%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI619_3 : 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 : n016.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 3.24s 1.22s
% Output : Refutation 3.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 44 ( 3 unt; 0 typ; 9 def)
% Number of atoms : 158 ( 51 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 165 ( 51 ~; 69 |; 29 &)
% ( 13 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 174 ( 18 atm; 20 fun; 110 num; 26 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 : 14 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 5 ( 1 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 19 !; 7 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_7,type,
sK0: $real > $real ).
tff(pred_def_1,type,
pow2: $real > $o ).
tff(f1,conjecture,
( ! [X0: $real] :
( pow2(X0)
<=> ( ( X0 = 1/1 )
| ( $lesseq(2/1,X0)
& ? [X1: $real] :
( pow2(X1)
& ( $product(2/1,X1) = X0 ) ) ) ) )
=> ~ pow2(5/1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_pow_of_2_5) ).
tff(f2,negated_conjecture,
~ ( ! [X0: $real] :
( pow2(X0)
<=> ( ( X0 = 1/1 )
| ( $lesseq(2/1,X0)
& ? [X1: $real] :
( pow2(X1)
& ( $product(2/1,X1) = X0 ) ) ) ) )
=> ~ pow2(5/1) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ! [X0: $real] :
( ( ( X0 = 1/1 )
| ( ~ $less(X0,2/1)
& ? [X1: $real] :
( pow2(X1)
& ( $product(2/1,X1) = X0 ) ) ) )
<=> pow2(X0) )
=> ~ pow2(5/1) ),
inference(theory_normalization,[],[f2]) ).
tff(f11,plain,
! [X0: $real,X1: $real] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) ),
introduced(definition,[],[tha_order_totality]) ).
tff(f21,plain,
( ! [X0: $real] :
( ( ( X0 = 1/1 )
| ( ~ $less(X0,2/1)
& ? [X1: $real] :
( pow2(X1)
& ( $product(2/1,X1) = X0 ) ) ) )
<=> pow2(X0) )
& pow2(5/1) ),
inference(ennf_transformation,[],[f3]) ).
tff(f22,plain,
( ! [X0: $real] :
( ( ( X0 = 1/1 )
| ( ~ $less(X0,2/1)
& ? [X1: $real] :
( pow2(X1)
& ( $product(2/1,X1) = X0 ) ) )
| ~ pow2(X0) )
& ( pow2(X0)
| ( ( 1/1 != X0 )
& ( $less(X0,2/1)
| ! [X1: $real] :
( ~ pow2(X1)
| ( $product(2/1,X1) != X0 ) ) ) ) ) )
& pow2(5/1) ),
inference(nnf_transformation,[],[f21]) ).
tff(f23,plain,
( ! [X0: $real] :
( ( ( X0 = 1/1 )
| ( ~ $less(X0,2/1)
& ? [X1: $real] :
( pow2(X1)
& ( $product(2/1,X1) = X0 ) ) )
| ~ pow2(X0) )
& ( pow2(X0)
| ( ( 1/1 != X0 )
& ( $less(X0,2/1)
| ! [X1: $real] :
( ~ pow2(X1)
| ( $product(2/1,X1) != X0 ) ) ) ) ) )
& pow2(5/1) ),
inference(flattening,[],[f22]) ).
tff(f24,plain,
( ! [X0: $real] :
( ( ( X0 = 1/1 )
| ( ~ $less(X0,2/1)
& ? [X1: $real] :
( pow2(X1)
& ( $product(2/1,X1) = X0 ) ) )
| ~ pow2(X0) )
& ( pow2(X0)
| ( ( 1/1 != X0 )
& ( $less(X0,2/1)
| ! [X2: $real] :
( ~ pow2(X2)
| ( $product(2/1,X2) != X0 ) ) ) ) ) )
& pow2(5/1) ),
inference(rectify,[],[f23]) ).
tff(f25,plain,
( ! [X0: $real] :
( ( ( X0 = 1/1 )
| ( ~ $less(X0,2/1)
& pow2(sK0(X0))
& ( $product(2/1,sK0(X0)) = X0 ) )
| ~ pow2(X0) )
& ( pow2(X0)
| ( ( 1/1 != X0 )
& ( $less(X0,2/1)
| ! [X2: $real] :
( ~ pow2(X2)
| ( $product(2/1,X2) != X0 ) ) ) ) ) )
& pow2(5/1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f24]) ).
tff(f26,plain,
pow2(5/1),
inference(cnf_transformation,[],[f25]) ).
tff(f29,plain,
! [X0: $real] :
( ~ pow2(X0)
| ( 1/1 = X0 )
| ( $product(2/1,sK0(X0)) = X0 ) ),
inference(cnf_transformation,[],[f25]) ).
tff(f30,plain,
! [X0: $real] :
( pow2(sK0(X0))
| ( 1/1 = X0 )
| ~ pow2(X0) ),
inference(cnf_transformation,[],[f25]) ).
