%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW632_2 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 01:30:59 PM UTC 2026
% Result : Theorem 2.49s 0.93s
% Output : Refutation 2.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 11 unt; 0 typ; 5 def)
% Number of atoms : 83 ( 29 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 97 ( 46 ~; 14 |; 20 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 114 ( 28 atm; 13 fun; 36 num; 37 var)
% Number of types : 6 ( 4 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 25 ( 22 usr; 15 con; 0-4 aty)
% Number of variables : 37 ( 22 !; 15 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
uni: $tType ).
tff(type_def_6,type,
ty: $tType ).
tff(type_def_7,type,
bool: $tType ).
tff(type_def_8,type,
tuple0: $tType ).
tff(func_def_0,type,
witness: ty > uni ).
tff(func_def_1,type,
int: ty ).
tff(func_def_2,type,
real: ty ).
tff(func_def_3,type,
bool1: ty ).
tff(func_def_4,type,
true: bool ).
tff(func_def_5,type,
false: bool ).
tff(func_def_6,type,
match_bool: ( ty * bool * uni * uni ) > uni ).
tff(func_def_7,type,
tuple01: ty ).
tff(func_def_8,type,
tuple02: tuple0 ).
tff(func_def_9,type,
qtmark: ty ).
tff(func_def_12,type,
power: ( $int * $int ) > $int ).
tff(func_def_16,type,
abs: $int > $int ).
tff(func_def_18,type,
div: ( $int * $int ) > $int ).
tff(func_def_19,type,
mod: ( $int * $int ) > $int ).
tff(func_def_20,type,
ref: ty > ty ).
tff(func_def_21,type,
mk_ref: ( ty * uni ) > uni ).
tff(func_def_22,type,
contents: ( ty * uni ) > uni ).
tff(func_def_23,type,
sK0: $int ).
tff(func_def_24,type,
sK1: $int ).
tff(func_def_25,type,
sK2: $int ).
tff(func_def_26,type,
sK3: $int ).
tff(func_def_27,type,
sK4: $int ).
tff(pred_def_1,type,
sort: ( ty * uni ) > $o ).
tff(f9,axiom,
! [X0: $int] : ( power(X0,0) = 1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_0) ).
tff(f37,conjecture,
! [X0: $int,X1: $int] :
( $lesseq(0,X1)
=> ! [X4: $int,X3: $int,X2: $int] :
( ( $lesseq(0,X2)
& ( $product(X4,power(X3,X2)) = power(X0,X1) ) )
=> ( ~ $less(0,X2)
=> ( X4 = power(X0,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wP_parameter_fast_exp_imperative) ).
tff(f38,negated_conjecture,
~ ! [X0: $int,X1: $int] :
( $lesseq(0,X1)
=> ! [X4: $int,X3: $int,X2: $int] :
( ( $lesseq(0,X2)
& ( $product(X4,power(X3,X2)) = power(X0,X1) ) )
=> ( ~ $less(0,X2)
=> ( X4 = power(X0,X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
tff(f42,plain,
~ ! [X0: $int,X1: $int] :
( ~ $less(X1,0)
=> ! [X4: $int,X3: $int,X2: $int] :
( ( ~ $less(X2,0)
& ( $product(X4,power(X3,X2)) = power(X0,X1) ) )
=> ( ~ $less(0,X2)
=> ( X4 = power(X0,X1) ) ) ) ),
inference(theory_normalization,[],[f38]) ).
tff(f61,plain,
~ ! [X0: $int,X1: $int] :
( ~ $less(X1,0)
=> ! [X2: $int,X3: $int,X4: $int] :
( ( ~ $less(X4,0)
& ( power(X0,X1) = $product(X2,power(X3,X4)) ) )
=> ( ~ $less(0,X4)
=> ( power(X0,X1) = X2 ) ) ) ),
inference(rectify,[],[f42]) ).
tff(f101,plain,
? [X0: $int,X1: $int] :
( ? [X2: $int,X3: $int,X4: $int] :
( ( power(X0,X1) != X2 )
& ~ $less(0,X4)
& ~ $less(X4,0)
& ( power(X0,X1) = $product(X2,power(X3,X4)) ) )
& ~ $less(X1,0) ),
inference(ennf_transformation,[],[f61]) ).
