first one will report.
% 2.88/1.11 % (2635081)Refutation found. Thanks to Tanya!
% 2.88/1.11 % SZS status Theorem for theBenchmark
% 2.88/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 2.88/1.11 % (2635081)------------------------------
% 2.88/1.11 % (2635081)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.88/1.11 % (2635081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.88/1.11 % (2635081)CaDiCaL version: 2.1.3
% 2.88/1.11 % (2635081)Termination reason: Refutation
% 2.88/1.11 % (2635081)Time elapsed: 0.025 s
% 2.88/1.11 % (2635081)Peak memory usage: 117 MB
% 2.88/1.11 % (2635081)Instructions burned: 19 (million)
% 2.88/1.11 % (2635081)------------------------------
% 2.88/1.11 % (2635081)------------------------------
% 2.88/1.11 % (2635070)Success in time 0.333 s
% 2.88/1.11 % Vampire exiting
%------------------------------------------------------------------------------