tff(f31,plain,
! [X0: $real] :
( ~ $less(X0,2/1)
| ~ pow2(X0)
| ( 1/1 = X0 ) ),
inference(cnf_transformation,[],[f25]) ).
tff(f36,definition,
( spl1_1
<=> pow2(5/1) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f38,plain,
( pow2(5/1)
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f36]) ).
tff(f39,plain,
spl1_1,
inference(avatar_split_clause,[],[f26,f36]) ).
tff(f45,plain,
( ( 1/1 = 5/1 )
| ( 5/1 = $product(2/1,sK0(5/1)) )
| ~ spl1_1 ),
inference(resolution,[],[f29,f38]) ).
tff(f47,plain,
! [X0: $real] :
( ~ pow2(X0)
| ( $product(2/1,sK0(sK0(X0))) = sK0(X0) )
| ( 1/1 = X0 )
| ( 1/1 = sK0(X0) ) ),
inference(resolution,[],[f29,f30]) ).
tff(f48,plain,
( ( 5/1 = $product(2/1,sK0(5/1)) )
| ~ spl1_1 ),
inference(evaluation,[],[f45]) ).
tff(f50,definition,
( spl1_3
<=> ( 5/1 = $product(2/1,sK0(5/1)) ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
tff(f53,plain,
( spl1_3
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f48,f36,f50]) ).
tff(f59,plain,
( ( 1/1 = sK0(5/1) )
| ( 1/1 = 5/1 )
| ( $product(2/1,sK0(sK0(5/1))) = sK0(5/1) )
| ~ spl1_1 ),
inference(resolution,[],[f47,f38]) ).
tff(f61,plain,
( ( 1/1 = sK0(5/1) )
| ( $product(2/1,sK0(sK0(5/1))) = sK0(5/1) )
| ~ spl1_1 ),
inference(evaluation,[],[f59]) ).
tff(f63,definition,
( spl1_4
<=> ( $product(2/1,sK0(sK0(5/1))) = sK0(5/1) ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
tff(f67,definition,
( spl1_5
<=> ( 1/1 = sK0(5/1) ) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
tff(f70,plain,
( spl1_4
| spl1_5
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f61,f36,f67,f63]) ).
tff(f73,definition,
( spl1_6
<=> pow2(sK0(5/1)) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
tff(f74,plain,
( ~ pow2(sK0(5/1))
| spl1_6 ),
inference(avatar_component_clause,[],[f73]) ).
tff(f77,definition,
( spl1_7
<=> pow2(sK0(sK0(5/1))) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
tff(f78,plain,
( pow2(sK0(sK0(5/1)))
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f77]) ).
tff(f79,plain,
( ~ pow2(sK0(sK0(5/1)))
| spl1_7 ),
inference(avatar_component_clause,[],[f77]) ).
tff(f85,plain,
( ( 1/1 = sK0(5/1) )
| ~ pow2(sK0(5/1))
| spl1_7 ),
inference(resolution,[],[f79,f30]) ).
tff(f86,plain,
( spl1_5
| ~ spl1_6
| spl1_7 ),
inference(avatar_split_clause,[],[f85,f77,f73,f67]) ).
tff(f115,plain,
( ( 1/1 = 5/1 )
| ~ pow2(5/1)
| spl1_6 ),
inference(resolution,[],[f74,f30]) ).
tff(f116,plain,
( ~ pow2(5/1)
| spl1_6 ),
inference(evaluation,[],[f115]) ).
tff(f117,plain,
( $false
| ~ spl1_1
| spl1_6 ),
inference(forward_subsumption_resolution,[],[f116,f38]) ).
tff(f118,plain,
( ~ spl1_1
| spl1_6 ),
inference(avatar_contradiction_clause,[],[f117]) ).
tff(f128,definition,
( spl1_14
<=> ( 1/1 = sK0(sK0(5/1)) ) ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
tff(f170,plain,
! [X0: $real] :
( ~ pow2(X0)
| ( 1/1 = X0 )
| ( 2/1 = X0 )
| $less(2/1,X0) ),
inference(resolution,[],[f11,f31]) ).
tff(f180,plain,
( $less(2/1,sK0(sK0(5/1)))
| ( 2/1 = sK0(sK0(5/1)) )
| ( 1/1 = sK0(sK0(5/1)) )
| ~ spl1_7 ),
inference(resolution,[],[f170,f78]) ).
tff(f191,definition,
( spl1_19
<=> ( 2/1 = sK0(sK0(5/1)) ) ),
introduced(definition,[new_symbols(definition,[spl1_19])],[avatar_definition]) ).
tff(f195,definition,
( spl1_20
<=> $less(2/1,sK0(sK0(5/1))) ),
introduced(definition,[new_symbols(definition,[spl1_20])],[avatar_definition]) ).
tff(f198,plain,
( spl1_14
| spl1_19
| spl1_20
| ~ spl1_7 ),
inference(avatar_split_clause,[],[f180,f77,f195,f191,f128]) ).
tff(f199,plain,
$false,
inference(avatar_smt_refutation,[],[f198,f118,f86,f70,f53,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI619_3 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n016.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 20:58:49 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 3.24/1.22 % (3998154)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.24/1.22 % (3998185)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1240503805:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.24/1.22 % (3998185)First to succeed.