tff(f102,plain,
? [X1: $int,X0: $int] :
( ~ $less(X1,0)
& ? [X2: $int,X4: $int,X3: $int] :
( ( power(X0,X1) = $product(X2,power(X3,X4)) )
& ~ $less(X4,0)
& ( power(X0,X1) != X2 )
& ~ $less(0,X4) ) ),
inference(flattening,[],[f101]) ).
tff(f114,plain,
? [X0: $int,X1: $int] :
( ~ $less(X0,0)
& ? [X2: $int,X3: $int,X4: $int] :
( ( $product(X2,power(X4,X3)) = power(X1,X0) )
& ~ $less(X3,0)
& ( power(X1,X0) != X2 )
& ~ $less(0,X3) ) ),
inference(rectify,[],[f102]) ).
tff(f115,plain,
( ~ $less(sK0,0)
& ( $product(sK2,power(sK4,sK3)) = power(sK1,sK0) )
& ~ $less(sK3,0)
& ( power(sK1,sK0) != sK2 )
& ~ $less(0,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f114]) ).
tff(f135,plain,
~ $less(0,sK3),
inference(cnf_transformation,[],[f115]) ).
tff(f136,plain,
power(sK1,sK0) != sK2,
inference(cnf_transformation,[],[f115]) ).
tff(f137,plain,
~ $less(sK3,0),
inference(cnf_transformation,[],[f115]) ).
tff(f138,plain,
$product(sK2,power(sK4,sK3)) = power(sK1,sK0),
inference(cnf_transformation,[],[f115]) ).
tff(f171,plain,
! [X0: $int] : ( power(X0,0) = 1 ),
inference(cnf_transformation,[],[f9]) ).
tff(f191,definition,
( spl5_3
<=> ( $product(sK2,power(sK4,sK3)) = power(sK1,sK0) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
tff(f193,plain,
( ( $product(sK2,power(sK4,sK3)) = power(sK1,sK0) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f191]) ).
tff(f194,plain,
spl5_3,
inference(avatar_split_clause,[],[f138,f191]) ).
tff(f196,definition,
( spl5_4
<=> $less(sK3,0) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
tff(f199,plain,
~ spl5_4,
inference(avatar_split_clause,[],[f137,f196]) ).
tff(f201,definition,
( spl5_5
<=> ( power(sK1,sK0) = sK2 ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
tff(f203,plain,
( ( power(sK1,sK0) != sK2 )
| spl5_5 ),
inference(avatar_component_clause,[],[f201]) ).
tff(f204,plain,
~ spl5_5,
inference(avatar_split_clause,[],[f136,f201]) ).
tff(f206,definition,
( spl5_6
<=> $less(0,sK3) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
tff(f209,plain,
~ spl5_6,
inference(avatar_split_clause,[],[f135,f206]) ).
tff(f253,definition,
( spl5_11
<=> ( 0 = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition]) ).
tff(f255,plain,
( ( 0 = sK3 )
| ~ spl5_11 ),
inference(avatar_component_clause,[],[f253]) ).
tff(f266,plain,
( ( power(sK1,sK0) = $product(sK2,power(sK4,0)) )
| ~ spl5_3
| ~ spl5_11 ),
inference(superposition,[],[f193,f255]) ).
tff(f274,plain,
( ( power(sK1,sK0) = $product(sK2,1) )
| ~ spl5_3
| ~ spl5_11 ),
inference(forward_demodulation,[],[f266,f171]) ).
tff(f275,plain,
( ( power(sK1,sK0) = sK2 )
| ~ spl5_3
| ~ spl5_11 ),
inference(evaluation,[],[f274]) ).
tff(f276,plain,
( $false
| ~ spl5_3
| spl5_5
| ~ spl5_11 ),
inference(forward_subsumption_resolution,[],[f275,f203]) ).
tff(f277,plain,
( ~ spl5_3
| spl5_5
| ~ spl5_11 ),
inference(avatar_contradiction_clause,[],[f276]) ).
tff(f278,plain,
$false,
inference(avatar_smt_refutation,[],[f277,f209,f204,f199,f194]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW632_2 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n015.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 14:26:32 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running first-order theorem proving
% 0.10/0.21 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
% 2.49/0.93 % (2662766)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.49/0.93 % (2662830)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3459723164:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.49/0.93 % (2662830)First to succeed.
% 2.49/0.93 % (2662830)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2662766"
% 2.49/0.93 % (2662827)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3410517830:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.49/0.93 % (2662826)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3936251111:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.49/0.93 % (2662825)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1255187670:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.49/0.93 % (2662828)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3147304619:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.49/0.93 % (2662828)Instruction limit reached!