% 3.24/1.22 % (3998185)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3998154"
% 3.24/1.22 % (3998184)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2751986452:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.24/1.22 % (3998180)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=661492810:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.24/1.22 % (3998183)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1434935182:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.24/1.22 % (3998181)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1719205730:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.24/1.22 % (3998183)Instruction limit reached!
% 3.24/1.22 % (3998183)------------------------------
% 3.24/1.22 % (3998183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.24/1.22 % (3998183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/1.22 % (3998183)CaDiCaL version: 2.1.3
% 3.24/1.22 % (3998183)Termination reason: Instruction limit
% 3.24/1.22 % (3998183)Termination phase: Saturation
% 3.24/1.22 % (3998183)Time elapsed: 0.006 s
% 3.24/1.22 % (3998183)Peak memory usage: 88 MB
% 3.24/1.22 % (3998183)Instructions burned: 4 (million)
% 3.24/1.22 % (3998182)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=4169192374:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.24/1.22 % (3998179)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1024499352:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.24/1.22 % (3998182)Instruction limit reached!
% 3.24/1.22 % (3998182)------------------------------
% 3.24/1.22 % (3998182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.24/1.22 % (3998182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/1.22 % (3998182)CaDiCaL version: 2.1.3
% 3.24/1.22 % (3998182)Termination reason: Instruction limit
% 3.24/1.22 % (3998182)Termination phase: Saturation
% 3.24/1.22 % (3998182)Time elapsed: 0.007 s
% 3.24/1.22 % (3998182)Peak memory usage: 88 MB
% 3.24/1.22 % (3998182)Instructions burned: 7 (million)
% 3.24/1.22 % (3998180)Refutation not found, incomplete strategy
% 3.24/1.22 % (3998180)------------------------------
% 3.24/1.22 % (3998180)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.24/1.22 % (3998180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/1.22 % (3998180)CaDiCaL version: 2.1.3
% 3.24/1.22 % (3998180)Termination reason: Refutation not found, incomplete strategy
% 3.24/1.22 % (3998180)Time elapsed: 0.038 s
% 3.24/1.22 % (3998180)Peak memory usage: 115 MB
% 3.24/1.22 % (3998180)Instructions burned: 6 (million)
% 3.24/1.22 % (3998184)Instruction limit reached!
% 3.24/1.22 % (3998184)------------------------------
% 3.24/1.22 % (3998184)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.24/1.22 % (3998184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/1.22 % (3998184)CaDiCaL version: 2.1.3
% 3.24/1.22 % (3998184)Termination reason: Instruction limit
% 3.24/1.22 % (3998184)Termination phase: Saturation
% 3.24/1.22 % (3998184)Time elapsed: 0.058 s
% 3.24/1.22 % (3998184)Peak memory usage: 116 MB
% 3.24/1.22 % (3998184)Instructions burned: 47 (million)
% 3.24/1.22 % (3998179)Instruction limit reached!
% 3.24/1.22 % (3998179)------------------------------
% 3.24/1.22 % (3998179)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.24/1.22 % (3998179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/1.22 % (3998179)CaDiCaL version: 2.1.3
% 3.24/1.22 % (3998179)Termination reason: Instruction limit
% 3.24/1.22 % (3998179)Termination phase: Saturation
% 3.24/1.22 % (3998179)Time elapsed: 0.041 s
% 3.24/1.22 % (3998179)Peak memory usage: 115 MB
% 3.24/1.22 % (3998179)Instructions burned: 12 (million)
% 3.24/1.22 % (3998185)Refutation found. Thanks to Tanya!
% 3.24/1.22 % SZS status Theorem for theBenchmark
% 3.24/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 3.24/1.22 % (3998185)------------------------------
% 3.24/1.22 % (3998185)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.24/1.22 % (3998185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/1.22 % (3998185)CaDiCaL version: 2.1.3
% 3.24/1.22 % (3998185)Termination reason: Refutation
% 3.24/1.22 % (3998185)Time elapsed: 0.038 s
% 3.24/1.22 % (3998185)Peak memory usage: 117 MB
% 3.24/1.22 % (3998185)Instructions burned: 27 (million)
% 3.24/1.22 % (3998185)------------------------------
% 3.24/1.22 % (3998185)------------------------------
% 3.24/1.22 % (3998154)Success in time 0.359 s
% 3.24/1.22 % Vampire exiting
%------------------------------------------------------------------------------