% 2.49/0.93 % (2662828)------------------------------
% 2.49/0.93 % (2662828)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.49/0.93 % (2662828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/0.93 % (2662828)CaDiCaL version: 2.1.3
% 2.49/0.93 % (2662828)Termination reason: Instruction limit
% 2.49/0.93 % (2662828)Termination phase: Saturation
% 2.49/0.93 % (2662828)Time elapsed: 0.005 s
% 2.49/0.93 % (2662828)Peak memory usage: 88 MB
% 2.49/0.93 % (2662828)Instructions burned: 7 (million)
% 2.49/0.93 % (2662829)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=211053430:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.49/0.93 % (2662829)Instruction limit reached!
% 2.49/0.93 % (2662829)------------------------------
% 2.49/0.93 % (2662829)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.49/0.93 % (2662829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/0.93 % (2662829)CaDiCaL version: 2.1.3
% 2.49/0.93 % (2662829)Termination reason: Instruction limit
% 2.49/0.93 % (2662829)Termination phase: Saturation
% 2.49/0.93 % (2662829)Time elapsed: 0.004 s
% 2.49/0.93 % (2662829)Peak memory usage: 88 MB
% 2.49/0.93 % (2662829)Instructions burned: 5 (million)
% 2.49/0.93 % (2662825)Instruction limit reached!
% 2.49/0.93 % (2662825)------------------------------
% 2.49/0.93 % (2662825)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.49/0.93 % (2662825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/0.93 % (2662825)CaDiCaL version: 2.1.3
% 2.49/0.93 % (2662825)Termination reason: Instruction limit
% 2.49/0.93 % (2662825)Termination phase: Saturation
% 2.49/0.93 % (2662825)Time elapsed: 0.030 s
% 2.49/0.93 % (2662825)Peak memory usage: 116 MB
% 2.49/0.93 % (2662825)Instructions burned: 12 (million)
% 2.49/0.93 % (2662826)Also succeeded, but the first one will report.
% 2.49/0.93 % (2662831)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3170747290:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.49/0.93 % (2662827)Instruction limit reached!
% 2.49/0.93 % (2662827)------------------------------
% 2.49/0.93 % (2662827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.49/0.93 % (2662827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/0.93 % (2662827)CaDiCaL version: 2.1.3
% 2.49/0.93 % (2662827)Termination reason: Instruction limit
% 2.49/0.93 % (2662827)Termination phase: Saturation
% 2.49/0.93 % (2662827)Time elapsed: 0.117 s
% 2.49/0.93 % (2662827)Peak memory usage: 116 MB
% 2.49/0.93 % (2662827)Instructions burned: 203 (million)
% 2.49/0.93 % (2662837)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1689849994:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.49/0.93 % (2662837)Instruction limit reached!
% 2.49/0.93 % (2662837)------------------------------
% 2.49/0.93 % (2662837)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.49/0.93 % (2662837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/0.93 % (2662837)CaDiCaL version: 2.1.3
% 2.49/0.93 % (2662837)Termination reason: Instruction limit
% 2.49/0.93 % (2662837)Termination phase: Saturation
% 2.49/0.93 % (2662837)Time elapsed: 0.011 s
% 2.49/0.93 % (2662837)Peak memory usage: 88 MB
% 2.49/0.93 % (2662837)Instructions burned: 14 (million)
% 2.49/0.93 % (2662831)Also succeeded, but the first one will report.
% 2.49/0.93 % (2662830)Refutation found. Thanks to Tanya!
% 2.49/0.93 % SZS status Theorem for theBenchmark
% 2.49/0.93 % SZS output start Proof for theBenchmark
% See solution above
% 2.49/0.93 % (2662830)------------------------------
% 2.49/0.93 % (2662830)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.49/0.93 % (2662830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/0.93 % (2662830)CaDiCaL version: 2.1.3
% 2.49/0.93 % (2662830)Termination reason: Refutation
% 2.49/0.93 % (2662830)Time elapsed: 0.024 s
% 2.49/0.93 % (2662830)Peak memory usage: 117 MB
% 2.49/0.93 % (2662830)Instructions burned: 18 (million)
% 2.49/0.93 % (2662830)------------------------------
% 2.49/0.93 % (2662830)------------------------------
% 2.49/0.93 % (2662766)Success in time 0.295 s
% 2.49/0.93 % Vampire exiting
%------------------------------------------------------------------------------